Direction-of-arrival estimates in the presence of wavelength, gain,and phase errors

Direction-of-arrival (DOA) estimation using an array of sensors relies on an accurate characterization of the array manifold. In the absence of characterization errors, established techniques like MUSIC can be shown to perform well both theoretically and in simulation. However, in the presence of unknown sensor and/or source characteristics, the performance of most methods degrades significantly. We consider the problem of estimating gain and phase errors of an array of sensors whose physical positions are known. Our algorithm assumes that the gain and phase characteristics of the sensors are independent of DOA and employs multiple calibration sources with known DOA's. It differs from other algorithms in that the signal wavelengths are unknown. A least-squares formulation of the problem is then shown to be NP-complete, implying that an efficient solution is unlikely to exist. An implicit, enumerative technique is used to obtain the exact solution. For the special case of collinear sensors, we further show that an inherent ambiguity in the model prevents exact phase characterization unless the wavelength of one calibration source is assumed known. A theorem is presented relating the error in DOA to the difference between the assumed and true wavelengths of this calibration source. Simulation results are presented for both noncollinear and collinear arrays