Low-rate multi-dimensional space-time codes for both slow and rapid fading channels

We consider the design of channel codes for improving the data rate and/or the reliability of communications using multiple transmit antennas over a fading channel. It is assumed that the transmitter does not know the channel but seeks to choose a codebook that guarantees a diversity gain of r₁ when there is no mobility and a diversity gain of r₂⩾r₁ when the channel is fast fading. A solution to this problem is unveiled in this paper. Here, the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The signal received at each receive antenna is a superposition of the faded versions of the n transmitted signals. We derive performance criteria for designing codes having the aforementioned properties. Performance is shown to be determined by diversity advantage quantified by a rank/distance and coding advantage quantified by a determinant/product criterion. The criteria is used to design codes for both slow and rapid fading channels. The constructed codes have remarkable performance in low signal to noise ratios and are suitable for improving the frequency reuse factor under a variety of mobility conditions