Average symbol error rate of cooperative spatial multiplexing in composite channels

Performance of cooperative spatial multiplexing systems over composite channels is presented. In particular, we derive the closed-form average symbol error rate (SER) expression for cooperative spatial multiplexing systems with linear equalization receiver (e.g. Zero-Forcing) and M-ary modulation scheme in the composite channel of log-normal shadowing and Rayleigh fading. Using the Gauss-Hermite quadrature integration, the average SER is expressed in the form of the Appell hypergeometric function. Applying the series representation of the Appell hypergeometric function, we derive a very tight approximation for the average SER. We also perform Monte-Carlo simulations to validate our analysis. Subsequently, we apply the obtained analytical SER expression to evaluate some representative cooperative spatial multiplexing scenarios in composite channels.