We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace can be estimated with the contaminated observations discarded. To this end, we employ a signal model which explicitly includes an interference term that is distinct from environmental noise. To detect when the interference term is nonzero, we estimate the interference term using an optimization problem with a sparsity-inducing group SLOPE penalty which accounts for simultaneous sparsity across all channels of the multichannel signal. We propose an iterative algorithm which efficiently computes the observations estimated to contain interference. Theoretical support for the accuracy of our interference estimator is provided by bounding its false discovery rate, the expected proportion of uncontaminated observations among those estimated to be contaminated. Finally, we demonstrate the empirical performance of our contributions in a number of simulated experiments.

翻译：我们考虑在存在干扰且干扰污染部分接收观测值的情况下估计信号子空间的问题。本文重点在于检测受污染的观测值，以便在剔除这些观测值后估计信号子空间。为此，我们采用了一种明确包含与环境噪声不同的干扰项的信号模型。为检测干扰项非零的时刻，我们通过一个带有稀疏诱导组SLOPE惩罚项的优化问题来估计干扰项，该惩罚项考虑了多通道信号所有通道的同步稀疏性。我们提出了一种迭代算法，能高效计算被估计为含有干扰的观测值。通过限定干扰估计量的错误发现率（即估计为受污染的观测值中未受污染观测值的预期比例），为干扰估计量的准确性提供了理论支持。最后，我们在多项模拟实验中展示了所提方法的实证性能。