On Feedback Resource Allocation in Multiple-Input-Single-Output Systems Using Partial CSI Feedback

Abstract—This paper studies the problem of feedback resource allocation in multiple-input-single-output (MISO) channels utiliz-ing partial channel state information (CSI) feedback. Considering low/moderate signal-to-noise ratios (SNRs), the optimal quantizers and the feedback bit allocation maximizing the throughput are obtained in the asymptotic case where the number of feedback bits increases. Moreover, the results are utilized to derive the op-timal retransmission rates in the automatic repeat request (ARQ) protocols and joint CSI-ARQ schemes are proposed for the MISO setups. We show that uniform channel amplitude quantization is asymptotically optimal in terms of throughput. Also, the optimal retransmission rates of the incremental redundancy (INR) ARQ protocols follow an arithmetic progression in the exponential do-main. Under certain conditions, a MISO system using quantized CSI can be mapped to a MISO or a SISO (S: single) setup using ARQ or joint CSI-ARQ feedback in the sense that they lead to the same throughput. Finally, to maximize the throughput, the optimal number of channel direction quantization bits should be (M−1) times the number of amplitude quantization bits, where M is the number of transmit antennas. Index Terms—CSI quantization, HARQ feedback, MIMO transmission, throughput, joint phase-amplitude information feedback, incremental redundancy (INR) ARQ. I