To evaluate the performance of the PAA systems, the downlink of a single-cell narrowband hybrid multi-user MIMO (MU-MIMO) system is modelled as shown in Figure 1. Each base station is assumed to be equipped with M analog beamforming PAA serves K ≤ M users, or equivalently, user equipment (UE) each provisioned with a single antenna. An analog beamforming network, a PA, a mixer, and a digital-to-analog converter (DAC) are the main components of a PAA.

Figure 1 shows a schematic of M analog beamforming networks, each of which consists of a planar array antenna with N _az × N _el elements and a total antenna gain of G _A in the broadside (BS) direction. The main beam is directed using phase shifters connected to each antenna element in the array. Each PAA selects one beam at a time to transmit information. All of the PAAs are connected to a centralized processing unit that handles the precoding scheme and selects the beams of the PAAs according to a beam selection algorithm (see Section 3.3).

Perfect channel state information (CSI) at the transmitter and receiver.

Based on Figure 1, the input-output relationship is given by y = H s + n , (1) where y ∈ C K × 1 is a vector comprising the received signal at each UE receiver, H ∈ C K × M is the downlink MU-MIMO channel matrix, s ∈ C M × 1 is the transmit signal vector after passing the PAs, and n ∈ C K × 1 is the Additive White Gaussian Noise (AWGN) vector at each UE receiver with zero means and σ _n standard deviation.

Let x ∈ C K × 1 be the transmit signal vector intended for the K UEs. The transmit signals are uncorrelated E x k x k ′ * = 0 , for k ≠ k′, and satisfy the power normalization E x k 2 = 1 . The operation E x denotes mathematical expectation of x, and x* is the complex conjugate of x. Hence, further expressing Eq. 1 as y = H G R F p + n (2) = H G R F W x + n , (3) where p ∈ C M × 1 is the linearly precoded transmit signal vector such that p = Wx. W ∈ C M × K is the precoding matrix with instantaneous power normalization, t r a c e W W H = 1 (Lim et al., 2015; Fatema et al., 2017). The proportionality constant G _RF ≥ 0 represents the gain of the amplifier in RF chains and is assumed to be constant across all RF chains.

This study considers two linear precoding schemes: the matched-filtering (MF) precoding and the zero-forcing (ZF) precoding. The precoding matrices are given by W = H † ‖ H † ‖ F  for  M F H † H H † − 1 ‖ H † H H † − 1 ‖ F  for  Z F , (4) where the instantaneous normalization of the precoding matrix mentioned above has been applied, see Eq. 3. H ^† denotes the hermitian (complex-conjugate) transpose operation on matrix H, and ‖H‖ _F is the Frobenius norm of the complex matrix H. The Frobenius norm in Eq. 4 above is defined as ‖ H ‖ F = t r a c e H H H = ∑ k = 1 K ∑ m = 1 M H k , m 2 . It is worthwhile to recall that MF precoding maximizes the received signal power at the UE, while the ZF eliminates the interference at the UE. (Lim et al., 2015) shows that W is independent of G _RF . It is worth noting that the selection of MF and ZF precoding schemes in this study is based on their well-established performance characteristics and relevance for comparison. While other more advanced schemes are known, like the minimum mean square error (MMSE), these schemes enable a focused and meaningful analysis of their strengths in various deployment scenarios that is sufficient to illustrate our main points.

The subsections below explain the three key performance metrics emphasized in this paper: the signal-to-interference-plus-noise ratio, radio frequency amplifier gains, and achievable sum rate.

The propagation channel model is essential to system performance evaluation because the latter will depend on multiple propagation channel characteristics. As mentioned above, the focus is on indoor systems. In the present evaluation, well-established, standardized channel models ensure that the obtained results are relevant to the wireless community and can be easier to understand and compare to future works. Therefore, the statistical 3GPP 38.901 channel model has been used to emulate indoor office propagation channels for frequencies from 0.5–100 GHz (3GPP, 2017). For completeness, some of the main characteristics of this channel model are reproduced below.

