A method for searching minimum Euclidean distances of respective substreams for different modulation orders of M-ary quadrature amplitude modulation signals in multiple-input and multiple-output systems is described. A channel matrix is cyclically-sorted sequentially and QR-decomposed. Using upper triangular matrices obtained by QR decomposition, minimum Euclidean distances are searched over trellis diagrams consisting of symbol-difference lattice points by computationally efficient multiple trellis-search algorithms. The simulation results demonstrate that per-substream minimum Euclidean distances can be detected with a high correct-estimation probability by path-re-searching controls over different modulation orders.

Multi-ary Trellis-Coded Modulation (TCM) schemes have been studied for use with digital radio communication systems. Among these TCM schemes, we have already reported the optimum signal constellation of a rate-3/4 trellis-coded (TC) 16-ary Amplitude and Phase Shift Keying (APSK) scheme and computed the minimum Euclidean distance: dfree. In this paper, we evaluate other performance parameters: Nfree and bit error rate (BER) over an additive white Gaussian noise channel, and further investigate the various signal constellations of rate-4/5 TC 32-APSK schemes. It is found that the BER performances of circular-type signal constellations are superior to that of rectangular-type in the TC 16-APSK, and a (24,8) circular type signal constellation is superior to other constellations in the TC 32-APSK.

This paper proposes a new signaling technique which employs multilevel block codes in conjunction with phase/frequency modulation. The proposed scheme exhibits an increased minimum squared Euclidean distances (MSEDs) and outperforms other conventional schemes in terms of asymptotic coding gain and decoding complexity. The proposed scheme is also considered for non-constant amplitudes, which turned out to show even better performances at small modulation indices in some cases. Examples are given to demonstrate how to optimize the signal set for a given block code to maximize the coding gain.