(4,12) Circular-Signal-Set constellation has been proposed for 16 APSK and its optimum ring ratio has been given by maximizing minimum Euclidean distance between mapped signal points in high channel SNR. But in order to get the best performance in low SNR, the optimum ring ratio should be calculated by using its symbol error rate (SER). Thus, we analyze its symbol error rates theoretically for several detection schemes, which are the ideal coherent detection, the envelope amplitude/coherent phase detection, and the envelope amplitude/differential phase detection.
Multiple-symbol differential detection (MSDD) based on the maximum likelihood (ML) criterion is proposed for APSK and its decision metric is given through the likelihood function, which is derived with no assumption. The SER performance of 16 APSK with this detection scheme shows better than that by using the approximated metric given in the past literature. To reduce the complexity and the computational efforts in the receiver
, the (M, L)-algorithm is applied to tree path search in this detection scheme. As the result, the sequence length of received signals to be estimated can be chosen quite large under a practicable receiver structure, and we confirm that the SER performance shows almost the same as that of the ideal coherent detection with the optimum ring ratio.
Lastly we propose a novel adaptive MSDD scheme that has excellent performance over frequency selective fading (FSF) channels. The adaptive MSDD scheme consists of an adaptive non-coherent least mean square channel estimator that can accomplish channel estimation without any decision delay and the MSDD. Because of the application of the adaptive channel estimator and the M-algorithm, this adaptive MSDD make it possible that channel estimation is accomplished for every symbol along M surviving paths without any decision delay. And the SER performance of this adaptive MSDD is not affected by phase fluctuation introduced by a channel because the MSDD and the non-coherent channel estimator are applied. The adaptive MSDD scheme is applied to typical constellation of 16 APSK, the (4,12) QAM and the star QAM. The excellent tracking performance of this adaptive MSDD scheme over FSF channels is confirmed by computer simulations.