The path gain in line-of-sight (LOS) is P G LOS [ d B ] = − 32.4 − 17.3 ⁡ log 10 d 3 D − 20 ⁡ log 10 f c , (11) where d _3D is the 3D distance in meters, and f _c is the frequency in Hz. The path gain model in non-line-of-sight (NLOS) is given by P G NLOS [ d B ] = min P G LOS [ d B ] , P G NLOS ′ [ d B ] , (12) where P G NLOS ′ [ d B ] = − 17.3 − 38.3 ⁡ log 10 d 3 D − 24.9 ⁡ log 10 f c . (13) Also, the main parameters for LOS and NLOS propagation conditions at 28 GHz are presented in Table 1. The parameters in the table include path loss exponent (PLE), shadow fading, delay spread, the azimuth angle of arrival (AoA) spread, the elevation angle of arrival (EoA) spread, the azimuth angle of departure (AoD) spread, the elevation angle of departure (EoD) spread, K-factor, cross-polarization ratio (XPR), and the number of paths (see Figure 2). In the table, μ and σ stand for mean and standard deviation, respectively.

The analysis will be approached in a specialized and systematic way. The considered office environments are subdivided into two main types:

• Indoor mixed office.

A structured and valuable implementation of the channel mentioned above models is available in the QuaDRiGa simulation package. QuaDRiGa can be regarded as a 3GPP 38.901 channel model reference implementation (Jaeckel et al., 2021). It incorporates full 3D propagation, including antenna modeling and scattering clusters, spherical wave propagation, and spatially correlated large and small-scale fading at both the transmitter and receiver sides of the communications link, i.e., the base station and the UE.

Figure 2 shows a sketch of the channel modeling approach in QuaDRiGa between a PAA and a UE. Given M PAAs and K UEs, the channel matrix H ̃ ∈ C K × Q a z × Q e l × M represents the channel responses between all PAAs beams and UEs. Each PAA has Q _az × Q _el beams within its scanning range, where Q _az and Q _el are the number of beams in the azimuth and elevation planes, respectively. One beam per PAA is chosen based on its ability to maximize SR (see Section 3.3 for the beam selection algorithm), and H is then generated from these beams using the details described below. To compute H, the k , q , m entry of H ̃ representing the multipath channel impulse response between the qth beam of the mth PAA and the kth UE is first computed as h ̃ k , q , m t = ∑ i = 0 I h i , k , q , m ′ δ t − τ i , (14) where h i , k , q , m ′ is the impulse-response corresponding to the ith path between the mth PAA when it is beam-steered towards the qth direction, q ∈ 1 , … , Q a z × Q e l and the kth UE, and τ _i is the time delay in the ith path. I + 1 is the number of channel paths: at most one LOS if it exists and I NLOS. When there is no LOS path between mth PAA and kth UE, h 0 , k , q , m ′ is zero. The parameters outlined in Table 1 are utilized to determine the angles and delays associated with the ith NLOS path. Consequently, it is possible to compute the precise locations of both the first bounce scatterer (FBS) and the last bounce scatterer (LBS), referring to the initial and final reflections along the path. It is worth noting that both the radiation pattern of the PAAs and the UEs are considered in the computation of Eq. 14. For the sake of simplicity, the UE antenna radiation pattern is considered isotropic. Thus, it does not affect the channel. Finally, h ̃ k , q , m t is converted to the frequency domain to obtain H ̃ k , q , m f , the k , q , m entry of the spatial channel transfer matrix H ̃ .

The complete channel matrix H is generated using the spatial channel transfer matrix H ̃ ((14)) in conjunction with a beam selection algorithm. In the implemented algorithm, beams maximize the MU-MIMO achievable sum-rate capacity because it is a fundamental figure of merit for a wireless system. The approach assumes an exhaustive search scheme, as suggested in (Han et al., 2017). It evaluates all the possible combinations of the beams and chooses the optimal selection. All channels from the PAAs’ beams to the UEs are assumed to be known. Each of M PAAs produces Q _az × Q _el beams, resulting in a total of Q a z × Q e l M beam combinations. After evaluating the achievable sum-rate capacity of each combination using Eq. 10, the optimum combination can be selected i 1 , … , i M = a r g m a x i 1 , … , i M = 1 , … , Q a z Q e l S R . (15) This approach optimizes the performance and gives an upper bound on performance. However, the algorithm represented by Eq. 15 is time-consuming and needs to be replaced in further studies to provide more practical results.

