**2.2 Single-site system model**

In wireless communication, the Base Station (BS) and User Equipment (UE) engage in point-to-point communication as shown in **Figure 1**. The BS may function

*Localization Techniques in Multiple-Input Multiple-Output Communication: Fundamental… DOI: http://dx.doi.org/10.5772/intechopen.112037*

as an Access Point (AP) or as another device in device-to-device communication. Typically, the BS has multiple antenna array elements while the UE may have one or more antenna elements. A general assumption is that the BS and UE are located in the far-field zones of each other, and multiple propagation paths exist between them. Multipaths arise from either reflection off objects or scattering [43]. Typically, there is a Line-of-Sight (LOS) path and several Non-LOS (NLOS) paths. The LOS path can be blocked, in which case only NLOS paths may exist.

Regardless of which side transmits the signal, the propagation path geometry between the BS and UE remains the same. Each path is characterized by an Angle-of-Departure (AoD), an Angle-of-Arrival (AoA), a Time-of-Arrival (ToA), and a complex gain. Since the signal geometry is invariant, it is possible to use AoA and AoD interchangeably. The AoD and AoA are vectors that define the azimuth and elevation angles in 3D space, while ToA represents the time it takes for the propagating signal to travel from the transmitter to the receiver. The ToA is sometimes referred to as the propagation path *delay*. ToA is equal to the length of the path traveled (*d*) divided by the speed of light (*c*):

$$
\mathfrak{r} = \mathfrak{d}/\mathfrak{c}.\tag{1}
$$

The 2D multipath propagation geometry is illustrated in **Figure 2**. In the LOS case, the shortest distance between the BS and UE represents the path traveled by the LOS signal. Furthermore, **Figure 2(a)** shows the AoD from the BS *θt LOS* and AoA at the UE *θr LOS*. On the other hand, the NLOS propagation path can be modeled using a *virtual BS* (BS') [43] as depicted in **Figure 2(b)**. A NLOS path can be thought of as direct path from a virtual node behind the reflecting surface. The virtual BS is on the opposite side of the reflecting surface, maintaining the same distance from it as the original BS, resulting in *dNLOS*1 ¼ *d*0 *NLOS*1. The total path traveled by the NLOS signal is *dNLOS* ¼ *dNLOS*1 þ *dNLOS*2. Furthermore, the AoD from the virtual BS can be calculated as *π* � *θ t NLOS*, where *θt NLOS* is the AoD at the original BS.

#### **2.3 Channel model**

The wireless communication community has widely adopted the COST 2100 MIMO channel model [44] as the predominant geometric channel model. This model

**Figure 2.**

*(a) LOS propagation path geometry for estimating relative location of the UE with respect to the BS. (b) NLOS propagation path and virtual BS (BS') geometry for estimating relative location of the UE with respect to the BS.*

expresses that a propagation environment can be defined by a set of scatterers that create clusters of multipath components. The model is applicable for both sub-6 GHz and mmWave band frequencies.

Consider a MIMO Orthogonal Frequency-Division Multiplexing (OFDM) wireless system, in which the BS and the UE are equipped with antenna arrays with *NB* and *NU* elements, respectively. The system uses OFDM signaling with *NC* subcarriers and the wideband channel has *L* taps. The received signal at the *l th* subcarrier of the UE antenna array can be expressed as

$$\mathbf{y}\left[l\right] = \mathbf{H}\left[l\right]\mathbf{s}\left[l\right] + \mathbf{n}\left[l\right].\tag{2}$$

Here, *y*½ �*l* ∈ *NU*�1 denotes the received signal, *H* ½ �*l* ∈ *NU*�*NB* represents the channel matrix, *s*½ �*l* ∈ *NB*�1 represents the transmitted signal, and *n*½��*l* **N 0**, , *σ*2 ð Þ*I* denotes the noise at the receiver.

The propagation paths between the BS and the UE can be split into *C* distinguishable path clusters, with each cluster containing *RC* distinguishable paths. Each path cluster is characterized by a mean time delay *τ* ð Þ*k m* , *k*∈ 1, … ,*C*, *m* ∈1, … , *RC*, a mean AoD *θtx c* , *ϕtx c* ∈ ½ Þ 0, *π* , and a mean AoA *θrx c* , *ϕrx c* ∈ ½ Þ 0, 2*π* . Each cluster contributes *RC* paths between the transmitter and the receiver, where each path has a relative time delay *τcm* (relative with respect to mean), a relative AOD *θ tx cm* , *ϕtx cm* , a relative AOA *θrx cm* , *ϕrx cm* , and a complex path gain *αcm* . The mean and relative paths are illustrated in **Figure 3**.

#### **2.4 Channel state information (CSI)**

Assuming the channel model defined above, the complex baseband delay-ℓ MIMO channel matrix *H* ½ � ℓ ∈ *NU*�*NB* can be written as [45, 46]

**Figure 3.** *The mean and relative paths of a NLOS path.*

*Localization Techniques in Multiple-Input Multiple-Output Communication: Fundamental… DOI: http://dx.doi.org/10.5772/intechopen.112037*

$$\mathbf{H}[\boldsymbol{\ell}^{\varepsilon}] = \sqrt{\frac{N\_{\mathrm{B}}N\_{\mathrm{U}}}{P\_{\mathrm{pl}}}} \sum\_{\varepsilon=1}^{C} \sum\_{c\_{\mathrm{m}}=1}^{R\_{\mathrm{C}}} a\_{\varepsilon\_{\mathrm{m}}} \mathbf{e}\_{\mathrm{x}} \Big(\boldsymbol{\theta}\_{\varepsilon}^{\mathrm{x}\mathrm{x}} + \boldsymbol{\theta}\_{\varepsilon\_{\mathrm{m}}}^{\mathrm{x}\mathrm{x}}, \boldsymbol{\theta}\_{\varepsilon}^{\mathrm{x}\mathrm{x}} + \boldsymbol{\phi}\_{\varepsilon\_{\mathrm{m}}}^{\mathrm{x}\mathrm{x}}\Big) \mathbf{e}\_{\mathrm{x}}^{H} \Big(\boldsymbol{\theta}\_{\varepsilon}^{\mathrm{x}\mathrm{x}} + \boldsymbol{\theta}\_{\varepsilon\_{\mathrm{m}}}^{\mathrm{x}\mathrm{x}}, \boldsymbol{\phi}\_{\varepsilon}^{\mathrm{x}} + \boldsymbol{\phi}\_{\varepsilon\_{\mathrm{m}}}^{\mathrm{x}\mathrm{x}}\Big) \delta(\boldsymbol{\ell}^{\prime}\boldsymbol{T}\_{\mathrm{s}} - n\_{\mathrm{c}}\boldsymbol{T}\_{\mathrm{s}}), \tag{3}$$

