In this paper. for $pi$/4 and $pi$/8 PSK. we proposed to condition to obtain coding gain increasing states, by design encoder of analytical method with minimal complexity in limited bandwidth and power channels. In order to improve the bit error rate(BER), comparing Ungerboeck designed the TCM. we propose MTCM(Multiple trellis-coded modulation) with multiplicity(k＝2), by optimum encoder design. By design encoder of analytical method. the trellis encoder can be minimal complexity and the decoder be used Viterbi decoder(MLSE). When compared to the TCM and MTCM with AWGN channels. the condition of performance enhancement of the MTCM with multiplicity(k＝2) is the case of parallel transition in TCM systems. without alternating data transmission rate in bandwidth and power limited channels.