As discussed above, the performance of various PAA systems is evaluated in two essentially different deployment scenarios:

• Collocated PAAs.

Results will be specialized to an indoor environment comprising a room of 80 × 80 × 3 m³ in size. The placement heights of the PAAs and the UE antennas are 3 m and 1 m, respectively. The UE positions in the room are random in the horizontal plane with a uniform distribution. The room parameters are defined according to Table 7.2-2 in (3GP, 2017), where a detailed scenario description is provided for channel model calibration. The center-to-center distance between neighboring PAAs in collocated scenarios is set to 20 cm, and they are aligned to have the BS direction towards the center of the room.

Three antenna system simulation cases are considered for each scenario and propagation environment mentioned above, as shown in Table 2. Hereafter, the number of UEs and PAAs in all simulations is K = M = 4. Cases 1 and 2 make use of the PAA presented in (Bagheri et al., 2023b), which is capable of analog beamforming within an angular range of ±60° and ±10° in the azimuth and elevation planes, respectively. A useful feature of this PAA is that it is modular with four identical and independent subarrays. Therefore, the PAA can function in two ways: first, all subarrays form one large PAA, corresponding to Case 1, and second, each subarray works as an independent PAA, as in Case 2. Case 1 has a high antenna gain of 29.4 dBi in the BS direction. Case 2 has a lower antenna gain of 23.4 dBi in the BS direction. As a result of the high antenna gain and larger aperture in Case 1, its half-power beamwidth (HPBW) is smaller than that of Case 2. Case 3 uses a PAA with a 23.1 dBi antenna gain in the BS direction (Bagheri et al., 2023a). This PAA can only beamform in the azimuth plane within an angular range of ±60°. The beam coverage of the PAAs is shown in Figure 4, where the antenna gain by the PAAs in the main beams at each angle Q a z , Q e l is shown.

Another important property of PAAs is effective isotropic radiated power (EIRP), which is defined as E I R P = P c G A , (16) where P _c is the conducted power and G _A is the total array antenna gain. Using Eq. 16 above and Eq. S2 in Supplementary Appendix S2, EIRP for each PAA in Figure 1 can be written as E I R P m = E s m 2 G A m = G R F W m : 2 G A m . (17) Therefore, the EIRP of the PAAs as given by Eq. 17 is limited by G _RF and total array antenna gain ( E I R P m < G R F G A m ) . The maximum EIRP values for the PAAs considered here are 9 dB backed off from their saturation points to preserve signal linearity. The simulations use these EIRP values with the conducted powers P _c . The maximum conducted power P _c,max is chosen to meet the maximum total radiated power (TRP) for local area base stations of 33 dBm (3GPP,2018).

A concise flow chart of the main simulation steps is shown in Figure 5. The structure follows the modeling approach outlined above, including the computation of the figures of merit of interest.

The simulation study compares the deployment of two different PAAs, realized in fundamentally two different spatial configurations of the PAAs in two different indoor propagation environments, and evaluated for two different beamforming algorithms.

The operational frequency chosen for the simulations is 28 GHz. The noise power and interference level play essential roles in the quality of the received signal. Here and for the rest of the paper, the noise power at the UEs is σ n 2 = N 0 B = − 99 dBm, where N ₀ = −174 dBm/Hz is the thermal noise power in a 1-Hz bandwidth at room temperature and B = 30 MHz is the signal bandwidth. The total number of samples for a single simulation is 500; hence, s = 1, …, 500. All computed parameters are shown as empirical cumulative distribution functions (CDFs). Corresponding mean values and standard deviations are also computed. For G _RF , the received signal, interference, and SINR, mean and standard deviation values are computed in the logarithmic domain. This is due to the log-normal distribution of these parameters in downlink cellular networks (Hadj-Kacem et al., 2020).

