Diversity of Coded Beamforming in MIMO-OFDM AF Relaying Systems with Direct Link

This paper investigates the diversity order of beamforming schemes in frequency-selective multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying channels with a nonnegligible direct link between the source and the destination. In this system, orthogonal frequency-division multiplexing and bit-interleaved coded modulation schemes are adopted to exploit multipath diversity. Due to a nonconvex property of the problem, the optimal performance of flat-fading MIMO relaying channels, which is imperative to derive the diversity order, is still unknown. To this end, we first identify upper and lower bounds of the signal-to-noise ratio (SNR) of the flat-fading channels, which lead to upper and lower bounds of diversity order of coded beamforming in frequency-selective channels. Then, we establish the diversity order as a closed form by showing that these bounds are tight. In addition, our analysis provides an insightful guideline for code constructions to achieve a proper diversity gain of the system. The accuracy of our analysis is validated through simulation results.