Trellis coded hybrid 2FSK/4PSK with expurgated phase code

The performance of trellis coded hybrid frequency and phase shift modulation (TC HFPSK) with the expurgated phase code and the asymmetric signal constellation is investigated by using the minimum squared free Euclidean distance d_free² and the bit error rate (BER). It is found that TC hybrid 2FSK/4PSK with the expurgated phase code shows larger d_free² than the corresponding TC hybrid 2FSK/4PSK with the complete phase code for varying the angle φ that determines the asymmetric signal constellation. The maximum value of d_free² of TC hybrid 2FSK/4PSK with the expurgated phase code can be obtained when the signal constellation is symmetric. The performance of BER is analyzed in additive white Gaussian noise (AWGN) and fading channels by using uniform error property and error bound based on transfer function. It is found that the coding gain of TC hybrid 2FSK/4PSK with the expurgated phase code over uncoded hybrid 2FSK/2PSK at BER = 10^-4 are 2.71 dB and 4.74 dB in AWGN and fading channels, respectively. The performance improvements of TC hybrid 2FSK/4PSK with the expurgated phase code over TC 8PSK at BER = 10^-4 are 0.68 dB and 4.07 dB in AWGN and fading channels, respectively.