Diversity analysis of bit-interleaved coded multiple beamforming

In this paper, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the case of general spatial interleavers, removing a condition on their previously known design criteria and quantifying the resulting diversity order. The diversity order is determined by a parameter Q_max which is inherited from the convolutional code and the spatial de-multiplexer used in BICMB. We introduce a method to find this parameter by employing a transfer function approach as in finding the weight spectrum of a convolutional code. By using this method, several Q_max values are shown and verified to be identical with the results from a computer search. The diversity analysis and the method to find the parameter are supported by simulation results. By using the singleton bound, we also show that Q_max is lower bounded by the product of the number of streams and the code rate of an encoder. The design rule of the spatial de-multiplexer for a given convolutional code is proposed to meet the condition on the maximum achievable diversity order.