A coded beamforming scheme for frequency-flat MIMO fading channels

In this paper, a coded beamforming scheme is considered for frequency-flat multiple-input-multiple-output (MIMO) fading channels. With channel state information (CSI) available at the transmitter, this scheme combines coded modulation (CM) with downlink transmission beamforming to exploit both diversity and coding advantages. In order to identify the appropriate code design criteria, the exact pairwise error probability and bit error rate upper bounds are derived for both frequency-flat slow and fast MIMO Rayleigh fading channels. It is shown that the minimum squared Euclidean distance of the code should be maximised in slow- fading channels, whereas the minimum effective code length and the product distances should be maximised in fast-fading scenarios. This conclusion indicates that the conventional Ungerboeck´s trellis-coded modulation codes originally designed for additive white Gaussian noise channels and single-antenna Rayleigh fading channels could be directly utilised in the proposed scheme for slow and fast MIMO fading channels, respectively. This eliminates the need for complicated code design. Simulation results are provided to substantiate the theoretical analysis. For an example, it is demonstrated that a trellis-coded beamforming scheme can outperform the published space-time trellis coded beamforming schemes by up to 4 dB, although it has a simpler encoder structure and requires no specific code design. Interference free is assumed in the analysis, while the impact of the imperfect CSI and antenna correlation on the system error performance is evaluated.