One-Bit Normalized Scatter Matrix Estimation For Complex Elliptically Symmetric Distributions

One-bit quantization has attracted attention in massive MIMO, radar, and array processing, due to its simplicity, low cost, and capability of parameter estimation. Specifically, the shape of the covariance of the unquantized data can be estimated from the arcsine law and one-bit data, if the unquantized data is Gaussian. However, in practice, the Gaussian assumption is not satisfied due to outliers. It is known from the literature that outliers can be modeled by complex elliptically symmetric (CES) distributions with heavy tails. This paper shows that the arcsine law remains applicable to CES distributions. Therefore, the normalized scatter matrix of the unquantized data can be readily estimated from one-bit samples derived from CES distributions. The proposed estimator is not only computationally fast but also robust to CES distributions with heavy tails. These attributes will be demonstrated through numerical examples, in terms of computational time and the estimation error. An application in DOA estimation with MUSIC spectrum is also presented.