Abstract: In order to improve the spectrum efficiency of random-polar modulated Extended Binary Phase Shift Keying with Continuous Phase (CP-EBPSK), a random-polar and M-ary CP-EBPSK modulation is proposed. The modulation principle of random-polar and M-ary CP-EBPSK is demonstrated. Based on the digital impacting filter, the demodulator on the basis of Multi-path decision method, greedy decision method and rational decision method is presented, respectively. The contrast and analysis of the power spectrum, the -60dB bandwidth, the spectral efficiency, and the demodulation performance among the CP-EBPSK, random-polar modulated CP-EBPSK, and the proposed modulation, are carried out. Simulation results show that: 1) under the premise of remaining the same spectral structure, the proposed modulation method can multiple the information transmission rate and spectral efficiency; 2) if taking bps/Hz/SNR(dB) as comprehensive indicator, CP-EBPSK is about 1.18*10-3, random-polar modulated CP-EBPSK is about 7.01, and the proposed modem is 13.8.