Performance Analysis and Power Allocation for Two-Way Amplify-and-Forward Relaying With Generalized Differential Modulation

Differential modulation has been proposed to mitigate the difficulties involved in estimating the channel state information (CSI) in a two-way relay network (TWRN). However, it suffers at least 3-dB performance loss compared with the coherent detection. This work proposes a new differential modulation and detection scheme to close the performance gap for TWRN using amplify-and-forward (AF) protocol. At two source nodes T₁ and T₂, a block-by-block differential encoder is employed, where each block consists of one reference symbol (RS) and several normal symbols (NSs). After two-way AF (TWAF) relaying, the information bits can be recovered without any knowledge of CSI. The bit-error-rate (BER) performance of the proposed scheme is analyzed, and closed-form expressions for the lower bound of BER and its high signal-to-noise ratio (SNR) approximation are derived. To minimize the lower bound of BER, we also investigate power allocation among the RS and the NSs in each block. Simulation results show that the performance gap between the proposed differential transmission scheme with a block length of 256 and the coherent receiver with perfect CSI is within 0.5 dB in quasi-static fading channels.