Cooperative spatial multiplexing (CSM) systems can achieve high spatial multiplexing gain in wireless relay networks since each single-antenna relay forwards simultaneously a different subset of source messages to the destination. In this paper, the performance of CSM with amplify-and-forward (AF) relays are presented. Specifically, we derive exact closed-form expressions for symbol error probability (SEP) and achievable spectral efficiency of CSM with linear receiver in dissimilar Rayleigh fading channels. Assessing the SEP performance in the high signal-to-noise regime, we further show that CSM with AF relays obtains the first order of diversity gain. Furthermore, it has been observed that CSM outperforms two well-known cooperative diversity systems, e.g., selection combining and maximal ratio combining, in term of spectral efficiency. We also perform Monte-Carlo simulations to validate our analysis.