Closed-form bounds on the ergodic capacity and symbol error probability of the opportunistic incremental relaying protocol

In this paper, we analyze the ergodic capacity (per unit bandwidth) and Average symbol error probability (ASEP) of an incremental relaying protocol used in conjunction with opportunistic relaying and consider a non-regenerative wireless relay network with Rayleigh fading channels. We consider a selection combining technique at the destination in order to combine the two signals, one from the direct path and the other from the best relay path. For a tractable analysis we upper bound the end-to-end signal-to-noise ratio (SNR) and then derive a new closed-form expression of its probability density function (PDF). Utilizing this statistical result we then derive new closed-form lower bounds of ASEP and upper bounds of ergodic capacity over independent and non-identical Rayleigh fading channels. It is shown that the opportunistic incremental relaying (OIR) protocol can considerably improve the ASEP and at the same time (depending upon the channel conditions) also slightly increase (or decrease) the ergodic capacity of the network. The improvement in the performance metrics comes only at the expense of an increase in the network's complexity. Furthermore, it is shown that our derived closed-form bounds are tight in a sense that they match with the exact curves obtained through Monte Carlo simulations and numerical integration techniques.