Device-based sensing approaches can as well be used to detect and track human beings and their activities [28,29]. However, requesting the subjects to carry a traceable device all the time is not always feasible or desirable. Passive, device-free sensing systems, instead, take advantage of the human body's property of disturbing the radio signals when partially or totally obstructing their trajectory, thus causing signal fluctuations. In principle, by analyzing such fluctuations, it could be possible to separate the influence of the human body from both the original signal and other causes of noise, thus allowing human detection, positioning and activity recognition. However, modeling the "baseline" noise and signal fluctuations that can be expected in the absence of the obstructing human body, thus allowing a reliable detection and tracking, is not a trivial process [30]. The Bluetooth standard stack only allows to measure the Received Signal Strength Information (RSSI), which is a scalar indication of the intensity of the received signal at a given time and is subject to fluctuations and fading during normal operation. The WiFi standard, instead, allows the measurement of the much more informative Channel State Information that, for the most recent devices, is a 3D matrix of complex values representing the amplitude attenuation and phase shift of multi-path WiFi channels [31]. Moreover, the CSI provides more stable information than the RSSI [32,33]. Consequently, the literature regarding the use of WiFi for passive human detection and activity tracking is much wider than the literature on Bluetooth for similar applications.

Human presence can influence a wireless signal in its spatial, temporal and frequency domains [34]. In particular, human motion can affect the frequency and temporal domains, whereas the location of the human body in the environment can affect the signal's phase. The RSSI alone does not provide phase information, and therefore, some other source of information is needed when the CSI is not directly available. Recently, Bluetooth v5.1 [35] introduced the possibility to measure the signal's Angle of Arrival and Angle of Departure, which can be used to improve both the positioning and activity tracking accuracy. However, to the best of the authors' knowledge, such an approach has not been reported in the literature so far.

Multiple RSSI samples can be used to extract more information, either in time or in space. In time, for example, by measuring through a fixed, static receiver a time sequence of RSSI samples emitted by a fixed, static transmitter, it is possible to track human body motion and recognize specific activities (see Figure 3a).

In space, instead, by deploying several transmitters and receivers, a very accurate positioning of a human body can be obtained by exploiting geometrical considerations [36] (see Figure 3b).

**Figure 3.** Moving humans counter and multi-transmitter, multi-receiver configurations. (**a**) Moving humans counter. The RSSI undergoes an abrupt change when a human body traverses the signal trajectory. (**b**) Multiple transmitters, multiple receivers.

A special case is based on the radio tomographic approach, where a very high number of transmitter/receiver couples over a spacial grid (see Figure 4) allows to use imaging techniques to obtain an extremely detailed and accurate positioning of the subject [37].

**Figure 4.** Tomographic sensing.

In principle, any wireless transmission technology can support some form of remote human sensing approach. In particular, an interesting comparison is reported in [6], where, curiously, Bluetooth is not mentioned. Table 1 summarizes the main pros and cons of exploiting some of the most popular communication technologies for wireless remote human sensing, such as the ones listed below.

*Radio Frequency Identification* (RFID) is a technology for contactless, short-range, twoway communications that is mainly used for tag detection and identification as well as for low datarate short message exchange. The main advantages of RFID technology are the reasonable resilience to radio frequency noise and the low cost of RFID tags. Conversely, the RFID reader is quite expensive [6]. The main disadvantage of using RFID for passive human sensing is the very short sensing range.

*Frequency Modulated Continuous Wave* (FMCW) radars are instead active sensing devices in which the sensor contains both a transmitter and a receiver [38,39]. The main advantages of applying FMCW to human sensing are the high sensitivity and distance accuracy [6]. However, FMCW-based devices are specifically aimed at sensing, and therefore, a

human sensing approach based on this technology cannot leverage existing communication infrastructures, but a separate deployment is needed. Moreover, FMCW-based human sensing is not in the scope of this study, as the focus here is on passive human sensing.

*Bluetooth and its low-energy version* (BLE) are among the most widely adopted wireless communication technologies. Their main advantages are low power consumption, which allows the installation of battery-operated nodes, and the relatively low deployment costs, even in case a specific infrastructure is required. Moreover, such technologies have the ability to support both regular communications and passive human sensing at the same time, as regular advertisement signals are exploited for sensing (see, for example, [40,41]). The main disadvantages of Bluetooth and BLE are that they currently do not provide CSI and an effective way to cope with the abrupt RSSI changes due to Frequency Hopping (see Section 3.2).

*WiFi* is the wireless communication technology that is most widely adopted for passive human sensing. Early works in the literature exploited the WiFi RSSI values, but the most accurate and effective applications are based on the ability of some recent devices to provide Channel State Information (CSI) multidimensional samples, thus supporting a more detailed extraction of human activity information [31]. The main advantages of using WiFi for human sensing are the wide diffusion of the WiFi communication technology and the reliable and fine-grained information provided by the CSI, which allows sensing low-amplitude activities (e.g., hand gestures) and vital signs (e.g., breathing). However, WiFi devices cannot be used for communications and passive sensing at the same time [6], and therefore, a separate infrastructure is needed for sensing or the same infrastructure must be multiplexed in time, thus reducing the time available for both services. Moreover, WiFi power consumption is sensibly higher than Bluetooth power consumption (this is particularly true for Bluetooth Low-Energy), and the deployment cost of an ad hoc infrastructure is also higher. Finally, WiFi is relatively less robust to changes in the environment and noise than other signals [6].

*Visible Light Communication* (VLC) technology is also being exploited for human sensing [42]. VLC technology uses low-cost, high-efficiency photodiodes (LED), is resilient to RF noise, and it can leverage the existing lighting infrastructure. However, such a technology requires a complex light sensing infrastructure that is hardly justifiable by its application to human sensing, as a large number of photodiodes need to be installed on the sensorized environment floor [6].

*LoRa* [43] is a radio frequency transmission technique based on a spread spectrum modulation, which enables long-range transmissions with low power consumption [44]. Both properties are interesting for human sensing. In the work in [45], LoRa is used for active remote human sensing in a radar-like fashion, by equipping the sensing device with both a transmitter and a receiver modified and adapted to the specific application. However, LoRa requires a dedicated infrastructure for sensing.

The *LTE* (long-term evolution) mobile communication system [46], which seamlessly covers almost all areas, both indoor and outdoor, can act as a diffused external illuminator for wireless human sensing [47].

The 6G communication networks also promise localization and human activity detection among their most relevant services [48]. The two main disadvantages of using LTE and 6G for remote human sensing are the long distance between the transmitter, the receiver and the human, which require complex filtering techniques to remove the noise and separate the signals [6], and the significant risk of privacy violation due to both the non-locality of the probing signal and the potential for receiving the sensing signal from a long distance, which would allow for mass monitoring.

**Table 1.** Pros and cons of the most relevant applications of wireless communication technologies to wireless remote human sensing, as reported in the literature.

One of the earliest and simplest applications of Bluetooth to deviceless human sensing is to support remote elderly care, by allowing the remote caregivers to monitor that their patients regularly take their prescriptions [40,41]. The described system consists of three principal components:

In this application, the Bluetooth beacon periodically transmits a message with a unique ID, while the tablet measures the received signal RSSI. When a human approaches the medicine calendar, thus disturbing the signal sent by the beacon, the RSSI suddenly drops, and the dedicated application running on the tablet records the event and sends a notification to the caregiver's smartphone. The detection accuracy obtained by the system in a real environment is higher than 90%.

More recently, by measuring and analyzing the fluctuations in the received signal RSSI, a passive device-free system based on a network of Bluetooth Low Energy (BLE) beacons was able to detect the presence [49] and estimate the number [50] of humans in a lecture room. With 24 beacons positioned under the seats in the room and four receivers positioned on the ceiling laterally to the seats, the detection accuracy was higher than 95%, while the accuracy of the number of people estimated was about 82%, with an average room occupancy of about 30 attendees.

In [51], a system to detect the presence of humans in a waiting queue is presented. Usually, waiting queues are controlled by barrier poles with retractable belts, which can be moved if needed, and the system described in [51] is able to detect the transit of people between two barrier poles so as to allow to estimate the queue waiting time. To this aim, the transmitting and receiving devices are positioned on the barrier poles, facing from the two opposite sides of the queue path, and two detection methods are studied:

The results reported in [51] show that the RSSI variance is better suited for detecting the transit of people between the two poles, i.e., the motion of a body traversing the ideal line connecting the two poles (see Figure 3a), while the RSSI average is more suitable for detecting people standing between the two poles. The accuracy of this system in detecting walking people is about 98% using variance and 96% using average. However, the second algorithm is also able to detect motionless people standing in the monitored area, whereas the first algorithm is only suitable for detecting moving people.

#### **3. Human Body Influence on the Bluetooth Signal**

In order to better understand the advantages and limitations of using the Bluetooth technology for passive human detection and tracking, this section recapitulates some relevant Bluetooth features.

#### *3.1. Bluetooth Recapitulation*

Bluetooth is a short-range wireless protocol that supports connections within a range from a few meters to a few dozen meters (depending on the antenna gain, the environment and the specific PHY adopted) [52].

The Bluetooth Classic protocol, also referred to as Bluetooth Basic Rate/Enhanced Data Rate (BR/EDR), works in the globally unlicensed Industrial, Scientific and Medical (ISM) 2.4 GHz short-range radio frequency band, which is divided into 79 channels with 1 MHz spacing. The Bluetooth technology is designed to work well even in very noisy environments, copying with fading and interference. To this end, Bluetooth uses the Frequency Hopping Spread Spectrum (FHSS) [53] technique, that forces two connected devices (master and slave) to frequently change the dedicated communication channel, so the devices hop from one channel to another according to a pseudo-random sequence. The channel sequence is maintained by the master device through a map in which the channels are marked as 'in use' if they work properly and 'unused' otherwise. This map is updated after a channel is found working well for a given time interval and is shared with the secondary devices so as to have the same information at both ends of the communication.

Two types of Bluetooth connections are available:

The most relevant advantages of the Bluetooth technology are the resilience to noise and interference, thanks to the FHSS technology, the low cost of the devices, and the low power consumption compared to other technologies. In particular, the introduction of Bluetooth Low Energy (BLE) has further reduced the power consumption, thus improving the lifetime of battery-powered devices. For this reason, BLE is also widespread in Internet of Things (IoT) applications.

#### 3.1.1. Bluetooth Low Energy

Bluetooth Low Energy divides the ISM band into 40 channels with 2 MHz spacing. Three channels are used as advertising channels (or primary channels) for broadcasting, while the remaining 37 data channels (or secondary channels) are used for data exchange after a connection event. Mobile devices can be designed to support both Bluetooth Classic and BLE (dual-mode device) or to only support BLE (single-mode device). Single-mode

devices are generally used in applications that require low power consumption as a major constraint. Moreover, the BLE stack is thinner compared to the Bluetooth Classic one, to reduce the firmware footprint and protocol management complexity for the applications that run directly on sensors [54].

The first version of BLE protocol was introduced with Bluetooth v4.0, and then, it was updated up to Bluetooth v5.3.

Comparing with the previous versions, in Bluetooth v5.0, major improvements were introduced. First, the coverage range was extended from about 50 m to more than 200 m for outdoor environments, whereas in indoor environments, the range changed from about 10 m to about 40 m. Furthermore, the Bluetooth Core Specification v5.0 [55] introduced a new way to perform advertising, called Extended Advertising, which allows the 37 channels previously reserved for data communication to be also used as secondary advertising channels. Traditional advertising transmits the same payload on the three primary channels, whereas the Extended Advertising transmits payload data only once on a secondary channel. This way, the total amount of transmitted data is lower, and therefore, the duty cycle is reduced. Another benefit of the Extended Advertising is that using a secondary channel to transmit the payload, 255-byte-long packets can be broadcast. In the previous versions of the protocol, instead, only 31-byte-long packets could be broadcast. With this version of BLE, it is also possible to chain packets together and transmit each chained packet on a different channel.

Bluetooth v5.0 also introduced the Periodic Advertising, which allows the receivers to synchronize their scanning for packets with the schedule of the transmitter device. In the previous versions, the advertising process included a degree of randomness in the timing of the advertising packet transmission to avoid repeated packet collisions. However, this implies that scanners could lose some packets, i.e., those transmitted out of their round of scan. In the Periodic Advertising, scanning is performed within the transmission window of the transmitter, thus avoiding such packet losses, and therefore in a more power-efficient way.

In addition, Bluetooth v5.0 reduced the minimum allowed Advertising Interval from 100 ms to 20 ms, thus allowing a rapid recognition of the advertising beacons.

Bluetooth v5.1 [35] introduced a new feature that allows Bluetooth devices to determine the direction of a Bluetooth incoming transmission.By equipping either the receiver or the transmitter with an array of antennas, the receiver can determine either the Angle of Arrival (AoA) or the Angle of Departure (AoD), respectively [56].

