Algebraic space-time codes for block fading channels

The availability of multiple transmit antennas allows for two dimensional channel codes that exploit the spatial transmit diversity. These codes were referred to as space-time codes by Tarokh et al. (see IEEE Trans. Inform. Theory, vol.44, no.2, p.744-65, March 1998). Thus far the main thrust has been to construct space-time codes that achieve maximum spatial diversity in quasi-static fading channels. In this paper, we extend the theory developed by Hammons et al. (see IEEE Trans. Inform. Theory, vol.46, no.2, p.524-42, March 2000) to block fading channels. We present base-band design criteria for space-time codes in block fading channels that encompass as special cases the quasi-static and fast fading design rules. Following the approach of Hammons et al., the diversity advantage base-band criterion is then translated into binary rank criteria for PSK modulated codes. Based on these criteria, we construct space-time codes that strive to optimally exploit the spatial and temporal diversity available in block fading channels. We also introduce the notion of universal space-time codes as a generalisation of the smart-greedy design approach proposed by Tarokh et.al