Beamforming is a spatial filtering technique using a sensor array to enhance the signal of interest (SOI) and suppress interferences and noise. It is widely used in radar, sonar, wireless communications, Global Positioning System (GPS) navigation, microphone array speech processing and many other areas. Most existing beamforming approaches are based on the minimum variance (MV) criterion. The MV approach is statistically optimal only when the desired signal, interferences and the noise are Gaussian-distributed. However, many real-world signals are non-Gaussian. For non-Gaussian signals, the higher-order statistics or fractional lower-order statistics contain useful information and can be utilized to improve the beamformer performance. In this thesis, a family of the minimum dispersion (MD) criterion-based robust beamforming algorithms, which minimize the Lp-norm (p>=1) of the array output subject to linear or nonlinear constraints, are proposed for non-Gaussian signals. The dispersion, which is a generalization of variance, implicitly exploits the higher-order statistics for p>2 or fractional lower-order statistics for p<2.
We utilize the MD criterion with a single linear constraint and multiple linear constraints, which gives us the minimum dispersion distortionless response (MDDR) beamformer and linearly constrained minimum dispersion (LCMD) beamformer, respectively. The MDDR and LCMD beamformers can be tailored to Gaussian, sub-Gaussian or super-Gaussian signals and noise by adjusting the value of p. Three efficient iterative algorithms, namely, the iteratively reweighted MVDR (IR-MVDR), complex-valued full Newton’s and partial Newton’s methods, are devised to solve the resulting convex optimization problems.
We extend the LCMD beamformer to the quadratically constrained minimum dispersion (QCMD) beamformer. The robustness against model uncertainty of the QCMD beamformer is significantly enhanced compared with the LCMD beamformer. A gradient projection algorithmic framework is developed to efficiently solve the resulting convex optimization problem. Furthermore, we derive a closed-form expression of the projection onto the constraint set.
Note that sub-Gaussian signals that are frequently encountered in practical applications. Therefore, a minimum infinity norm criterion is then adopted by the robust linear programming beamformer (RLPB). In this way, the sub-Gaussianity of the signals can be fully exploited. We model the uncertainty region as a rhombus in which the L1-norm of the steering vector error is bounded. As a result, the proposed RLPB beamformer can be obtained by solving a linear programming (LP) problem. We also present the theoretical explanation to the reason why the RLPB can implicitly exploit the high-order statistics from the statistical perspective. / Dissertation / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/16226 |
| Date | 28 October 2014 |
| Creators | Jiang, Xue |
| Contributors | Kirubarajan, T., Electrical and Computer Engineering |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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