Union Bound for Linear Space-Time Codes


Robert W. Heath Jr, Sumeet Sandhu, and Arogyaswami J. Paulraj


Proc. of Allerton Conf. on Comm. Control and Comp., Sept. 30 - Oct. 2, 2000.


Design of practical coding and modulation techniques for the multiple antenna fading wireless channel is a challenging problem. A number of interesting solutions have been proposed recently ranging from block codes to trellis codes for the MIMO (multiple input, multiple output) fading channel. We address the general problem of linear code design
for the quasi-static, flat-fading, coherent MIMO channel. A linear code refers to an encoder that is linear with respect to scalar input symbols. The decoder performs ML (maximum likelihood) decoding of the received matrix symbols and is not assumed to be linear.

We provide a cohesive framework for analysis of linear codes in terms of a union bound on the conditional probability of symbol error. The error bound is conditioned on the channel realization and does not make any assumptions on channel statistics. Our analysis incorporates all existing linear spatial modulation techniques such as
spatial multiplexing, space-time block codes, and truncated delay diversity. We show that space-time block codes achieve the lowest error bound among all orthogonal codes and are in fact optimal.


MIMO systems, space-time block codes, space-time trellis codes

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