On Space-Time Coding with Finite-Bit Feedback

Space time coding for a multiple input, multiple output (MIMO) system with finite-bit feedback and maximum-likehood (ML)-decoding is considered. Based on the analysis of union bound of error probability of the system, it is shown that designing the system with good performance can be divided into the following three steps: (1) efficiently packing finite points into a dynamic ellipsoid in a finite dimensional real Euclidean space; (2) effectively quantizing a Stiefel manifold; (3) optimally quantizing a cone in a real Euclidean space. Furthermore, criteria and methods to implement the above steps are given. A design example for a system, which has 2 transmit and 2 receive antennas, 2 time slot delay and 4 bits transmission rate, shows that 5 bits feedback can derive 1.8 dB gain over the system without feedback.