A simple near-capacity concatenation scheme over MISO channels

This paper proposes a capacity-approaching, yet simple scheme over a multiple-input single-output (MISO) wireless fading channel, which is very common in the downlink of a cellular system. The proposed scheme is based on a concatenation of a mixture of short memory-length convolutional codes or repetition codes and a short, and simple rate-1 linear block code, followed by either 1-dimensional (1-D) anti-Gray or Gray mapping of quadrature phase-shift keying (QPSK) modulation. By interpreting rate-1 code together with 1-D mapping as a multi-D mapping performed over multiple transmit antennas, the error performance is analyzed in the turbo pinch-off region using EXIT chart. At first, a simple design criterion on the bit-wise mutual information with perfect a priori information is derived. Based on the obtained design criterion, an optimal rate-1 code for each 1-D mapping is then constructed to maximize the bit-wise mutual information with perfect a priori information. The combination of optimal rate-1 code and 1-D mapping results in a steep inner detector's EXIT curve over an MISO channel, which matches very well to that of a simple outer code. It is demonstrated that the simple concatenation scheme can achieve a near-capacity performance over the MISO channels. In some cases, the selected mixed code is just a simple repetition code.