Bezout-based robust precoding for MIMO frequency selective channel using imperfect channel knowledge

In this paper, the problem of MIMO precoding is addressed for the case of single user, frequency selective wireless channel. Based on Bezout identity, two robust precoder designs are proposed that aim to inverse the effects of channel Intersymbol Interference (ISI) under two different scenarios of imperfect channel knowledge at the transmitter side. In the first one, specific statistical quantities of the channel are known at the transmitter while in the second one, a worst case scenario is adopted assuming that channel uncertainty falls within a given bounded set. Using standard optimization tools, both precoders are expressed in closed forms which are applicable for a wide range of channel conditions w.r.t. correlation in space and/or time, antenna numbers etc. Simulation results have shown that the proposed precoders perform comparably to the perfect channel knowledge case, offering at the same time some benefits in required transmitted power.