To illustrate the impact of the propagation channels on the received signals when beamforming is employed, the received signal has been computed at several positions evenly distributed over the simulated room for two different propagation channels. Figure 6 shows the distribution of the link path gain plus antenna gain (in dB) for the PAAs in all cases based on the corresponding Eqs 11–13 given above. Results are shown when the arrays transmit in the BS direction. Two propagation channels are considered:

The path gains in these cases are spatially correlated. The effects of the main lobe, side lobes, and nulls of the antenna’s radiation pattern are visible in Figures 6A,C,E. Multipath propagation has changed the path gain distribution considerably. As a result, the gain has increased at some positions, more visibly in the direction of pattern nulls. The distribution of the received signal has become more even. In Figures 6B,D,F, the effect of the radiation pattern is not visible anymore, and the values of the path gain plus antenna gain have dropped significantly. Computing the average path gain in linear scale over all the simulated room positions gives the following values in dB scale: −75.5, −100.6, −75.2, −96.7, −75.6. These values correspond to Figure 6A through F. These average values are well correlated with the respective PLEs. As seen from the above results, the propagation channel behaves differently in different environments, which may negatively impact the system performance, as evaluated next. Moreover, as multipath propagation becomes predominant, digital beamforming that adapts the communication link to the spatially selective channel becomes more relevant. The optimized performance might be achieved through the scatters, i.e., the environment, instead of forming a well defined beam towards the users.

The CDFs of RF power amplifier gains G _RF Eq. 9 of all PAAs (see Supplementary Appendix S2) are shown in Figure 7 for Case 1 (see Table 2). The other two cases are omitted because the main shapes are the same. On the other hand, the mean value and standard deviation corresponding to computed CDFs for all three cases are presented in Table 3.

It can be seen from Table 3 that the PAA distributed deployment scenario (Dist.) requires lower G _RF than the collocated scenario (Coll.) regardless of the propagation scenario, the precoding scheme, and the antennas and beams used. The required power is on the order of ≈ 1.45 dB lower on average, i.e., about 40% lower power amplifier (PA) gain needed across all cases. The computed G _RF difference in dB between the Dist. scenario and the Coll. scenario in the mixed environment varies from 1.6–2.4 dB (45–74%), observed across all the cases and precoding algorithms. In contrast, in the open propagation environment, it goes from 0.2–1.7 dB (5–48%). A similar comparison shows that for the MF precoding, the reduction is from 0.2–2.4 dB (5–74%), and for the ZF precoding, it is from 1.6–2.0 dB (45–58%), observed across the propagation environments and cases.

As can be seen above, the choice of precoding scheme affects the PA gains G _RF , too. Looking at Table 3, it becomes apparent that, indeed, ZF requires, in general, a higher G _RF than MF. This is expected because MF is well-known to optimize the link power while ZF minimizes interference. The MF requires ≈ 1.11  dB (29%) less power than the ZF, regardless of the propagation scenario, the antennas and beams used, and the deployment scenario (i.e., Coll. or Dist.). More specifically, comparing the reduction of G _RF with MF compared to the ZF precoding in the mixed scenario is from 1.2–1.6 dB (32–45%), while it is from −0.1 − 1.6 dB (−2 − 45%) in the open propagation scenario. It is worth reminding that the negative values −0.1 dB (−2) % indicate an increase rather than a decrease, which was observed for only one of the twenty possible simulated instances, i.e., for Case 2 [16,1] open propagation scenario.

The reduction of G _RF depends on the propagation environment, the antenna type, and the deployment scenario, as illustrated above. As shown in Table 2, Case 1 and 3, having the same P _c,max , use an equal amount of RF power. Case 2 transmits roughly 6 dB (300%) less than the other cases, with 6 dB less P _c,max as well. On the other hand, the spatial beam arrangement of each PAA ( Q a z , Q e l ) shows no significant change in the total conducted RF transmit power. In this context, the most significant reduction of G _RF is for Case 2 with 16,1 and 8,2 beams using MF precoding in the mixed propagation environment.

Regarding the standard deviation, it can be seen from Table 3 that it remains almost unchanged across Cases 1, 2, and 3 and that the values are relatively low. There is an increment when using distributed antennas compared to collocated for most considered instances, but the MF precoding in the open space propagation scenario. The latter might be explained by the fact that it becomes more likely to be in a focused beam with slight channel variation.

The SINRs at the UE locations are computed using Eq. 5 and are shown in Figure 8 for Case 1 only because of the same reasons as above. Table 4 shows the mean value and standard deviation.

As seen from Table 4, the SINR increases with deploying distributed antennas compared to collocation with an average of 12.7 dB, as seen across all the results. The SINR increment is larger in the open propagation environment with an average of 19.3 dB compared to 6.1 dB in the mixed environment computed over all the cases and precoding schemes.

