Error analysis of differentially modulated cooperative systems under generalized fading

This paper analyzes the average bit error rate performance of dual-hop cooperative systems over generalized multipath fading conditions. The considered system is differentially modulated and is assumed to operate based on the amplify-and-forward relaying protocol. Therefore, its main advantage is that it does not require any channel state information neither at the relay nor at the destination nodes. Novel closed-form expressions are derived for the end-to-end statistics for the case of generalized multipath fading conditions that follow the η-μ, distribution, which includes as special cases the well-known Nakagami-m, Rayleigh and Nakagami-g (Hoyt) fading models. Capitalizing on this, a closed-form expression is subsequently derived for the corresponding average bit-error-rate, which is given in terms of known elementary and special functions. The derived analytic expressions are then employed in evaluating the performance and behavior of the considered system and thus quantify the corresponding effects of generalized fading conditions on the achieved bit error rate performance. It is shown that the effect of multipath fading is detrimental at both high and low signal-to-noise ratio regimes as the corresponding deviations are often close to an order of magnitude. This indicates that accurate channel characterization is essential in effective design of cooperative communications as well as that differential modulation can be a suitable modulation scheme for relay systems since it can provide adequate performance at a reduced implementation complexity.