The effect of wireless channel on network coding opportunities

The impact of wireless network coding on multiuser diversity gain is investigated. A generic framework to calculate the CDF of the opportunistic channel gain, for different communication scenarios with a single relay, when scheduling or network coding are used, is presented. The CDF and PDF of the lognormal and Rayleigh opportunistic channels for these scenarios are calculated and the average system capacity is derived. Numerical results show that while wireless network coding most of the time can provide significant throughput gain, for low mean received SNR and high channel variations it may result to lower ergodic capacity than simple opportunistic scheduling, especially when transmission overhearing is required. For these cases, we show that although a coding gain is achieved, there may be a larger reduction on the multiuser diversity gain which results to overall lower average system capacity compare to traditional opportunistic scheduling.