2L-symbol 8-dimensional constellations

By utilizing four consecutive symbol periods at a time, eight-dimensional constellations can be generated. Here, such 2^L -symbol constellations (8D-L) are proposed, where L is any integer ⩾8. Actually, two constellations are given for L=8: one which requires an optimum detector, 8D-8B, and the other, 8D-8A, which can be detected by the general detector provided for 8D-L. It is demonstrated that 8D-8B provides 0.37-dB improvement as far as signal-to-noise ratio is concerned over 8D-8A which, in turn, provides 1.78 dB improvement over the corresponding QPSK (quadrature-phase-shift-keying) system. Furthermore, 8D-12 is better than 8-QAM (quadrature amplitude modulation)/by 3.17 dB, whereas 8D-16 achieves 2.55 dB improvement over 16-QAM