Downlink Training Sequence Design for FDD Multiuser Massive MIMO Systems

We consider the problem of downlink training sequence design for frequency-division-duplex multiuser massive multiple-input multiple-output systems in the general case where users have distinct spatial correlations. The training sequences leverage spatial correlations and are designed to minimize the channel estimation weighted sum mean square error (MSE) under the assumption that users employ minimum MSE estimators. Noting that the weighted sum MSE function is invariant to unitary rotations of its argument, a solution is obtained using a steepest descent method on the Grassmannian manifold. We extend the proposed design to scenarios with temporal correlations combined with Kalman filters at the users, and design sequences exploiting the multiuser spatio-temporal channel structure. Finally, we consider scenarios where only a limited number of bits B are available at the base station (BS) to inform the users of each chosen sequence, e.g., sequences are chosen from a set of 2(B) vectors known to the BS and users, and develop a subspace version of matching pursuit techniques to choose the desired sequences. Simulation results using realistic channel models show that the proposed solutions improve user fairness with a proper choice of weights, lead to accurate channel estimates with training durations that can be much smaller than the number of BS antennas, and show substantial gains over randomly chosen sequences for even small values of B.