Probing signal waveforms play a central role in the signal processing performance of a multiple-input multiple-output (MIMO) radar. In practice, for a given desired beam pattern, we need to design a probing signal waveform whose beam pattern closely matches the desired one and whose autocorrelation and cross-correlation sidelobes are kept low. The latter properties are important to mitigate undesirable interference caused by multiple targets or scatterers. In this correspondence, we present an efficient optimization method to design a constant modulus probing signal which can synthesize a desired beam pattern while maximally suppressing both the autocorrelation and cross-correlation sidelobes at/between given spacial angles. We formulate this problem as an unconstrained minimization of a fourth order trigonometric polynomial and propose an efficient quasi-Newton iterative algorithm to solve it. Besides, we provide an analysis of the local minima of the fourth-order trigonometric polynomial and prove that any local minima is a 1/2-approximation of its global optimal solution. Numerical examples show that the proposed approach compares favorably with the existing approach.
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Manuscript received June 06, 2011; revised November 17, 2011 and February 03, 2012; accepted April 10, 2012. Date of publication May 03, 2012; date of current version July 10, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Visa Koivunen. Y.-C. Wang started this work while he was a postdoctoral fellow at the University of Minnesota. This research is supported in part by the National Key Science Technology Project, Grant. 2011ZX03004-001-01, Research Fund of ISN Lab., Grant ISN1102004, the Fundamental Research Funds for the Central Universities, Grant K50510010009, and by the 111 Project, Grant B08038. The research of Z.-Q. Luo is supported in part by the National Science Foundation, Grant DMS-1015346.
- Beam pattern
- constant modulus probing signal
- multiple-input multiple-output (MIMO) radar
- spatial auto/cross-correlation