Optimal Pilot Design for MIMO Broadcasting Systems Based on the Positive Definite Matrix Manifold

In the MIMO broadcasting system, channel state information (CSI) is often used for data detection at the receiver or preprocessing techniques such as the power control and user scheduling at the transmitter and hence, the study of its acquisition is important. Usually, the CSI can be obtained by the training-based channel estimation. Assuming that the users have the channels' statistical information and adopt the minimum mean-square-error (MMSE) receivers, this paper studies how to design an optimal training sequence to minimize the total weighted mean square error (MSE) of channel estimation. Following this objective, we formulate this problem as a positive semidefinite problem (SDP) with two constraints, and further transform it into a dual problem. In the solving process of the dual problem, we model it as an optimization problem on the positive definite matrix manifold and solve it by use of the iterative geodesic equation on the matrix manifold. The convergence and correctness of the proposed method are demonstrated by computer simulation; the effects of key system parameters on the weighted MSE are also investigated. Under various system configurations, the superiority of the proposed method is shown by comparing with a few other existing schemes.