The exact average complexity analysis of the basic sphere decoder for generalspace-time codes applied to multiple-input multiple-output (MIMO) wirelesschannel is known to be difficult. In this work, we shed the light on thecomputational complexity of sphere decoding for the quasi-static, LAtticeSpace-Time (LAST) coded MIMO channel. Specifically, we drive an upper bound ofthe tail distribution of the decoder's computational complexity. We show that,when the computational complexity exceeds a certain limit, this upper boundbecomes dominated by the outage probability achieved by LAST coding and spheredecoding schemes. We then calculate the minimum average computationalcomplexity that is required by the decoder to achieve near optimal performancein terms of the system parameters. Our results indicate that there exists acut-off rate (multiplexing gain) for which the average complexity remainsbounded.
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