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Wideband Signal Delay and Direction of Arrival Estimation using sub-Nyquist Sampling

Chaturvedi, Amal
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416231079

Abstract Details

2014, PhD, University of Cincinnati, Engineering and Applied Science: Electrical Engineering.
This work is dedicated towards finding time delay and the Direction of Arrival (DOA) of Wideband signals impinging on a sensor array using sub-Nyquist sampling. Compressed Sensing or Compressive Sampling (CS) has recently emerged as a breakthrough technique. The strength of CS lies in solving an underdetermined problem with a very high probability and almost no error, provided the solution is sparse. The problem of estimating DOA of sources has been under focus of researchers worldwide. Most of the methods for estimating DOA exist for narrowband signals. Several methods solving the same problem have been proposed for wideband signals where usually the wideband signal is decomposed into multiple frequency bins and the concept of narrowband signals is applied on all the bins. In a sensor array, the time delay between two sensors depends on the position of sources and thus estimating the time delay could be used in finding the Direction of Arrival of the sources. In this research work, I have estimated the time delay between the sensors using the cross-correlation of the signals received at the sensor array to estimate the DOA. The wider the bandwidth of the signal, the sharper will be the peak of its autocorrelation. Thus, it would be safe to say that the autocorrelation of the wideband signal is sparse. This property of sparsity together with the CS reconstruction algorithm is used in this dissertation to solve the underdetermined system of equations to estimate the autocorrelation and hence the DOA of the signals. For sub-Nyquist rate sampling, the architecture of Modulated Wideband Converter\cite{eldar4} is being used. We show that the correlation of sub-Nyquist samples could be used to reconstruct the sparse correlation of Nyquist samples. The peaks in the reconstructed Nyquist correlation are used to estimate the time delay and hence the DOA. Another very important area of research involving time delay estimation is radar. In radar, the receiver receives a time delayed and doppler shifted signal which then samples the received signal at a very high rate. Such high sampling rates put a huge burden on the sampling devices. Assuming there are only a few targets at a time, the radar system could be modeled as a sparse system in the context of time delays and doppler shifts. We show three different methods of doing so. The first method uses a simple dictionary of time and doppler shifted signal. The second method uses a dictionary made of sub-Nyquist correlation terms of the transmitted signal and the signal with all possible time and doppler shifts. An entirely different approach is used in the third method where we get rid of the analog high-rate mixing and shift it to the digital low-rate mixing after sub-Nyquist rate sampling (much simpler and cheaper). In all the methods the known signal is used to create a dictionary with all possible time delays and doppler shifts is created and the greedy CS reconstruction algorithms are used to estimate the delay and doppler shift pair.
H. Howard Fan, Ph.D. (Committee Chair)
James Caffery, Ph.D. (Committee Member)
Donald French, Ph.D. (Committee Member)
William Wee, Ph.D. (Committee Member)
Xuefu Zhou, Ph.D. (Committee Member)
219 p.
Electrical Engineering
Sub-Nyquist Sampling; Compressed Sensing; DOA; Time Delay Estimation; Radar

Recommended Citations

Citations

  • Chaturvedi, A. (2014). Wideband Signal Delay and Direction of Arrival Estimation using sub-Nyquist Sampling [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416231079

    APA Style (7th edition)

  • Chaturvedi, Amal. Wideband Signal Delay and Direction of Arrival Estimation using sub-Nyquist Sampling. 2014. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416231079.

    MLA Style (8th edition)

  • Chaturvedi, Amal. "Wideband Signal Delay and Direction of Arrival Estimation using sub-Nyquist Sampling." Doctoral dissertation, University of Cincinnati, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416231079

    Chicago Manual of Style (17th edition)

ucin1416231079
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This open access ETD is published by University of Cincinnati and OhioLINK.