Combining Pre- and post-processing with Tomlinson-Harashima precoding in downlink MU-MIMO with each user having arbitrary number of antennas

In downlink multiuser (MU) MIMO (multiple-input multiple-output) system, precoding at the transmitter should be such that the data symbols meant for ith user do not cause interference at kth user, k ≠ i, while ensuring that the transmitted power is unchanged by the precoding. Dirty paper coding (DPC) meets these conditions, but its practical implementation is very complex. Tomlinson-Harashima precoding (THP) ensures interference-free communication to the users like DPC, with very little increase in the transmitted power, and its implementation is much less complex compared to that of DPC. Block diagonalization based precoding also meets these conditions, but at the cost of increased number of antennas at the transmitter, and the increase depends on the number of antennas of the users. In the downlink MU-MIMO with THP, it is known that the transmitter with Nt antennas can serve Nt users, with each user having one antenna, thereby transmitting one stream of symbols (we refer to this as one layer) to each user. To the best of our knowledge, MU-MIMO with THP has not addressed the case of Nt users, with each user having arbitrary number of antennas. In this paper, we first show that by combining pre-processing with THP at the transmitter and performing post-processing at each user, Nt users, each with arbitrary number of antennas, can be served with one layer each. Pre-processing involves vectors, matched to the coefficients of the user channels from an a priori chosen transmitter antenna for each user, which serve as the postprocessing vectors for the users. Next, we show that if number of users, say M, is less than the number of antennas at the transmitter, then the Nt layers can be distributed among M users, provided the total number of receiving antennas of M users is ≥ Nt. The transmitter has to send minimal information to the users to enable decoding of their layers.