Optimum Training for MIMO BPSK Transmission

Abstract

In this paper, we derive an analytical expression for the bit error rate (BER) of binary phase shift keying (BPSK) symbols transmitted over a multiple-input multiple-output (MIMO) system under channel estimation errors. In this wireless communications system, the receiver uses the linear minimum mean squared error (LMMSE) estimator to estimate the channel matrix. The error in this estimation affects the following estimation that is used to recover the transmitted symbols. It is shown that the channel estimation error is Gaussian and hence the convex Gaussian min-max theorem (CGMT) can be applied to analyze the error of the signal estimation stage and finally obtain an expression for the BER. We use the BER expression to obtain the optimal pilot power allocation under a total transmit energy constraint. Numerical results show close matching between theory and simulations.