Full-diversity full-rate space-frequency codes with optimum coding gain for distributed-transmission OFDM systems

Distributed transmission is a way of simultaneously transmitting the same signal from multiple distributed antennas. This paper focuses on the design of full-rate space-frequency (SF) codes for improving the performance of distributed-transmission OFDM systems over asynchronous multipath channels. Analyzing the conditional pairwise error probability, we show the achievable diversity order Z for distributed-transmission OFDM systems is upper bounded by the total number of delay paths between M_T transmit antennas and M_R receive antennas. SF codes based on lattice theory are constructed to achieve the diversity order Z. Then, we propose two full-diversity (maximum diversity) SF code design methods. The first method is a cyclic shift coding approach employing different shift lengths for different transmit antennas, and the second method is a cyclic shift superposition coding approach using same shift lengths for different transmit antennas. In order to reduce the decoding complexity while preserving the diversity order, subcarrier grouping based on interleaved partition is performed to the SF codes designed above, which divides all subcarriers into disjoint subsets to carrier different SF code blocks. Moreover, we show that different interleaving methods result in different coding gain due to the effect of the asynchronous delays. Therefore, the detailed design criteria of subcarrier grouping are provided to achieve optimum coding gain. Simulation results show that the proposed full-diversity SF codes induce about 6 dB performance improvement, and optimum subcarrier grouping can achieve 5-9 dB gain.