In this letter, a relay-assisted transmission scenario over frequency-selective fading channels perturbed by different random carrier frequency offsets is considered. OFDM and block-double differential (BDD) design are implemented to overcome the problem of intersymbol interference (ISI) and carrier frequency offsets (CFOs). We analyze the symbol error rate (SER) performance of decode-and-forward relaying with BDD design in wireless cooperative communications over frequency-selective fading channels and derive a theoretical upper bound for average SER when the relay (R) is error free. It can be seen from our analysis that the system performance is influenced by the ability of R to decode, and when R decodes without error, both spatial and multipath diversity can be obtained without requiring any knowledge of channel state information and CFO information at the receivers. Numerical examples are provided to corroborate our theoretical analysis.

A new high-rate space-time block code (STBC) with full transmit diversity gain for four transmit antennas based on a generalized Alamouti code structure is proposed. The proposed code has lower Maximum Likelihood (ML) decoding complexity than the Double ABBA scheme does. Constellation rotation is used to maximize the diversity product. With the optimal rotated constellations, the proposed code significantly outperforms some known high-rate STBCs in the literature with similar complexity and the same spectral efficiency.