Wireless MIMO switching with zero forcing and network coding

Abstract — A wireless relay with multiple antennas is called a multiple-input-multiple-output (MIMO) switch if it forms a one-to-one mapping from the inputs (uplinks) to the outputs (downlinks). This paper studies the case with N source stations and N destination stations (which may be the same set), so that the mapping is any permutation of the N inputs. Moreover, the switching is achieved by “precode-and-forward”, i.e., the relay precodes the received vector signal by a zero-forcing matrix and transmits it, so that each destination station receives only its desired signal with enhanced noise but no interference. Assuming full channel state information is available at the switch, the design of the zero-forcing precoder for maximizing some performance metric based on the received signal-to-noise ratios is investigated. The problem with two stations is completely solved in closed form in certain cases. In other cases, heuristic algorithms are proposed to optimize the precoder. These algorithms are shown to be near-optimal. Index Terms—Beamforming, fairness, maxmin, MIMO switch-ing, relay, zero-forcing. I