Direction Finding and Power Estimation of Electromagnetic Sources on a Cross-Dipole Array Using 1.5-Bit Measurements

Cross-dipole arrays can estimate the directions of arrival (DOAs) and polarizations of electromagnetic sources, but they need twice as many analog-to-digital converters as scalar arrays. One-bit quantization with a zero threshold reduces this cost but records only the signs of the samples, so the source powers cannot be estimated, and a single non-zero threshold cannot estimate the powers and the DOAs both accurately. We apply 1.5-bit quantization—which maps each real sample to one of three levels by two symmetric thresholds—to the cross-dipole array and propose a joint DOA and power estimator. Two second-order statistics of the 1.5-bit data are derived: the fraction of zero outputs gives the received power of each dipole array, and a relation obtained from Price’s theorem gives the correlation of two 1.5-bit samples with different powers, such as those of an x-axis dipole and a y-axis dipole. With these two results, the covariance and cross-covariance matrices of the unquantized data are reconstructed on their true scale, and the DOAs and the source powers are estimated by spatial-smoothing MUSIC and by least squares. Simulations show that the proposed estimator is more accurate than one-bit estimators in DOA estimation and estimates the source powers almost as accurately as unquantized data, with one extra comparator per in-phase or quadrature branch.