Blind Equalization Based on Modified Third-Order Moment Algorithm for PAM-PPM Optical Signals in FSO Communication

In order to mitigate the influence of turbulence on pulse amplitude modulation–pulse position modulation (PAM-PPM) optical signals, which represents a promising avenue for future high-speed free-space optical (FSO) communication, this paper proposes a novel blind equalization scheme based on a modified third-order moment algorithm (MTOMA). The MTOMA is more robust to noise compared with the current fourth-order moment algorithms, such as the constant modulus algorithm (CMA) and the modified constant modulus algorithm (MCMA). Moreover, it will not increase the implementation complexity compared with the CMA and MCMA. The simulation results show that the MTOMA effectively reduces the distortion of PAM-PPM optical signals in atmospheric turbulence channels with a pointing error. Under different turbulence conditions, the MTOMA has a faster convergence rate than the CMA and MCMA. For example, when the signal-to-noise ratio (SNR) is 15 dB, the MTOMA requires about 530 iterations to reach convergence in moderate turbulence, which is about 230 and 170 fewer iterations than required by the CMA and MCMA, respectively; in addition, the differences in the number of iterations required by the MTOMA and those required by the CMA and MCMA, respectively, are 140 and 100 in weak turbulence and 150 and 90 in strong turbulence. Moreover, when the algorithms converge, the bit error rate (BER) performance of the PAM-PPM signals with MTOMA is also superior to that with CMA and MCMA. For example, when SNR = 20 dB, the BER performance of the PAM-PPM signals with MTOMA improves by 6.5 dB and 1.7 dB, respectively, compared to that with CMA and MCMA in moderate turbulence; this value improves by 4.3 dB and 1.4 dB in weak turbulence and 4.8 dB and 1.5 dB in strong turbulence. In addition, when the MTOMA reaches convergence, the decision-directed least mean square (DDLMS) algorithm can continue to be utilized to further improve the BER performance of PAM-PPM optical signals.