Performance of multiple-input wireless channels with limited feedback

Channel knowledge at a transmitter can be used to optimize transmit waveforms, exploit channel conditions, and avoid interference. A receiver, which has channel state information, can compute and relay the optimal transmit waveform to the transmitter via a feedback channel. Here we study the performance of various communication systems with limited feedback.; In Code Division Multiple Access (CDMA), the feedback specifies the signature sequence that maximizes the signal-to-interference plus noise ratio (SINR) for the desired user. The signature is selected from a set of quantized signatures or codebook, which is known a priori at both the transmitter and receiver. We show that a Random Vector Quantization (RVQ) codebook, whose entries are independent and isotropically distributed, is optimal in a large system limit in which the number of users, processing gain, and feedback bits tend to infinity with fixed ratios. We derive the asymptotic SINR for RVQ and show that, with one feedback bit per signature coefficient, the performance of RVQ is close to the performance with unlimited feedback. To reduce the quantizer complexity, we propose a simpler, but suboptimal reduced-rank quantization scheme in which the optimal signature vector is projected onto a lower dimensional subspace before element-wise scalar quantization.; We extend the results for CDMA to a point-to-point multi-antenna channel. The receiver optimizes and quantizes a transmit precoding matrix. For a rank-one precoding matrix or beamformer, the RVQ codebook is optimal in the large system limit and the associated asymptotic capacity is derived. The asymptotic sum rate with RVQ and a precoding matrix with arbitrary rank is approximated. In addition to an optimal receiver, we also consider the performance of a quantized precoding matrix with the matched filter and Minimum Mean Square Error (MMSE) receivers. We show how much additional feedback is needed by linear receivers to achieve a target rate, relative to the optimal receiver.; We also examine the capacity of beamforming with finite training for channel estimation and limited feedback. The receiver computes an MMSE estimate of the channel from a training sequence and selects the optimal beamformer from an RVQ codebook based on the channel estimates. We derive capacity bounds as functions of the number of feedback and training symbols and optimize the bounds over those variables. The optimal amount of feedback and training and the corresponding capacity are characterized for a large number of transmit antennas. With a single receive antenna, the number of training and feedback symbols are asymptotically the same. Both feedback and training lengths, normalized by the number of transmit antennas, tend to zero as the number of transmit antennas tends to infinity.