O&7PSK modulation and its bit error rate performance

This paper studies a phase shift keying (PSK) modulation scheme that employs an eight symbol alphabet consisting of the origin and seven equally spaced phases along a circle on the complex-number plane, carrying three bits per symbol. This constellation was first presented more than thirty years ago, but has not been fully investigated for implementation since then. We present the optimum bit mapping and derive a formula for calculating bit error rate (BER), to find that this "0&7PSK" modulation achieves better BER performance than the conventional 8PSK by 1.7 dB in E_b/N₀ at BER of 10 6. The paper also proposes a differential coding method to be applied to the 0&7PSK. We further evaluate BER performance degradation of the 0&7PSK due to transmitter nonlinearity, and find that the 0&7PSK still outperforms the 8PSK by about 2 dB in E_b/N₀ at the optimum output back-off (OBO) even for a small roll-off factor. We also examine increase in the out-of-band emission of the power spectrum at the transmitter output in the presence of the nonlinear distortion. Through our study, the 0&7PSK is found to be a better alternative to the 8PSK and is promising for practical use.