Trellis coded hybrid frequency and phase modulation with expurgated phase code and asymmetric signal constellation

The performance of trellis coded hybrid frequency and phase shift modulation (TC HFPSK) with expurgated phase code and asymmetric signal constellation is investigated by using minimum squared free Euclidean distance d_free² and bit error rate (BER). It is found that TC HFPSK with expurgated phase code shows a larger d_free ² than the corresponding TC HFPSK with the complete phase code for varying the angle φ that determines the asymmetric signal constellation. The maximum value of d_free² of TC HFPSK with expurgated phase code is obtained when the signal constellation is symmetric. The BER performance is analyzed in additive white Gaussian noise (AWGN) and fading channels by using uniform error property (UEP) and error bounds based on the transfer function. It is found that the performance improvements of TC HFPSK are 2.1 dB and 5.0 dB in AWGN and fading channels respectively, at BER=10^-4, compared to uncoded HFPSK