In both methods, a special signal, called a direction-finding signal, is transmitted by the transmitting device and used by the receiving device to calculate the direction of the received signal, which in ideal conditions corresponds to the direction along which the transmitting device lays. In the AoA method, the receiving device (that is connected to an array of antennas) receives different copies of the same signal from different consecutive antennas in the array. The received signals are phase-shifted due to the different distances of the receiving antennas to the single transmitting antenna. The Angle of Arrival *θ* is computed from the phase difference according to Equation (1), where *λ* is the wavelength, *ψ* is the phase difference and *d* is the distance between two consecutive antennas in the array [56].

$$\theta = \arccos(\frac{\psi \lambda}{2\pi d})\tag{1}$$

In the AoD method, instead, the transmitting device is equipped with an antenna array which emits a signal from each of the antennas. The receiving device, which is equipped with a single antenna, given that *λ* is the wavelength and *d* is the distance between two consecutive antennas in the transmitting array, determines the phase difference *ψ* from two received signals and computes the direction *θ* according to Equation (2).

$$\theta = \arcsin(\frac{\psi \lambda}{2\pi d})\tag{2}$$

In Bluetooth 5.1, the direction-finding signals are generated by both defining a new Link Layer Protocol Data Unit (PDU) for direction finding between two connected devices, and a way to use the existing advertising PDUs for connectionless direction finding. In both cases, a special field, known as the Constant Tone Extension (CTE), is added to the end of the PDUs.

Bluetooth v5.1 also introduced the Randomized Advertising Channel Indexing, which allows the devices in advertising state to randomize the selection of advertising channels so that they are not selected in strict order (37, 38, 39) as in the previous Bluetooth versions but in a random order. This feature improves packet collision avoidance.

In Bluetooth v5.2 [57], the LE Power Control feature was introduced. This new feature allows the transmitting devices to dynamically change their transmission power level and inform the receiving device that this has happened. This process is useful to keep high the signal quality and low the error rates, respectively. Moreover, the process also improves coexistence in general, thus benefiting all the protocols working in the 2.4 GHz frequency band.

Bluetooth v5.3 [58] introduced some improvements in the Periodic Advertising, i.e., the host of a receiving device can inform the controller that a packet has been found to contain data that has already been received in an earlier packet. The controller can, therefore, disregard the current periodic advertising packet and immediately switch to another channel.

#### *3.2. Influence on Bluetooth Signal*

Numerous studies proved that radio signals in the 2.4 GHz frequency band are easily influenced by the human body. An experiment explicitly aimed at demonstrating the effects of a human body occluding the Line-of-Sight between a transmitter and a receiver (see Figure 1a) was reported in 2014 [59], where the received signal power was measured with and without obstruction, and the measured attenuation was approximately 10 dB. However, signal fluctuations were exploited to detect the presence of people in an environment already in 2006 [60].

Received signal fluctuations can be caused by changes in the environment, in the state of the transmitter or the receiver, or by design, e.g., because the protocol requires actions that produce such fluctuations. In order to exploit the signal fluctuations for passive human sensing, it is mandatory to exclude the unwanted causes or, at least, to find a way to separate their effects from the effects of the targeted human body. Compared to WiFi, Bluetooth appears to be better suited for this purpose, because it is less subject to electromagnetic noise thanks to the FHSS technique. However, the FHSS itself by design generates fluctuations in the received signal due to the communication channel switch. In fact, measurements at the receiver side of the signal emitted by a Bluetooth beacon in advertising mode showed that different channels have different noise and attenuation characteristics [20]. To reduce the influence of the channel hopping on the signal RSSI, each Bluetooth channel should be modeled and processed separately [16]. In the reported experiments, four BLE beacons were used. In particular, three beacons were modified to allow a separate RSSI measurement for each advertising channel, while the other one was not modified. After measuring the RSSI values of all beacons, the RSSI variance was calculated for each beacon. The modified beacons allowed the calculation of separate variances for each channel, while the non-modified beacon only allowed the calculation of the variance of the hybrid signal resulting from the channel hopping. As the Bluetooth protocol does not allow the determination of the time instant at which the hopping takes place, and it does not report the current advertising channel, it was not possible to filter out the RSSI fluctuations produced by the hopping. Consequently, the hopping contributed to the overall RSSI variance. As it was expected, the RSSI variance calculated over the signal transmitted by the unmodified beacon was significantly larger than the per-channel RSSI variances obtained by the modified beacons.

The described study demonstrated that the FHSS causes a significant increase of the RSSI fluctuations, which would heavily impact the reliability of a passive human detection approach based on a set of unmodified Bluetooth devices. For this reason, most of the research works in this area rely on some way to manage each advertising channel separately.

#### **4. Data Preprocessing**

The demonstration that the wireless signal generally suffers from the noise due to the surrounding environment is introduced in [61]. Moreover, endogenous fluctuations, i.e., the ones coming from inside the device, always affect the received signal. The aim of the preprocessing stage is ideally the elimination, and more in general the attenuation, of noise and endogenous fluctuations, so that the only fluctuations present in the signal after this step are those generated by the human presence between the connected devices.

In [62], a Kalman filter was used for signal noise reduction. The Kalman filter uses linear models, i.e., linear transformations both in the transitions from the current state to the next state and in the transformation from state to measurement, and it also assumes that the noise associated to both the measurements and state of the system is Gaussian. Unfortunately, the hypotheses of linearity and Gaussian noise are not always satisfied in wireless passive human sensing, as shown in [61], where the Kalman filter and the Moving Average filter were compared.

In [62], the Kalman filter performed well with the available data, whereas in [61], such a filter performed poorly, flattening the signal to the point where relevant peaks corresponding to the presence of a human body were deleted. The Moving Average filter, instead, is simpler and less accurate than the Kalman filter under linearity and Gaussian noise hypotheses, but it performed better on RSSI data [61].

An advanced version of the Moving Average filter, i.e., the Exponential Weighted Moving Average filter, was adopted in [22]. Unlike the Moving Average filter, this filter assigns different weights to the values of the considered time series according to an approximated exponential law. The filtered RSSI value is computed according to Equation (3), where *α* ∈ [0, 1] is the smoothing factor. In particular, the value of *α* in [22] is 0.05.

$$f\_{i,j}[n] = aRSSI\_{i,j}[n] + (1 - a)f\_{i,j}[n-1] \tag{3}$$

A similar principle is used in [51], where data preprocessing consists of computing the weighted average according to Equation (4), where *α* = 0.9 produces a larger weight for the previous values than for the current value, thus reducing the effect of noisy outliers.

$$Mean\_{current} = aMean\_{old} + (1 - a) RSSI\_{current} \tag{4}$$

In [63], a passive detection system is described, in which the signal is preprocessed using an *α*-trimmed mean filter. The *α*-trimmed filter is generally used in very high noise conditions. In this case, calculating the mean of the signal as the average of the samples is not recommended, because an outlier might significantly alter it. Instead, given a sliding window with *q* RSSI values, this filter sorts the RSSI values and then removes *α* extremes. After this process, the average of the remaining values is computed according to Equation (5), where 0 ≤ *α* ≤ 0.5.

$$f(q;a) = \frac{1}{q - 2\lceil aq \rceil} \sum\_{i=\lceil aq \rceil + 1}^{q - \lfloor aq \rfloor} RSS\_i \tag{5}$$

The described process has an offline phase, which produces an estimate of the initial parameters of the system, and an online phase, which produces an estimate of the detected human bodies location, according to the received RSSI samples. Since the environment may significantly change between the offline estimation phase and the online phase, the Analysis of Variance (ANOVA) [64] is adopted to check if the estimate of the initial parameters is still valid.

In [16], a localization system is discussed that uses BLE beacons with a modified firmware able to select a specific channel (either 37, 38, or 39) to send the advertising packets through. This way, one of the causes of increased RSSI variance is removed, but a new problem is introduced. In fact, some packets may get lost in some channels during a scan round due to the fact that the transmitter might send its packet out of the receiver scan interval. At each scan round, the receiver stores the RSSI values from each channel in a vector of RSSI values that represents the RSSI sample for that round. If a packet is lost, the vector has one component missing, and this leads to errors in the analysis steps. As a consequence, some method to fill the missing component of the vector is needed. First, the missing sample component must be detected, and then, an adequate value must be selected to replace the missing value. The chosen solution is that the missing sample component is replaced by the median value of the last *WL*<sup>1</sup> samples from the same channel.

Other preprocessing methods based on statistic techniques are available in the literature. The works in [49,50] describe a passive system that is able to detect the presence, and count the number, of human beings in a lecture room. To train and test this system, three datasets were used:

The first dataset was produced by collecting five measurement sessions for each lecture, thus obtaining a total of 80 × 5 = 400 sessions. The installation was composed of 24 transmitting beacons and four receivers. Provided that each beacon sent one frame per second, and that each session lasted 300 s, for each session, a total of 24 × 4 × 300 = 28,800 samples were collected. To reduce the dataset size, a summarized dataset DS2 was built by calculating, for each measurement session, four features, i.e., mean, variance, trimmedmean, and trimmed-variance, which were calculated according to Equation (5). Next, the position of the beacons was taken into account by introducing a weighting factor depending on the receiver–transmitter distance. The weighting factor was a normalization matrix *W*, which is used to apply a Min/Max normalization to the data. The set of normalized data was the third dataset DS3. Experimental results show that with the described preprocessing approach, the performance improved from 70% to 98%.

Recently, Deep Neural Networks are being applied also to passive human sensing. The main advantage of deep learning techniques is that they do not need, in general, to manually build specific features for the classification process. Instead, such features are calculated by a neural network that is adequately trained over large amounts of data [65], thus consistently reducing the amount of preprocessing. In [66], for example, raw RSSI values are simply averaged over one-minute intervals and then fed to a deep neural network that is trained to output an estimate of the initial and final position of a human moving in the monitored area.

#### **5. Classification Methods**

The lack of protocol support to gather the Channel State Information (CSI) sensibly reduces the amount of information that can be obtained by analyzing the received signal. Most likely for this reason, to the best of the authors' knowledge, as reported in Section 6, the current literature regarding human body sensing through Bluetooth mainly focuses on indoor passive people detection, counting, and approximate motion tracking, whereas complex activities recognition and vital signs sensing have not yet been investigated.

For the considered applications, statistic techniques, Machine Learning techniques, and Artificial Neural Networks are adopted in the literature, as described in the following subsections.

#### *5.1. Statistical Methods*

The approaches defined as "statistic" use methods based on the analysis of either the mean or the variance of the RSSI values. In [51], two algorithms based on these techniques are presented. The first algorithm, based on the analysis of the variance of a stream (sequence) of RSSI values, is more suitable to detect the motion of a human body, for example, when entering an area of interest. In this case, the RSSI values are detected in subsequent time instants, and therefore, their sequence represents the evolution of the Bluetooth signal perturbation when a human body moves in the area between the receiver and the transmitter devices.

In general, the RSSI variance is calculated over a sliding window always containing the last *n* samples according to Equation (6), where *xi* represents the current RSSI value and *μ* is the average of all the RSSI values within the sliding window.

$$Var(\mathbf{x}) = \frac{1}{n} \sum\_{i=1}^{n} (\mathbf{x}\_i - \mu)^2 \tag{6}$$

The size *n* of the sliding window must be chosen according to the specific application. If *n* is too large, too old RSSI values are considered in the calculation, and this could lead to delayed detection. If *n* is too small, the smoothing effect of previous samples on the calculation is not sufficient to remove the measurement noise, thus leading to false positives or false negatives in the classification. In [51], the optimal value of *n* is 10. It was determined considering the time it takes a human to cross the monitored area and the number of messages received for second. Moreover, the mean *μ* in Equation (6) is replaced with a weighted average computed according to Equation (4).

In the second algorithm reported in [51], the weighted average calculated according to Equation (4) is subtracted from each new RSSI sample and, if the resulting value exceeds a given threshold *Tm*, then a detection event is triggered. The weighted average is not updated when a detection event is triggered, because the average is intended to represent the "background" condition, where no human body is present in the monitored area.

The threshold *Tm* is critical and requires a complex calculation involving a preliminary calibration, which is repeated every time something changes in the system deployment, and an initial stabilization time interval that is needed every time the system is turned on or reset. Moreover, the formulation of *Tm* includes some constants that were experimentally determined on the basis of the available data and setup and that might potentially undermine the generality of the proposed approach.

#### *5.2. Machine Learning Methods*

Machine Learning techniques include both classification and regression algorithms, so they can be used both for presence detection and counting people. For example, K-Means and Gradient Boosting were adopted in [67], whereas Artificial Neural Networks, regression models and Decision Trees (Random Forest) were adopted in [68], and Random Forest were applied in [69]. Passive, BLE-based presence detection systems in the literature exploit Logistic Regression, k-Nearest Neighbor (KNN), and Support Vector Machine (SVM) with linear, polynomial and Radial Basis Function kernel. In [49], a presence detection system was developed, and the algorithms mentioned above were compared on three different datasets. Such datasets, here called DS1, DS2, and DS3, were built according to the process formerly described in Section 4, i.e.,

The best accuracy was obtained with the (SVM) algorithm [70] using a Radial Basis Function (RBF) kernel applied to the third dataset. An RBF kernel [71] is a function used when the boundaries of the classes are hypothesized to be curve-shaped and nonlinear. An RBF kernel involves the choice of two hyperparameters, i.e., the penalty parameter and the kernel width. In [49], such parameters are auto-optimized in the SVM implementation. In 98.97% of cases, this algorithm recognized the presence of a subject between two nodes. The KNN algorithm, instead, was more efficient with the first and second datasets and obtained higher accuracy than the other algorithms.

