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.

中文翻译：

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通过基于两级分数程序的波束形成进行恒模波形估计和干扰抑制

在雷达和通信系统中，存在一大类具有恒模特性的信号，包括BPSK、QPSK、LFM和相位编码信号。在本文中，我们重点研究天线阵列接收信号的联合恒模波形估计和干扰抑制问题。不是通过 Capon 方法寻求干扰抑制和输出噪声功率降低之间的折衷，或者在 ID 处放置完美零点之前利用干扰方向 (ID)，然后通过线性约束最小方差 (LCMV) 波束形成器最小化输出噪声功率，我们设计了一种新颖的功率比标准，即波束形成器输出中的干扰加噪声比（INNR），以实现完美的干扰归零和最小的输出噪声功率，如 LCMV 中但在未知 ID 情况下。开发了一种基于两阶段分数程序的方法来联合抑制干扰并估计恒模波形。在第一阶段，我们制定一个带有分数目标函数的优化模型，以最小化 INNR。然后，在第二阶段，建立另一个分数约束优化问题，以从受 INNR 界限约束的解空间细化权向量，以实现近似完美的零点和最小输出噪声功率。此外，该解决方案还进一步扩展以解决具有转向矢量误差的情况。数值结果证明了我们的方法的优异性能。