Training sequence optimization in MIMO systems with colored noise

In this paper, we address the problems of channel estimation and optimal training sequence design for MIMO systems over flat fading channels in the presence of colored noise. In practice, knowledge of the unknown channel is often obtained by sending known training symbols to the receiver. During the training period, we obtain the best linear unbiased estimates of the channel parameters based on the received training block. Under the assumption that we can express the noise covariance matrix as a Kronecker product of temporal and spatial correlation matrices, we determine the optimal training sequence set that minimizes the mean square error (MSE) of the channel estimator under a total transmit power constraint, in order to obtain the advantage of the optimal training sequence design, long-term statistics of the noise correlation are needed at the transmitter. Hence this information needs to be estimated at the receiver and fed back to the transmitter. Obviously it is desirable that only a minimal amount of information needs to be fed back from the receiver to gain the advantage in reducing the estimation error of the short-term channel fading parameters. We develop such a feedback strategy in this paper.