4-dimensional PSK trellis coding scheme using M-ary orthogonal modulation with a frequency-reuse technique

The 16 and 32-state trellis-coded M-ary 4-dimensional (4-D) orthogonal modulation schemes with a frequency-reuse technique have been investigated. Here, 5 coded bits from a rate 4/5 convolutional encoder provide 32 possible symbols. Then the signals are mapped by a M-ary 4-D orthogonal modulator, where each signal has equal energy and is PSK modulated. In the M-ary 4-D modulator, we have employed the vectors which are derived by the optimization technique of signal waveforms (OSW) in a 4-D sphere. This technique is used in maximizing the minimum Euclidean distance between a set of signal points on a multidimensional sphere. By combining trellis coding with M-ary 4-D modulation and proper set-partitioning, we have obtained a considerable improvement in the free minimum distance of the system over an AWGN channel. The 16-state scheme obtains coding gains up to 5.5 dB over the uncoded two-independent QPSK scheme and 2.5 dB over the two-independent 2-D TCM scheme. And, the 32-state scheme obtains coding gains up to 6.4 dB over the uncoded two-independent QPSK scheme and 3.4 dB over the two-independent 2-D TCM scheme