An adaptive differential codebook using M-PSK constellations for slowly varying channels

We propose an adaptive scheme of a differential codebook for temporally correlated channels. The codeword entries of the proposed codebook are selected among the set of M-PSK constellations and the values of M proposed in this paper are 8, 16, or 32. Firstly, we analyze mathematically how the optimal spherical cap radius of the proposed codebook is tracked. Then, we explain how to implement the proposed differential equal-gain codebook practically. Among the candidate differential codebooks designed for various temporal correlation coefficients, the proper codebook can be chosen (or switched) according to the temporal correlation coefficients of wireless channels. We assume that the correlation coefficients of the channels are known to the receiver and the properly (or optimally) chosen differential codebook can show the best system throughput performance. Monte-Carlo simulations demonstrate that the achievable throughput performance employing the proposed codebook is always superior to those of the differential codebooks employing M-PSK constellations and non-adaptive differential codebooks with the same amount of feedback information.