Maximum Likelihood DOA Estimation Aided by Magnitude Measurements

This paper proposes a maximum likelihood (ML) direction of arrival (DOA) estimator for a magnitude-aided antenna array (MA-AA), which incorporates magnitude-only radio frequency (RF) chains into the traditional AA to obtain magnitude measurements. The magnitude observations are further quantized by low-resolution (2-bit) analog-to-digital converters (ADC) in quantized MA-AA (QMA-AA) to further reduce the circuit power of magnitude RF chains. In ML, the multi-signal classification (MUSIC) method is firstly used to get estimates of DOA based on complex measurements from AA. Secondly, the angle region around the MUSIC DOAs is gridded uniformly and their likelihood values are calculated based on complex-valued and (quantized) magnitude observations. Since the channel response is modeled as continuous random variables, it is impractical to search over its value range. Therefore, the channel response estimate is obtained by the least-square (LS) method before calculating the likelihood function. Finally, the DOA with the highest likelihood function value is the DOA estimate of ML. Simulation results show that both the magnitude measurements from MA-AA and low-resolution quantized magnitude measurements from QMA-AA can enhance the DOA estimation accuracy of ML. ML outperforms the traditional DOA estimators and does not require a reference source. MA-AA is more energy-efficient than the traditional AA under the ML estimator.