Use of the Gerchberg-Saxton Algorithm for Denoising of Constant-Envelope OFDM Signals

A constant-envelope OFDM signal offers significant performance advantages on both transmit and receive. Our method for constructing such a signal using complementary sequences is reviewed, along with iterative nonlinear methods of exploiting the magnitude constraint for enhanced performance. The Fourier transforms involved in OFDM modulation/demodulation motivate an investigation of the merits of employing the Gerchberg-Saxton algorithm for phase retrieval in image processing, also known as the Gerchberg-Papoulis algorithm for sample interpolation in signal processing. The parallels enable a reduction of the AWGN with oversampled constant-modulus OFDM signals. The results can be further enhanced by using nonlinear point-wise mappings to iteratively exploit the constant magnitude constraint.