Design of Optimized Radar Codes With a Peak to Average Power Ratio Constraint

Abstract

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 non-convex 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

MERIT: A monotonically error-bound improving technique for unimodular quadratic programming

“…This type of behavior, which is not unexpected, is due to the fact Table 2. Comparison of the performance of MERIT (see Table 1) and SDR [22] when solving the UQP for 20 random positive definite matrices of different sizes n and ranks d.…”

“…Note that, in general, the provided sub-optimality guarantees γ are considerably larger than π/4 of SDR. We also employ SDR [22] to solve the same UQPs. In this example, we continue the randomization procedure of SDR until reaching the same UQP objective as for MERIT.…”

“…Studies on polynomial-time (or efficient) algorithms for UQP have been extensive (e.g. see [9]- [22] and the references therein). In particular, the semi-definite relaxation (SDR) technique has been one of the most appealing approaches to the researchers.…”

MIMO Radar Transmit Beampattern Design with PAR constraint in a Spectrally Crowded Environment

“…In this case, the rank-one relaxation in problem 2 P is tight and the solution ★ x is optimal. Otherwise, a suboptimal procedure can be adopted following the proposed algorithm in [18]. Interested readers can refer to [18] for more details, we will present the synthesis algorithm in the sequel to make the letter self-contained.…”

“…Hence, the semidefinite relaxation (SDR) is used to solve this nonconvex QCQP problem in polynomial time. Then, with the optimized covariance matrix, the final transmit waveforms which satisfy those practical constraints can be synthesized directly through the randomization procedure [18]. Finally, some interesting case studies are analyzed to assess the performance of the proposed algorithm.…”