Gradient-Descent Based Optimization of Constant Envelope OFDM Waveforms

This paper describes a gradient-descent based optimization algorithm for synthesizing Constant Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM) waveforms with low Auto-Correlation Function (ACF) sidelobes in a specified region of time-delays. The algorithm optimizes the Generalized Integrated Sidelobe Level (GISL) which controls the mainlobe and sidelobe structure of the waveform's ACF. The operations of this Gradient-Descent GISL (GD-GISL) algorithm are FFT-based making it computationally efficient. This computational efficiency facilitates the design of large dimensional waveform design problems. Simulations demonstrate the GD-GISL algorithm on CE-OFDM waveforms employing Phase-Shift Keying (PSK) symbols that take on a continuum of values (i.e, $M_{\text{PSK}} = \infty$). Results from these simulations show that the GD-GISL algorithm can indeed reduce ACF sidelobes in a desired region of time-delays. However, truncating the symbols to finite M-ary alphabets introduces perturbations to the waveform's instantaneous phase which increases the waveform's ACF sidelobe levels.