On Source Transmission Over MIMO Channels With Limited Feedback

The problem of source-channel coding over a multiple-antenna (MIMO) channel with quantized channel state information at the transmitter (CSIT) is considered. Upper bounds on the distortion exponents achieved with partial CSIT under a long-term power constraint are developed. It is shown that the distortion exponent with perfect CSIT grows unbounded as the ratio between the channel and source bandwidth increases, while the exponent achieved with any feedback link of fixed, finite resolution is bounded above by a polynomial of the product between the number of transmit and number of receive antennas. The resolution of the feedback link should grow with the bandwidth ratio to make the distortion exponent scale as fast as that in the perfect-CSIT case. We show that in order to achieve the optimal scaling the CSIT feedback resolution must grow logarithmically with the bandwidth ratio for MIMO channels, and faster than linear for the single-input single-output channel. The achievable distortion exponent of some hybrid schemes with heavily quantized feedback is also derived. The results demonstrate that dramatic performance improvement over the case of no CSIT can be achieved by combining simple schemes with a very coarse CSIT feedback.