where ℓ ¼ 0, 1, … , *L* � 1*:* Furthermore, *Ppl* indicates the pathloss between the transmitter and the receiver, while *etx*ð Þ *θ*, *ϕ* ∈ *NB*�1 and *erx*ð Þ *θ*, *ϕ* ∈ *NU*�1 denote the antenna array response vectors of the transmitter and the receiver, respectively. *δ*ð Þ*t* is the Dirac function, *Ts* is the signaling time, and *ncm* ¼ ⌊ *τc*þ*τcm Ts* ⌋.

The channel matrix at subcarrier *k*, denoted as H½ � *k* , can be written as H½ �¼ *k* P*L*�1 ℓ¼0 *H* ½ � ℓ *e* �*j* 2*πk NC* ℓ . The overall Channel Frequency Response (CFR) matrix, denoted as **H**, can be expressed as H ¼ ½ � H½ � 0 , H½ � 1 , … , H½ � *NC* � 1 , where *Nc* is the number of subcarriers. This matrix is also known as the Channel State Information (CSI) and its estimation is referred to as the channel estimation problem.

The direct measurement of CSI is possible using MIMO-OFDM systems with fully digital beamforming which is available at sub-6 GHz bands. However, in the mmWave band, only analog beamforming is available, making direct CSI measurement not feasible. Instead, estimation techniques are used to obtain the CSI indirectly [47]. Channel estimation in mmWave massive MIMO channel is under extensive research and several CSI estimation methods have been proposed to this end [48–50]. Accurate estimation of these parameters is crucial for effective localization.

#### **2.5 Angle-delay-profile (ADP)**

Assuming a single antenna at the UE and a uniform linear array antenna at the BS, the ADP is a linear transformation of the CSI computed by multiplying it with two Discrete Fourier Transform (DFT) matrices *V* ∈ *NB*�*NB* and *F* ∈ *NC*�*NC* . The ADP matrix *G* ∈ *NB*�*NC* is defined as follows [51]

$$\mathbf{G} = \mathbf{V}^{H} \mathcal{H} \mathbf{F},\tag{4}$$

where *V* ∈ *NB*�*NB* is defined as

$$[\mathbf{V}]\_{i,k} \stackrel{\Delta}{=} \frac{\mathbf{1}}{\sqrt{N\_B}} e^{-j2\pi \frac{\left(i\left(k - \frac{N\_B}{2}\right)\right)}{N\_B}},\tag{5}$$

and *F* ∈ *NC*�*NC* as

$$[\mathbf{F}]\_{i,k} \stackrel{\Delta}{=} \frac{1}{\sqrt{N\_C}} e^{-j2\pi \frac{ik}{N\_C}},\tag{6}$$

where *i* ¼ 0, … , *NC* � 1 and *k* ¼ 0, … , *NB* � 1.

This transformation has proven to be quite useful for various localization applications. **Figure 4** illustrates an example of the magnitude of the raw CSI ∣H∣ and its ADP transformation ∣*G*∣. The transformation converts the data into a sparse representation which has shown to improve the performance and generalizability of data-driven models [52]. Furthermore, in the visual representation of the raw CSI data, the scattering characteristics of the multipaths are ambiguous [53]. In contrast, the ADP

**Figure 4.**

*(a) Raw CSI data of a OFDM-MIMO system with 30 sub-carriers. The BS is equipped with a uniform linear array antenna with 30 antenna elements, and UE with single antenna. (b) the ADP transformation of the CSI in (a) with LOS and NLOS path clusters labeled.*

provides semantic visual interpretation of the channel multipath, where ½ � *G i*,*k* denotes the power of path associated with the angle

$$\theta\_k = \arccos\left(\frac{2k - N\_B}{N\_B}\right),\tag{7}$$

and delay

$$
\pi\_i = iT\_s.\tag{8}
$$

The semantic visual interpretation means that the path clusters can easily be identified visually in the ADP. Referring to **Figure 4(b)**, the strongest peak in the ADP is the LOS path cluster and the remaining peaks are NLOS path clusters. This information is not visually observable in the raw CSI in **Figure 4(a)**.

#### **2.6 Received signal strength indicator (RSSI)**

The RSSI is a metric used in wireless communication systems that measures the strength of a received signal. RSSI parameters are typically used in distributed (or cell free) MIMO localization systems. Cell-free MIMO uses a large number of distributed antennas and MIMO techniques to improve coverage, capacity, and reliability compared to single-site MIMO system shown in **Figure 1**. Specifically, it aims to improve the performance of single-site MIMO systems by dynamically assigning antennas to users based on their location and available resources.

An example of a distributed MIMO system is illustrated in **Figure 5**. In this example, there are multiple BSs distributed in the environment. The RSSI is measured for each BS to create a RSSI vector **p** ¼ *p*1, *p*2, … , *pM* , where *M* represents the number of BSs and *pi* is the RSSI from the *i th* BS. The RSSI vector should be unique for every location in the environment. To ensure the uniqueness of the RSSI vector, multiple BSs are necessary.

