Publication Date


Document Type


Committee Members

Fred Garber (Committee Member), Muralidhar Rangaswamy (Committee Member), Brian Rigling (Committee Chair), Arnab Shaw (Committee Member), Michael Temple (Committee Member)

Degree Name

Doctor of Philosophy (PhD)


Passive bistatic radar can be an attractive choice relative to monostatic radar because it provides the ability to operate covertly; immunity to jamming and interference; the ability to operate outside of traditional radar bands; and reduced cost. The benefits of noise waveforms versus classic radar waveforms such as linear frequency modulation (LFM) are discussed in the literature. Noise waveforms, with their thumbtack ambiguity functions, are ideal for use in non-cooperative passive radar. Since many digital waveforms are randomized to make their spectra approximately white, noise-like waveforms may be readily available for opportunistic use by non-cooperative passive radar receivers. For instance, the literature points out that digital television transmitters offer a powerful, well-defined signal with sufficient bandwidth for reasonable precision in range and are noise-like, thereby allowing for good, consistent range compression and Doppler estimation of targets. Much of the literature assumes that the transmitted noise (or noise-like) waveform is white (flat spectrum) over a finite bandwidth, and with good reason. However, some illuminators may emit waveforms that are not white. When the transmitted waveform's spectrum is colored (correlated), the cross-correlation process is likely to produce unacceptably high sidelobes. Meanwhile, LMS may produce more acceptable sidelobes. Until now, no theoretical expressions for the SNR at the output of the LMS family of algorithms existed in the literature for cases in which variants of the LMS algorithm are used to process colored Gaussian noise input data. The original contribution of this research is as follows. An equation is derived which predicts the theoretical output SNR when processing colored Gaussian noise input data using conventional LMS, valid at steady-state. Theoretical results have been corroborated by simulation results, and this contribution has been completed. The equation which predicts the steady-state theoretical output SNR when conventional LMS processes colored Gaussian noise input data should also apply at steady-state when block LMS and fast block LMS (fast LMS) are used to perform the processing. Additionally, promising simulation results using L1 LMS are presented, which highlight the previously known fact that L1 LMS's performance when processing sparse input data may be robust even when the transmit waveform's spectrum is notched, while results from other algorithms (including conventional LMS) noticeably degrade. These simulation results prompt future research to extend the contribution documented herein by deriving the steady-state theoretical output SNR when processing sparse colored Gaussian noise input data using L1 LMS.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons