On the ergodic capacity of cooperative spatial multiplexing systems in composite channels

The ergodic capacity of cooperative spatial multiplexing systems over composite channels is presented. Specifically, we derive the exact closed-form expressions for ergodic capacity of cooperative spatial multiplexing systems with linear receiver in the composite channel of log-normal shadowing and Rayleigh fading. Using the Gauss-Hermite quadrature integration, the final analytical result of ergodic capacity is described in a closed-form expression. We also perform Monte-Carlo simulations to validate our analysis. Subsequently, we apply the obtained analytical expression to evaluate some representative scenarios regarding to spatial multiplexing gain in relay composite channels.