Angular Spread Statistics for 6.75 GHz FR1(C) and 16.95 GHz FR3 Mid-Band Frequencies in an Indoor Hotspot Environment
Dipankar Shakya Mingjun Ying Theodore S. Rappaport






Angular Spread Statistics for 6.75 GHz FR1(C) and 16.95 GHz FR3 Mid-Band Frequencies in an Indoor Hotspot Environment
    
Dipankar Shakya, Mingjun Ying, and Theodore S. Rappaport
NYU WIRELESS, Tandon School of Engineering, New York University, Brooklyn, NY, 11201

 {dshakya, yingmingjun, tsr}@nyu.edu

    September 9, 2024
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§ ABSTRACT 
We present detailed multipath propagation spatial statistics for next-generation wireless systems operating at lower and upper mid-band frequencies spanning 6–24 GHz. The large-scale spatial characteristics of the wireless channel include Azimuth angular Spread of Departure (ASD) and Zenith angular Spread of Departure (ZSD) of multipath components (MPC) from a transmitter and the Azimuth angular Spread of Arrival (ASA) and Zenith angular Spread of Arrival (ZSA) at a receiver. The angular statistics calculated from measurements were compared with industry-standard 3GPP models, and ASD and ASA values were found to be in close agreement at both 6.75 GHz and 16.95 GHz. Measured LOS ASD was found larger than 3GPP ASD indicating more diverse MPC departure directions in the azimuth. ZSA and ZSD were observed smaller than the 3GPP modeling results as most multipath arrivals and departures during measurements were recorded at the boresight antenna elevation. The wide angular spreads indicate a multipath-rich spatial propagation at 6.75 GHz and 16.95 GHz, showing greater promise for the implementation of MIMO beamforming systems in the mid-band spectrum. 




		6G, angular spread, ASA, ASD, FR3, FR1(C), indoor, upper mid-band, ZSA, ZSD 




§ INTRODUCTION



The progression towards 6G wireless communications has generated significant interest in the 6 to 24 GHz spectrum, as these frequency bands offer a promising balance between coverage and capacity. Regulatory bodies such as the ITU, NTIA, and FCC have emphasized the strategic importance of these bands, particularly the 7.125-8.4 GHz, 4.40-4.80 GHz, and 14.8-15.35 GHz segments, for future wireless networks <cit.>. 
As the industry gears up for cellular deployments in these mid-band frequencies, understanding the propagation characteristics and angular spread statistics in indoor and outdoor environments is crucial for effective network planning and optimization. 


Angular spread (AS) is a crucial parameter in wireless communication, significantly influencing key performance metrics such as beamforming effectiveness, channel hardening, spatial correlation, and channel estimation accuracy. In beamforming systems, narrower AS, typically observed at higher frequencies in the mmWave and sub-THz bands, enhance beamforming performance by focusing the signal within the narrow beams. Conversely, broader spreads at lower frequencies with omnidirectional (omni) antennas, such as 3.5 GHz, introduce challenges due to increased signal scattering, which can degrade the signal-to-interference-plus-noise ratio (SINR) <cit.>. Research has shown that AS has a non-monotonic effect on achievable rates in MIMO systems, particularly when transmit antenna array sizes are moderate between 20 and 50 antennas <cit.>. Pilot contamination is another aspect of MIMO communications where wider AS is known to degrade the channel estimation accuracy requiring longer pilot lengths <cit.>. In dense urban environments, AS plays a significant role in determining the power distribution and spectral efficiency for radio links <cit.>. Especially considering higher frequencies in upper mid-band and mmWave spectrum, wider half-power beamwidth (HPBW) is shown to be desirable for larger AS when accounting for beam misalignment in beamforming systems<cit.>.  

Moreover, AS affects the spatial correlation in antenna arrays having closely spaced elements, with lower AS leading to higher spatial correlation and reduced scattering of MPC.  This increased correlation due to lower AS can improve channel estimation accuracy, however, can negatively impact the performance of MIMO systems by reducing the effectiveness of spatial multiplexing and diversity techniques <cit.>. Additionally, the frequency-dependent nature of AS, where higher frequencies are associated with smaller AS due to increased directionality and reduced scattering, is a critical factor as wireless communications advance towards upper mid-band, mmWave, and THz frequencies. Understanding this behavior is essential for enhancing channel estimation accuracy and optimizing network performance in these higher frequency bands <cit.>.

