# Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing
## 3 Numerical Results
### Full-Array vs. Sub-Array Architecture  
First, the full- and sub-array architectures are investigated. To this end, a dominant LOS channel is considered, where the power of the LOS component is significantly larger than the sum power of the multi-path components originating from local clusters around the users. The LMR is set to \(10\,\mathrm{dB}\) and the spatial spread of the multi-path components is \(\sigma_{5}=2^{\circ}\). The PSPs of the users are assumed to be perfectly known and the beamforming weights are chosen optimally, i.e., the beams are evenly distributed in the given FoV \(\Phi=\pi/2\), whereby one of the generated beams is perfectly aligned to a respective user. For comparison, the SER performance of coherent detection via Bell Laboratories layered space-time (BLAST) [45, 46] with perfect channel knowledge is included in the following considerations. Applying the digital beamspace preprocessing, the induced power of the users at the BS, which has been uniformly distributed over the receive antennas due the to far-field location, is spatially redistributed and focused onto a smaller subset of the \(N_{\mathrm{r}\mathrm{r}}\) receive branches. First, regarding the full-array architecture, the resulting PSPs show a very narrow peak as depicted in Figure 4a, where user 2 is located at boresight (\(\phi_{2}=0^{\circ}\)). In case of conventional beamforming, the PSPs follow a squared sinc function, which is minimally broadened due to the low-power multi-path components. A combination with eigenspace-based beamforming yields even narrower power peaks, where most of the user power is concentrated at one receive branch. A difference in the total power of the users can be observed, which is due to a loss in received power for non-boresight users since directional patch antennas are employed at the BS. The SER performance as function of the SNR is illustrated in Figure 4b when user 2 is again at the boresight location. While noncoherent detection fails without beamspace preprocessing due to uniform PSPs, the spatial redistribution of the user power in the digital domain via beamforming allows almost identical performance compared to the coherent detection with perfect channel knowledge. Here, no performance gains are observed when eigenspace-based processing is applied in addition. The worse performance of the users 1 and 3 is again related to the power loss using directional antennas. Analyzing the SER as function of the angular position \(\phi_{2}\) of user 2 (see Figure 4c), the performance of the noncoherent detection scheme deteriorates when approaching one of the other users due to the overlapping of the respective PSPs. Here, additional eigenspace-based beamforming exhibits a significant improvement in terms of user separability since the digital redistributed user power is  
\begin{table}
\begin{tabular}{c c} \hline \hline
**System Configuration** & \\ \hline number of users \(N_{\mathrm{u}}\) & 3 \\ number of BS antennas \(N_{\mathrm{r}\  
almost located at one receive branch. Noteworthy, coherent detection using BLAST exhibits a minor degradation in performance when the users are exactly at the same angular position. Next, the sub-array architecture is considered allowing a low-complexity LO distribution network since each sub-array can employ its own LO. To this end, the antenna array of the BS is splitted into \(N_{\text{sub}}=8\) sub-arrays each comprising \(N_{\text{rc,sub}}=16\) antennas. Consequently, 16 different spatial beams can be generated, which are assumed to be the same for each sub-array. This leads to a periodic pattern of the PSPs as depicted in Figure 4(a). The SER as function of the SNR remains almost unchanged when compared to the full-array architecture using Bartlett beamforming (see Figure 4(b)). A saturation is observed at high SNR, where the residual inter-user interference due to non-orthogonal beams begins to dominate, deteriorating the performance. A slight performance degradation is observed for Bartlett-eigenspace beamforming.