Symbol error outage for spatial multiplexing systems in Rayleigh fading channel and lognormal shadowing

In this paper, we deal with the analytical performance study of spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems experiencing flat Rayleigh fading and log-normal shadowing. We address the problem of finding a tractable expression for the symbol error outage (SEO) in this environment. In order to obtain the SEO, a symbol error probability (SEP) inversion w.r.t. the signal to noise ratio (SNR) is needed. We propose a new tight approximation for the SEP holding for M-PSK and M-QAM signals which is accurate for all SNRs of interest. These new approximations are invertible w.r.t. the SNR and we derive a new generic expression for the SNR which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.