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 E_b/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 E_b/N₀ and simulate performance with and without differential coding. The required E_b/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).