In general, all the analyzed algorithms performed similarly when applied to the same dataset, apart from a few exceptions. In particular, for the dataset DS1, the highest accuracy obtained was 70.15% with the KNN algorithm, while the Logistic Regression algorithm obtained 69.81%. If we look only at the accuracy that the two algorithms achieve, the KNN performed better than the Logistic Regression, but the KNN is a parametric algorithm in which the execution time increases with an increasing amount of data. The Logistic Regression algorithm, instead, is a linear algorithm and is faster than the KNN. The SVM algorithm performed slightly worse than the other algorithms on DS1, especially with the linear kernel (62.67%). The reason for this could lay in the distribution of the data. The linear SVM algorithm assumes that a linear boundary can be found between two classes, whereas the kernel trick supports different, nonlinear models of the data. However, in some cases, even the nonlinear kernels struggle in approximating the strongly nonlinear distribution of real data.

For the dataset DS2, containing four features for every transmitter–receiver couple, the KNN resulted as the best performing algorithm with 96.90% accuracy, whereas the SVM with an RBF kernel produced 96.46% accuracy.

The situation changed for dataset DS3, which was normalized to keep in account the distance between the transmitter and the receiver. The SVM with the RBF kernel performed better than the other algorithms (98.97%).

An analysis of the accuracy obtained by applying the described algorithms to all the datasets evidences that the preprocessing stage is always useful to increase the classification accuracy. In fact, as it is shown in Figure 5, the classification accuracy obtained with DS1 is 70%, with DS2 approaches 97%, and with DS3 approaches 99%.

**Figure 5.** Comparison of the classification models used in [49] with the datasets DS1 (without any processing), DS2 (after aggregation and preprocessing), and DS3 (after normalization with weight factors).

The regression algorithms used to develop the counting system, instead, are the KNN Regression, the Least Squares Regression (LSR), the Polynomial Regression, and the Support Vector Regression. These algorithms were compared in [50], in which a counting system was developed and the same preprocessing approach of the previous paper was adopted, obtaining similar performance improvements. In fact, for the dataset DS1, the lowest Root Mean Square Error (RMSE) among all the considered approaches was 18.78, for the second dataset DS2, it was 6.40, and for DS3, it was 5.42. Notably, for DS2 and DS3, the LSR algorithm performed considerably worse than the others, as shown in Figure 6.

As a consequence, the selection of the best algorithm requires further considerations regarding the resource requirements or other specific characteristics of the intended application. In particular, the computational complexity of the considered approach, and therefore its execution time and memory requirements, can sensibly influence the choice of the approach, depending on the hardware that will be used for implementing the system.

#### *5.3. Artificial Neural Networks*

Artificial Neural Networks are still little used in Bluetooth-based passive counting and detection, whereas the development of a Bluetooth-based localization system exploiting Artificial Neural Networks is described in [66].

In [18], a system for obstruction detection between two nodes, aimed at RSSI signal correction, was developed. Two Artificial Neural Networks were compared to detect obstructions, i.e., a Multi-Layer Perceptron (MLP) network, with two hidden layers of 20 neurons, and a Radial Basis Function (RBF) network, with only one layer of 20 neurons. The comparison demonstrated that both the neural networks detected the obstructions between nodes with high accuracy, with the MLP performing better (91%) than the RBF (89%) according to an estimate based on the data reported in the paper. The detection rate of the proposed approaches in discriminating clear Line-of-Sight, i.e., when no human body was present in the LoS between transmitter and receiver, was also measured. The MLP obtained a 94% detection rate, while the RBF obtained a 92% detection rate.

#### **6. Overall Performance Comparison**

Table 2 provides a comparison of the different approaches addressed in this paper. Presence detection refers to methods able to reveal the presence of a human body either still or in motion, whereas motion detection refers to methods that only reveal moving human bodies. People counting, instead, refers to methods able not only to reveal the presence of a human body but also to count the number of human bodies present in the monitored area. Finally, clean Line-of-Sight (LoS) detection refers to approaches able to detect the presence of a human body obstructing the line of sight between the transmitter and the receiver (see Figure 1a).

The approaches discussed in this section were trained and tested on different datasets and with different sensors set up. As the codebase and the datasets of the cited studies are not publicly available, the comparison is based on the data reported in the cited works.

**Table 2.** Performance comparison of the considered approaches.

<sup>1</sup> This value is not an accuracy value, but the Root Mean Square Error. In [50], such an error metrics was chosen because it represents the misestimation in counting the number of people in the room. <sup>2</sup> These percentages are detection rates and not accuracy values. Accuracy is the sum of the true positives and true negatives over the whole set of samples, whereas here, the true positives over the whole set are considered.

The comparison shows that the accuracy of all the techniques is above 87%, and in some cases, it approaches 100%. Nevertheless, some significant differences need to be taken into account. In [40], a simple statistical approach was used for human detection, i.e., when the value of the average RSSI was above a threshold, a detection event was triggered. With this approach, the detection rate was slightly above 90%. Conversely, in [51], a more complex statistical approach was used, and two algorithms were implemented based on the RSSI-variance and RSSI-mean. The first algorithm is more suitable to detect a human crossing the LOS between two nodes, and it obtains an accuracy of 98%. The second algorithm, instead, is best suited for detecting a human that stands between two devices, and it obtains an accuracy of 96%.

In [49], different Machine Learning algorithms for human detection were compared. The best result was obtained with the SVM algorithm using an RBF kernel (98.97%) on a set of preprocessed data. However, the other algorithms perform similarly on the same type of preprocessed data (≈98%). On raw RSSI data, all the tested algorithms performed worse, with accuracy values between ≈70% and 62%. As stated in Section 5, this result supports the observation that appropriate preprocessing is generally needed to improve the accuracy of the classification and regression algorithms and reduce the size of the final dataset, thus shortening the execution time of more complex algorithms, such as the k-Nearest Neighbor one. In [50], a very similar approach was applied to human counting, obtaining an RMSE of 5.42.

In [18], Artificial Neural Networks were used to detect a human body obstructing the space between a transmitter and a receiver, although the system was indeed intended for the correction of the RSSI signal in case of obstructions. The proposed networks, an MLP and an RBF, reached 91% and 89% accuracy, respectively, thus underperforming compared to the statistical approaches. However, the proposed Artificial Neural Networks were only tested on raw data. In principle, they could benefit from data preprocessing, thus further improving their performance. Consequently, more experiments are needed to better understand which approach has the higher potential over the others.

#### **7. Discussion**

In the previous sections, some applications of the Bluetooth technology (in particular, BLE) to passive human detection, counting and tracking in indoor environment were described and analyzed. Moreover, a comparative overview of their performance was provided.

As the signal RSSI depends on the position and distance between two Bluetooth devices and on the geometric and physical characteristics of the environment, the development of a "generic" passive human sensing system able to cope with all the possible variations in the environment and spatial deployment of the transmitting and receiving devices would require a generalization ability that is hardly obtainable.

Current approaches, instead, rely on some training or initialization process that builds a model of the received signal RSSI that is able to explain all the possible fluctuations of the RSSI values, thus allowing their classification. Such a model can be either explicit, e.g., defined in terms of statistical parameters, or implicit, e.g., obtained by training an ANN.

Building a data-driven model, however, requires that a suitable dataset is gathered from the specific environment where the system will be deployed; i.e., a long data collection process is needed to initialize the system. Furthermore, if Neural Networks are exploited, the data collection process becomes longer and longer, because large datasets are needed to train Neural Networks. The lack of universal datasets to train and test the developed systems makes the comparison of existing techniques difficult.

Another issue often highlighted in the literature is the impossibility of independently extracting the RSSI signal values from each advertising channel of the BLE beacons. The BLE beacons need to be modified at the hardware or firmware level in order to transmit on a certain preset channel and to allow the researcher to discriminate the variation in the signal due to the presence of a human body from other fading effects.

According to Table 2, the RSSI-variance and RSSI-mean approaches used in [51] might be considered as the best performers for presence detection. The reported accuracy results are even better than those reached by more recent Artificial Neural Networks approaches. However, in this study, the BLE transmitters were modified to transmit only on one advertising channel, so that the channel information can be transmitted to the receiver into the payload of the advertising message. Such a modification allows to separately analyze each advertising channel, thus substantially reducing the variance in the RSSI signal and dramatically improving the detection stability and reliability. However, the proposed modification, although being frequently adopted in the relevant literature, is not allowed by the Bluetooth standard, and therefore, it represents a substantial violation of the protocol. In other words, the proposed approach would not work with off-the-shelf beacons.

The Machine Learning techniques used in [49] obtained about 98% accuracy. In particular, as already stated in Section 5, 98% accuracy was reached by using the SVM algorithm with an RBF kernel on a reduced and normalized dataset. In this case, unlike the previous approach, only standard devices were used, and only four receivers were used with 24 transmitters, instead of requiring the same number of receivers and transmitters. As a consequence, the approach proposed in [49] can be applied to a much wider range of cases and environments while performing close to best in class.

#### **8. Conclusions**

This paper provided a reasoned overview of the Bluetooth-based approaches for passive remote sensing of the human body reported in the literature. The work illustrated and commented on the pros and cons of each approach. Moreover, the experimental results and performance of the considered approaches were described, compared and discussed.

Although the inherent limitations imposed by the Bluetooth protocol may affect its applicability to passive human sensing, a number of recent research works proposed specific preprocessing and non-parametric classification and regression techniques, and they demonstrated the effectiveness and accuracy of the proposed approaches. In general, the adoption of BLE-based remote passive wireless human sensing approaches should be

preferred whenever the power consumption of the sensing devices, the deployment cost, and the simultaneous communication and sensing capability are very relevant. However, some interesting aspects still need to be investigated. In particular, the FHSS mechanism significantly affects the reliability of RSSI-based human sensing, and therefore, several works in the literature address modifications of the transmitting device original firmware in order to either bypass the FHSS mechanism or include the channel information in the transmitted frame. Such modifications, however, violate the Bluetooth protocol and should be avoided, also because bypassing FHSS reduces the robustness to noise of the proposed approach. A possible alternative approach can be to estimate, at the receiver side, the transmitter channel mapping and, therefore, to foresee the next hop. Effective techniques are available to obtain such an estimate, such as the ones in [72–74].

Furthermore, the recent introduction in the Bluetooth standard of the direction-finding technology has a potential for supporting the development of novel approaches able to extract more information from the BLE signal, thus allowing for more accurate and detailed human sensing applications, similarly to what happened with WiFi. In particular, when determining the Direction of Arrival (DoA) of the received signal (see Section 3.1.1), the receiver can compute a suitable estimate of the phase shift of the reflected, scattered and refracted signal components, and leverage such information to produce a more accurate sensing, thus allowing for complex activity recognition, vital signs detection, and multiperson tracking.

**Author Contributions:** Conceptualization, methodology, investigation, formal analysis, writing original draft preparation, writing—review and editing, G.I. and L.L.B.; investigation, M.M.; investigation, data curation, A.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Multilink Operation in IEEE 802.11be Wireless LANs: Backoff Overflow Problem and Solutions**

**Wisnu Murti and Ji-Hoon Yun \***

Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul 01811, Korea<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** The next-generation wireless LAN standard named IEEE 802.11be supports a multilink operation to cost-efficiently boost throughput performance, for which an efficient multilink channel scheme is essential. The synchronous channel access scheme with an enhancement allowing multilink transmission before backoff completion greatly enhances the performance of multilink devices with no simultaneous transmit and receive capability, for which, however, backoff count compensation is necessary for coexistence with legacy and other multilink devices. In this paper, we identify the backoff count overflow problem of the enhanced synchronous channel access scheme with backoff compensation, which becomes aggravated once triggered due to repeated compensations. Then, we propose four solutions to mitigate this problem: limiting consecutive free-riding transmissions, limiting a compensated backoff value, using the contention window value of a main link, and balancing transmissions between links. Through comparative evaluation and analyses for dense single-spot and indoor random deployment scenarios, we demonstrate in terms of throughput and latency that the proposed solutions successfully mitigate the problem while preserving the coexistence performance.

**Keywords:** IEEE 802.11be; multilink operation; channel access; backoff; coexistence

#### **1. Introduction**

A multilink operation (MLO) is a salient feature of the upcoming next-generation wireless LAN (WLAN) standard, i.e., IEEE 802.11be (also called extremely high throughput (EHT)) [1,2], that enables the simultaneous utilization of multiple links using individual frequency channels for both transmission and reception. The benefit of MLO is the simultaneous utilization of multiple frequency bands at a lower hardware cost than the approach of using a single multiband radio. Designing an efficient channel access operation for the presence of radio frequency (RF) power leakage between links to best exploit the benefit of MLO is still a challenge. In the IEEE 802.11be working group (WG), it was agreed that the multiple links involved in MLO may or may not have RF power leakage between them. A multilink device (MLD), which has links with power leakage between them, is unable to simultaneously transmit and receive (STR) across different links, as the power leakage from one link will make the other links unable to sense each's channel medium. This type of MLD is called a non-STR MLD. On the other side, an MLD with no RF power leakage between its links will be able to simultaneously transmit and receive signals and thus is called an STR MLD.

