Efficient gradient method for locally optimizing the periodic/aperiodic ambiguity function

Algorithms for Designing Unimodular Sequences with High Doppler Tolerance for Simultaneous Fully Polarimetric Radar

“…The requirements of Doppler tolerance, autocorrelation and cross-correlation properties make the optimization problem difficult. This paper extends the approaches in [19] and proposes new cyclic algorithms for designing sequences with good correlation properties and Doppler tolerance. The rest of this paper is organized as follows: Section 2 presents the problem formulation; in Section 3, the Cyclic Algorithm-Gradient I (CAGI) and Cyclic Algorithm-Gradient II (CAGII) algorithms are introduced to design the sequences with good properties; the numerical examples are provided in Section 4 to verify the performance of the proposed algorithms, followed by the conclusions in Section 5.…”

“…In other words, even if the velocity of the target is low, the output of the matched filters will still significantly deteriorate compared with the processing results of the static target’s echoes. In a recent work, an efficient gradient algorithm has been proposed to optimize the autocorrelation property of the sequences in different Doppler shift [19]. However, this algorithm cannot optimize the cross-correlation properties of the sequences, which is important for the measurement of simultaneous polarimetric radar as mentioned before.…”

“…However, this algorithm cannot optimize the cross-correlation properties of the sequences, which is important for the measurement of simultaneous polarimetric radar as mentioned before. Cui et al [20] proposed an accelerated iterative sequential optimization (AISO) algorithm that can minimize the ISL of the autocorrelation function in different Doppler shift of interest and reduce the computations compared with the algorithm in [19]. However, the AISO algorithm also does not consider the optimization of the cross-correlation properties of the sequences.…”

“…In addition, Doppler tolerant complementary code sets are also developed these days because of their potential of making all the autocorrelation side-lobes sum to zero, at least in theory, but the orthogonality of the complementary sequences are not considered in most articles [21,22]. In addition, the Doppler frequency in [19,20] is considered to be a constant in one PRT, which means that the target is assumed to be in a uniform rectilinear motion state. However, the instantaneous acceleration of maneuvering targets, such as missile and spacecraft, can reach 10 g ( g is the gravitational acceleration).…”

Optimization of the Radar Ambiguity Function-Application to Chaotic Sequences: Invited Paper

“…In radar systems the search for transmitted waveforms leading to the "best possible" ambiguity function, particularly in terms of low side lobes, has already been addressed in the literature [1], [2]. In some works the considered waveforms are defined by a set of sequences; these works aim to design good waveforms by synthesizing sequences having suitable autoand cross-correlation functions [3], [4], [5], [6], [7]. However, the ambiguity function also depends on parameters concerning the shaping pulse, the geometry of the transmission antenna array and the targets angles of arrival.…”