TY - JOUR
T1 - Design of optimized radar codes with a peak to average power ratio constraint
AU - De Maio, Antonio
AU - Huang, Yongwei
AU - Piezzo, Marco
AU - Zhang, Shuzhong
AU - Farina, Alfonso
PY - 2011/6
Y1 - 2011/6
N2 - 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.
AB - 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.
KW - Approximation bound
KW - nonconvex quadratic optimization
KW - nonnegative trigonometric polynomials
KW - radar waveform design
KW - randomized algorithm
KW - semidefinite programming relaxation
KW - waveform diversity
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U2 - 10.1109/TSP.2011.2128313
DO - 10.1109/TSP.2011.2128313
M3 - Article
AN - SCOPUS:79957508879
SN - 1053-587X
VL - 59
SP - 2683
EP - 2697
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 6
M1 - 5732713
ER -