A Holistic Approach to Wireless Design Through Physics Based Simulations
Maximal Ratio Combining (MRC) Detector
The MRC detection technique uses the hermitian (conjugate transpose) of the channel matrix to multiply the received symbol vector. Similar to the matched filter, it leverages the fact that different user channels have low correlation to decode separate data streams. From the bar graph of the SINR we can see that the interference power from user 2, after MRC, when user 1 is decoded is about 14 dB above the signal power of user 1. Noise power can be neglected as we are in a high SNR regime. This points to the weakness of MRC as a very simple linear architecture and could be improved by the use of ZF or LMMSE detection.
Zero Forcing (ZF) Detector
The ZF detection technique uses the left pseudo-inverse of the channel matrix to multiply the received symbol vector. From the bar graph of SINR we see that the signal power of user 1, after ZF, is about 7 dB above the interference power from user 2 when user 1 is decoded (high SNR regime). ZF detector is therefore able to separate the two UEs in space at sufficiently large SINR to allow for space-division multiple access.
Linear Minimum Mean Squared Error (LMMSE) Detector
The LMMSE detection technique uses a minimum mean squared error estimate of the transmitted symbol vector with processing confined to linear operation (vector matrix multiplication). Since both MRC and ZF are both linear, LMMSE would have a higher spatial resolution than either MRC or ZF. Moreover, in the limit of high SNR, LMMSE reduces to ZF which is can be seen from the bar graph.