Sensor array calibration for uniform rectangular array in presence of mutual coupling and sensor gain-and-phase errors

Abstract

The sensor array calibration methods tailored to uniform rectangular array (URA) in the presence of mutual coupling and sensor gain-and-phase errors were addressed. First, the mutual coupling model of the URA was studied, and then a set of steering vectors corresponding to distinct locations were numerically computed with the help of several time-disjoint auxiliary sources with known directions. Then, the optimization modeling with respect to the array error matrix (defined by the product of mutual coupling matrix and sensor gain-and-phase errors matrix) was constructed. Two preferable algorithms (called algorithm I and algorithm II) were developed to minimize the cost function. In algorithm I, the array error matrix was regarded as a whole parameter to be estimated, and the exact solution was available. Compared to some existing algorithms with the similar computation framework, algorithm I can make full use of the potentially linear characteristics of URA’s error matrix, thus, the calibration precision was obviously enhanced. In algorithm II, the array error matrix was decomposed into two matrix parameters to be optimized. Compared to algorithm I, it can further decrease the number of unknowns and, thereby, yield better estimation accuracy. However, algorithm II was incapable of producing the closed-form solution and the iteration operation was unavoidable. Simulation results validate the excellent performances of the two novel algorithms compared to some existing calibration algorithms.

Keywords

array calibration / uniform rectangular array (URA) / mutual coupling / sensor gain-and-phase errors / closed-form solution / Newton-type iteration

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