This paper deals with the design of coded waveforms which optimize radar performances in the presence of colored Gaussian disturbance. We focus on the class of phase coded pulse trains and determine the radar code which approximately maximizes the detection performance under a similarity constraint with a prefixed radar code. This is tantamount to forcing a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence. We consider the cases of both continuous and finite phase alphabet, and formulate the code design in terms of a nonconvex, NP-hard quadratic optimization problem. In order to approximate the optimal solutions, we propose techniques (with polynomial computational complexity) based on the method of semidefinite program (SDP) relaxation and randomization. Moreover, we also derive approximation bounds yielding a "measure of goodness"of the devised algorithms. At the analysis stage, we assess the performance of the new encoding techniques both in terms of detection performance and ambiguity function, under different choices for the similarity parameter. We also show that the new algorithms achieve an accurate approximation of the optimal solution with a modest number of randomizations.
Bibliographical noteFunding Information:
Manuscript received January 07, 2008; revised September 24, 2008. First published November 7, 2008; current version published January 30, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Daniel P. Palomar. This work was supported in part by the Hong Kong RGC Earmarked Grants CUHK418505 and CUHK418406. The work of Z.-Q. Luo was supported in part by the National Science Foundation by Grant DMS 2416. This work was performed while A. De Maio and S. De Nicola were visiting the Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong.
- Nonconvex quadratic optimization
- Radar signal processing
- Semidefinite program relaxation