#### **2.7 Channel parameters summary**

The common channel parameters discussed above are summarized in **Table 1**. These parameters can be used individually or in combination to estimate the location *Localization Techniques in Multiple-Input Multiple-Output Communication: Fundamental… DOI: http://dx.doi.org/10.5772/intechopen.112037*

#### **Figure 5.**

*Illustration of a distributed MIMO system with four BSs and one UE.*

#### **Table 1.**

*List of MIMO channel parameters utilized in localization techniques.*

of a UE. For instance, to define a propagation path, AoD or AoA is often used in conjunction with ToA.

### **3. Localization techniques**

Localization is an extensive area of research in wireless MIMO communication and several different approaches have been proposed to solve this problem. This section provides an overview of the common localization techniques in sub-6 GHz and mmWave MIMO systems.

#### **3.1 Map-assisted localization**

Map-assisted localization techniques leverage 2D or 3D environment maps along with channel parameters to determine the location of UEs. The map provides information about the scattering surfaces and other obstacles in the environment. Then, by utilizing the AoD and delay of the signal path, multiple beam paths can be traced from the BS to the UE. This is illustrated in **Figure 6**. The paths are traced using the geometry defined in **Figure 2**. The point where these paths intersect is the UE's

**Figure 6.**

*Map-assisted localization using propagation path tracing. The figure illustrates the LOS path and three NLOS paths between the BS and UE. The intersection of these four paths represents the UE's location.*

location. The minimum requirement to localize the UE is the AoD of two different paths. Alternatively, the UE can be localized if the angle and delay of a single path are known. The delay is used to estimate the length of the path by solving for *d* in (1). However, more precise localization is achieved by utilizing multiple paths and incorporating both angle and delay information. Furthermore, since the communication is bi-directional, either AoD or AoA can be used to estimate the UE's location.

When analog beamforming is available, which is typically at lower frequency bands (i.e. sub-6 GHz), the angle and delay can be directly measured. However, the mmWave bands digital beam forming is still prevalent, which does not enable measuring angle and delay directly. Therefore, angle and delay parameters have to be estimated. One approach to this problem is to estimate CSI and convert it to ADP. Then, the angle and delay can be estimated using (7) and (8), respectively.

#### **3.2 Localization using compressive sensing techniques**

*Compressive Sensing* (CS), also known as compressed sensing or sparse sampling, is a signal processing technique that allows for the reconstruction of a sparse signal from a small number of measurements or samples. CS has found its way in many applications [54, 55]. *Sparsity* is the property of a signal or data representation whereby a small number of coefficients or elements carry most of the signal's energy or information content, while the majority of coefficients or elements are zero or close to zero [56]. In fact, many real-world signals are sparse or compressible in either their original domain or some transform domain, such as Fourier or wavelet transforms [57]. An example is shown in **Figure 4**, where the raw CSI data is transformed into ADP to create a sparse representation. As may be observed in the ADP, the multipath components are concentrated into only a few clusters creating a sparse representation.

CS techniques have found many applications in wireless MIMO communication by exploiting the sparsity of channel model parameters [57, 58]. These applications include channel estimation, spectrum sensing, and localization. Channel estimation provides information on the AoA/AoD and ToA of the paths and thus the relative location of the UE with respect to the BS can be estimated.

In mmWave MIMO communication, channel estimation and localization are typically combined. The idea behind sparse channel estimation is that the system can make only a few random measurements which are then used to reconstruct channel model parameters using CS techniques. A commonly used CS technique in mmWave

*Localization Techniques in Multiple-Input Multiple-Output Communication: Fundamental… DOI: http://dx.doi.org/10.5772/intechopen.112037*

MIMO channel estimation is Distributed Compressive Sensing - Simultaneous Orthogonal Matching Pursuit (DCS-SOMP). DCS-SOMP is typically used to estimate AoA/AoD and ToA [59–61]. Once the angle and delay channel parameters are recovered, the relative UE location can be estimated from the LOS path directly as shown in **Figure 2(a)**. When LOS is not available, the location can be estimated from the NLOS path by applying the virtual BS concept as shown in **Figure 2(b)**.

#### **3.3 Fingerprinting-based localization**

*Fingerprinting* is a data-driven localization technique that typically consists of two phases: offline phase and online phase. During the offline phase, the locations in the environment are mapped to a unique wireless measurement to create geo-tagged fingerprint database [62]. The unique wireless measurements are referred to as fingerprints. The measurements can be any wireless parameter such as RSSI, CSI/ADP, AoA/AoD or ToA. Then, during the online phase, the new measurement (fingerprint) is compared to the geo-tagged database to estimate the UE's location. The underlying principle behind fingerprinting is that the wireless channel between the UE and BS is uniquely determined by the scattering environment surrounding the UE's location [63]. Therefore, each location has a unique fingerprint. Matching a new wireless measurement to the measurements in the geo-tagged dataset typically involves a machine learning model. The training is performed during the offline phase. The most common fingerprinting models are based on Deep Learning (DL), Gaussian Progress Regression (GPR), or clustering and classification models.

RSSI-based fingerprinting is commonly used in wireless systems that have rich AP distributions such as Wireless Sensor Networks (WSNs) [64–66], Wi-Fi networks [67, 68], or Distributed Massive MIMO (DM-MIMO) systems [69, 70]. Since the RSSI provides a single measurement from the BS or AP, multiple APs are required to generate a unique fingerprint. On the other hand, single-site localization takes advantage of the multipath characteristics of the MIMO channel which are captured in CSI data or the angle and delay parameters that define the multipath. Furthermore, the CSI fingerprint can be used in its original form or it can be transformed into ADP.

#### *3.3.1 Application of deep learning techniques*

Deep Learning Neural Networks (DL NNs) require a large training dataset that covers the entire environment. The input to the NN is the wireless measurement and the output is the UE location. Several different NN architectures have been proposed in fingerprinting-based localization, including Multiple-Layer Perception (MLP) networks, [71, 72], Convolutional Neural Networks (CNNs), [51, 63, 73–75] and Recurrent Neural Networks (RNNs) [53].

