Codebook Design for Memory-Based Quantization of Precoder Matrix in Low-Rate Feedback MIMO Systems with Temporally Correlated Fading

An important transmitter adaptation technique used in multiple-input multiple-output (MIMO) communication systems is precoding based on the dominant right-singular vectors of the channel matrix. These vectors are typically estimated at the receiver, quantized, and fed-back to the transmitter via a low-rate feedback channel. We present a method for designing an efficient low-rate quantizer for the dominant right singular vectors of a MIMO channel matrix, which exploits the memory in the slow-varying channel fading process. A memory-based (recursive) quantizer is considered which quantizes the time-trajectory of points representing the channel subs-spaces on a Grassmannian manifold. The quantizer codebook is optimized with respect to an objective functions which can be directly related to MIMO channel capacity. The main contribution of this paper is the derivation of a stochastic gradient-based algorithm for codebook optimization. Numerical results obtained with channel simulations are presented, which demonstrate the MIMO channel capacity improvement achieved by using the codebooks optimized as proposed in this paper.