Multiple-input multiple output (MIMO) communication systems can have dramatically higher throughput than singleinput, single-output systems. Unitary space-time codes for MIMO fading channels have been shown to be optimal under certain conditions when neither the transmitter or receiver has channel state information. Previous work on constructing unitary space-time codes has focused on the diversity product or diversity sum of the unitary space-time code constellation. This paper shows how these min-max design criteria may produce sub-optimal codes in terms of minimizing symbol-error rate (SER). A union bound design metric based on a union bound of pairwise error probabilities is presented, and a bound on its optimal value is derived. Examples suggest this new metric can more accurately distinguish good constellations than the diversity product and diversity sum. The complexity of the union bound design metric is reduced by using recently derived tight bounds, and a desirable -incremental property of the union bound design metric is demonstrated in an example.
We propose a construction technique for unitary space-time codes that use Givens rotation matrices. These constellations have a desirable weak group property that leads to reduced construction and decoding complexity. The newly constructed constellations have the best known diversity product and diversity sum for a wide range of constellation sizes and number of transmit antennas.
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