Calibration in Array Processing
Book chapter, 2009
High-resolution direction-or-arrival estimation has been an active area of research since late 1970's. The methods find a wide range of applications, including passive listening arrays, radar and sonar, and spatial (or space-time) characterization of wireless communication channels. Conventional beamforming-based techniques for direction estimation are limited by the aperture (or physical size) of the array. In contrast, parametric methods promise an unlimited resolution in theory. These methods take advantage of a precise mathematical model of the received array data, for example due to incoming plane waves. In practice, the resolution and estimation accuracy is limited by noise as well as errors in the assumed data model. The focus of this chapter is on modeling errors, and in particular calibration techniques to mitigate such errors. Perhaps the most natural and common approach is to measure the response of the array in an anechoic chamber. These calibration measurements are then used to update the data model, either in the form of explicit unknown parameters or in a non-parametric way. Under favorable conditions it is also possible to estimate the response model together with the unknown directions, so-called auto-calibration. The purpose of this chapter is to give an overview of existing techniques and discuss their respective pros and cons. We will also elaborate on how the methods can be extended to more general situations, for example including frequency and polarization dependence. It should be mentioned that practical calibration also involves hardware adjustments, to compensate for temperature drift etc. The methods considered here can be classified as software calibration, where errors are handled by adjusting the assumed data model rather than correcting for it.
Array Signal Processing