Recently proposed coded bi-directional relaying protocols increase the spectral efficiency by using network codes, which rely on joint packet encoding and exploitation of previously transmitted and stored information. In this letter, we derive the cumulative density function (CDF) and the probability density function (PDF) of received signal-to-noise ratios (SNRs) for two-phase and three-phase bi-directional coded relaying protocols, respectively, over Rayleigh fading channels. Using these results, we compare the outage performances as well as the average capacities of the protocols. From the numerical observations, we can see that the two-phase protocol has better link-level performances than the three-phase protocol when required data rate is greater than 2 for outate performance and transmit SNR at each node is greater than 18 dB for average capacity, respectively. Otherwise, the three-phase protocol performs better.

Combining relaying and multi-input multi-output (MIMO) transmission is a generic way to overcome the channel-fading impairments. Best antenna selection is a simple but efficient MIMO method that achieves the full diversity and also serves as a lower bound reference of MIMO performance. For a dual-hop MIMO system with an ideal amplify-and-forward (AF) relaying gain and best antenna selection, we provide a probability density function (PDF) of received signal-to-noise ratio (SNR) and an analytic BER equation when using M-ary PSK in Rayleigh fading channels. The analytic result is shown to exactly match with simulated one. Furthermore, the effect of link unbalance between the first hop and the second hop, due to differences in the number of antennas deployed in both hops as well as in the average power of channel coefficients, on the BER performance is numerically investigated and the results show that the links with better balance give better performance.

In this letter, we first provide the closed-form exact outage probability of opportunistic single relay selection in decode-and-forward (DF) relaying with the direct source-destination link under arbitrarily distributed Rayleigh fading channels. The signals from the source and the selected relay are combined at the destination by using maximal ratio combining (MRC). We derive the probability density function (PDF) and the cumulative density function (CDF) of received SNR at the destination. Numerical results show that the analytic results exactly match with the simulated ones.