Optimal Training Sequences for Large-Scale MIMO-OFDM Systems

Abstract

This paper considers the optimal design of training sequences for channel estimation in large-scale multiple-input multiple-output orthogonal frequency-division multiplexing systems. The application scenario of interest is when the number of transmit antennas for the downlink (or the number of receive antennas for the uplink) is large, but not large enough to benefit the asymptotical optimality of using equipower training sequences (e.g., due to practical constraints on deployment costs, space, and antenna size). Under the criterion of minimizing the mean square error of the channel estimate, the optimal design of training sequences for such systems poses a truly large-scale optimization problem, to which existing optimization solvers are not applicable. We develop a fast convex programming (FCP) procedure to find its global optimal solution. In each iteration of the proposed FCP procedure, a solution is found in a scalable and closed form. The singularity and ill-conditionedness of the channel correlation matrices are also exploited to improve the computation efficiency. Furthermore, we also examine the design of reduced-length training sequences and develop a successive quadratic programming procedure to find the solutions. Intensive simulation results are provided to illustrate the performance of our methods.