The channel access scheme of IEEE 802.11be is classified into an asynchronous operation (Async) and a synchronous operation (Sync). In Async, each of the links belonging to an MLD independently performs a channel access process (backoff procedure, BO). Therefore, different links finish their BOs at different times; thus, their transmissions will be asynchronous between them, which is ideal for STR MLDs. In Sync, all links also perform individual BOs. When a link finishes its BO earlier than other links, it waits until the other

**Citation:** Murti, W.; Yun, J.-H. Multilink Operation in IEEE 802.11be Wireless LANs: Backoff Overflow Problem and Solutions. *Sensors* **2022**, *22*, 3501. https://doi.org/10.3390/ s22093501

Academic Editor: Peter Han Joo Chong

Received: 29 March 2022 Accepted: 1 May 2022 Published: 4 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

links also finish their BOs. If the waiting link sees its channel busy, the link must rerun its BO. Because only simultaneous transmission initiation is allowed on all links, the RF power leakage between links does not affect the operation of Sync. However, Sync does not utilize multiple channels better than Async, since it requires all links to have zero backoff counts for transmission.

There has been a notable discussion on the enhancements of Sync for better multilink exploitation and a hybrid of the Sync and Async schemes for faster transmission (FT), called Sync-FT [3]. In this work, the coexistence issue of Sync-FT was discussed since legacy single-link devices (SLDs) may coexist with EHT MLDs in practical WLANs, and multiple solutions were proposed. This is because, with Sync-FT, a link of the MLD can transmit before its BO completion, which is called free-riding. This behavior prioritizes channel access for the MLD, resulting in long and frequent wait times for the legacy device. It was shown in the work that compensating the backoff count for each free-riding transmission achieved the best coexistence performance while having a marginal throughput decrease in MLDs. However, there may arise a backoff count overflow problem where the accumulated backoff count of an MLD resulting from repeated compensations becomes too large; thus, the MLD is not able to obtain a transmission opportunity by its own BO completion once an overflow occurs.

This paper aims to identify the backoff count overflow problem of the enhanced multilink channel access scheme (Sync-FT) with backoff compensation in an IEEE 802.11be WLAN and propose solutions applicable to both STR and non-STR MLDs. First, we describe the Sync scheme of an MLO and its design variants including Sync-FT. Next, we demonstrate the backoff count overflow problem of backoff compensation for Sync-FT and identify that the problem is aggravated once triggered due to continuing free-riding transmissions and compensations. Subsequently, we propose four solutions to mitigate this problem: limiting consecutive free-riding transmissions, limiting a compensated backoff value, using the contention window (CW) value of a main link, and balancing transmissions between links. Through comparative evaluation and analyses for dense single-spot and 3GPP indoor random deployment scenarios, we demonstrate in terms of throughput and latency that the proposed solutions successfully mitigate the backoff count overflow problem. We also investigate the coexistence performance of the solutions and demonstrate that the proposed solutions preserve coexistence performance with other MLDs and legacy SLDs while solving the backoff count overflow problem.

In summary, the main contributions of our work are listed as follows:

The rest of the paper is organized as follows. Section 2 explains the multilink Sync operation and Sync-FT modification, and its coexistence issue and a backoff compensation solution are presented in Section 3. Section 4 describes the backoff count overflow problem. Section 5 details the proposed solutions, and Section 6 evaluates them via simulation compared with other channel access schemes in coexistence scenarios. Finally, Section 7 concludes the paper.

#### **2. Synchronous Multilink Channel Access**

Sync is one of the multilink channel access mechanisms for EHT that has been considered to be used for transmissions of non-STR MLD. This operation uses both links in the backoff process, but a transmission is triggered only if the backoff counters of both links are zero. Once a link finishes its BO, it waits until the other link finishes BO. If another device occupies the channel while an MLD is in the waiting mode, the backoff count of the

waiting link should be rechosen, and its BO is initiated with the new count. This means that a multilink transmission aligns the transmission start time in each link; thus, RF power leakage does not affect channel access and transmission. However, the requirement of the availability of both links at the same time leads to severe performance degradation especially when the channels are crowded. The inability to perform independent transmission in individual links may cause an MLD to suffer from waiting. Therefore, the use of Sync may not be able to exploit the potential of MLO for throughput enhancement.

In what follows, we describe two design variants of Sync.

#### *2.1. Synchronous Operation with a Primary Link*

The Sync with a primary link scheme (Sync-PL) is similar to the conventional wideband operation of IEEE 802.11 [4,5] In this scheme, an MLD runs a single BO in a primary link (PL) only and does not run in other links. When the primary link is about to reach a zero backoff count, the MLD performs a short clear channel assessment (CCA) for a point coordination function interframe space (PIFS) on each of the other links to check each's availability. The links that are clear to send (idle) in a given short CCA period will then be able to send simultaneously with the primary link. The links in which the MLD transmits frames are the primary link and the other idle link(s). The MLD starts transmission in these links at the same time and ends transmission at the same time as well to avoid RF power leakage between the links. If all other links are found to be busy, the MLD transmits in the primary link only. Since only the primary link performs BO, a single link transmission is available only in the primary link. Sync-PL is expected to have better throughput performance than the basic Sync since at least a single link transmission is enabled. One concern is that a transmission is triggered only by the backoff completion of the primary link; thus, transmission opportunities highly depend on the load condition of the corresponding channel.

#### *2.2. Synchronous Operation for Faster Transmission*

Another enhancement of Sync is called Sync for faster transmission (Sync-FT) and has proven to be better in throughput performance than Sync. Sync-FT is a hybrid of Sync-PL and Async. As in Async, it lets the links of an MLD run individual backoff processes. When a link finishes its BO earlier than the others, the MLD performs a short CCA in each of the other links and starts a multilink transmission in a set of links sensed idle as in Sync-PL while freezing the backoff counts of the links. Once the links finish transmission, they resume individual backoff processes. The links that completed backoff at the time of transmission choose a new backoff count and initiate a new backoff process, while the other links resume BO with their remaining counts. We call the transmission of a link with BO completion as a main transmission and the transmission of a link before BO completion as a free-riding transmission. This operation enhances the multilink utilization of non-STR MLDs by avoiding the failure of link utilization due to RF power leakage. The operation is applicable to both STR and non-STR MLDs. Sync-FT enables both single-link and multilink transmissions in all links.

#### **3. Coexistence Issue of Sync-FT and Backoff Count Compensation Solution**

In this section, we describe the coexistence issue of Sync-FT and the backoff compensation solution.

#### *3.1. Coexistence Issue*

There may coexist legacy SLDs and EHT MLDs with different channel access schemes in networks. Therefore, the main coexistence scenarios are given below:

Suppose that a legacy device starts a backoff process with the same backoff count as an MLD with Sync-FT. However, while the legacy station obtains a single transmission opportunity (TXOP), the MLD may obtain more TXOPs. This is because Sync-FT enables the MLD to transmit in a link before the backoff completion of the link. Such behavior prioritizes the channel access of the MLD and gives more TXOPs to it, resulting in long and frequent waiting times of the legacy device. When two MLDs, one with Sync-PL (MLD1) and the other with Sync-FT (MLD2) coexist, MLD2 is likely to obtain more TXOPs than MLD1 due to the aggressiveness of Sync-FT against Sync-PL.

In the basic design of Sync-FT, a link performing transmission by another link's BO completion, which we call a free-riding link, resumes its ongoing backoff process after finishing transmission, with the remaining count value. This behavior makes the links under Sync-FT transmit more frequently than others that have to complete BO before transmission (e.g., legacy SLDs). In other words, this behavior makes the free-riding link go through a relatively deflated backoff count on average.

#### *3.2. Sync-FT with Backoff Compensation*

One of the proposed designs to tackle the coexistence issue of Sync-FT is having backoff count compensation after free-riding of a link [3]. This is a straightforward modification where the backoff count of a free-riding link is compensated for by an appropriate amount such that it finally goes through the backoff time given by its backoff counts on average. Before the additional backoff count value is added to the current count by compensation, a new backoff count should first be chosen. After a free-riding transmission finishes, the link stores the current backoff count value and rechooses a new backoff count. Then, it performs a new backoff process with an initial count as the sum of the stored backoff count and the rechosen one. This solution is simple in implementation, since it reuses existing functions of the backoff mechanism and can resolve the coexistence issue caused by Sync-FT's aggressive behavior.

#### **4. Backoff Count Overflow Problem**

The backoff compensation solution described in the previous section leads to another problem called a backoff count overflow problem. This problem is that a link has a very large value of its backoff count, thus preventing it from finishing its countdown and transmission. In general WLANs, a greater backoff value is usually caused by consecutive transmission failures, causing a CW value to rise and in turn increasing a random backoff value chosen within the CW. This backoff count overflow problem, however, happens in Sync-FT with backoff compensation implementation even without consecutive transmission failures.

The problem is illustrated in Figure 1. Upon completion of each free-riding transmission, the link compensates for its backoff count value by the remaining amount of the previous value. There is a possibility that one link may become stuck in consecutive free-riding transmissions and keep compensating its backoff count value, thus making the count increase indefinitely. This phenomenon happens especially when the channels of the links have heterogeneous load conditions; hence, some links in low load conditions keep decreasing their backoff values and make the other links keep free-riding with no chance of transmitting via their own BO completion. This is the case when links tend to have different backoff stages (i.e., different CW values) and thus heterogeneous backoff counts. As a free-riding transmission makes a link rechoose a backoff count from its current CW value (without a change in its backoff stage), a link with a higher backoff stage will statistically choose a larger backoff count value and, thus, have a higher chance of free-riding again. In other words, once a link performs a free-riding transmission, it will retain half of the current backoff count value on average (assuming that the BO completions of links are independent from each other and, thus, randomized between them) and add a new rechosen value, which is highly likely to make the resulting backoff count larger than the other links; If this happens consecutively, the link will always be a free-riding link.

Figure 2 shows the time evolution of the backoff count values of the two links of an MLD. In the figure, Link 1 and 2 have similar backoff count ranges in the beginning, but Link 2 suddenly keeps increasing its backoff count, while Link 2 still has a similar backoff count range. This is due to consecutive free-riding transmissions of Link 2. As mentioned above, a free-riding transmission of a link inflates the link's backoff count when backoff count compensation is applied, which in turn increases the possibility of the link's recurrent free-riding transmissions. This happens even when links are in the same load condition, but it is aggravated when they are in different load conditions. In such a condition, the backoff stages of links may be different from each other because of different occurrence rates of collisions.

**Figure 1.** Illustration of the backoff count overflow problem (backoff count values after compensation are colored red).

**Figure 2.** Backoff count evolution example for two links of an MLD.

#### **5. Solutions to Backoff Count Overflow Problem**

In this section, we describe the proposed solutions with additional design variants. Figures 3–5 (Proposals 1, 2, and 3, respectively) illustrate the changed operation of Link 2 against the Sync-FT operation with compensation illustrated in Figure 1 (the operation of Link 1 remains the same as Figure 1, since only Link 2 performs free-riding) while Figure 6 (Proposal 4) illustrates another example operation of Sync-FT (with backoff compensation) and the changed operation side by side. We assume in the figures that Link 1 is in the first backoff stage (CW = 16) and Link 2 is in the second backoff stage (CW = 32).

#### *5.1. Proposal 1: Limiting Consecutive Free-Riding Transmissions*

The main cause of an indefinite increase of a backoff count value, resulting in a backoff overflow, is consecutive free-riding transmissions of a link. This solution is made to alleviate the problem by limiting the number of allowed consecutive free-riding transmissions of each link. As illustrated in Figure 3, if a link performs a free-riding transmission, it starts its consecutive counter with value one. The next free-riding transmission right after the first one will result in an increment of the consecutive counter by one. The counter will keep increasing through consecutive free-riding transmissions of the link. Once the counter reaches its limit, the link will block its next free-riding transmission and reset the counter to zero. The counter will also be reset if there is a transmission caused by the link's own BO completion. The blocked free-riding transmission will keep its remaining backoff count value and continue to decrease the value after a main transmission finishes without a compensation. Setting the limit to one is the same as disabling any consecutive free-riding transmission, i.e., one link can free-ride only once, then must finish its own backoff process to transmit.

**Figure 3.** Proposal 1: limiting consecutive free-riding transmissions (backoff count values after compensation are colored red).

#### *5.2. Proposal 2: Limiting a Compensated Backoff Value*

A backoff overflow is caused by adding compensation to what is already a large backoff count value. In order to prevent that from happening, we designed the second solution to limit the compensated backoff count value itself. There are two ways of limiting the compensated backoff count value:

In both solutions, we can ensure the new backoff value remains at a smaller value and increase the chance of a free-riding link to complete its backoff process the next time.

