4-dimensional modulation for a bandlimited channel using Q/sup 2/PSK

We introduce M-ary orthogonal modulation for a bandlimited channel with non-linearity. A set of 16 vectors which have the minimum distance is symmetrically constructed on the surface of a 4-dimensional (4-D) sphere. For the modulation, we have used 4-D orthogonal basis signals whose power efficiency is maximized within a fixed bandwidth. We compare the performance of 4-D constant amplitude signals in terms of transmission parameters on the additive white Gaussian noise (AWGN) channel. After mapping the derived 4-D vectors into the modulation without coding, we have obtained 2.7 dB gain over QPSK and 0.9 dB over Q/sup 2/PSK in signal-to-noise ratio (SNR) while maintaining the minimum bandwidth.