Thus far, CNN models have demonstrated the highest localization accuracy performance. The CNN model treats the input fingerprint as a 2D image and performs series of convolutions over multiple layers to establish the spatial correlation in the 2D input. Typically, raw CSI or transformed ADP fingerprints are used for this application. The sparsity of ADP enhances the CNN model both from a computational complexity and a learning point-of-view [76]. RNN models are time series models that can track the changes of the input over time to predict the next UE location. RNN models can predict changes in the environment and account for these changes in the location estimation. RNN models are also used to predict the future location of the UE.

**Figure 7.** *Fingerprinting based multi-level classification grid of the environment map.*

These networks can either be postulated as classification or regression models. In the classification models, the environment is usually divided into grids where each grid represents a class. If the area is larger, it is not uncommon to have multiple levels of classification, where each grid may be subdivided into smaller grids as shown in **Figure 7**. In general, the first level employs a CNN classification model (coarse search), whereas the second level utilizes a different machine learning algorithm to perform a fine search. In addition to increasing the complexity of the model, the multi-layer approach is more susceptible to errors. If at the first stage, the grid is classified incorrectly, then the error propagates into the second stage. Furthermore, the accuracy of the classification model is limited to the size of the grid. On the other hand, the goal of regression is to find a function or equation that best describes the relationship between the input and output variables. Therefore, regression models predict a continuous output variable and the accuracy is not limited to the grid as in classification.

#### *3.3.2 Application of Gaussian process regression models*

A *Gaussian Process* (GP) is a collection of random variable functions indexed by time or space. The key property of a GP is that any finite subset of the random variables is jointly Gaussian distributed. That is, for any finite set of vector elements **x**1, … , **x***n* ∈ X, the associated set of random variables *f*ð Þ **x**1 , … , *f*ð Þ **x***n* follow a joint Gaussian distribution. The following notation is commonly used in literature to represent the GP

$$f(\mathbf{x}) \sim \mathcal{GP}(m(\mathbf{x}), k(\mathbf{x}, \mathbf{x}')),\tag{9}$$

where the mean and covariance functions are defined as

$$m(\mathbf{x}) = \mathbb{E}[f(\mathbf{x})],\tag{10}$$

$$k(\mathbf{x}, \mathbf{x}') = \mathbb{E}\left[ (f(\mathbf{x}) - m(\mathbf{x}))(f(\mathbf{x}') - m(\mathbf{x}')) \right] \tag{11}$$

for any **x**, **x**0 ∈ X [77]. Therefore, the GP is entirely defined by its mean and covariance functions [78].

A Gaussian Process Regression (GPR) model is a non-parametric statistical model that uses a GP to model a continuous function and provides a probabilistic prediction with uncertainty estimates [79]. To define the GPR model, assume D*train* ¼ Δ **X**, **y** ¼ Δ **x***i*, *yi n i*¼1 , **x***i* ∈ ℝ*d*, *yi* ∈ ℝ to be an input–output pair training dataset. Furthermore,

*Localization Techniques in Multiple-Input Multiple-Output Communication: Fundamental… DOI: http://dx.doi.org/10.5772/intechopen.112037*

assume that a latent function *f*ð Þ� is responsible for generating the observed output *yi* given the input vector **x***i*. Then, GPR model can be defined as

$$y\_i = f(\mathbf{x}\_i) + \varepsilon\_i,\tag{12}$$

where *f*ð Þ� **x** GP *m*ð Þ **x** , *k* **x**, **x**0 ð Þ ð Þ , *ϵ* � **N** 0, *σ*2 ð Þ**I** is the noise of the system that has an independent, identically distributed (i.i.d.) Gaussian distribution with zero mean and variance *σ*2, and *i* refers to the *i th* observation.

GPR models often assume zero mean as default. The correlation between input points is defined by the covariance function (also known as the kernel). There is a variety of kernels, including exponential, matern, quadratic, and more, each with hyperparameters that can be fine-tuned during training [80]. Given a new testing sample **x ∗** , the mean and variance (uncertainty) of the unknown output **y ∗** are predicted as

$$\overline{\mathbf{y}}\_{\*} = \mathbf{K}\_{\*}^{\mathbf{T}} \left(\mathbf{K} + \sigma\_{n}^{2}I\right)^{-1} \mathbf{y},\tag{13}$$

$$\mathbb{V}\left[\overline{\mathbf{y}}\_{\*}\right] = \mathbf{K}\_{\*}\, \mathop{\mathbf{s}}\nolimits - \mathbf{K}\_{\*}^{\mathrm{T}}\left(\mathrm{K} + \sigma\_{n}^{2}I\right)^{-1}\mathbf{K}\_{\*}\, \mathrm{s},\tag{14}$$

where **K** ¼ *K*ð Þ **X**, **X** , **K∗** ¼ *K*ð Þ **X**, **X∗** , and **K∗ ∗** ¼ *K*ð Þ **X∗** , **X∗** [81]. **K** is the covariance matrix (also known as Gram matrix) whose entries are the kernel functions *k* **x***i*, **x***j* � � [79].

In localization, the objective of the GPR model is to define the latent function *f*ð Þ� in (12), where **x***i* is the channel parameter (fingerprint) and *yi* is the UE location. Given a new fingerprint **x**∗ , the UE location is predicted using (13), while the level of uncertainty in the prediction is estimated by (14). The fingerprint in distributed MIMO systems is usually the RSSI vector as proposed in [69, 70, 82]. On the other hand, the input in singlesite MIMO systems can be AoA/AoD vector, CSI or ADP data as proposed in [83, 84].

The main advantage of GPR models over DL CNN models is that they can be trained on substantially smaller datasets. GPR models have shown the ability to train models with small-scale datasets due to the small number of hyper-parameters that define the model [84]. However, the GPR model does have its drawbacks. The main weakness of the GPR model lies in its training complexity, which is characterized by high computational and memory demands. Specifically, GPR training has a computational complexity of *O n*3 ð Þ and a memory complexity of *O n*2 ð Þ, where *n* represents the number of training points in the dataset [85].