**Figure 4.** Proposal 2: limiting a compensated backoff value.

#### *5.3. Proposal 3: Using the CW Value of a Main Link*

As explained previously, the backoff overflow problem is aggravated if the links of an MLD have different backoff stages. The case is especially true when a free-riding link has a higher backoff stage than the link of the main transmission, because this can cause the randomly chosen count value of the free-riding link to become higher. In the solution illustrated in Figure 5, a free-riding link will use the same CW value as that of the link performing a main transmission, without considering its own backoff stage or current CW value. By using the same CW value as the main link, the free-riding link will have a higher probability to finish its own backoff process at a similar time as the main link. The same CW value with the main link will only apply to the new compensated rechosen value and will not affect transmissions by other means.

**Figure 5.** Proposal 3: using the CW value of a main link (backoff count values after compensation are colored red).

#### *5.4. Proposal 4: Balancing Transmissions between Links*

The main idea of this solution is to balance the number of TXOPs between links so that equal opportunities are given between them. The solution introduces a FR\_COUNT value. This is a variable that increases when a link performs a free-riding transmission and decreases when it skips a transmission caused by its own BO completion, but it can never be lower than zero. Skipped transmissions will be excluded from compensation, thus mitigating the backoff overflow problem. The solution has several optional features to be implemented according to what to skip when the FR\_COUNT of a link becomes higher than a limit as illustrated in Figure 6:

(**d**) Sync-FT vs. Option 3

**Figure 6.** Proposal 4: balancing transmissions between links (backoff count values after compensation are colored red).

#### **6. Performance Evaluation**

We evaluated and compared the performance of MLO with Sync-FT with the proposed solutions. Both throughput and latency performance were observed in the evaluation. The coexistence of MLDs with legacy SLDs was also considered. In addition, backoff count values were observed as a way to determine the effectiveness of the proposed solutions to the backoff overflow problem.

#### *6.1. Environmental Setup*

Each MLD had two links (Link 1 and Link 2) working in individual channels. RF power leakage between the links of an MLD was considered, so all MLDs were non-STR MLDs. Each EHT basic service set (BSS) was composed of an access point (AP) and connected device(s) (a single device in a single-spot scenario and multiple devices in a 3GPP indoor scenario). APs and MLDs were equipped with MLO capability, while legacy devices were not. All devices used the modulation and coding scheme (MCS) 7 in 80 MHz (i.e., data bit rate of 680.6 Mbps) with the aggregation MAC service data unit (AMPDU) of 64 MPDUs, where each MPDU was 1500 bytes long. We considered full-buffer traffic conditions. Proposal 1 used one as a consecutive free-riding transmission limit, Proposal 2 used Option 1, and Proposal 4 used Option 1 with the FR\_COUNT limit set to five. The operation frequency band of the network was 5 GHz, and the channel bandwidth was 20 MHz. Other system parameters followed those for the simulation scenario [6] and evaluation methodology [7] used for IEEE 802.11ax as listed in Table 1. All simulation results were obtained by averaging over five runs; in each run, 50 s were simulated.

**Table 1.** Simulation parameters.

We considered two deployment scenarios:

Each deployment scenario had two coexistence scenarios:

**Figure 7.** 3GPP indoor deployment scenario.

## *6.2. Single-Spot Deployment*

## 6.2.1. MLD vs. MLD

Figure 8 shows the performance results with one MLD BSS with Sync-PL and the other with various channel access schemes. Sync-PL was chosen as the benchmark, because it suits a non-STR MLD better than the basic Sync operation. In the figure, along with the proposed solutions, we also considered Sync-FT (with no backoff compensation), Sync-FT with a rechoose option (Sync-FT-Repick), and with backoff compensation (Sync-FT-Repick+Comp). From the throughput and latency results, we see that Sync-FT and its modified rechoose design (MLD1) had a significantly higher performance than Sync-PL, while the other schemes (except Proposal 4) showed only slightly better performance than Sync-PL. This is because the earlier designs are highly aggressive against Sync-PL. On the contrary, the proposed solutions (except Proposal 4) coexisted better with Sync-PL. One point to note is that Proposal 4 had a worse performance than Sync-PL, which was caused by the excessive penalties given to the free-riding link. Figure 8c shows that our solutions alleviated the backoff overflow problem. The problem was severe, with Sync-FT-Repick+Comp showing the largest value of the average backoff count. Sync-FT and Sync-FT-Repick did not show the problem since they did not use backoff compensation and, thus, showed aggressive behavior. The proposed solutions achieved both harmonized coexistence and alleviation of backoff overflow.

#### 6.2.2. MLD vs. Legacy SLD

The results of this scenario are presented in Figure 9. The case of legacy BSSs only (with no MLD BSS) is shown first labeled as "Legacy Only" in the graphs as a comparative measure to examine whether an EHT BSS has a positive or negative effect on the legacy performance. Compared to Sync-FT and Sync-FT-Repick, Sync-FT-Repick+Comp had a lower MLD performance in throughput and latency. This can be considered as due to the conservative behavior of Sync-FT-Repick+Comp; however, it is due to the backoff overflow problem as shown in Figure 9c. All the proposed solutions succeeded in suppressing the Sync-FT's channel access aggressiveness, while still maintaining good performance. Their average backoff count values were well limited compared to Sync-FT-Repick+Comp. The performance enhancement by mitigating the problem was especially noticeable in terms of latency; Figure 9b shows that Proposal 2 had 21.5% lower latency than Sync-FT-Repick+Comp. This implies that the proposed solutions were effective in solving the backoff overflow problem, while supporting the coexistence with legacy SLDs. On the other hand, it is also shown that the performance of legacy BSSs was also higher when half of them were replaced with an EHT BSS. This is due to the higher effectiveness of MLO in utilizing the channel medium and, thus, more room given to remaining legacy BSSs for channel access.

#### *6.3. 3GPP Indoor Deployment*

The indoor path loss model of the IEEE 802.11ax simulation scenario was used as given below:

$$PL(d) = 40.05 + 20\log\_{10}(f\_c/2.4) + 35\log\_{10}(d/5) \tag{1}$$

where *d* is a transmitter–receiver distance in meters, and *fc* is the center frequency in GHz. Then, the receive power (*Pr*) is obtained as

$$P\_r = P\_t + A\_t - PL(d) + A\_r \tag{2}$$

where *Pt* is the transmit power, and *At* and *Ar* are the antenna gains of the transmitter and receiver, respectively. The noise figure is 7 dB, and the noise floor is −94 dBm. We considered the transmission bit rates of IEEE 802.11ac (6.5 to 78 Mbps). The signal–to– noise ratio (SNR) vs. packet error rate (PER) curves of the IEEE 802.11ax's evaluation methodology [7] were used for packet error generation. For link adaptation, the highest bit rate with a PER lower than 10% was selected [9,10]. The control frames were transmitted at the lowest bit rate.

#### 6.3.1. MLD vs. MLD

With the same reasoning as the single-spot deployment, Sync-PL was also used as a comparative benchmark in this scenario. The evaluation results are given in Figure 10. From both throughput and latency results, we can see that Sync-FT-Repick+Comp had the worst performance compared to Sync-PL because of the backoff overflow problem. All of the proposed solutions showed increased performance that was similar to Sync-FT and Sync-FT-Repick. This means that they alleviated the backoff overflow problem. Another proof that the proposed solutions effectively alleviated the problem is shown in Figure 10c. The problem happened with Sync-FT-Repick+Comp, showing a significantly large value of the average backoff count. The problem was considerably alleviated by the proposed solutions, as they showed small average backoff count values. Among the solutions, Proposal 2 (limiting a compensated backoff value) showed a relatively high backoff count value, meaning it was less effective than the other solutions.

#### 6.3.2. MLD vs. Legacy SLD

The evaluation results of this scenario are presented in Figure 11. In the figure, Sync-FT-Repick+Comp showed lower performance than Sync-FT and Sync-FT-Repick, especially in the latency performance, which was possibly caused by backoff overflow. Figure 11c shows that Sync-FT-Repick+Comp suffered the backoff overflow problem. All proposed solutions mitigated the problem without ruining coexistence with the legacy BSSs. Proposals 1 and 4 showed slightly worse MLD performance, which was more noticeable in the latency performance. It is shown in Figure 11c that the average backoff count values of all proposed solutions were as small as Sync-FT and Sync-FT-Repick, thus proving that

they were effective in solving the backoff overflow problem. As observed in the results of the single-spot deployment scenario, the performance enhancement in this deployment scenario was also noticeable in terms of latency; Figure 11b shows that Proposal 2 had 13.5% lower latency than Sync-FT-Repick+Comp.

(**a**) Throughput

(**b**) Latency

(**c**) Average backoff count

**Figure 8.** MLD vs. MLD performance in the single-spot deployment scenario.

(**a**) Throughput

**Figure 9.** MLD vs. legacy SLD performance in the single-spot deployment scenario.

(**a**) Throughput

**Figure 10.** MLD vs. MLD performance in the 3GPP indoor deployment scenario.

285

(**a**) Throughput

**Figure 11.** MLD vs. legacy SLD performance in the 3GPP indoor deployment scenario.

#### **7. Conclusions**

Sync-FT is one of the best options for multilink channel access in IEEE 802.11be WLANs, especially for non-STR MLDs. Due to the raised coexistence issue of Sync-FT resulting from its aggressive channel access behavior, the backoff count compensation solution can be applied to it. In this paper, we identified the backoff count overflow problem of Sync-FT with backoff count compensation, which happens due to continuing free-riding transmissions and backoff count compensations, thus causing an unlimited increase in the backoff count value. We proposed four solutions to alleviate the problem and showed through comprehensive evaluation that all proposed solutions were effective in mitigating the problem while still preserving coexistence with other MLDs and legacy SLDs.

**Author Contributions:** This work was realized through the collaboration of all authors. W.M. contributed to the main results and simulation. J.-H.Y. organized the work, provided the funding, supervised the research, and reviewed the draft of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Research Program funded by the SeoulTech (Seoul National University of Science and Technology).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **References**

## *Article* **Popularity-Aware Closeness Based Caching in NDN Edge Networks**

**Marica Amadeo 1,2, Claudia Campolo 1,2,\*, Giuseppe Ruggeri 1,2 and Antonella Molinaro 1,2,3**

	- 91190 Gif-sur-Yvette, France

**Abstract:** By enabling name-based routing and ubiquitous in-network caching, Named Data Networking (NDN) is a promising network architecture for sixth generation (6G) edge network infrastructures. However, the performance of content retrieval largely depends on the selected caching strategy, which is implemented in a distributed fashion by each NDN node. Previous research showed the effectiveness of caching decisions based on content popularity and network topology information. This paper presents a new distributed caching strategy for NDN edge networks based on a metric called popularity-aware closeness (PaC), which measures the proximity of the potential cacher to the majority of requesters of a certain content. After identifying the most popular contents, the strategy caches them in the available edge nodes that guarantee the higher PaC. Achieved simulation results show that the proposed strategy outperforms other benchmark schemes, in terms of reduced content retrieval delay and exchanged data traffic.

**Keywords:** Named Data Networking; information centric networking; caching; edge networks; 6G

#### **1. Introduction**

A multitude of innovative applications, ranging from holographic telepresence to extended reality (XR), are expected to be delivered on top of sixth-generation (6G) networks, which would highly challenge the existing Internet infrastructure. Disruptive solutions are needed to cope with the demands of such future bandwidth-hungry and low-latency applications. By supporting name-based routing and ubiquitous in-network caching, the Named Data Networking (NDN) [1] paradigm is identified as a key enabler of 6G network architectures aimed at improving content distribution.

NDN is an information centric networking (ICN) architecture that promotes a communication model directly based on topology-independent content names, instead of internet protocol (IP) addresses. Content retrieval is based on the exchange of two named packets: the Interest, transmitted by the end-clients to retrieve the content, and the Data, transmitted by any node owning a copy of the content. Each Data packet is uniquely named and secured and, therefore, it can be cached by any NDN node in the path between the requester and the original source.

More specifically, NDN nodes are provided with a Content Store (CS) to cache incoming Data packets. The default caching strategy in NDN is Cache Everything Everywhere

(CEE) coupled with Least Recently Used (LRU) replacement, i.e., each node caches each incoming Data packet and, if the CS is full, the LRU policy is applied to remove an existing item and make room for the new one. Although this strategy can speed up the data retrieval, several studies have showed that better performance can be obtained if selective decision strategies are implemented that improve the cache diversity [2].

