Bounds on optimal end-to-end distortion of MIMO links

For transmitting a continuous-amplitude source, quadratic distortion is the primary performance metric. Its lower bound decreases with channel capacity which can be increased by multiple antennas. In this paper, assuming the transmitter perfectly knows the instantaneous channel rate by feedback from the receiver and a white thermal noise source is transmitted over a quasi-static Rayleigh fading AWGN channel, we give the compact analytic expression of the tight lower bound on the optimal end-to-end mean quadratic distortion at any SNR, in terms of antenna numbers, the ratio of source-bandwidth to channel-bandwidth (SCBR), the ratio of signal power to noise power (SNR) and the source power. We analyze the expression of the lower bound to obtain the SNR exponent and the SNR coefficient at the asymptotically high SNR. Results indicate that the optimal distortion does necessarily decrease with both antenna numbers for any SCBR, the commutation between the transmit antenna number and the receive antenna number can affect the optimal distortion, and the frequency-selectivity can benefit the optimal distortion.