Space-time coding with feedback

Space-time coding for a Multiple-Input, Multiple-Output (MIMO) system with feedback and Maximum-Likehood (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 cut, 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 I 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.