We consider sparse array beamformer design achieving maximum signal-to interference plus noise ratio (MaxSINR). Both array configuration and weights are attuned to the changing sensing environment. This is accomplished by simultaneously switching among antenna positions and adjusting the corresponding weights. The sparse array optimization design requires estimating the data autocorrelations at all spatial lags across the array aperture. Towards this end, we adopt low rank matrix completion under the semidefinite Toeplitz constraint for interpolating those autocorrelation values corresponding to the missing lags. We compare the performance of matrix completion approach with that of the fully augmentable sparse array design acting on the same objective function. The optimization tool employed is the regularized $l_1$-norm successive convex approximation (SCA). Design examples with simulated data are presented using different operating scenarios, along with performance comparisons among various configurations.

我们认为稀疏阵列波束形成器设计可实现最大的信干噪比（MaxSINR）。阵列配置和权重都可以适应不断变化的传感环境。这是通过同时在天线位置之间切换并调整相应的权重来实现的。稀疏阵列优化设计需要在整个阵列孔径的所有空间滞后上估计数据自相关。为此，我们在半定Toeplitz约束下采用低秩矩阵补全，以内插与缺失滞后相对应的自相关值。我们将矩阵完成方法的性能与作用于相同目标函数的完全可扩展的稀疏阵列设计的性能进行比较。使用的优化工具是正则化的${升}_{\mathrm{1个}}$-范数连续凸逼近（SCA）。使用不同的操作场景介绍了带有仿真数据的设计示例，并比较了各种配置之间的性能。