Limited Feedback for Temporally-Correlated Channels: Feedback Rate and Delay

Limited feedback systems send quantized channel state information (CSI) from the receiver to the transmitter for improving either the throughput or the link reliability. This paper proposes a framework for analyzing multiantenna limited feedback systems with temporally-correlated flat-fading channels. Developed on a Markov chain modeling quantized CSI, the proposed framework consists of analytical results concerning the feedback rate, the feedback compression, the capacity with feedback delay, and the decay rate of the capacity gain due to feedback delay. These results constitute a set of useful tools for designing a wide-range of limited feedback system. The application of the proposed framework is illustrated for a multiple-input-single-output (MISO) beamforming system, where the feedback consists of the quantized channel gain and direction. Feedback rates are shown to increase linearly with the Doppler frequency in a Rayleigh fading channel with Clarke’s spectrum. Furthermore, capacity gains are found to decrease exponentially with feedback delay. From theses results, useful design guidelines can be derived for choosing system parameters ranging from the reception vehicular speed to the feedback channel rate.