Variable step size decision feedback equalizer-cascaded multi-modulus algorithm blind equalization technology based on avalanche photodiode gain control for multi-level pulse amplitude modulation modulated atmospheric laser communication

The traditional cascaded multi-modulus algorithm (CMMA) struggles to compensate for nonlinear inter-symbol interference (ISI) in atmospheric laser communication systems based on multi-level pulse amplitude modulation (M-PAM). To address this issue, we propose an adaptive blind equalization algorithm based on avalanche photodiode (APD) gain control. We derive the relationship among the channel scintillation index (SI), the optimal gain of the APD, and the optimal output signal-to-noise ratio (SNR) of the system. According to the real-time measured SI, we adjust the APD gain to optimize the system’s output SNR. The receiver uses CMMA to blindly adjust the decision feedback equalizer (DFE) tap weights to reduce nonlinear ISI, which is named the DFE-CMMA algorithm. To enhance the performance of the DFE-CMMA with fixed step size, we have made improvements and named the improved algorithm as variable step size DFE-CMMA (VS-DFE-CMMA). The iterative step size of the VS-DFE-CMMA is determined by the optimal output SNR of the system after APD gain control. We build a gamma–gamma channel model to simulate the transmission of M-PAM signals. The simulation results show that APD gain control can effectively improve the output SNR of the system. The VS-DFE-CMMA can converge quickly under various turbulence intensity channels, and convergence can be achieved in as few as 200 iterations. Compared with DFE-CMMA, the bit error rate (BER) of the system equalized by VS-DFE-CMMA is reduced by up to one to two orders of magnitude. In terms of algorithm convergence and BER performances, the VS-DFE-CMMA significantly outperforms the DFE-CMMA. The proposed scheme can solve practical problems in atmospheric laser communication and provide a reference for practical engineering applications.