Performance of optimal beamforming with partial channel knowledge in correlated fading

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 maximal ratio combining (MRC) at the receiver, where the receiver antennas experience correlated fading. 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. In addition, the transmitter is endowed with knowledge of the receive channel correlations. We derive the optimal beamformer for a single stream transmission case and show that it is the principal eigenvector of the known channel submatrix and the expected value of the unknown channel submatrix given the known channel. We show that the diversity order of a transmission scheme where such a preceder 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. We further show that, as expected, the effect of the correlation is only an array gain reduction. All the results are supported by simulations.