496 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 47, NO. 3, MARCH 1999 Receiver Array Calibration Using Disparate Sources Ishan Samjeva Daniel Solomon, Member, IEEE, Douglas A. Gray, Member, IEEE, Yuri I. Abramovich, Member, IEEE, and Stuart J. Anderson Abstract— In this paper, we present a new array calibration procedure for over-the-horizon (OTH) radar, using disparate sources. Unlike previous array calibration methods, which re- quire a specific type or class of sources for calibrating the array, the method we propose can use combinations of single- mode, multimode, and near-field sources; each source with either known or unknown DOA’s (directions-of-arrival). Multidimen- sional MUSIC is exploited for time-invariant DOA sources, while single-snapshot techniques are used for sources that have time- varying DOA’s. A nonlinear separable least-squares solution to the array calibration problem is used to estimate the array coupling matrix and sensor positions. Simulation results indicate that good estimates are obtained for the unknown parameters and further the array sidelobe levels and bearing errors are significantly reduced when these estimated parameters are used in array processing. The algorithm performance was also compared with the Cramer–Rao lower bound and found to be statistically efficient. Index Terms— Array calibration, Cramer–Rao lower bound, Jindalee, meteors, OTH radar. I. INTRODUCTION A RRAY calibration has been an active area of research in array processing for the last few decades with many papers relating mainly to sonar and radar being published in [1]–[29]. For towed sonar hydrophone arrays, receiver gain/phase errors and the time-varying sensor position er- rors, degrade performance. Radar arrays generally have time- invariant sensor position errors, but have the additional prob- lem of mutual coupling. In this paper, we consider radar receiver arrays, for example, for bistatic over-the-horizon (OTH) radar applications. For OTH radar arrays errors in sensor positions, unknown mutual coupling and receiver gain/phase variations are known to degrade performance [30]. Hence, for such radars currently being developed for coastal surveillance, which incorporate antenna arrays that can be erected quickly on unprepared sites, array calibration is essential. While gain/phase errors may be calibrated relatively easily by the injection of signals at the receiver inputs, both sensor position errors and mutual coupling require more sophisticated calibration methods. Manuscript received September 22, 1997; revised May 26, 1998. I. S. D. Solomon is with the CRC for Sensor Signal and Information Processing (CSSIP), The Levels, 5095 Australia, and also with the Defence Science and Technology Organization, Salisbury, 5108 Australia. D. A. Gray is with the University of South Australia, and also with the University of Adelaide, 5000 Australia. Y. I. Abramovich is with the University of South Australia, The Levels, 5095 Australia. S. J. Anderson is with the Defence Science and Technology Organization, Salisbury, 5108 Australia. Publisher Item Identifier S 0018-926X(99)04427-0. Fig. 1. Illustration of disjoint clusters: and are disjoint clusters, each of which may contain a number of sources/signals. For OTH radar array calibration one may use special sources such as beacons, noise sources such as radio stations, and sources of opportunity such as backscattered echoes from meteors. These sources have widely varying properties, which must be accounted for when used for array calibration [31], [32]. For example, in [28], [29] we showed how backscattered echoes from ionized meteor trails may be used for array calibration. Unlike previous array calibration methods, which require a specific type or class of sources for calibrating the array, the method we propose here can use all available sources for array calibration. For example, the methods proposed by See and Ng [21]–[23], [27] to estimate sensor positions and mutual coupling, need disjoint single-mode sources of known DOA’s and the DOA’s must be time-invariant. The method we propose here, however, can use disjoint 1 clusters (see Fig. 1) of nondisjoint single-mode, multimode, and/or near-field sources, with either known or unknown DOA’s. Further, the DOA of each source may be either time-varying or time-invariant. In Section II, we describe the signal model. In Section III, we consider the case of a cluster of time-varying DOA sources. In Section IV, the case of a cluster of time-invariant DOA sources are considered and we formulate the problem for each case. Then, in Section V, we show how to combine cost func- tions from a number of clusters of either type into an overall cost function. In Section VI, the proposed algorithm is given with a simulation example in Section VII. Statistical analysis of the algorithm is conducted in Section VIII and the algorithm is compared with the Cramer–Rao lower bound in Section IX. Section X contains the conclusion, while the Appendix give an example and contain mathematical derivations. 1 By disjoint we mean that they do not occupy both the same time snapshots and the same radar range cells. U.S. Government work not protected by U.S. copyright.