Improving Angle Estimation via Feedback for Hybrid mmWave Systems Using Beamforming Virtual Arrays

It is known that when there is some rough knowledge on the angles of arrivals (AoAs) and angles of departures (AoDs), beamforming can increase the received SNR for finer angle estimation. Beamforming aided angle estimation generally requires two stages or more. Estimation performance depends on the allocation of training time and feedback bits between the two stages. In this paper, we consider the allocation of training time and feedback bits of a two-stage angle estimation scheme for a hybrid mmWave system that has limited feedback rate. Banded Toeplitz matrices are used for precoding and combining to obtain beamforming virtual uniform linear arrays (BV-ULA). Using properly designed banded Toeplitz precoders and combiners, the equivalent path gains are boosted by beamforming gain while the overall system is equivalent to one equipped virtual ULAs but without precoding and combining. Virtual ULAs allow us to conduct angle estimation as if there are no precoder and combiner; most existing angle estimation methods can be applied. Due to finite feedback rate, the AoDs are quantized before they are fed back to the transmitter. The AoD estimates available to the transmitter contain both quantization and angle estimation errors. We derive the overall error, which depends on how the training time and feedback bits are allocated to the two stages. For the useful case of high feedback rate, we show that the training vectors should be equally allocated to the two stages. Simulations show that the proposed BV-ULA approach can considerably improve the SNR at the second stage and achieve high resolution.