Publication Date


Document Type


Committee Members

Arnab Shaw (Advisor), Joshua Ash (Advisor), Steve Gorman (Committee Member), Brian Rigling (Committee Member), Marty Emmert (Committee Member)

Degree Name

Doctor of Philosophy (PhD)


Direction of Arrival (DoA) estimation of chirp sources has many applications in radar, sonar and medical imaging. This work considers DoA and parameter estimation of wide- band chirp sources by the use of Discrete Chirp Fourier Transform (DCFT), its Compres- sive Sensing formulation (CS-DCFT) and Distributed CS. DCFT is similar to traditional Discrete Fourier Transform (DFT) but with chirp ba- sis and two-dimensional search over chirp rate and chirp frequency. For chirp parame- ters estimation, the proposed Compressive Sensing (CS) formulation uses the parametric DCFT basis to achieve superior estimator performance in polynomial time using Orthog- onal Matching Pursuit (OMP) for fast recovery. Simulation results show superior perfor- mance as compared to original DCFT. For chirp DOA estimation, three different wide band chirp-model based DoA algo- rithms have been proposed. The first approach is a novel idea utilizing CS-DCFT for DOA parameter estimation where frequency-shift is used instead of typical phase shifts to measure the signal time-delays between sensors. Mathematical formulation of this new approach has been given, and the effectiveness has been studied via simulation. The pro- posed novel frequency-shift based approach eliminates certain limitations that arise due to phase ambiguity such as, Nyquist spatial sampling, which in turn limits the DoA resolution to theoretical Rayleigh limit. This is because in this case, the distance between sensors can be increased to more than Nyquist spatial sampling criteria limits because the estimation process is not affected by phase ambiguity. The proposed approach eliminates the need for correlation, iterations, time-frequency analysis, and θ-quantization. Comparison with well- established DoA algorithms has been performed via simulations and it has shown superior performance. The second DoA algorithm is formulated in the typical array signal processing form of solving Ax = b, where A is the steering matrix as defined in all classical DoA techniques except, the steering vectors are defined specifically for chirp sources considered in this work. Our steering matrix is a function of unknown chirp parameters, f, β and θ. Results showed better performance when compared with that of the first algorithm. The third algorithm is meant for DoA estimation in active signaling scenario, where prior knowledge of f and β are assumed to be available as would be the case in active signaling. It can be considered as chirp transforms across the spatial array and this feature helped to achieve single snapshot DoA estimation, a result that would be important for real time DoA and/or energy saving mode applications. For distributed-CS, a fourth DoA Algorithm has been developed by utilizing the dis- tributed network principle, where a new message passing (sum, count) distributed algo- rithm was introduced. A new CS-recovery algorithm, named distributed-GAMP, was de- veloped and implemented. Simulation results show excellent performance and convergence compared to the original algorithms. For this case also, it is possible to estimate DoAs with a single measurement per sensor, and results showed accurate DoA estimation. The distributed-CS algorithm developed in this part of the work can be used in other parallel processing and wireless sensor network applications as well as in the case of fusion center absence, or if communication to/from a fusion center is costly or unsecured.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons