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For RF-pilot-assisted PDM-CO-OFDM systems, we propose and demonstrate a carrier recovery method applying a simple moving average filter (MAF) to extract the central RF-pilot for phase noise compensation. Because only two additions per output sample would be required to implement such a MAF, its computational complexity is rather simple compared to any other direct-form finite impulse response (FIR) filter. To handle its weak side-lobe attenuation, which would cause the spectrally nearby OFDM signal to interfere with the extracted pilot signal, we further propose using multiple MAFs in cascade to enhance the side-lobe attenuation. We evaluate the performance of a 16-QAM and 40-Gbps PDM-CO-OFDM signal, in terms of the bandwidth tolerance, optical signal to noise ratio (OSNR) tolerance, nonlinear tolerance, linewidth tolerance, and residual carrier frequency offset (RFO) tolerance, with different filters including the simple MAF, cascaded MAFs, and the previously-demonstrated multi-stage decimation and interpolation filter (MDIF). We've found that 1) all the filters exhibit similar performance to the ideal brick-wall filter in terms of noise and nonlinear tolerances, 2) the MAF1 exhibits the worse tolerances against linewidth and RFO, and 3) the MDIF has to be carefully designed to enhance its tolerances against both the linewidth and RFO.