#### *3.3.3 Clustering and classification*

*Clustering* is a class machine learning algorithms used to group similar objects or data points together into clusters. The groupings are based on some similarity or distance measures. The goal of clustering is to identify patterns or structures in the data that may not be immediately apparent, and to group similar data points into clusters that can be easily analyzed or visualized. In localization, clustering techniques can be used to compare the test fingerprints to the fingerprints in the training database. Kmeans clustering and K-Nearest Neighbor (KNN) classification have widely been used in fingerprinting-based wireless localization and have shown to provide excellent accuracy given enough data point [86, 87]. The KNN location estimation is given by

$$
\hat{\mathbf{p}} = \frac{1}{K} \sum\_{i=1}^{K} \mathbf{p}\_i,\tag{15}
$$

#### **Table 2.**

*Methods in MIMO localization, categorized according to the localization technique employed and the parameters utilized.*

where *K* is the number of surrounding neighbors considered and *pi* is the coordinate of the *i th* nearest reference point. Weighted KNN (WKNN) is an extension of KNN where the contribution of each neighbor is weighted. The WKNN is defined as

$$
\hat{\mathbf{p}} = \sum\_{i=1}^{K} w\_i \mathbf{p}\_i,\tag{16}
$$

where *wi* is the weight of the *i th* reference point. Typically, the weight corresponds to the distance between the reference point and the input point. The closer the neighbor is to the input point, the more weight it carries in the final prediction. The weights can also be defined by some similarity criteria calculated between the input and the reference fingerprint. Various similarity criteria have been established in wireless MIMO communication, such as normalized correlation [53, 86, 88], Joint Angle Delay Similarity Coefficient (JADSC) [63], Angular Similarity Coefficient Weight (ASCW) [89], and Weighted Mean Square Error (WMSE) [90].

#### **3.4 Summary of methods**

**Table 2** provides a summary of the methods proposed in recent years that apply the localization techniques discussed in the previous subsection. The techniques are also grouped by the type of communication parameter used with the associated technique.


*3.1. Microstructure Observation*

Figure 2 displays the X-ray diffraction patterns of TA15 titanium alloys subject to various heat treatments. All samples exhibit α phase, while some also exhibit β phase. However, after TriAC or TriWQ treatment, only α phase is detected. Figure 3 illustrates the microstructures of TA15 titanium alloys under different heat treatment methods. Combined with XRD diffraction results and SEM images, it is evident that the initial sample comprises primary equiaxed α phase and β grain microstructures (Figure 3a). However, the microstructures present various morphologies after different heat treatments. Figure 3b–d demonstrate that the microstructures comprise secondary α phase and transformed β phase after 810AC, 810WQ, and 940WQ treatments, respectively. Figure 3e,f indicate that the main microstructure after TriAC and TriWQ treatments is acicular α phase, with the α phase being slenderer after TriWQ treatment than after TriAC treatment.

To better illustrate the variation in elemental content between the α and β phases, we conducted an EDS scanning analysis of the initial sample's microstructure, as presented in Figure 4. The TA15 alloy consists predominantly of Ti, Al, and V. The EDS mapping results indicate that the α phase is primarily composed of Ti and Al elements, whereas the β phase contains more Mo and O. Additionally, V is found to be evenly distributed across the entire surface.

**Figure 2.** X-ray diffraction patterns of the TA15 Titanium Alloy under different heat treatment conditions.

**Figure 3.** SEM images of the TA15 Titanium Alloy under different heat treatment methods: (**a**) None, (**b**) 810AC, (**c**) 810WQ, (**d**) 940WQ, (**e**) TriAC, (**f**) TriWQ.


Intraocular Refractive Surgery - Special Cases

#### **Chapter 5**

## Surgical Correction of Ametropia with AddOn™ Intraocular Lens in Post-Penetrating Keratoplasty Pseudophakia

*Iva Dekaris, Ivan Gabrić and Doria Gabrić*

#### **Abstract**

Cataract surgery is the most common surgery in ophthalmology. The aim of cataract surgery is to restore vision in eyes in which the natural lens became opacified mostly due to the aging of the lens, or the presence of other ocular diseases, which promote earlier cataract formation. During cataract surgery, artificial intraocular lens (IOL) is implanted into the lens capsule and the value of the IOL is planned before surgery based on the preoperative IOL calculation. However, in the significant number of patients, cataract surgery may end up with a postoperative refractive error in which case patients have to wear glasses to reach the full vision for both distance and near correction (if monofocal IOL is used during cataract surgery!). Modern cataract surgery becomes more and more a refractive procedure as well, especially when multifocal and/or toric IOLs are implanted. However, in some specific cases where such IOLs are not applicable, high postoperative refractive error after cataract surgery can significantly influence the quality of the obtained vision. One such example is cataract surgery after penetrating keratoplasty. In this chapter, results of a novel approach of post-PK ametropia correction, namely implantation of sulcus placed AddOn IOLs (also called a piggyback lens) will be presented.

**Keywords:** AddOn IOL, penetrating keratoplasty, ametropia, refractive error, piggyback lens

#### **1. Introduction**

In patients who have had penetrating keratoplasty (PK) cataract surgery cannot end up in emmetropia due to the fact that they all have significant postoperative astigmatism due to the presence of corneal graft. In eyes without corneal graft, which have significant astigmatism, the problem can be solved with the implantation of monofocal toric IOL, which can correct higher amounts of astigmatism. However, in patients with corneal graft, it is questionable whether to use monofocal toric IOL since we never know whether corneal graft will survive throughout patient life, or the graft will need to be changed later during patients' life. If the graft needs to be changed and we have already implanted toric IOL during cataract surgery adjusted to the refractive error of the first corneal graft, the patient would have non-appropriate toric IOL in the eye. Thus, for patients with corneal graft, which develop cataract, we need a "reversible" correction of pre-existing astigmatism and, for that purpose, piggyback or AddOn IOLs are almost ideal option. Namely, AddOn IOLs can be easily and safely implanted in the ciliary sulcus over the already existing "in-the-bag" monofocal IOL, and if needed, they can be safely removed later on [1]. Thus, our method of choice for ametropia correction in post-PK patients who cannot wear contact lenses or spectacles to solve their ametropia is the implantation of AddOn IOL in the ciliary sulcus. This type of lens is used in eyes that already have had cataract surgery with implantation of conventional monofocal IOL in-the-bag. In this chapter, all the main aspects of add-on IOL usage in such cases are clarified.