AS behavior is of considerable importance for Air-to-Ground (A2G) links for 6G communications. Studies on A2G channels reveal that AS varies with UAV altitude, where azimuth spread of arrival (ASA) decreases and elevation/zenith spread of arrival (ZSA) increases. These findings highlight the unique characteristics of A2G channels, particularly the significant impact of ground reflections, which are crucial for designing reliable 6G networks involving UAV communications <cit.>. 

Despite such broad implications, there is a notable scarcity of empirical data on the propagation characteristics within the frequency ranges of 6-24 GHz. Previous studies conducted in environments such as office corridors and university hallways have explored path loss exponents and RMS delay spreads at various frequencies, but comprehensive indoor measurements at FR1(C) and FR3 bands remain limited. This paper presents spatial statistics for indoor hotspot (InH) environments, evaluated from an extensive measurement campaign encompassing indoor, factory, and outdoor environments at 6.75 GHz (FR1(C)) and 16.95 GHz (FR3) using a 1 GHz bandwidth sliding correlation channel sounder. Conducted at the NYU WIRELESS Research Center, the indoor measurements provide detailed insights into the spatial propagation behavior and angular spread characteristics, encompassing both line-of-sight (LOS) and non-LOS (NLOS) scenarios. Over 30,000 power delay profiles (PDPs) were collected to analyze angular statistics, offering unique propagation insights at these frequencies and suggesting potential revisions to existing models.

The organization of this paper is as follows: Section <ref> describes the channel sounding system and the indoor hotspot scenario. Section <ref> details the angular statistical channel model at 6.75 and 16.95 GHz. The paper concludes with a summary of findings and implications for future wireless communication systems.



§ MEASUREMENT SYSTEM, ENVIRONMENT, AND PROCEDURES





 §.§ Channel Sounding System

Measurements were conducted with a wideband sliding correlation channel sounder at 6.75 and 16.95 GHz. Key system features are described in <cit.> and include:

    
  * 500 Mcps PN sequence sliding correlation baseband with 1 GHz RF bandwidth for high temporal resolution of MPC delays (1 ns)
    
  * Dual-band co-located RF front-end modules for efficient frequency switching. One band is active at a time, while the other front-end module is powered off.
    
  * 31 dBm EIRP for adequate coverage, while staying within FCC licensed limits.
    
  * Directional horn antennas with 15 dBi (6.75 GHz) and 20 dBi (16.95 GHz) gain mounted on mechanically rotatable gimbals with a one-degree spatial resolution for directional measurements.




 §.§ Indoor Hotspot Scenario

Measurements were performed in the open office environment of the NYU WIRELESS Research Center. Total of 20 TX-RX locations were measured covering the entire office space spanning distances between 11 and 97 m. Cubicles, offices, labs, and conference rooms in the research center were partitioned with drywall and glass panels with wooden or glass doors.  A map of the environment is shown in Fig. <ref> (a) <cit.>.



 §.§ Measurement Procedure

The channel sounder calibration process ensures accurate capture of the multipath power, delay, and direction, and is performed at the start and end of each day of propagation measurements. At each TX-RX location pair, the strongest azimuth and elevation pointing directions are determined by carefully observing changes in the recorded power level as the TX and RX antennas are moved in one-degree steps. The careful stepping ensures capturing the strongest MPC with maximum power. Keeping the same zenith of departure (ZOD) elevation angle, TX angles of departure (AOD) with significant RX received power are determined through rapid scans, as detailed in <cit.>. 

For each TX AOD pointing direction, the RX is swept 360^∘ in the azimuth in antenna HPBW steps. Following the stepped sweep at boresight 
 zenith of arrival (ZOA) elevation, the RX is up and down tilted by the antenna HPBW and swept again across the azimuth. Next, the ZOD elevation is changed by down-tilting the TX by the antenna HPBW. RX azimuth sweeps in HPBW steps are performed for the down-tilted TX ZOD at RX boresight and HPBW down-tilted ZOAs. 










