Maximum achievable diversity of coded MIMO-OFDM amplify-and-forward relaying systems

In this paper, we consider multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) amplify-and-forward relay channels. We analyze the maximum achievable diversity of the coded beamforming scheme in MIMO-OFDM relaying systems, and provide proper code designs and the subcarrier pairing criteria that yield the maximum diversity. The pairwise error probability is analyzed based on the assumption of correlated fadings among subcarriers. For systems with N_t source, N_r relay and N_d destination antennas with proper code design, we show that the maximum achievable diversity order is obtained as min(L_hN_tN_r, L_gN_rN_d), where L_h and L_g denote the number of channel taps of the first hop and the second hop channel, respectively.