  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.