§ ANGULAR STATISTICS MEAUSURED AT 6.75 AND 16.95 GHZ











The double directional channel impulse response for multipath propagation between the TX and RX can be defined with (<ref>) <cit.>.

    h_omni(t,Θ,Φ)=    ∑_n=1^N∑_m=1^M_na_m,ne^jφ_m,n·δ(t-τ_m,n) 
       ·δ(Θ-Θ_m,n)·δ(Φ-Φ_m,n),

where t is the absolute propagation time, Θ=(ϕ_AOD,θ_ZOD) represents the 3D TX pointing direction vector, and Φ=(ϕ_AOA,θ_ZOA) is the RX pointing direction vector. N and M_n denote the number of time clusters (TCs) and the number of cluster subpaths (SPs), respectively, as defined in <cit.>; a_m,n is the magnitude of the m^th SP belonging to the n^th TC, while φ_m,n and τ_m,n represent the phase and propagation delay of the SP, respectively. Likewise, Θ_m,n and Φ_m,n are the vectors representing AOD/ZOD and azimuth of arrival (AOA)/ZOA for the SP, respectively. The terms MPC and SP are used interchangeably <cit.>.

The propagation behavior of the multipath is characterized through primary statistics including the number of time clusters and spatial lobes, cluster delay and multipath delay, received power of each SP in a cluster, and direction of arrival and departure of SPs. The secondary statistics for temporal and spatial propagation behavior including the RMS angular spread (AS) at both TX and RX help characterize the wireless channel at a large scale and are crucial parameters for cellular network and radio system designs. The RMS AS provides a measure of the spatial dispersion of angles at which MPCs arrive or depart from a receiver or transmitter. The azimuth angular spread of arrival (ASA) and the zenith angular spread of arrival (ZSA) characterize the spread of multipath arriving at the RX in horizontal and vertical planes, respectively. Similarly, at the TX side, the azimuth angular spread of departure (ASD) and the zenith angular spread of departure (ZSD) describe the spread of MPCs being transmitted over the wireless channel that are captured at the RX. 

The NYU WIRELESS channel measurements include directional measurements, which are carefully combined to synthesize the omnidirectional antenna pattern, removing antenna gains <cit.>. The power angular spectrum (PAS) resulting from the synthesis of directional measurements is presented in Fig. <ref> (b) and (c) for the RX AOAs and TX AODs, respectively. The omni directional antenna patterns facilitate the implementation of arbitrary antenna patterns for simulations, with 3GPP providing omnidirectional models for the same reason <cit.>. 

The blue dots on the PAS in Fig. <ref> represent the channel sounder RX AOA/ TX AOD pointing directions during the directional measurements at the T-R location. The AOA/AOD powers between the measured directions are obtained through linear interpolation of the measured powers, as the PAS has a spatial resolution corresponding to the antenna HPBW. Based on circular statistics, the omnidirectional RMS AS is evaluated in radians using (<ref>) for the circular standard deviation of the multipath departure/arrival directions<cit.>. Considering the PAS in Fig. <ref>, omni RMS AS considers all spatial directions with power above the threshold defined 10 dB below the peak power (“-10 dB Threshold" in Fig. <ref> (b) and (c)) in the PAS, which was proven sufficient for statistical analysis in <cit.>. 

Using the same “-10 dB Threshold" on the PAS as the spatial lobe threshold (SLT), a spatial lobe (SL) is defined as contiguous spatial directions with powers above the SLT. The SLs in a PAS are illustrated in Fig. <ref> (b) and (c) as the orange-filled region constituting AOA/AOD directions with received powers above the SLT. Several SLs are observed in AOA and AOD PAS in both 6.75 GHz and 16.95 GHz measurement campaigns.

    AS_omni = √(-2× ln|∑_l=1^L∑_m=1^M_le^(j(ϕ_l,m or θ_l,m)) a^2_l,m/∑_l=1^L∑_m=1^M_l a^2_l,m|),


ϕ_l,m in (<ref>) can represent the AOA or AOD and θ_l,m can represent ZOA or ZOD for the m^th MPC in the l^th SL. Evaluating the AS for each SL defined from the PAS, as shown in Fig. <ref> (b) and (c), results in the lobe AS for the SL. For each SL, the lobe AS is evaluated using (<ref>), as the circular standard deviation of the departure/arrival directions of MPCs within the SL<cit.>.   


    AS_lobe,l = √(-2× ln|∑_m=1^M_le^(j(ϕ_m or θ_m)) a^2_m/∑_m=1^M_l a^2_m|),


 







§ ANGULAR STATISTICS OF 3GPP TR38.901 MODELS


Table <ref> compares the RMS AS evaluated from the InH measurements, with the results from 3GPP TR 38.901 models for 0.5-100 GHz <cit.>.