### **2. Characteristics of 1stQ AddOn lens**

The 1stQ AddOn is a single-piece hydrophilic monofocal IOL for implantation into the ciliary sulcus in addition to a primary IOL in the patient's pseudophakic eye (Medicontur). This lens is implanted into the ciliary sulcus in addition to the IOL in the capsular bag and it is compatible with common capsular bag IOL, irrespective of design or material (**Figure 1**). Due to the lens convex-concave design, a space between AddOn IOL and posterior chamber IOL is approximately 0.5 mm, so there is no touch between the optics of the two implanted lenses. 1stQ AddOn lens is appropriate for the correction of both spherical refractive errors and astigmatism [1, 2]. The AddOn power calculation is typically made with the help of 1stQ AddOn®Calculator for the calculation of sulcus-fixated AddOn® IOLs. However, due to the fact that the amount of astigmatism is unusually "high" after PK, the calculation of the lens power for our specific cases was made by the manufacturer (Medicontur) and not by the operating surgeon. In post-penetrating keratoplasty cases, it was always implanted in the pseudophakic eye, although this type of lens can also be implanted in a single procedure namely together with the extraction of cataract (for example if the lens is used to correct presbyopia!). This type of IOL is very safe to implant into the sulcus due to the four important features: the lens has four flexible haptics, very good rotational stability due to its non-torque design, it is of convex-concave optic design enabling no IOL touch of adjacent eye structures, and it has square design making it safe regarding

**Figure 1.** *Position of 1stQ Addon lens in the ciliary sulcus (www.medicontur.com).*

*Surgical Correction of Ametropia with AddOn™ Intraocular Lens in Post-Penetrating… DOI: http://dx.doi.org/10.5772/intechopen.104782*

#### **Figure 2.**

*main characteristics of 1stQ Addon lens (www.medicontur.com).*

touch of the iris ("no iris capture" design) (**Figure 2**). The lens can be positioned safely irrespective of the size and shape of the ciliary sulcus [1–3].

#### **3. Surgical procedure**

Implantation of AddOn IOL was always performed under topical anesthesia. The anterior chamber was filled with dispersive (on the corneal endothelium!) and cohesive viscoelastic after side-ports were formed. The incision size was 2.4–2.7 mm. The lens was loaded into the lens injector with viscoelastic and the tip of the injector was placed intracamerally prior to the insertion of AddOn IOL. The lens was injected very slowly in order to allow the leading haptic to unfold in a controlled manner and then the haptic was guided under the iris (**Figure 3**) [1]. During the injection procedure, care was taken not to push against the primary lens to maintain zonular stability. Due to its design, toric versions of the lens are easier to rotate into position without all four haptics positioned in the sulcus; thus, the lens was rotated into its desired position before placement of the other two haptics behind the iris. The lens could be rotated in either direction. Once the desired position of the toric lens was obtained, the other 2 haptics were also gently placed into the sulcus behind the iris, and a careful check-up was made to be sure that all four haptics are positioned behind the iris. It was very important to check that all

**Figure 3.** *Implantation of a 1stQ Addon lens with the Medicel Accuject 2.1 injector (www.medicontur.com).*

four haptics are positioned behind the iris before removing the viscoelastic, particularly in our patients with corneal transplants, as it may be difficult to see the haptics behind the corneal scar. Some pearls for insertion include the use of the microscope with an integrated OCT image; thus, the surgeon can visualize the sulcus and position of the AddOn lens in the sulcus intraoperatively with the highest precision. It is also important to have good pupil dilation, and careful manipulation with the lens since in post-PK eyes special attention is needed not to destroy any endothelial cells during lens implantation. The advantage of post-PK eyes was that all the eyes had a very deep anterior chamber with enough space for manipulation with the lens.

### **4. Ametropia correction in post-PK eyes**

We have used AddOn IOL in post-PK eyes with a significant refractive error that could not be corrected by contact lens or spectacle wear. All of our post-PK eyes in which AddOn lens was implanted gained significant improvement in their non-corrected distance visual acuity and the satisfaction rate was extremely high. Implantation of the AddOn lens had no influence on near visual acuity and low-contrast

#### **Figure 4.**

*Slit-lamp image of the eye in which penetrating keratoplasty and cataract surgery with posterior chamber IOL implantation was done.*

#### *Surgical Correction of Ametropia with AddOn™ Intraocular Lens in Post-Penetrating… DOI: http://dx.doi.org/10.5772/intechopen.104782*

acuity. A typical example of a post-PK eye in which cataract was already removed and posterior chamber IOL implanted in the capsular bag is shown in **Figure 4**, together with its corneal topography (measured by Pentacam) showing significant post-PK astigmatism (**Figure 5**). For each post-PK eye an individual Addon lens is ordered and produced according to patients' individual measurements (**Figure 6a** and **b**). Lens implantation is made according to the previously described surgical procedure. The position of the lens after the surgery can be precisely checked postoperatively on the OCT scan of the anterior eye chamber to control for a proper distance between AddOn lens and PCIOL (**Figure 7**). The results of the significant increase in visual acuity in our first 3 post-PK eyes implanted with Addon IOL are represented in **Figure 8**. A dramatic increase in visual acuity from preoperative non-corrected (VA sc preop) is represented.

#### **Figure 5.**

*Corneal topography of a post-PK pseudophakic eye showing significant astigmatism which can be corrected with Addon lens implantation.*

#### **Figure 6.**

*(a, b) Individual patient data and the outcome measurements for the individually designed Addon provided by manufacturer.*

#### **Figure 7.**

*OCT image showing position of AddOn IOL and the already existing PCIOL with adequate distance between the two lenses.*

#### **Figure 8.**

*Change in visual acuity after AddOn lens implantation in 3 representative post-PK cases.*

The preoperative best-corrected (VA cc preop) is a vision tested by an eye doctor in the office; however, none of the patients could in fact wear such a correction in a real-life situation since their eyes did not support correction with either contact lens or spectacles. Therefore, their vision of 5–15% prior to AddOn lens implantation increased to 80–100% vision after AddOn lens implantation. As expected, with such a dramatic change in vision all patients were extremely satisfied with the outcome of the surgery. Those results are comparable with other publications [3–5].

