Distributed Beamforming in Wireless Relay Networks with Quantized Feedback

摘要

This paper is on quantized beamforming in wireless amplify-and- forward relay networks. We use the Generalized Lloyd Algorithm (GLA) to design the quantizer of feedback information and specifically to optimize the bit error rate (BER) of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedbask scheme based on relay selection can achieve full-diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by the approximations and modified forwarding schemes. Then, for high-rate feedback, we find an upper bound on the average signal-to-noise ratio (SNR) loss and show that it decays at least exponentially with the number of feedback bits, B. Using this result, we also demonstrate that the capacity loss also decays exponentially with B. We also derive approximate upper and lower bounds on the BER, which can be calculated numerically. With R relays, our designs achieve full-diversity when B is greater than or equal to log(R). Moreover, simulations show that our BER approximations are reliable estimations of the simulation results, even for moderate values of B. This paper is on quantized beamforming in wireless amplify-and-forward relay networks. We use the Generalized Lloyd Algorithm (GLA) to design the quantizer of feedback information and specifically to optimize the bit error rate (BER) of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedbask scheme based on relay selection can achieve full-diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by the approximations and modified forwarding schemes. Then, for high-rate feedback, we find an upper bound on the average signal-to-noise ratio (SNR) loss and show that it decays at least exponentially with the number of feedback bits, B. Using this result, we also demonstrate that the ca.