Design of optimized radar codes with a peak to average power ratio constraint

Antonio De Maio, Yongwei Huang, Marco Piezzo, Shuzhong Zhang, Alfonso Farina

Research output: Contribution to journalArticlepeer-review

167 Scopus citations


This paper considers the problem of radar waveform design in the presence of colored Gaussian disturbance under a peak-to-average-power ratio (PAR) and an energy constraint. First of all, we focus on the selection of the radar signal optimizing the signal-to-noise ratio (SNR) in correspondence of a given expected target Doppler frequency (Algorithm 1). Then, through a max-min approach, we make robust the technique with respect to the received Doppler (Algorithm 2), namely we optimize the worst case SNR under the same constraints as in the previous problem. Since Algorithms 1 and 2 do not impose any condition on the waveform phase, we also devise their phase quantized versions (Algorithms 3 and 4, respectively), which force the waveform phase to lie within a finite alphabet. All the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints. We prove that these problems are NP-hard and, hence, introduce design techniques, relying on semidefinite programming (SDP) relaxation and randomization as well as on the theory of trigonometric polynomials, providing high-quality suboptimal solutions with a polynomial time computational complexity. Finally, we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to Doppler shifts.

Original languageEnglish (US)
Article number5732713
Pages (from-to)2683-2697
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number6
StatePublished - Jun 2011


  • Approximation bound
  • nonconvex quadratic optimization
  • nonnegative trigonometric polynomials
  • radar waveform design
  • randomized algorithm
  • semidefinite programming relaxation
  • waveform diversity


Dive into the research topics of 'Design of optimized radar codes with a peak to average power ratio constraint'. Together they form a unique fingerprint.

Cite this