Multiple-Symbol Differential Sphere Detection for the Amplify-and-Forward Cooperative Uplink

It is widely recognized that the differential amplify-and-forward (DAF) transmission scheme is capable of providing a superior performance compared to classic direct transmissions employing differential detection in slow-fading channels and in fact it may even outperform coherent detection aided systems relying on realistic imperfect channel estimates. However, in reality the channels connecting the multiple nodes of a cooperative system typically become time-selective due to the relative mobility of the cooperating terminals. Hence, the performance gain achieved may erode as the environment becomes more time-selective. On the other hand, multiple-symbol based differential sphere detection (MSDSD) has been proposed to mitigate the channel-induced performance loss suffered by classic direct transmission schemes employing the conventional differential detection (CDD) scheme. Hence in this paper, we specifically design the MSDSD based on a multidimensional tree search, which is capable of achieving a significant performance gain in the context of a DAF-aided cooperative system for transmission over time-selective channels. For example, given a target BER of 10 3, a performance gain of about 10 dB can be attained by the proposed MSDSD for a two-user cooperative system in a channel having a normalized Doppler frequency of 0.03.