Counter-Based Scatter Matrix Estimation for One-Bit Centered Bivariate Cauchy Signals

Scatter matrix or covariance matrix estimation under data with outliers is crucial to signal processing applications. These data can be modeled as Cauchy or elliptically symmetric (ES) distributions, under which many estimators have been developed. However, these estimators primarily assume continuous-valued data. For implementation purposes, these data are quantized into discrete levels, which can be represented by finite bits. The complexity of the estimators is also restricted. These hardware constraints degrade the performance of existing scatter matrix estimators. This paper proposes the Cauchy onebit scatter matrix estimator (COSME). The COSME is founded on the proposed integral expressions of the marginal and joint probability for one-bit centered bivariate ES (CB-ES) data. These probabilities are simplified in closed forms for one-bit centered bivariate Cauchy (CB-Cauchy) data. For equal normalized quantization thresholds, these forms admit the COSME with lowcomplexity steps. In particular, these steps involve counting the occurrences of the events in the one-bit CB-Cauchy data and evaluating trigonometric functions. The minimum number of snapshots and the multivariate extension of the COSME are also investigated. Numerical examples demonstrate that the COSME exhibits shorter CPU time under the same number of snapshots and improved estimation performance under the same number of bits, compared to several existing estimators. Empirical results show the robustness of the COSME to Student’s t distributions and parameter variations.