Physical layer reliability vs ARQ in MIMO block-fading channels

In today´s wireless communication systems, automatic repeat request (ARQ) is implemented at the MAC layer in order to retransmit packets that have been erroneously transmitted at the physical (PHY) layer. Following a joint PHY-MAC design, information provided by the ARQ scheme can be exploited at the PHY layer in order to improve the system´s performance. This paper extends the work presented in the context of SISO channels to the context of MIMO block-fading channels. Based on statistical channel knowledge at the transmitter, it provides an analysis of the natural tradeoff that exists between the PHY layer transmission rate and the number of ARQ retransmissions. We derive a very accurate analytical formulation of the optimum transmission rate (and, equivalently, the optimum PHY packet error-rate) that maximizes the goodput, as a function of the system parameters, namely the SNR, the number of antennas and the diversity order of the channel. Interestingly, we find that the PHY layer has to be made more reliable for MIMO channels than for SISO channels, and also that the MIMO ARQ system is less sensitive to a wrong choice of the rate of transmission than the SISO ARQ system.