Linear Beamforming for the Spatially Correlated MISO broadcast channel

A spatially correlated broadcast setting with M antennas at the base station and M users (each with a single antenna) is considered. We assume that the users have perfect channel information about their links and the base station has only statistical information about each user's link. The base station employs a linear beamforming strategy with one spatial eigen-mode allocated to each user. The goal of this work is to understand the structure of the beamforming vectors that maximize the ergodic sum-rate achieved by treating interference as noise. In the M = 2 case, we first fix the beamforming vectors and compute the ergodic sum-rate in closed-form as a function of the channel statistics. We then show that the optimal beamforming vectors are the dominant generalized eigenvectors of the covariance matrices of the two links. It is difficult to obtain intuition on the structure of the optimal beamforming vectors for M > 2 due to the complicated nature of the sum-rate expression. Nevertheless, in the case of asymptotic M, we show that the optimal beamforming vectors have to satisfy a set of fixed-point equations.Comment: Published in IEEE ISIT 2010, 5 page

Quantized Multimode Precoding in Spatially Correlated Multi-Antenna Channels

Multimode precoding, where the number of independent data-streams is adapted optimally, can be used to maximize the achievable throughput in multi-antenna communication systems. Motivated by standardization efforts embraced by the industry, the focus of this work is on systematic precoder design with realistic assumptions on the spatial correlation, channel state information (CSI) at the transmitter and the receiver, and implementation complexity. For spatial correlation of the channel matrix, we assume a general channel model, based on physical principles, that has been verified by many recent measurement campaigns. We also assume a coherent receiver and knowledge of the spatial statistics at the transmitter along with the presence of an ideal, low-rate feedback link from the receiver to the transmitter. The reverse link is used for codebook-index feedback and the goal of this work is to construct precoder codebooks, adaptable in response to the statistical information, such that the achievable throughput is significantly enhanced over that of a fixed, non-adaptive, i.i.d. codebook design. We illustrate how a codebook of semiunitary precoder matrices localized around some fixed center on the Grassmann manifold can be skewed in response to the spatial correlation via low-complexity maps that can rotate and scale submanifolds on the Grassmann manifold. The skewed codebook in combination with a lowcomplexity statistical power allocation scheme is then shown to bridge the gap in performance between a perfect CSI benchmark and an i.i.d. codebook design.Comment: 30 pages, 4 figures, Preprint to be submitted to IEEE Transactions on Signal Processin

Illinois Center for Wireless Systems (ICWS)

unpublishednot peer reviewe