Since patients with AddOn IOL in fact have two lenses in the eye; and despite the fact that AddOn IOL is very gentle and thin, we checked whether intraocular pressure (IOP) is increased by implantation of such lens and according to our results AddOn lens did not change values of IOP in 6 postoperative months of patients' follow-up (**Figure 9**). A typical sample of corneal endothelial cell count pre- and post- Addon IOL implantation is shown in **Figure 10**. Due to the very deep anterior chamber in all post-PK eyes, the surgery of Addon IOL implantation did not influence the regularity and count of corneal endothelial cells.

*Surgical Correction of Ametropia with AddOn™ Intraocular Lens in Post-Penetrating… DOI: http://dx.doi.org/10.5772/intechopen.104782*

#### **Figure 9.**

*Intraoperative pressure (IOP) values before and after Addon IOL implantation.*

#### **5. Discussion**

Penetrating keratoplasty can be a life-changing procedure for those patients who suffer from significant vision loss due to a corneal disease involving all corneal layers. Despite the fact that the success of this procedure may be limited by some postoperative complications like graft rejection, postoperative rise in intraocular pressure, or cataract formation, most of the patients with a clear corneal graft are extremely satisfied with their improvement of vision. In some cases, however, despite of the fact that the corneal graft is perfectly clear and there have been no postoperative complications jeopardizing the quality of the grafted tissue, we may end up with very unsatisfied patients with very low uncorrected visual acuity equal to or even worse as compared to preoperative vision. This happens in eyes with a corneal graft having very high postoperative astigmatism which cannot be corrected with a contact lens. Most often such cases develop after suturing of the graft with interrupted sutures or with the unexpected change in astigmatism after suture removal. We must bear in mind that the astigmatism is not only the result of the suture placement, but also a result of the type of healing process in each particular eye, so it may be that the patient has good vision and a low amount of astigmatism for a several months after surgery and then, unfortunately, develops a high astigmatism. Similarly, at the time of suture removal, we cannot judge the amount of astigmatism which will remain after suture removal. Recently new types of contact lens such as scleral lens has been developed to help in cases with very high astigmatism, but still, some patients remain who are not able to wear such lenses and who are in fact without any solution to improve their vision after PK. With the invention of AddOn lenses, which were primarily designed to correct refractive errors after more often performed surgeries like cataract surgery, corneal surgeons could also start to use such lenses for their post-PK patients. AddOn lenses are produced in a personalized manner as previously said, and according to individual patient refractive error. However, due to the high amount of astigmatism in some of post-PK cases it may happen that the manufacturer does not have an option of producing a lens for full astigmatism correction. We have also had such patients which were consequently "under-corrected" regarding their astigmatism. However, even if the full amount of astigmatism is not corrected with the AddOn lens, those patients still gained significantly better postoperative vision and were perfectly happy with obtained vision. Moreover, since in many of post-PK cases we do not have a regular type of astigmatism, we were worried that the outcome may not be as good as if the regular astigmatism is corrected. This is easily visible in **Figure 5**, where the irregularity of the post-PK astigmatism is clearly visible. However, clinically, despite the irregularity of post-PK astigmatism the visual outcome was better than expected and the patient satisfaction rate was high. Therefore, the AddOn lenses are the best and truly speaking the only currently available option for post-PK cases with high astigmatism, being of regular type (which is in fact rarely seen) or of the irregular type. The drawback of AddOn lenses that we have noticed was that the lens is not produced for extremely high amounts of astigmatism (>10 dioptres) and such high astigmatism may be seen in post-PK patients. Thus, the production of AddOn lens able to correct even higher amounts of astigmatism would be an improvement in 1stQAddOn lens portfolio. All the operated eyes, as mentioned before, were pseudophakic. We do know from the literature that refractive errors in pseudophakic eyes can sometimes be corrected with the replacement of the existing IOL. However, in post-PK cases, this is not an option since we would need to replace the IOL with toric IOL. However, in post-PK cases, the graft may be replaced in the future and then

*Surgical Correction of Ametropia with AddOn™ Intraocular Lens in Post-Penetrating… DOI: http://dx.doi.org/10.5772/intechopen.104782*

the toric IOL in the eye would be certainly not appropriate since astigmatism after repeated PK cannot be the same. Since AddOn lenses are not in use for a longer period of time for post-PK cases we still cannot comment on the performance of those lenses in a longer follow-up and this remains to be studied in the future. Namely, a follow-up of 6 months (which we have presented in this chapter) on the effect of AddOn lenses on postoperative IOP and on the state of endothelial cells should be studied in a long run as well.

#### **6. Conclusion**

Implantation of AddOn IOL in pseudophakic eyes with post-PK refractive error is safe and easy procedure to significantly improve visual acuity in post-PK cases unable to wear contact lenses or spectacles (at least for the shorter follow-up). Also, there was no adverse effect or IOP rise, and one of the main advantages is its reversibility in case of the next transplantation.

