Channel State Feedback Over the MIMO-MAC

In order to exploit the full multiplexing gain of multi-antenna multi-user downlink schemes, accurate channel state information at the transmitter (i.e., at the base station) is required. We consider the design of a closed-loop channel state information feedback scheme, where user terminals feed back their channel state information simultaneously to a multi-antenna base station. The underlying information theoretic problem consists of lossy source-channel coding of multiple independent analog sources (i.e., the users' channel coefficients) over a Gaussian multiple-input multiple-output multi-access channel (MIMO-MAC). Unlike the classical source-channel coding setting, this application requires low latency, otherwise the channel state information would be outdated. Hence, source-channel codewords can span only a single fading state of the uplink (feedback) channel. Furthermore, the transmitters are ignorant of the realization of the uplink channel coefficients. In this scenario, the scaling of the maximum of the estimated downlink channel mean-square errors with the SNR dominates the performance of the multiuser downlink. This scaling is described by the distortion SNR exponent, previously introduced in a single-user MIMO setting. This paper analyzes the max-min distortion SNR exponent of the MIMO-MAC for both separated source-channel coding, and a particular hybrid digital-analog joint source-channel coding scheme. For the case of single-antenna users, we prove that the distortion SNR exponent of separated source-channel coding can be achieved by the concatenation of scalar quantization and uncoded quadrature-amplitude modulation (QAM) transmission, with lattice decoding at the base-station receiver. The resulting scheme has very low encoding latency (only a few symbols of the uplink slot) and generally outperforms currently proposed channel state feedback schemes based on analog unquantized transmission or vector quantization with fixed codebooks.