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Performance evaluation of multi-level four-dimensional Q/sup 2/PSK in Gaussian noise

This paper considers the expansion of a well known four-dimensional quadrature-quadrature phase-shift keying (Q/sup 2/PSK) signalling scheme by introducing multiple amplitudes and/or phases per dimension to increase the effective data throughput rate and spectral efficiency of the former system. The performance of the new multi-level Q/sup 2/PSK modulation schemes, denoted by quadrature-quadrature amplitude-phase-shift keying (Q/sup 2/APSK), is compared to the original Q/sup 2/PSK modulation scheme, as well as to conventional two-dimensional QPSK and QAM modulation strategies under realistic bandlimiting conditions in the presence of additive white Gaussian noise. The performance comparisons are made in terms of spectral efficiency (or data throughput rate) versus symbol error probabilities. The results presented exhibit an expected signal to noise penalty for Q/sup 2/APSK compared to modulation schemes with two levels per dimension, such as QPSK and Q/sup 2/PSK, but with a considerable increase in spectral efficiency.