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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 onebit 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. 

In array processing, minimum redundancy arrays (MRA) can identify up toO(N2) uncorrelated sources (theO(N2) property) withN physical sensors, but this property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are robust, but they resolve only O(N) sources. Recently, the robust MRA (RMRA) was shown to possess the O(N2) property and to be as robust as ULA. But finding RMRA is computationally difficult for large N. This paper proposes a novel array geometry called the composite Singer array, which is related to a classic paper by Singer in 1938, and to other results in number theory. For large N, composite Singer arrays could own theO(N2) property and are as robust as ULA. Furthermore, the sensor locations for the composite Singer array can be readily computed by the proposed recursive procedure. These properties will also be demonstrated by using numerical examples. 

Sparse arrays have received considerable attention due to their capability of resolving O(N2) uncorrelated sources with N physical sensors, unlike the uniform linear array (ULA) which identifies at most N − 1 sources. This is because sparse arrays have an O(N2)-long ULA segment in the difference coarray, defined as the set of differences between sensor locations. Among the existing array configurations, minimum redundancy arrays (MRA) have the largest ULA segment in the difference coarray with no holes. However, in practice, ULA is robust, in the sense of coarray invariance to sensor failure, but MRA is not. This paper proposes a novel array geometry, named as the robust MRA (RMRA), that maximizes the size of the hole-free difference coarray subject to the same level of robustness as ULA. The RMRA can be found by solving an integer program, which is computationally expensive. Even so, it will be shown that the RMRA still owns O(N^2) elements in the hole-free difference coarray. In particular, for sufficiently large N, the aperture for RMRA, which is approximately half of the size of the difference coarray, is bounded between 0.0625N^2 and 0.2174N^2.