The Throughput-Reliability Tradeoff in MIMO Channels

In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse’s elegant formulation of the diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between the probability of error, transmission rate, and signal-to-noise ratio. In particular, we identify the limitation imposed by the multiplexing gain notion and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of MIMO channels. 1 Problem Formulation This paper revolves around the following question: What does a 3 dB increase in the signal-to-noise ratio (SNR) buy in an outage limited Multi-Input Multi-Output (MIMO) channel? In an Additive White Gaussian Noise (AWGN) setting, it is well known that a 3 dB increase in SNR translates into an extra bit in channel capacity in the high SNR regime. The scenario considered in this paper, however, is more involved. We study an outage limited channel where the randomness of the instantaneous mutual information results in a non-zero lower bound on the probability of error, for non-zero constant transmission rates. Hence, a fundamental tradeoff between the throughput, as quantified by the transmission rate, and reliability, as quantified by the so-called outage probability, arises. Our work explores this tradeoff in the high SNR regime. To be more specific, we consider a MIMO wireless communication system with m transmit and n receive antennas. We adopt a quasi-static flat-fading setup where the path gains remain constant over l consecutive symbol-intervals (i.e., a block), but change independently from one block to another. We further assume a coherent communication model implying the availability of channel state information (CSI) only at the receiver. Under these assumptions, the channel input-output relation is given by: