Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may he quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.
Bibliographical noteFunding Information:
Manuscript received October 17, 2001; revised October 10, 2002. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada, Communications and Information Technology Ontario (CITO), Premier’s Research Excellence Award Program of the Ministry of Energy, Science, and Technology (MEST) of Ontario, Canada Research Chairs Program, and Wolfgang Paul Award Program of the Alexander von Humboldt Foundation. The associate editor coordinating the review of this paper and approving it for publication was Dr. Rick S. Blum.
- Optimal diagonal loading
- Robust adaptive beamforming
- Second-order cone programming
- Signal mismatch problem
- Worst-case performance optimization