Furthermore, on average, the SINR with ZF is 19 dB higher than with MF computed over all the propagation scenarios and cases. In the open propagation environment, the average SINR increase is 25.5 dB compared to 12.5 dB in the mixed propagation environment. It should be noted here that ZF precoding produces a SINR distribution with a lower standard deviation than MF. This gives the benefit of a more reliable link between PAAs and UEs.

The signal power by UEs also increases when the PAAs are distributed in all cases. This is due to the higher path gain in the distributed deployment scenario. In addition, the standard deviation of the received signal power decreases when PAAs are distributed. The LOS probability is higher in the open propagation environment; therefore, the received signal level also generally increases. Almost always, in the distributed deployment scenario in the open propagation environment, the UEs are within LOS distance of at least one PAA. Still, in the collocated scenario, there is a high probability that the UEs do not see any PAA in their LOS. While not shown here, it was observed that the mean of the received signal level in the distributed deployment of the open propagation environment is ≈ 20 dB higher than the mixed environment.

The most significant increase of SINR is for Case 1 with 16,1 and 8,2 beams using ZF precoding in the open propagation environment.

As in the case of the PA gains above, the variability is similar for the antenna types and beam configurations. As seen from Table 4, the ZF precoding has a much lesser standard deviation than the MF precoding. Moreover, the standard deviation is larger in the open propagation environment than in the mixed environment. The comparison of distributed versus collocated is less straightforward and depends on the case.

Figure 9 shows the CDF of the achievable sum rate computed by Eq. 10 for Case 1. All the curves have been obtained from 500 simulated data points, i.e., channel realizations. Table 5 summarizes the simulations’ mean value and standard deviation.

It can be immediately seen from the shown results that the distributed deployment scenario always leads to higher SR because of the similar behavior of the SINR. On average, the SR in the distributed deployment scenario is 11.1 bps/Hz larger than in the collocated scenario for all the propagation scenarios, cases, and precoding schemes. The numbers in open and mixed propagation environments are 16 bps/Hz and 6.2 bps/Hz, respectively. The distribution of PAAs increases the chance for UEs to make a LOS link with at least one PAA in the open propagation environment.

The ZF precoding shows a larger SR increase than the MF precoding. It is mainly because ZF removes the interference at UE positions. On average, ZF SR is 12.5 bps/Hz larger than the MF for all the cases and propagation environments. The corresponding improvements in the open and mixed environments are 18.5 bps/Hz and 6.4 bps/Hz, respectively, because of the higher LOS probability.

The largest SR are observed for both scenarios of Case 1 when 16,1 and 8,2 . Since the vertical spread of the UE locations in the indoor environment is limited, it is advantageous that all of the beams are in the same plane when the HPBW is small—with 16,1 beams covering the azimuth plane within their HPBW (look at Figures 4A,B). Meanwhile, the opposite effect can be seen in both scenarios of Case 2, where beams with larger HPBW are employed. When 8,2 beams are used, SR increases in both collocated and distributed deployment scenarios. Figures 4C,D show the beam coverage by the antenna of Case 2.

In terms of the standard deviation of the sum-rate capacity, it can be see from Table 5 that it is larger for the ZF precoding employed in a distributed antenna scenario than for the MF in a collocated scenario. Moreover, the standard deviation is larger in the open environment than in the mixed environment. As in the case of the power amplifier gain and the SINR, the standard deviation is relatively stable across the antenna types and beam configurations.

Table 6 overviews the top four simulation instances, ranked according to the SR mean in 3GPP-defined indoor mixed and open propagation environments. The table also shows the SR values corresponding to a CDF probability level equal to 0.05, denoted as CDF_SR = 0.05 in the table. As established above, PAA distributed deployment scenarios consistently perform better than collocated scenarios. In addition, the ZF precoding scheme offers a higher average achievable SR capacity due to a higher SINR. At the same time, a lower PA gain is needed in distributed than collocated scenarios, as established above. Also, when comparing the ZF precoding in the indoor scenarios, a higher SR can be expected from the open propagation environment than the mixed propagation environment. We believe it is mainly due to the higher probability of the LOS condition.