 §.§ 3GPP Omnidirectional RMS Angular Spread


3GPP calculates the AS using a formulation identical to (<ref>). Based on the evaluation of AS across various frequencies, 3GPP provides frequency-dependent models to characterize AS up to 100 GHz. These models are specifically detailed in <cit.> under “Table 7.5-6 Part-2" and “Table 7.5-10."




    
  * Omnidirectional RMS ASA:
    
    log_10 (μ_ASA, LOS  [^∘] )= -0.19 log_10(1 + f_c) + 1.781,

    
    log_10 (μ_ASA, NLOS  [^∘] )= -0.11 log_10(1 + f_c) + 1.863,

    
    log_10 (σ_ASA ) = 0.12 log_10(1 + f_c) + 0.119,

    
    log_10 (σ_ASA, NLOS ) = 0.12 log_10(1 + f_c) + 0.059.

    

    
  * Omnidirectional RMS ZSA:
    
    log_10 (μ_ZSA, LOS  [^∘] )= -0.26 log_10(1 + f_c) + 1.44,

    
    log_10 (μ_ZSA, NLOS  [^∘] )= -0.15 log_10(1 + f_c) + 1.387,

    
    log_10 (σ_ZSA, LOS) = -0.04 log_10(1 + f_c) + 0.264,

    
    log_10 (σ_ZSA, NLOS) = -0.09 log_10(1 + f_c) + 0.746.

    

    
  * Omnidirectional RMS ASD:
    
    μ_ASD, LOS  [^∘] = 10^1.60 = 39.8,

    
    μ_ASD, NLOS  [^∘] = 10^1.62 = 41.7,

    
    σ_ASD, LOS = 10^0.18 = 1.51,

    
    σ_ASD, NLOS = 10^0.25 = 1.78.

    

    
  * Omnidirectional RMS ZSD:
    
    log_10 (μ_ZSD, LOS  [^∘]) = -1.43 log_10(1+f_c) + 2.228,

    
    log_10 (μ_ZSD, NLOS  [^∘]) = 1.08,

    
    log_10 (σ_ZSD, LOS) = 0.13 log_10(1+f_c) + 0.3,

    
    log_10 (σ_ZSD, NLOS) = 0.36.

    
    ZOD  offset, LOS = ZOD  offset, NLOS = 0.





























































































        





        





        





        





        










        





















§ DISCUSSIONS AND COMPARISON WITH 3GPP MODELS


The AS measured from the InH campaign showed wider spatial spreads at 6.75 GHz compared to 16.95 GHz in both azimuth and elevation planes. When compared to 3GPP models, NYU ASAs at the RX are similar, whereas NYU ASDs at the TX are wider. The 3GPP zenith spreads are wider than the NYU measured ZSA and ZSD. 



The omni RMS ASA at 6.75 GHz was observed to be 40.9^∘ in LOS and 58.2^∘ in NLOS, which is nearly identical to the 3GPP values, with a negligible difference of 0.03^∘ in both cases, as shown in Table <ref>.
At 16.95 GHz, the NYU measured omni ASA was 34.2^∘ in LOS and 43.5^∘ in NLOS. The 3GPP omni ASA values were obtained as 34.89^∘ in LOS and 53.09^∘ in NLOS, showing a difference of 0.69^∘ in LOS and 9.59^∘ in NLOS, indicating slightly smaller ASA values in the NYU measurements at 16.95 GHz compared to the 3GPP models.

The mean lobe RMS ASA for SLs was measured at 9.4^∘ in LOS and 24.5^∘ in NLOS at 6.75 GHz, and 5.4^∘ in LOS and 14.3^∘ in NLOS at 16.95 GHz. 
The wider SLs in NLOS suggest that MPCs arrive from multiple azimuth directions.



In terms of omni ASD, at 6.75 GHz, 67^∘ spread was recorded in LOS, while 47^∘ in NLOS. At 16.95 GHz, omni RMS ASD was obtained as 63^∘ in LOS and 44.2^∘ in NLOS. The mean of the LOS omni ASD is observed wider than the NLOS omni ASD for both 6.75 GHz and 16.95 GHz, which indicates the multipath-rich propagation over several different transmit angles across the azimuth plane in LOS in addition to the direct LOS path. The NYU measurements are consistently wider than the 3GPP values. At 6.75 GHz, the 3GPP LOS omni ASD of 39.8^∘ is 27.2^∘ narrower than the NYU value. In NLOS, the NYU omni ASD is 47^∘, which is 5.3^∘ wider than the 3GPP value of 41.7^∘. At 16.95 GHz, the NYU omni ASD is 63^∘ in LOS and 44.2^∘ in NLOS, while the 3GPP model results 39.8^∘ and 41.7^∘ in LOS and NLOS, respectively, showing a difference of 23.2^∘ in LOS and 2.5^∘ in NLOS. 3GPP models the omni ASD as a constant value across frequency, which may need revision. Further, the wider measured NYU ASDs, particularly in LOS, compared to 3GPP values at both 6.75 GHz and 16.95 GHz, indicate greater diversity in the TX AODs and spatial richness of MPCs.

The mean lobe ASD at 6.75 GHz was observed at 8.4^∘ in LOS and 13^∘ in NLOS. At 16.95 GHz, LOS lobe ASD was observed at 4.8^∘, and NLOS lobe ASD was 9.8^∘, which are on average 3.2^∘ narrower than the lobe ASDs at 6.75 GHz. 

In the zenith plane, the lobe RMS ZSA at 6.75 GHz was observed to be 5.2^∘ in LOS and 8^∘ in NLOS, and at 16.95 GHz it was 3.6^∘ in LOS and 4.1^∘ in NLOS. Similarly, considering omni ZSA, at 6.75 GHz the zenith AS is 3.6^∘ in LOS and 5.1^∘ in NLOS, and at 16.95 GHz the spread is 3^∘ in LOS and 3.3^∘ in NLOS. At 6.75 GHz, the 3GPP models resulted in 17.3^∘ in LOS, and 17.9^∘ in NLOS. At 16.95 GHz, 3GPP RMS ZSA values were obtained as 13.93^∘ in LOS and 15.8^∘ in NLOS, respectively. On average, the NYU-measured ZSAs are observed smaller than the 3GPP values by 13.2^∘ at 6.75 GHz and 11.7^∘ at 16.95 GHz. The measured zenith spread of MPC departure angles was also observed to be small with lobe ZSD of 0.4^∘ in LOS and 1.8^∘ in NLOS at 6.75 GHz, and 0.5^∘ in LOS and 0.6^∘ in NLOS at 16.95 GHz. Considering all departing MPC angles and evaluating the omni ZSD, in LOS the spread was found to be 0.9^∘ and 3.7^∘ in NLOS at 6.75 GHz, while at 16.95 GHz the omni ZSD spread was evaluated to be 1.6^∘ and 3.6^∘ in LOS and NLOS, respectively. The 3GPP models yielded 9^∘ and 12^∘, respectively at 6.75 GHz, and 2.7^∘ and 12^∘, respectively at 16.95 GHz. 

The NYU-measured zenith spreads are smaller than the 3GPP zenith spreads. The reasoning for this observation lies in the underlying measurement methodology behind the NYU measurements. As highlighted in Section II. C, the strongest pointing direction is determined at each TX-RX location by adjusting the TX and RX pointing angles in azimuth and elevation in 1-degree steps until the maximum power is captured at the RX. The RX performs azimuth sweeps at the boresight elevation angle and is up-tilted and down-tilted by the antenna HPBW. As a result, most of the MPC received power for a TX-RX location pair is captured in the azimuth measurement sweep at the boresight elevation. MPCs captured during the azimuth sweep at this elevation are assigned the boresight elevation of the antenna. The zenith spread is, therefore, smaller than that modeled in 3GPP. Individual MPC elevations can be further extracted from the captured PDPs through the use of post-processing methods such as ADME<cit.>, R-CLEAN<cit.>, or SAGE<cit.>.



































§ CONCLUSION

This paper presented detailed large-scale spatial statistics of wireless channels at 6.75 GHz and 16.95 GHz for InH environments extracted from comprehensive measurements conducted at the NYU WIRELESS Research center. The AS statistics obtained were compared with the industry standard 3GPP models. The LOS ASA, NLOS ASA, and NLOS ASD were found to be in close agreement with 3GPP models. The measured LOS ASD was found to be larger than the 3GPP model result by 25.2^∘ on average, indicating a greater diversity in the TX AODs in the azimuth plane. Moreover, in the zenith plane, LOS and NLOS ZSAs and ZSDs were measured smaller than the 3GPP modeled values as most MPCs were captured in the azimuth sweep at boresight elevation. The wide azimuth spreads clearly indicate spatial richness of MPCs and potential for implementation of spatial multiplexing techniques with MIMO systems in the upper mid-band. 













    

    


























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