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 Qmax 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 Qmax 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 Qmax 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.