Non-unique differential turbo matrix modulation

We consider differential matrix modulation with forward error control coding and iterative (turbo) detection. Optimized mappings of bits to matrices which allow turbo gains are given for different unitary differential matrix modulation schemes. Particularly, we propose a differential matrix modulation where the number of possible transmit matrices is smaller than the number of possible bit sequences. The ambiguities are resolved in an iterative ("turbo") detector. The proposed scheme enables improved performance compared to existing proposals particularly in the error floor region. Since the number of possible transmit matrices is reduced compared to state of the art schemes, the detection complexity is reduced. Furthermore, the peak to average power ratio is reduced which relaxes the requirements for linearity of amplifiers. The backoff of amplifiers can be reduced which results in lower battery consumption and costs