Seiichi Noda

Optimum Binary to Symbol Coding for 6PSK and Bit Error Rate Performance

This paper proposes the optimum binary to symbol coding for 6PSK (senary PSK) that minimizes bit errors. 6PSK is expected to be able to transmit data at a higher information rate than QPSK with lower required Eb/N0 compared with 8PSK. In this paper, after discussing general principles of 6PSK, the authors propose the optimum 5 bit to 2 symbol coding for 6PSK (2.5bit/symbol). The authors derive a theoretical formula for bit error rate (BER) versus Eb/N0 and simulate performance with and without differential coding. The required Eb/N0 for 6PSK is 1.4dB less than that for 8PSK at BER of 10-6. Penalty of differential coding is estimated about 0.2dB at BER of 10-6. The authors study BER performance of 6PSK in the presence of transmitter nonlinearity. 6PSK still outperforms 8PSK even for a small value of output back-off (OBO).

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 “O&7PSK” modulation achieves better BER performance than the conventional 8PSK by 1.7 dB in Eb/N0 at BER of 10–6. The paper also proposes a differential coding method to be applied to the O&7PSK. We further evaluate BER performance degradation of the O&7PSK due to transmitter nonlinearity, and find that the O&7PSK still outperforms the 8PSK by about 2 dB in Eb/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 O&7PSK is found to be a better alternative to the 8PSK and is promising for practical use.