Circulant space-time codes for integration with beamforming

This paper provides a framework for designing space-time codes to take advantage of a small number of feedback bits from the receiver. The new codes are based on circulant matrices and simple conditions are derived that guarantee full rate and full diversity. In the absence of feedback, Symbol Error Rate (SER) performance is shown to be similar to that of Diagonal Algebraic Space-Time (DAST) codes, both for Maximum Likelihood (ML) decoding and for suboptimal linear decoding. Decoding complexity of circulant codes is similar to the DAST codes and encoding is slightly less complex. In the presence of a small number of feedback bits from the receiver the circulant construction is shown to permit integration of space-time coding with a fixed set of beams by simply advancing the phase on one of the antennas. This integration is not possible within the DAST framework. Integration of space-time codes with beamforming makes it possible to achieve ML decoding performance with only linear decoding complexity or to improve upon ML performance of the original code.