Constant Modulus Waveform Estimation and Interference Suppression via Two-Stage Fractional Program-Based Beamforming

In radar and communication systems, there exist a large class of signals with constant modulus property, including BPSK, QPSK, LFM, and phase-coded signals. In this paper, we focus on the problem of joint constant modulus waveform estimation and interference suppression from signals received at an antenna array. Instead of seeking a compromise between interference suppression and output noise power reduction by the Capon method or utilizing the interference direction (ID) prior to place perfect nulls at the IDs and subsequently minimize output noise power by the linearly constrained minimum variance (LCMV) beamformer, we devise a novel power ratio criterion, namely, interference-plus-noise-to-noise ratio (INNR) in the beamformer output to attain perfect interference nulling and minimal output noise power as in LCMV yet under the unknown ID case. A two-stage fractional program-based method is developed to jointly suppress the interferences and estimate the constant modulus waveform. In the first stage, we formulate an optimization model with a fractional objective function to minimize the INNR. Then, in the second stage, another fraction-constrained optimization problem is established to refine the weight vector from the solution space constrained by the INNR bound, to achieve approximately perfect nulls and minimum output noise power. Moreover, the solution is further extended to tackle the case with steering vector errors. Numerical results demonstrate the excellent performance of our methods.