Space-Time Coding with Feedback

Space-time coding for a multiple-input, multiple-output (MIMO) system with feedback and maximum-likelihood (ML)-decoding is considered. In the case that complete feedback from the receiver to the transmitter is available, the optimal structure of the codes is shown to have the form cu^dagger, where c is a T-dimensional complex vector (T is a time delay), and u is a unit-norm eigenvector corresponding to the largest eigenvalue of matrix HH^dagger (H is the channel matrix and ^dagger means the transpose and conjugate). Moreover, criterion for designing vector c is obtained. In the case that only finite-bit feedback is available, the optimal structure of the codes is proved to have the form cp^dagger, where c is also a T-dimensional complex vector and p is a M-dimensional vector with unit-norm (M is the transmit number of the system). Furthermore, criteria for designing vectors c and p are given. A Lloyd-like algorithm to approach p is introduced