# Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing
## 4 Conclusions  
In this paper, the application of digital beamspace preprocessing to a massive MIMO system is assessed, where noncoherent detection is performed in the uplink. First, the fundamentals and the requirements are discussed when both concepts are treated jointly and when a full-array or a sub-array architecture is considered. Then, the symbol error rate performance is analyzed for a three-user scenario on the basis of a cluster-based channel model capturing its principal behavior under physically accurate conditions. It is demonstrated that digital beamspace preprocessing transforms the unsuitable uniform PSPs, when the users are located in the far-field of the BS, into PSPs with a narrow peak located at the receive branch associated with the corresponding angle of arrival of the incoming wave. Hence, the users can be spatially separated when the signals impinge at the BS from sufficiently different angular directions enabling again the noncoherent detection scheme. An improved performance in terms of angular user separability is achieved when the conventional processing is extended by means of eigenspace-based beamforming. At the costs of higher computational complexity, this procedure reduces the inter-user interference in case of closely spaced users. Regarding a sub-array configuration, the PSPs exhibit a periodic pattern and the angular user separation is less due the reduced aperture size. Furthermore, a small performance degradation is observed.  
The characteristics of the propagation channel can have a large impact on the system performance. Best results in terms of user separability are obtained in dominant LOS channels, which allows an accommodation of a large number of users. On the contrary, better overall SER performance is achieved in multi-path scenarios since the channel correlations are lower. However, a higher level of inter-user interference can occur for larger spatial spreads of the multi-path components reducing the total number of users, which can be served optimally.  
Generally, the knowledge of the PSPs for noncoherent detection are unknown in practice. However, the estimation is straightforward when the angular position of the users is known beforehand. Otherwise, the common known concept of DOA estimation can be employed extracting the respective angular directions via a peak search in the angular spectrum. This works particularly in dominant LOS channels. The extracted knowledge of the angular position can also be used for the downlink transmission afterwards.  
Comparing the results to coherent detection with perfect channel knowledge, the performance gap is minimal. However, the estimation overhead and potential channel estimation errors are not taken into account, which severely degrades its performance. When considered, the presented combination of the noncoherent detection scheme and digital beamspace preprocessing outperforms the CSI-based detection.  
Conceptualization, S.B.; methodology, S.B.; software, S.B.; validation, S.B.; formal analysis, S.B.; investigation, S.B.; resources, C.W.; data curation, S.B.; writing--original draft preparation, S.B.; writing--review and editing, S.B. and C.W.; visualization, S.B.; supervision, C.W.; project administration, C.W.; funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) grant number WA 3506/5-1.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.