In order to study frequency offset estimation and Bit Error Rate(BER) of 8 Phase Shift Keying(8PSK) and 16 Amplitude Phase Shift Keying(16APSK) signals，two high-order constant envelope digital modulation methods 8PSK and 16APSK are introduced firstly，and then their frequency offset estimation is investigated. The communication link model is built to simulate the performance. Matrix Laboratory(Matlab) is utilized to simulate and analyze the frequency offset estimation of 8PSK and 16APSK modulation signals, under Additive Gaussion White Noise. Then coherent demodulation is conducted with the carrier frequency obtained by the frequency offset estimation. Finally, the actual bit error rate and theoretical bit error rate are compared and analyzed. Simulation results demonstrate that the noise immunity of 8PSK is better than that of 16APSK, under the condition of Additive Gaussion White Noise channel with different Signal-Noise Ratios(SNR). The performance of the frequency offset estimation method proposed in this paper approaches the theoretical value. This paper provides a reference for the design of communication systems.