Differential coding for non-orthogonal space-time block codes with non-unitary constellations over arbitrarily correlated rayleigh channels

In this paper, we propose a maximum likelihood (ML) decoder for differentially encoded full-rank square nonorthogonal space-time block codes (STBCs) using unitary or non-unitary signal constellations, which is also applicable to full-ranked orthogonal STBC (OSTBC). As the receiver is jointly optimized with respect to the channel and the unknown data, it does not require any knowledge of channel power, signal power, or noise power to decode the signal, and the decision is purely based on two consecutively received data blocks. We analyze the effect of channel correlation on the performance of the proposed system in Rayleigh fading channels. Assuming a general correlation model, an upper bound of the pair-wise error probability (PEP) of the differential OSTBCs is derived. An approximate bound of the PEP for the differential nonorthogonal STBCs is also derived. We propose a precoder designing criterion for differential STBC over arbitrarily correlated Rayleigh channels. Precoding improves the system performance over the correlated Rayleigh MIMO channels. Our precoded differential codes differ from the previously proposed precoder designs for differential OSTBC in the following ways: 1) We propose a precoder design for arbitrarily correlated Rayleigh channels, whereas the previous work considers only for transmit correlation. 2) The previous work is only applicable to the OSTBCs with PSK constellations, whereas our precoder is applicable to any type of full-rank square STBCs with unitary and non-unitary signal constellations.