On the Decoding Complexity of D-TR-STBC for Single Carrier Relay-Assisted Transmissions

In this paper, we present a low complexity maximum likelihood (ML) detection based on the sphere decoder (SD) for distributed time-reversal space-time block code (D-TR-STBC) with frequency selective fading links. Unlike direct transmission, the relay-assisted transmission results in higher number of taps for the resultant end-end channel. The complexity of Viterbi algorithm (VA) grows exponentially with the channel memory and the signal modulation order. Hence makes it prohibitive for the above scenario. On the other hand, the complexity of SD is a low-degree polynomial in the block length and does not vary significantly with the channel memory and the modulation order over the signal to noise ratio (SNR) range of interest. This offers a significant computational reduction over VA specifically for relay networks that provide higher diversity. To corroborate our claims, we have shown the simulation results comparing the average complexities of SD and VA for various system settings. A further reduction in the average complexity of SD is achieved for D-TR-STBC with multiple relays and with relay selection.