Performance of Optimal Beamforming with Partial Channel Knowledge

Abstract

Multiple antenna techniques are used to enhance wireless links and therefore have been studied extensively. Many practical systems that differ from ideal schemes have been discussed in the literature. One example is a system that lacks precise channel information at the transmitter. We evaluate analytically the performance of a multiple input multiple output (MIMO) technique that uses partial channel knowledge. Specifically, we analyze a scheme with M transmit antennas and N receive antennas, employing eigenbeamforming at the transmitter and MRC at the receiver. We assume that only partial channel matrix is known to the transmitter, specifically only P out of N rows of the channel matrix are known. We derive the optimal beamformer for a single stream transmission case and show that it is the singular vector of the known channel submatrix. We show that the diversity order of a transmission scheme where such a precoder is used is MP+N-P and further show that increasing the value of P by one increases the diversity order by M-1. We also derive the array gain for this scheme. All the results are supported by simulations.