Explicit Space-Time Codes Achieving the Diversity-Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesn t +n r -1 where T is the number of time slots over which coding takes place and n t ,n r are the number of transmit and receive antennas, respectively. For Tn t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all Tgesn t is the same as that previously known to hold for Tgesn t +n r -1