Maria Lanne

Calibration in Array Processing

High-resolution direction-or-arrival estimation has been an active area of research since late 1970s. 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.

Optimized Beamforming Calibration in the Presence of Array Imperfections

For arrays with position and channel errors the calibration becomes very crucial. In the traditional calibration methods one can choose between an optimal SNR and a beam pattern with low side lobes. In this paper we formulate a beam pattern synthesis method which optimize the trade-off between the two criteria. A classical problem with position errors in an array, is that it is difficult to get low side lobes over the whole side lobe region, since the position errors give rise to direction dependent errors. In this paper this problem is solved by using local (direction dependent) correction matrices in the beam pattern optimization. The new way of using local correction matrices leads to the lowest possible uniform side lobe level, for the chosen SNR, beamwidth and beam pointing direction.

Moment method analysis of circular-cylindrical array of waveguide elements covered with a radome

We have developed a moment method program that analyzes arrays of waveguide elements on circular-cylindrical surfaces. The presence of a radome is rigorously taken into account by using the Greens function of a multilayer circular cylindrical structure. Special attention is given to numerical treatment of the Greens function when analyzing cylindrical antennas of large radii. The calculated results are compared with the measured S-parameters of the array with 54 waveguide elements. The agreement between measured and calculated results is very good.

Adaptive beamforming using calibration vectors with unknown gain and phase

The importance of taking the direction dependent amplitude and phase of the received signals (due to the mutual coupling) into account in the calibration is demonstrated using adaptive beamforming (Capons method). The method is compared to a direction dependent (local) calibration method, which is shown to be the preferred method if there are position errors in the array. In reality, robust versions of Capons method is always used. The calibration is considered as a complement to these robust methods, to reduce the array steering vector errors and thereby further improve the performance of the robust Capon methods. The calibration also allows for larger errors in the array, which translates to a potential to decrease the manufacturing cost.

Two-Step Esprit with Compensation for Modelling Errors using a Sparse Calibration Grid

In arrays with scan dependent errors, such as large position errors, a dense calibration grid can become necessary. Calibration time is, however, very expensive and keeping the measured calibration grid as sparse as possible is important. In this paper it is shown how interpolation using local models can be used to make the calibration grid more dense without increasing the number of measurements. Furthermore, it is shown how the performance of the DOA estimation with ESPRIT using arrays with large position errors can be improved by a second step including weighted calibration.

T/R-module mismatch and antenna pattern characteristics

Phased array antennas are complex systems, with a large number of components. It is essential to understand how the performance of the included components influences the performance of the overall antenna system. In this work, we have studied the effects of T/R-module front-end mismatch in connection with array characterization and active T/R-module calibration. This paper will emphasize issues regarding how maintenance at the array element level can influence antenna pattern characteristics. Simulated results from a linear array with 200 active elements are presented.