**Citation:** Amadeo, M.; Campolo, C.; Ruggeri, G.; Molinaro, A. Popularity-Aware Closeness Based Caching in NDN Edge Networks. *Sensors* **2022**, *22*, 3460. https:// doi.org/10.3390/s22093460

Academic Editor: Peter Han Joo Chong

Received: 29 March 2022 Accepted: 28 April 2022 Published: 2 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

One of the most important caching decision metrics is the content popularity. Typically, Internet contents show a skewed popularity distribution [3]: only a few contents are highly requested and deserve to be cached. Another crucial caching decision metric is the centrality of the nodes. The work in [4] focuses on the betweenness centrality metric and demonstrates that caching at the most central nodes can increase the cache hit probability and decrease the cache eviction rate, as these nodes are traversed by the majority of content requests. However, from the perspective of content retrieval, the node centrality should be re-defined by taking into account the capability of the node of satisfying the content requests, in addition to its topological feature [5,6].

So far, existing work [5–7] defined a popularity-aware betweenness centrality metric to enable coordinated caching decisions between distributed cachers. Basically, these strategies weight the betweenness centrality of a node with the popularity of the contents that can be transmitted through it. By introducing a relevant signalling among the nodes, collaborative decisions are deployed, where the most popular contents are cached in the most central nodes. However, in edge topologies, typically characterized by hierarchical topologies [6,8], the nodes with the highest betweenness centrality are also far away from the end-clients, i.e., the content consumers. Therefore, they cannot guarantee a low retrieval delay and a small network traffic. Instead, it would be crucial to cache the content as close as possible to the consumers to meet the proximity requirements of upcoming 6G applications.

In this paper, we define a new caching scheme based on a popularity-aware closeness (*PaC*) metric, which allows to cache the most popular contents in the edge nodes according to their proximity to the majority of requesters. Thanks to lightweight signalling piggybacked in Interest and Data packets, the potential cachers are ranked according to the *PaC* metric, and the best available cacher per path is selected. Performance evaluation shows that the conceived strategy is able to limit the retrieval delay while maintaining low exchanged traffic and the signalling overhead, compared to related literature based on the betweenness centrality metric [6].

The remainder of this paper is organized as follows. Section 2 provides background material on caching strategies in NDN. The proposal is discussed in Section 3 and evaluated in Section 4. Final remarks are reported in Section 5.

#### **2. Background and Motivations**

#### *2.1. NDN in a Nutshell*

In NDN, caching operations are embedded in the forwarding process of the Interest and Data packets, which is shown is Figure 1.

**Figure 1.** Forwarding process in NDN.

At the reception of an Interest packet, the node looks in the CS and, in case of a name matching, it immediately sends the Data back. Vice versa, the node checks if an equal request is pending in the Pending Interest Table (PIT) and, in case of a positive outcome, the incoming interface of the Interest is added to the PIT entry and the packet is discarded, thus reducing the traffic in the network. If the PIT matching fails, the Interest is forwarded according to named-based forwarding rules towards the original source.

When the Data packet arrives, the node checks for a name matching in the PIT and, in case of a positive outcome, the packet is cached and then forwarded towards the consumer(s). Vice versa, if the PIT matching fails, the Data is considered unsolicited and it is discarded.

The vanilla NDN caching strategy, CEE, typically leads to poor performance due to the lack of cache diversity [2]. A conventional scheme that limits the cache redundancy without introducing much complexity is Fixed Probability-based caching, where the Data packets are cached according to a fixed probability, usually set to 0.5 [9].

#### *2.2. Caching Strategies in the Literature*

To improve the content retrieval performance, several NDN caching strategies have been proposed in the last few years [2]. Among them, we can identify two major categories, namely popularity-based schemes and centrality-based schemes, which leverage, respectively, content popularity information and network topology information to select which contents to cache and where.

In popularity-based schemes [10–14], NDN nodes cache the most popular contents according to the locally measured rate of received Interests, which is stored in a Popularity Table. Typically, a threshold based mechanism is considered: contents that are requested a number of times higher than the threshold are cached.

In centrality-based schemes [4], instead, the caching decision depends on the *importance* of the nodes, expressed in terms of topological centrality. For instance, the pioneering proposal called *Betw* [4] leverages the betweenness centrality of the nodes as decision metric and replaces contents with the least recently used (LRU) policy. According to the graph theory, given a set *V* of network nodes, the betweenness centrality (*CB*) of a node *vi* ∈ *V* is defined as:

$$\mathcal{C}\_{B}(v\_{i}) = \sum\_{\upsilon\_{k} \neq \upsilon\_{j} \neq \upsilon\_{i} \in V} \frac{\sigma\_{\upsilon\_{k}, \upsilon\_{j}}(v\_{i})}{\sigma\_{\upsilon\_{k}, \upsilon\_{j}}},\tag{1}$$

with *σvk*,*vj* (*vi*) and *σvk*,*vj* being, respectively, the number of shortest content delivery paths from the two endpoints *vk* and *vj* that pass through *vi* and the total number of shortest content delivery paths between the same endpoints. *Betw* strategy is built on the following intuition: if a node *vi* is traversed by many content delivery paths, then it is more likely to get a cache hit. Therefore, contents are cached in the nodes with the higher betweenness centrality.

In [5], however, the authors observe that the topological centrality metric alone does not reflect the importance of a node from the content delivery perspective. Therefore, the authors define a new popularity-aware centrality metric, which aims at placing the most popular contents at high central nodes, and the remaining contents with decreasing popularity at nodes with decreasing centrality score. With the same target, the Betweenness and Edge Popularity caching (BEP) strategy [6] leverages a coordinated signalling mechanism piggybacked into Interest and Data packets. In BEP, the edge nodes (i.e., the leaf nodes directly connected to the consumers) track the number of received requests and periodically compute the content popularity with an exponential weighted moving average (EWMA) formula. The information is maintained in a Popularity Table, where contents are also ranked in terms of popularity. When a content request arrives, the edge node includes the correspondent popularity ranking in the Interest and forwards it towards the origin source. In addition, the Interest carries an array of betweenness centrality values, which is filled by all on-path routers. When the origin source receives the Interest, it compares the popularity ranking against the available betweeneess values and identifies the cacher by matching the two metrics, i.e., if the content has the highest popularity, it will be cached in the node with the highest centrality, and so on.

Despite their differences, all the noted approaches consider the betweenness centrality in the caching decision. However, this metric does not guarantee the minimum retrieval delay for the consumers. Indeed, especially when considering edge domains, typically characterized by hierarchical topologies [8], the nodes with the highest betweenness centrality are usually far away from the leaf nodes, where the consumers are attached. Instead, a peripheral edge node, e.g., a base station (BS), has typically low betweenness centrality, but it can be very close to the consumers and cover a key role as cacher.

Given a content *x*, the closest node to the requesters of *x* would be able to deliver the content with the lowest delay. Therefore, to take advantage of the limited cache capacity at the edge, it is necessary to select the most popular contents and cache them in the closest nodes along the delivery paths. In addition to reducing the content retrieval latency, caching contents close to the consumers allows for the reduction of intra-domain traffic. Indeed, contents may traverse a lower number of hops and free bandwidth resources over edge links.

Table 1 compares the main features of the related caching strategies available in the literature and our proposal.

**Table 1.** Comparison of caching strategies based on popularity and/or topology metrics.

#### **3. PaC-Based Caching**

*3.1. Main Pillars and Assumptions*

To capture the aforementioned needs and overstep the limitations of existing solutions, we propose a different topological metric that accounts for *the proximity of potential cachers to the consumers and is weighted by the content popularity*. We leverage the resulting metric, namely *PaC*, in a new strategy aimed at caching the most popular contents as close as possible to the majority of consumers in order to limit the data retrieval delay and the exchanged data traffic.

As shown in Figure 2, the reference scenario of our study is an edge domain, e.g., the backhaul network of a mobile network operator, a campus network, composed of a set *V* of NDN nodes [8]. A subset of nodes denoted as *I* ⊂ *V* act as ingress nodes that consumers are connected to. A few other nodes, instead, act as egress nodes towards the content sources, i.e., remote servers hosting the contents. A catalogue *X* of cacheable contents is considered.

For ease of reference, the key notations used in the paper are summarized in Table 2.

**Table 2.** Summary of the main notations.

**Figure 2.** Reference scenario.

All the nodes have caching capabilities and implement the traditional NDN forwarding fabric with the *best route* strategy, i.e., Interests are forwarded along the shortest path between ingress and egress nodes. A routing protocol, e.g., named-data link state routing protocol (NLSR) [15], is enabled for intra-domain dissemination of both connectivity and name prefix information.

To enable the PaC-based caching (PaCC), the following main modifications are foreseen to the legacy NDN routines, data structures, and packet fields:

Figure 3 shows the new fields introduced in the Interest and Data packets, respectively, that enable the PaC-based caching thanks to an implicit signalling mechanism, which will be clarified subsequently.

**Figure 3.** Overhauled NDN packets (fields with text in orange are those added by the PaCbased caching).

#### *3.2. Tracking Content Popularity*

Similarly to other schemes [6,10,11,13], the edge nodes track in the Popularity Table the received requests in order to identify the most popular contents.

Basically, the ingress nodes (green devices in Figure 2) counts the Interests received from consumers they are connected to, in order to determine the average request rate of each content. At the ingress node *vj* ∈ *I*, the average request rate for content *xn* is denoted as *Rvj* (*xn*).

The node periodically updates the average request rate, with a time interval *T* set to one minute, similarly to [13], to properly infer potential changes in the request patterns. Therefore, we assume each entry in the Popularity Table includes three fields: content name, average request rate, and current counter of requests.

In our design, the ingress nodes are also in charge of identifying the most popular contents that should be cached along a delivery path. More specifically, a content is considered popular by the ingress node *vj* if it is requested a higher number of times than a popularity threshold Θ*P*. This latter is computed as the EWMA of the average request rate per each requested content:

$$
\Theta\_P = (1 - \alpha)\Theta\_{P\_{\text{Old}}} + \alpha \overline{R\_{v\_{\text{j}}}} \tag{2}
$$

with

$$\overline{R\_{v\_j}} = \frac{\sum\_{n=1}^{M\_{v\_j}} R\_{v\_j}(\mathbf{x}\_n)}{M\_{v\_j}},\tag{3}$$

with *Mvj* being the number of distinct contents requested during the last time interval *T*, as perceived by node *vj*, and *α* ∈ (0, 1) set to 0.125 to avoid large fluctuations in the computation and give relevance to the historical values.

Because the Interest aggregation in the PIT hides the actual number of consumers requesting the same contents, a specific signalling mechanism is deployed to let intermediate nodes effectively track the request rate. More specifically, each time an ingress node *vj* forwards an Interest for content *xn* to the next on-path node *vi*, it includes the average request rate information in the RATE field. Of course, the same edge node *vi* can be in multiple shortest delivery paths towards the same content. For instance, node *v*<sup>4</sup> in Figure 2 is traversed by two shortest paths from the ingress nodes *v*<sup>8</sup> and *v*9. Instead, node *v*<sup>2</sup> is traversed by three shortest delivery paths from the ingress nodes *v*8, *v*9, and *v*10.

We denote as <sup>ˆ</sup>*Ii*(*xn*) <sup>⊂</sup> *<sup>I</sup>* the set of ingress nodes forwarding Interests for content *xn* to *vi*. In other words, *vi* belongs to the shortest paths connecting the ingress nodes belonging to ˆ*Ii*(*xn*), which receive the requests from the consumers, and the egress node towards the origin source. Since NDN implements only on-path caching, *vi* is a candidate cacher for a content *xn* for which requests are received by ingress nodes in ˆ*Ii*(*xn*). For instance, a content cached at *v*2, in Figure 2, may serve the requests coming from the three ingress nodes, *v*8, *v*9, *v*10.

The intermediate node *vi* (e.g., *v*<sup>4</sup> in Figure 2) collects the *Rvj* (*xn*) values from the Interests received through the incoming interfaces and calculates the local average request rate as:

$$R\_{v\_i}(\mathbf{x}\_n) = \sum\_{j \in \mathcal{I}\_i(\mathbf{x}\_n)} R\_{v\_j}(\mathbf{x}\_n). \tag{4}$$

When re-transmitting the Interest packet, *vi*, in its turn, overwrites the RATE field with the new cumulative value, thus the next-hop node will be aware of the average number of requests that can be satisfied with a Data packet over that incoming interface. The next-hop node (e.g., *v*<sup>2</sup> in Figure 2) also calculates the cumulative request rate, and so on.

#### *3.3. Popularity-Aware Closeness Metric*

The PaC metric of a potential cacher *vi* for content *xn*, *PaC*(*vi*, *xn*), considers the distance, in terms of hop count, between *vi* and the ingress nodes connected to the consumers. Since, in NDN, *vi* receives Interests for *xn* from an ingress node *vj* only if it is in the forwarding path between *vj* and the origin source, *PaC*(*vi*, *xn*) takes into account only the set of ingress nodes ˆ*Ii*(*xn*).

In parallel, the metric considers the number of consumers that could be satisfied by the potential cacher. The higher is the number of requests for *xn* that cross *vi*, the higher should be the PaC metric.

