Diversity and multiplexing tradeoff in general MIMO fading channels
The optimal diversity-multiplexing tradeoff (DMT) has provided a comprehensive view for multiple-input multiple-output (MIMO) systems with multiple transmit and receive antennas. It is widely used as a benchmark to evaluate different space-time schemes in high signal-to-noise ration (SNR) regime. However, previous results depend on the assumption of independent and identical distributed (i.i.d) Rayleigh fading while practical channel models may be more complicated. In this thesis, we investigate for a family of MIMO fading channels the optimal DMT, which is characterized by the near zero and near infinity behaviors of its bounded probability density function (pdf). We believe this family is quite general since it includes i.i.d Rayleigh as well as many other known models as special cases. The progress we have made is built upon our analysis of the probability of the outage set. We find the relation between the parameters of a channel model and the probability of the dominant events in the outage set in high SNR regime. Two different methods are used to obtain the asymptotic outage probability for low and high multiplexing gains. Based on the outage result, we show that optimal DMT can be characterized exactly in a simple piece-wise linear function given long enough channel coherent length while we only provide lower and upper bounds for the optimal DMT when the channel coherent length is short. In the extension section, we consider the effect of correlation on optimal DMT given that the transmit correlation and receive correlation are separable. We also discuss the effect of non-zero-mean channel and derive the optimal DMT result for some specific fading types added with a determinant channel mean.