#### **Author details**

Iva Dekaris\*, Ivan Gabrić and Doria Gabrić University Eye Hospital Svjetlost, Zagreb, Croatia

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Instruction for use 1stQ addon IOL ... – implantecinsumos.com [Internet]. 1stQ AddOn® IOL. 1stQ GmbH; 2015. Available from: https:// implantecinsumos.com/wp-content/ uploads/2019/10/ifu\_1stq\_iol\_addon\_ en\_20150908.pdf. [Accessed: March 19, 2022]

[2] Themes UFO. Addon® intraocular lenses [Internet]. Ento Key. 2017. Available from: https://entokey.com/ addon-intraocular-lenses/. [Accessed: March 19, 2022]

[3] Gundersen KG, Potvin R. Refractive and visual outcomes after implantation of a secondary toric sulcus intraocular lenses. Clinical Ophthalmology. 2020;**14**:1337-1342

[4] Hassenstein A, Niemeck F, Giannakakis K, Klemm M. Torische addon-Intraokularlinsen zur Korrektur Hoher Astigmatismen nach Pseudophaker Keratoplastik. Der Ophthalmologe. 2016;**114**(6):549-555

[5] Srinivasan S, Ting DS, Lyall DA. Implantation of a customized Toric intraocular lens for correction of post-keratoplasty astigmatism. Eye. 2013;**27**(4):531-537

#### **Chapter 6**


**4.3 Plasma syn-irradiation of biodegradable polyesters**

As described in section 3.2.3, a polymer can also be grafted on the surface of a biodegradable polyester by pre-adsorption of the monomer followed by a plasma treatment. However for the specific case of biodegradable polymers, we were able to track only one research paper using this plasma approach (Ding et al., 2004). In this paper, Ding et al. tried to modify the surface of PLLA films with a chitosan layer. However, results indicated poor cell adhesion, but acceptable cell proliferation.

### **4.4 Plasma polymerization on biodegradable polyesters**

Plasma polymerization differs from plasma grafting in that respect that it coats the substrate rather than covalently binds species to a plasma-modified polymer surface (Barry et al., 2005). Allylamine is one of the most frequently used monomers to plasma polymerize on biodegradable polymers such as PLLA, PCL and PHBV (Barry et al., 2005, Guerrouani et al., 2007, Carlisle et al., 2000). Plasma polymerized allylamine films on biodegradable polymers resulted in highly hydrophilic surfaces with contact angles of 20° or lower due to the amine groups on the surface.

As there is a great interest in the surface modification of 3D implants, plasma polymerization has also been performed on the surface of 3D PLA scaffolds. Plasma grafting has been compared with plasma polymerization using allylamine (Barry et al., 2005). In the case of plasma grafting, the scaffolds were first pre-treated with an oxygen plasma and afterwards exposed to allylamine vapour, while plasma polymerization was carried out by exposing the scaffolds to an allylamine vapour plasma after an oxygen plasma pretreatment. XPS measurements of the scaffolds at different points across the scaffold diameter demonstrated that the grafting process resulted in a more homogeneous nitrogen concentration through the scaffold while the concentration of nitrogen on the internal surface of the scaffold on which the plasma deposit was formed decreased from the edge to the core of the scaffold, as can be seen in Figure 6. However, at the lowest nitrogen concentration, the nitrogen concentration on the internal surface of the plasma-polymerized scaffold was still greater than that of the grafted surface. The plasma-coated scaffolds also showed a higher metabolic activity than the plasma-grafted samples. Moreover, fibroblasts were detected in the centre of the plasma-coated samples, which was not the case for the grafted scaffolds (Barry et al., 2005).

### **5. Conclusion**

The growing research fields of tissue engineering and regenerative medicine are a leverage for surface engineering of biodegradable polymers. Next to chemical surface modification techniques which encounter problems with the use of hazardous organic solvents in relation to cell viability, non-thermal plasma technology knows a steep growth as solvent-free technique. Plasma treatments are already commonly performed on biodegradable polymers such as PLA and PLGA, while treatment of more advanced biodegradable polymers (such as PCL, PHBV, PBS and composites) and other plasma-based techniques (such as plasma grafting and plasma polymerization) are only at the verge of breaking through. Nonthermal plasma technology can greatly enhance cell-material interactions, however, a better understanding of these interactions is of crucial importance. This knowledge can provide us information on which plasma-based strategies should exactly be pursued.

Fig. 6. Nitrogen concentration as determined by XPS at set points across the internal diameter of grafted and plasma-polymerized allylamine (ppAAm) scaffolds (Reprinted from (Barry et al., 2005) with permission from Wiley-VCH Verlag GmbH & Co. KGaA).

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The growing research fields of tissue engineering and regenerative medicine are a leverage for surface engineering of biodegradable polymers. Next to chemical surface modification techniques which encounter problems with the use of hazardous organic solvents in relation to cell viability, non-thermal plasma technology knows a steep growth as solvent-free technique. Plasma treatments are already commonly performed on biodegradable polymers such as PLA and PLGA, while treatment of more advanced biodegradable polymers (such as PCL, PHBV, PBS and composites) and other plasma-based techniques (such as plasma grafting and plasma polymerization) are only at the verge of breaking through. Nonthermal plasma technology can greatly enhance cell-material interactions, however, a better understanding of these interactions is of crucial importance. This knowledge can provide us

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*Review* **Is Protein Folding a Thermodynamically Unfavorable, Active, Energy-Dependent Process?**

**Irina Sorokina 1,\*, Arcady R. Mushegian 2,3 and Eugene V. Koonin 4,\***

**Abstract:** The prevailing current view of protein folding is the thermodynamic hypothesis, under which the native folded conformation of a protein corresponds to the global minimum of Gibbs free energy *G*. We question this concept and show that the empirical evidence behind the thermodynamic hypothesis of folding is far from strong. Furthermore, physical theory-based approaches to the prediction of protein folds and their folding pathways so far have invariably failed except for some very small proteins, despite decades of intensive theory development and the enormous increase of computer power. The recent spectacular successes in protein structure prediction owe to evolutionary modeling of amino acid sequence substitutions enhanced by deep learning methods, but even these breakthroughs provide no information on the protein folding mechanisms and pathways. We discuss an alternative view of protein folding, under which the native state of most proteins does not occupy the global free energy minimum, but rather, a local minimum on a fluctuating free energy landscape. We further argue that Δ*G* of folding is likely to be positive for the majority of proteins, which therefore fold into their native conformations only through interactions with the energydependent molecular machinery of living cells, in particular, the translation system and chaperones. Accordingly, protein folding should be modeled as it occurs in vivo, that is, as a non-equilibrium, active, energy-dependent process.

**Keywords:** protein folding; entropy; free energy; free energy landscape; energy-dependent protein folding; co-translational protein folding; molecular chaperones; physical model of protein folding