Beamforming in Wireless Networks Using Quantized Channel State Information

We study quantized beamforming schemes for single and multiple user wireless networks with quasi-static fading channels. The main goal is to design a reliable communication system that can achieve low symbol error rates (SERs) by utilizing the quantized channel state information (CSI) provided by the receiver(s') feedback. We focus on the high signal-to-noise ratio (SNR) regime, where the goal of achieving low error rates is equivalent to achieving high diversity and array gains.;First, we consider quantized beamforming in one-hop amplify-and-forward (AF) relay networks with a single transmitter-receiver pair. We provide necessary and sufficient conditions on the structure of SER-optimal quantizers. In particular, we show that it is necessary and sufficient to use single-relay selection (SRS) to achieve maximal diversity.;We also prove that the average SNR loss and the capacity loss due to quantization decays at least exponentially with the number of feedback bits. We then study the quantized beamforming problem in multiuser networks. In general, the optimal beamforming policy requires the global CSI of the network. However, in a network with multiple receivers, none of the receivers can have access to the global CSI, each can only know its local CSI. As a result, quantizer design in multiuser networks much more difficult than the one in single-user networks. We resolve this difficulty by introducing a new local (distributed) quantizer (LQ) design method, called localization, in which one synthesizes the LQ out of an existing global quantizer (GQ).;We apply the localization method to multiple-input multiple-output (MIMO) broadcast channels, where a single multiple-antenna transmitter intends to send a common message to multiple single-antenna receivers using quantized beamforming. Using the localization method, we design the LQ to minimize the probability that at least one receiver incorrectly decodes its desired symbol. Our LQ designs provide full-diversity and high-array gain with very low feedback rates. They also reveal a surprising property of finite rate feedback schemes for multiple-input single-output (MISO) systems that was previously unexplored: For MISO systems, one can achieve the performance of almost any quantized beamforming scheme with an arbitrarily low feedback rate, when the transmitter power is sufficiently large.;Finally, we consider quantized beamforming in multiuser relay-interference networks with any number of single-antenna transmitters, relays, and receivers. We introduce a generalized diversity measure that encapsulates the conventional one as the first-order diversity. Additionally, it incorporates the second-order diversity, which is concerned with the transmitter power dependent logarithmic terms that appear in the error rate expression. First, we show that, relay-interference networks suffer a second-order diversity loss compared to interference-free networks. Then, two different quantization schemes are studied: First, using a GQ, we show that the SRS scheme can achieve full-diversity. Then, using the localization method, we construct both fixed-length and variable-length LQs (fLQs and vLQs). Our fLQs achieve maximal first-order diversity, whereas our vLQs achieve maximal diversity. As in the MIMO broadcast system, we show that all the promised diversity and array gains can be obtained with arbitrarily low feedback rates when the transmitter powers are sufficiently large.