Waveform techniques for improved delay -Doppler radar measurement

Chieh-Fu Chang, Purdue University

Abstract

This thesis consists of three topics related to the improvement of delay-Doppler resolution in radar measurement systems. In the first topic, we propose techniques for the construction of frequency coding sequences that give rise to frequency coded waveforms having ambiguity functions with a clear area—containing no sidelobes—in a connected region surrounding the main lobe. These constructed sequences are called pushing sequences. Next, two important properties of pushing sequences are investigated: the group D4 dihedral symmetry property and the frequency omission property. Using the group D4 dihedral symmetry property, we show how to construct additional pushing sequences from a given pushing sequence. Using the frequency omission property, we show how to construct pushing sequences of any length N and design proper frequency coded waveforms that meet specific constraints in the frequency domain. We also note that Costas sequences also has the former property while extended sonar sequences have both properties and the implication of this are investigated. Finally, we show how to construct pushing sequences with any desired power using the Lempel T 4 construction and Lee codewords. Because these arbitrary-power pushing sequences constructed using Lee codewords do not have the Costas property, we derive expressions for the pattern of hits in the geometric array. Based on this, the general form of the positions and levels of all the sidelobe peaks are derived. In the second topic, we propose the frequency division multiplexing technique, the clean algorithm and time frequency division multiplexing technique to achieve a delay-Doppler response that approximates the composite ambiguity function. First, the channel estimate based on maximum likelihood estimation (MLE) for each subband of frequency division multiplexing system is provided. Also, the signal to noise power ratio (SNR) needed to achieve the specific variance requirement of the MLE is derived. Next, using the Doppler transformation, we show how to combine the output response of each subband suffering a different Doppler shift effect induced by each different carrier frequency. Then the composite ambiguity function approximation of each target is derived based on the clean algorithm. Finally, the composite ambiguity function approximation of all the targets is obtained and provides a way to resolve initially undetected targets using the recursive procedure. In the third topic, we propose an approach to detect masked targets. First, in terms of computation, the proposed approach implements the CLEAN process efficiently because only a few selective samples are used, instead of all the samples of matched filter response. In some situations that the signal strength and phase need to be estimated, we propose a slightly modified data model so that these parameters and image residues can be estimated simultaneously. Hence the computation complexity is further reduced. Secondly, we provide a hypothesis-test based detector and a quantitative way to select detection samples such that the detection performance is optimized. The selection of residue samples and transmitted waveforms are also investigated.

Degree

Ph.D.

Advisors

Bell, Purdue University.

Subject Area

Electrical engineering

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