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The new paradigm of cooperative communications is a promising resolution to carry out MIMO technique. In this work, we study the performance of cooperative relay networks in which the transmission from a source to a destination is assisted by one or several relaying nodes employing amplify-and-forward (AF) and decode-and-forward (DF) protocols. The performance of two-way (or bi-directional) AF relay networks, which are proposed to avoid the pre-log factor 1/2 of spectral efficiency, is latter investigated. Specifically, the exact closed-form expressions for symbol error rate (SER), outage probability, and average sum-rate of bi-directional AF relay systems in independent but not identically distributed (i.n.i.d.) Rayleigh fading channels are derived. Our analyses are verified by comparing with the results from Monte-Carlo simulations.