Title:
Slepian Array Processing: Concepts and Practical Considerations
Slepian Array Processing: Concepts and Practical Considerations
Author(s)
DeLude, Coleman Buchanan
Advisor(s)
Romberg, Justin K.
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Abstract
In recent years, there has been substantial focus placed on how to integrate multi-sensor arrays into a variety of applications. The motivation for this is simple, acquiring a signal with multiple sensors induces redundancy that can be leveraged in downstream tasks. However, particularly in radio frequency (RF) applications, there is also a demand for higher bandwidths and larger arrays. This has the capacity to greatly complicate several key problems in array processing. In turn, this motivates the development of new processing techniques that can be applied to arrays with high bandwidth and possibly a large number of elements. In this thesis, we aim to develop new techniques of broadband source localization, beamforming, and RF channel emulation.
The thesis begins with an introduction to the concept broadband source localization. We then develop an iterative algorithm for localizing broadband sources. It is shown that this algorithm is applicable to localization in time, or space and time. The latter case envelopes the array processing scenario, where we wish to estimate the spectral support of an impinging signal as well as where is it coming from. A key part of the technique is the use of \emph{Slepian spaces} to model signals as a union of subspaces. Leveraging this model, we show that our technique performs far better than standard Fourier based methods. The advantage is even greater as the dynamic range between sources becomes more substantial.
In the next chapter of the thesis we return to this Slepian space model and show how it can be used to perform broadband beamforming. The technique, which we call Slepian beamforming, is an entrely new paradigm for beamforming. It differs drastically from traditional approaches by not requiring any notion of filtering or presteering. Furthermore it is shown that Slepian beamforming convincingly outperforms existing techniques of conventional and adaptive beamforming. All of this is achieved while not being any more computationally expensive than traditional filter based methods.
The following chapter of the thesis shows how the Slepian beamforming technique can be extended to operating from dimensionality reducing measurements. In this scenario we form measurements by linearly combining sensor outputs across space, or space and time. This collapses the dimension of the array output, reducing the amount of data that must be processed. We then show that leveraging our Slepian beamforming model we can compensate for quantization errors in the measurements. The impact of this is substantial, and we can achieve exceptional performance with very low precision measurements. For example, in the adaptive beamforming case we can achieve in excess of $60$ dB of interference cancellation with measurements quantized to $1$-bit.
In the final chapter before the conclusion we address the problem of system testing and validation by developing an efficient computational framework for RF channel emulation. It leverages a novel ``direct path" model that can account for all physical interactions necessary to properly emulate a RF channel. The proposed computational model is shown to efficiently scale to multi-object scenarios, and can be easily distributed. Obtaining these favorable properties required the development of several innovative modeling techniques, which allows us to carefully factor computations. Additionally, the model is shown to be no less accurate than more conventional RF emulation models.
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Date Issued
2024-11-19
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Text
Resource Subtype
Dissertation