In mathematical terms, the PaC metric for a node *vi* ∈ *V* and a content *xn* can be expressed as:

$$\text{PaC}(v\_i, \mathbf{x}\_n) = \frac{R\_{v\_i}(\mathbf{x}\_n) |f\_i(\mathbf{x}\_n)|}{\sum\_{j \in \vec{I}\_i(\mathbf{x}\_n)} (h\_{(v\_i, v\_j)} + 1)} \tag{5}$$

where <sup>|</sup>ˆ*Ii*(*xn*)<sup>|</sup> is the cardinality of the set of ingress nodes in <sup>ˆ</sup>*Ii*(*xn*), used to normalize the metric, and *h*(*vi*,*vj*) is the hop distance between *vi* and the ingress node *vj*.

It can be observed that *PaC*(*vi*, *xn*) increases with the request rate of *xn* and it is equal to zero if *vi* does not receive any request for *xn*. At the same time, the metric decreases if *vi* is far from the consumers.

#### *3.4. Caching Algorithm*

When an Interest for content *xn* arrives at an ingress node *vj*, the latter updates the corresponding entry in the Popularity Table, checks if the content is popular, and then accesses the CS to find a matching Data packet to send back immediately. If the CS lookup fails, then *vj* checks the PIT. If this lookup also fails, then *vj* acts differently depending whether the content is popular, i.e., its average request rate is higher than the popularity threshold, or not. If it is not popular, then there is no need to cache it along the path. Therefore, *vj* increases by one the HOPCOUNT field of the Interest, fills the RATE field, in order to allow the next hop updating the Popularity Table, but leaves the PAC field to the default zero value, to indicate that the content is not popular. The request will be forwarded towards the origin server according to the standard NDN forwarding fabric. Of course, it may happen that an edge on-path node belonging to multiple delivery paths has cached the content (because it is considered popular by another ingress node) and, therefore, the request can be still satisfied at the edge.

The returning Data packet, being not popular, should not be cached. However, to make the best of the available storage space, unpopular Data packets can be cached in case the CS is not full, e.g., during the network bootstrap phases.

Vice versa, if *xn* is popular, then *vj* updates all the new fields of the Interests, i.e., HOPCOUNT, RATE, and PAC, and transmits the packet to the next-hop, according to the FIB entry.

The subsequent node *vi* receiving the Interest performs a slightly different processing. First, it accesses the information from the Interest header fields and checks if the Popularity

Table needs to be updated. In NDN, Interests cannot loop, therefore a newly received Interest carries consistent information in the header fields. The latter can be equal to the previously recorded one, if the request pattern has not changed. The node then performs a lookup in the CS for a match. If the Data packet is found, then *vi* computes its PaC metric and compares it with the value in the PAC field. If its value is greater, then it overwrites the field and sends the packet back. Vice versa, if its PaC value is smaller, it simply sends the Data packet without altering it. The receiving node with the highest PaC will also cache the Data, thus moving the copy closer to the consumers.

In case the CS and the consequent PIT matching fail, *vi* computes its PaC and, if its value is greater than the current one, it updates the PAC, HOPCOUNT, and RATE fields. Conversely, if the PaC is lower than the current one, it only updates the HOPCOUNT and RATE fields. It then re-transmits the request according to the FIB and waits for the Data packet.

When finally receiving the Interest, the origin server, or an intermediate cacher, copies the PaC value from Interest to the corresponding field in the Data packet header and transmits the packet. The first node with the corresponding PaC will cache the Data. If the CS if full, an existing item is replaced according to the LRU policy.

The flowcharts summarizing the Interest processing and Data processing for the PaC-based caching are depicted in Figure 4 and Figure 5, respectively.

**Figure 4.** Interest processing in the presence of PaC-based caching.

**Figure 5.** Data processing in the presence of PaC-based caching.

#### *3.5. A Toy Example*

To better understand the PaC metric, we consider the toy example in Figure 6 that includes eight edge nodes in a hierarchical topology. The nodes *v*1, *v*2,...,*v*<sup>5</sup> are ingress nodes tracking the average content request rate. For the sake of simplicity, we assume that three distinct popular contents, namely *x*1, *x*2, *x*3, should be cached at the edge and their request rate is stable. The available storage space at each node allows for caching only one content.

It can be observed that the average request rate for *x*1, the most requested content at the edge, is 22 at *v*<sup>1</sup> and 20 at *v*2, *v*3, whereas it is 6 at *v*5. When computing the PaC metric for the nodes traversed by the Interests for *x*1, according to Equation (5), it results in *PaC*(*v*1, *x*1) = 22, *PaC*(*v*2, *x*1) = *PaC*(*v*3, *x*1) = 20, *PaC*(*v*5, *x*1) = 6, *PaC*(*v*6, *x*1) = <sup>62</sup>·<sup>3</sup> <sup>6</sup> = 31, *PaC*(*v*7, *x*1) = <sup>6</sup>·<sup>1</sup> <sup>2</sup> <sup>=</sup> 3, and *PaC*(*v*8, *<sup>x</sup>*1) = <sup>68</sup>·<sup>4</sup> <sup>12</sup> = 22.66. The node with the highest PaC metric for *x*<sup>1</sup> is *v*6, which is indeed the node closer to the majority of consumers that are attached to the ingress nodes *v*<sup>1</sup> − *v*3. If instead we consider the path {*v*<sup>5</sup> → *v*<sup>7</sup> → *v*8}, the node with the highest PaC is *v*8. However, caching *x*<sup>1</sup> at *v*<sup>6</sup> would imply that the node at the upper layer, *v*8, will not receive further Interests for *x*<sup>1</sup> and therefore, its local request rate will decrease. As a consequence, in a subsequent time window, *x*<sup>1</sup> will be cached at *v*5.

Vice versa, an approach based on the betweenness centrality, like BEP, would be considered as best cacher for *x*<sup>1</sup> node *v*8, which has the highest centrality, but it is also the farthest away from the consumers. Therefore, caching *x*<sup>1</sup> at *v*<sup>8</sup> would highly increase the retrieval delay and the intra-domain traffic.

Content *x*<sup>2</sup> is requested only at *v*<sup>4</sup> and *v*<sup>5</sup> and it results in *PaC*(*v*4, *x*2) = 15, *PaC*(*v*5, *x*2) = 3, *PaC*(*v*7, *x*2) = <sup>18</sup>·<sup>2</sup> <sup>4</sup> <sup>=</sup> 9, *PaC*(*v*8, *<sup>x</sup>*2) = <sup>18</sup>·<sup>2</sup> <sup>6</sup> = 6. The node with the highest PaC metric is *v*<sup>4</sup> which, again, is the one closer to the majority of consumers. Therefore, the majority of requests will be served with minimum delay and with minimum intra-domain traffic. To serve requests coming from path {*v*<sup>5</sup> → *v*<sup>7</sup> → *v*8}, instead, *v*<sup>7</sup> would be selected as cacher.

By following the same procedure, it can be found that the higher PaC for content *x*<sup>3</sup> is obtained at *v*8.

**Figure 6.** Toy example: an edge network with eight nodes.

#### **4. Performance Evaluation**

#### *4.1. Simulation Settings*

The proposed caching strategy has been implemented in ndnSIM, the official simulator of the NDN research community [16]. As representative edge domain, we consider a tree topology randomly generated with the Georgia Tech Internetwork Topology Models (GT-ITM) [17]. The topology includes 20 intermediate nodes and 8 leaves acting as ingress nodes. The root node connects the edge domain with a remote server acting as content producer. Because the performance assessment is focused on the edge domain, the external network is simply simulated as a link, with latency of 30 ms [18], between the root node and the server. The latency of edge links is instead uniformly distributed in the range [2–5] ms.

We consider a catalog of 15,000 contents, each one consisting of 1000 Data packets 1 Kbyte-long. A variable number of consumers attached to the leaf nodes of the topology, request contents according to the Zipf's law [3], with skewness parameter *α* set to 1. In these settings, we consider two distinct simulation scenarios.

• In the first scenario, we assume that the total caching capacity of the edge domain, uniformly distributed among the nodes, is varying from 0.25% to 2% of the overall catalog size, similarly to the values reported in [19]. The number of consumers is set to 60.

• In the second scenario, we assume that the cache capacity is fixed to 0.5% of the overall catalog size, whereas the number of consumers range from 20 to 70. The main simulation settings are summarized in Table 3.

**Table 3.** Main simulation settings.

We compare the proposed model (labeled as *PaCC* in the plots) against the following benchmark solutions:

For all the noted schemes, the replacement policy is LRU. The following performance metrics are considered:

The first two metrics capture the effectiveness of the compared schemes in caching content copies in proximity to the consumers. The last metric provides insights about the efficiency of the schemes, in terms of traffic exchanged in the network. Results are averaged over 10 runs and reported with 95% confidence intervals.

#### *4.2. Results*

#### 4.2.1. Impact of the Cache Size

Figure 7 shows the performance metrics when varying the cache size of the edge domain from 0.25% to 2% of the content catalogue size. As expected, it can be observed that, as the cache size increases, performance improves for all the considered schemes. Indeed, the higher the storage space at the edge, the higher is the number of contents that can be stored, with consequent advantages in terms of reduced retrieval delay, number of hops, and exchanged traffic.

**Figure 7.** Metrics when varying the cache size of the edge domain from 0.25% to 2% of the content catalogue size (number of consumers equal to 60).

Being oblivious of content popularity and topology information, the simplest CEE solution shows the worst performance in terms of content retrieval delay, due to higher number of hops traversed to reach the requested content. It generates the highest load of exchanged NDN packets. The Prob scheme slightly outperforms CEE, because it does not cache indiscriminately contents but it tries to better distribute them in the CS of edge nodes.

As the cache size of the edge domain increases, differences among the two decrease, because there is higher chance to find storage space for caching contents within nodes.

PaCC outperforms all the other schemes in terms of all the considered metrics. However, the gap with BEP reduces as the edge domain is more capable to cache contents.

To conclude the analysis, Figure 8 shows the percentage of Interest packets that reach the origin server because it has not been found a CS matching at the edge. Reasonably, the traffic to the cloud reduces when the storage space at the edge increases, with PaCC outperforming all the benchmark schemes.

**Figure 8.** Percentage of Interest packets that are forwarded to the origin server.

#### 4.2.2. Impact of the Number of Consumers

The second set of results, reported in Figure 9, measures the metrics of interest when varying the number of consumers.

Under such settings, the proposed PaCC solution achieves the best performance in terms of content retrieval delay, number of hops, and exchanged NDN packets.

It can be observed that, as the number of consumers increases, all schemes experience a shorter delay and a lower number of hops. Such a behaviour has to be ascribed to the fact that under the simulated settings, due to the Zipf distribution, a higher number of requests, from different consumers, concentrate on the same few contents, the most popular ones. Hence, such contents are more likely to be cached in the edge domain, instead of being retrieved from the original producer. The number of exchanged packets, instead, reasonably increases with the number of consumers, to account for the increasing number of Interests issued by more consumers and number of Data packets forwarded to each single consumer.

#### 4.2.3. Overhead Analysis

To better show the pros and cons of the conceived solution, we summarize in Table 4 the main differences between the compared schemes in terms of incurred overhead, i.e., additional signalling bytes piggybacked in the exchanged NDN packets. A high signalling overhead introduced by a caching strategy could deteriorate the content retrieval performance, e.g., by increasing the content retrieval delay due to the transmission of larger packets that occupy the channel for a longer time and may generate a higher channel load and resulting congestion. It is worth observing that the blind CEE and Prob schemes incur no additional overhead. Similarly to PaCC, BEP foresees one additional field in the Data packet to convey the maximum betweenness to be compared with that of the nodes along the backforwarding path. It is the PaC metric in our proposal. Three additional fields per Interest are foreseen by PaCC, for a total of 10 bytes (less than 1% overhead per packet). For BEP, the overhead per Interest is a function of the number of nodes traversed along the path (|Π|) by the packet carrying the BETWEENNESSARRAY field. For a path made of 5 nodes the overhead gets equal to 24 bytes. Under the majority of settings (|Π| > 1), PaCC is also more efficient than BEP in terms of exchanged bytes in the network per packet. Therefore, the signalling overhead introduced by PaCC is extremely low, which contributes to limit

the retrieval delay metric, as showed in Figures 7 and 9.

**Figure 9.** Metrics when varying the number of consumers (cache size equal to 0.5% of the catalogue size).

**Table 4.** Additional fields per packet: PaCC vs. benchmark schemes.

#### **5. Conclusions**

In this work we have proposed a novel caching strategy for edge domains, called PaCC, which accounts for content popularity and proximity to the consumers. Achieved results, collected under a variety of settings, confirm that the devised solution allows more judicious content caching decisions that are particularly crucial when the storage capabilities of the edge domain are small. As a consequence, the content retrieval delay experienced by PaCC is reduced compared to the considered benchmark schemes.

As a further benefit, the proximity of contents to consumers achieved by PaCC allows for reduction in the overall amount of exchanged data traffic at the expense of a negligible additional overhead per NDN packet. Such a finding is relevant because future networks will be overwhelmed by a myriad of (huge) contents exchanged by massively deployed devices and requested by increasingly demanding users.

