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Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative method. In particular, we learn illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method. Coded diffraction phase retrieval is a physically realistic system in which the signal is first modulated by a sequence of codes before the sensor records its Fourier amplitude. We represent the phase retrieval method as an unrolled network with a fixed number of layers and minimize the recovery error by optimizing over the measurement parameters. Since the number of iterations/layers are fixed, the recovery incurs a fixed cost. We present extensive simulation results on a variety of datasets under different conditions and a comparison with existing methods. Our results demonstrate that the proposed method provides near-perfect reconstruction using patterns learned with a small number of training images. Our proposed method provides significant improvements over existing methods both in terms of accuracy and speed.