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The impact of carrier frequency offset on second-order algorithms for blind channel identification and equalization

Research has shown that second-order statistics (SOS) are sufficient to blindly identify or equalize a broad class of channels. We relax the assumption of perfect carrier recovery and determine if SOS are sufficient for channel identification, equalization, and carrier recovery in the presence of frequency offset. We show that while equalization may still be possible, channel identification and carrier recovery require use of higher-order statistics. We show that SOS-based channel identification is possible only with knowledge of the carrier frequency offset, and conversely, that SOS-based carrier-offset identification is possible only with knowledge of the channel. We describe algorithms and present simulation results to demonstrate these claims.