The performance of the conceived solution can be further improved by addressing the following aspects: (i) optimizing the method for tracking the content popularity, (ii) optimizing the computation of the popularity-aware closeness metric. In PaCC, a threshold-based mechanism is implemented to track the popularity of contents based on the number of received content requests. However, more accurate mechanisms could be introduced in our design, for instance based on artificial intelligence (AI) content popularity prediction algorithms [20]. In parallel, more accurate metrics could be considered to estimate the proximity of the cachers to the consumers. In our design, we leverage the hop count metric, which, however, cannot reflect the presence of congested links or congested nodes. The proximity information could be improved by taking into account other additional metrics like the round-trip-time over the network links and/or the load on the nodes.

**Author Contributions:** Conceptualization, M.A., C.C., and G.R.; methodology, M.A. and C.C.; software, M.A.; validation, M.A.; investigation, M.A., C.C., and G.R.; writing—original draft preparation, M.A. and C.C.; writing—review and editing, M.A. and C.C.; supervision, A.M. and G.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **New Results for the Error Rate Performance of LoRa Systems over Fading Channels**

**Kostas Peppas 1,\*, Spyridon K. Chronopoulos 2,3,\*, Dimitrios Loukatos <sup>4</sup> and Konstantinos Arvanitis <sup>4</sup>**

**Abstract:** Long Range (LoRa) systems have recently attracted significant attention within the research community as well as for commercial use due to their ability to transmit data over long distances at a relatively low energy cost. In this study, new results for the bit error rate performance of Long Range (LoRa) systems operating in the presence of Rayleigh, Rice, Nakagami-*m*, Hoyt, *η*-*μ* and generalized fading channels are presented. Specifically, we propose novel exact single integral expressions as well as simple, accurate expressions that yield tight results in the entire signal-to-noise ratio (SNR) region. The validity of our newly derived formulas is substantiated by comparing numerically evaluated results with equivalent ones, obtained using Monte-Carlo simulations and exact analytical expressions.

**Keywords:** bit error rate; fading channels; Internet of things; LoRa; performance evaluation

#### **1. Introduction**

In recent years, the exponential growth in the number of inexpensive, Internetconnected devices has given birth to the Internet of things (IoT) and its numerous applications, including autonomous farming, wearable health monitoring, smart homes and cities. Nevertheless, the increasing number of connected devices in conjunction with memory, bandwidth and energy availability constraints has revealed the limits of traditional connectivity technologies, namely ZigBee, Bluetooth and WiFi, in terms of energy consumption, scalability and throughput [1].

In order to fulfill the communication requirements of the IoT, the so-called Low-Power Wide Area Networks (LPWAN) have recently attracted significant attention within the research community as well as for commercial use, due to their ability to complement traditional cellular and short-range wireless technologies in an efficient manner [2–5].

Among all available LPWAN protocols, the so-called LoRa (Long Range) technology [6] has emerged as a promising candidate for smart sensing technology for civil (e.g., environment and health monitoring, smart metering, precision agriculture) and industrial applications, in urban and rural environments, due to its long-range and low-power capabilities. LoRa modulation is a 3GPP standard based on the chirp spread-spectrum (CSS) technology [7–20] and uses the industrial, scientific and medical (ISM) frequency bands at 433 MHz, 868 MHz or 915 MHz with data rates of up to 50 kbps.

Although the LoRa technology is well documented in [6], there are still relatively few studies on its theoretical performance. A summary of related works is presented in Table 1.

**Citation:** Peppas, K.; Chronopoulos, S.K.; Loukatos, D.; Arvanitis, K. New Results for the Error Rate Performance of LoRa Systems over Fading Channels. *Sensors* **2022**, *22*, 3350. https://doi.org/10.3390/ s22093350

Academic Editor: Peter Han Joo Chong

Received: 27 March 2022 Accepted: 25 April 2022 Published: 27 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Table 1.** Related works on theoretical performance of LoRa systems in the presence of fading and noise.

Specifically, the mathematical representation of the LoRa modulation/demodulation process and its performance in terms of the symbol and bit error rates for additive white Gaussian noise (AWGN) and frequency selective fading channels were addressed in [7]. In [21], a moment matching method was employed to obtain accurate closed-form approximations for AWGN and Rayleigh fading channels. Multi-antenna LoRa systems were addressed in [11,24]. The performance of relay-based LoRa networks was addressed in [25]. A first attempt to provide exact BER expressions for Rayleigh, Rice and Nakagami-*m* fading is available in [22]. Nevertheless, as was pointed out in [21,23], the proposed methodology for channels other than Rayleigh may suffer from numerical stability issues, due to the computation of large values of binomial coefficients. To this end, ref [23] leveraged the properties of the Marcum Q-function to provide accurate approximations for the BER of LoRa systems over Rice and Nakagami-*m* fading channels.

However, several results obtained using this method, i.e., for Nakagami-*m* fading, require the computation of hypergeometric functions with two arguments [23], which in turn are not available as built-in functions in standard mathematical software packages such

as Matlab or Mathematica [26]. Moreover, for the numerical evaluation of the underlying mathematical expressions, the computation of an approximation threshold parameter is required. Nevertheless, the exact computation of this threshold is rather complicated and therefore, a heuristic method for its computation was proposed by the authors in the same work. The above facts motivate simpler, yet accurate expressions for the evaluation of the BER of LoRa systems in the presence of noise and fading. On the other hand, analytical results for the error performance of LoRa systems in the presence of fading channels other than Rayleigh, Rice and Nakagami-*m*, are—to the best of our knowledge—not available in the open technical literature. Indeed, as it was pointed out in [27], the above mentioned classical fading models do not always fit well measured data, especially at the tail portion. This motivates research on performance evaluation over generalized fading models that include the classical ones as special cases.

Motivated by the above facts, in this study we present new analytical expressions for the average bit error rate evaluation of LoRa systems in the presence of fading. More specifically, the novel research contributions of this work can be summarized as follows.

In order to validate the correctness of the proposed mathematical analysis, all analytical results are substantiated by means of Monte-Carlo simulations. Note that the proposed analytical framework provides accurate results in the entire SNR range, thus circumventing the need for evaluating system performance via time consuming Monte-Carlo simulations (It is a common practice to use Monte-Carlo simulations in order to verify the correctness of analytical results. Please note that although Monte-Carlo simulations may also be used to obtain performance evaluation results, they suffer from two significant disadvantages, as compared to analytical results. First, one has to specify the system model using software defined components, i.e., to simulate channel, noise, modulation, demodulation and detection. Although this process provides further insights on the system structure, it is computationally very intensive, time consuming and requires large amounts of memory to achieve a given accuracy. Specifically, as a rule of thumb, in order to obtain exact BER results of the order of 10<sup>−</sup>6, random samples of two orders of magnitude larger, namely 108, are required. Such large vectors are difficult to be handled by software tools such as Matlab. On the other hand, analytical results in the form of equations yield accurate results within a large range of system level parameters). The remainder of this work is structured as follows. Section 2 presents an overview of the LoRa modulation and its BER performance. Section 3 presents the main results of this work. Numerical results are presented in Section 4 whereas Section 5 concludes the work. *Notations:* A list of mathematical notations used in this work is available in Table A1.

#### **2. Overview of the LoRa Modulation**

In this section, an overview of the LoRa modulation and the corresponding bit error probability are presented. LoRa systems employ the shift chirp modulation scheme, also known as spread spectrum modulation. The number of samples within the duration of a symbol, *Ts*, is determined by the spreading factor (SF). It holds that *Ts* = 2SF/*B*, where *B* is the signal bandwidth. In typical applications, SF ∈ {6, 7, ... , 12}. Note that the coverage of LoRa is determined by SF. Specifically, increasing SF results in wider coverage but also in a reduction in the data rate.

The modulation encoder maps a group of SF bits to a symbol, *sk*, *k* ∈ {0, 1, ... *L*} where *<sup>L</sup>* <sup>=</sup> <sup>2</sup>SF <sup>−</sup> 1. The transmitted waveform can be expressed as [21]

$$s\_k(nT) = h\sqrt{E\_s}\omega\_k(nT\_s) \tag{1}$$

$$\eta = h \sqrt{\frac{E\_s}{N}} \exp\left\{ j2\pi\frac{n}{N} [(k+n) \mod N] \right\} \tag{2}$$

where *<sup>N</sup>* <sup>=</sup> 2SF, *Ts* <sup>=</sup> 1/*<sup>B</sup>* is the sampling period, *<sup>n</sup>* ∈ {0, 1, ... *<sup>L</sup>*} is the sample index at time *nTs*, *Es* is the signal energy, *h* is the fading channel coefficient and *ωk*(*nTs*) are orthonormal basis functions.

Figure 1 depicts the main functional blocks of a LoRa non-coherent demodulator. Specifically:

**Figure 1.** A simplified overview of the LoRa non-coherent demodulator.

Using the orthogonal properties of *sk*(*nT*), the correlator output at the demodulator is given as [21]

$$\sum\_{n=0}^{L} r\_k(nT)\omega\_i^\*(nT) = \begin{cases} h\sqrt{E\_s} + \phi\_i & \text{if } k=i\\ \phi\_i & \text{if } k \neq i \end{cases} \tag{3}$$

where *rk*(·) is the received signal and *φ<sup>i</sup>* is the complex Gaussian noise. The decision rule for the detected index symbol can be expressed as [21]

$$\hat{k} = \{i \vert \arg\_i \max\left( \vert \delta\_{k,i} h \sqrt{E\_s} + \phi\_i \vert \right)\}. \tag{4}$$

The conditional symbol error probability given the squared channel coefficient *h* is given as [21–23]

$$P(e|h) = \Pr\{\rho^2 > |h\sqrt{E\_s} + \phi\_i|^2\}\tag{5}$$

where *<sup>ρ</sup>*<sup>2</sup> <sup>=</sup> max{|*φi*|}|*<sup>i</sup>*<sup>=</sup>*<sup>k</sup>* is the maximum of *<sup>L</sup>* independent and identically distributed (i.i.d) exponential random variables with CDF given by

$$F\_{\rho^2}(\mathbf{x}) = \left[1 - \exp(-\mathbf{x}/2)\right]^L. \tag{6}$$

Moreover, the RV *R* |*h* <sup>√</sup>*Es* <sup>+</sup> *<sup>φ</sup>i*<sup>|</sup> <sup>2</sup> conditioned to *h*<sup>2</sup> follows a non-central chi-square distribution with PDF given by [21–23]

$$f\_{R|h^2}(\mathbf{x}) = \frac{1}{2} \exp\left(-\frac{\mathbf{x} + 2Nh^2\gamma}{2}\right) I\_0\left(\sqrt{2Nh^2\gamma\mathbf{x}}\right),\tag{7}$$

where *<sup>γ</sup>* <sup>=</sup> 1/E|*φi*<sup>|</sup> <sup>2</sup> is the SNR. The CDF of *<sup>R</sup>* conditioned to *<sup>h</sup>*<sup>2</sup> can be expressed in terms of the Marcum Q-function as

$$F\_{R|h^2}(\mathbf{x}) = 1 - Q\_1\left(\sqrt{2Nh^2\gamma\_\prime}\sqrt{\mathbf{x}}\right). \tag{8}$$

Finally, using (5)–(7), the average symbol error probability is given in terms of the following two-fold integral [21–23]

$$P\_s = \frac{1}{2} \int\_0^\infty \int\_0^\infty \left\{ 1 - \left[ 1 - \exp(-x/2) \right]^L \right\} $$

$$\times \exp\left( -\frac{x + 2Ny\gamma}{2} \right) I\_0\left( \sqrt{2N\gamma xy} \right) f\_{h^2}(y) \text{dxdy}.\tag{9}$$

The resulting bit error probability can be expressed as [21,23]

$$P\_b = \frac{2^{\text{SF}-1}}{2^{\text{SF}} - 1} P\_s. \tag{10}$$

#### **3. Main Results**

In this section, exact analytical expressions for *Ps* in terms of a single integral as well as accurate approximations will be obtained for Nakagami-*m*, Ricean and Hoyt fading channels.

#### *3.1. Symbol Error Probability for Nakagami-m Fading Channels*

Under Nakagami-*m* fading, the RV *h*<sup>2</sup> follows a gamma distribution with PDF given as [28]

$$f\_{h^2}(y) = \frac{m^m}{\Gamma(m)} y^{m-1} \exp(-my) \tag{11}$$

where *m* > 0 is the fading parameter. For *m* = 1, i.e., for Rayleigh fading, (11) reduces to the exponential distribution. An exact analytical expression for *Ps* is given in the following proposition.

**Proposition 1.** *The exact symbol error probability of LoRa systems under Nakagami-m fading in terms of a single integral is given as*

$$\begin{split}P\_s^{\text{Nak}} &= \frac{1}{2} \left(\frac{m}{N\gamma + m}\right)^m \int\_0^\infty e^{-\mathbf{x}/2} [1 - (\mathbf{1} - e^{-\mathbf{x}/2})^L] \\ &\times \mathcal{L}\_{-m} \left[\frac{N\gamma \mathbf{x}}{2(N\gamma + m)}\right] \mathbf{d}x \end{split} \tag{12}$$