Low ambiguity zone property of generalized chirp-like sequences under fractional doppler

In radar sensing and communications, designing Doppler resilient sequences (DRSs) with low ambiguity function for delay over the entire signal duration and Doppler shift over the entire signal bandwidth is an extremely difficult task. However, in practice, the Doppler frequency range is normally much smaller than the bandwidth of the transmitted signal, and it is relatively easy to attain quasi-synchronization for delays far less than the entire signal duration. Motivated by this observation, we propose a new concept called low ambiguity zone (LAZ) which is a small area of the corresponding ambiguity function of interest defined by the certain Doppler frequency and delay. Such an LAZ will reduce to a zero ambiguity zone (ZAZ) if the maximum ambiguity values of interest are zero. In this paper, we derive a set of theoretical bounds on periodic LAZ/ZAZ of unimodular DRSs with and without spectral constraints, which include the existing bounds on periodic global ambiguity function as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of sequences against Doppler effect. We then introduce four optimal constructions of DRSs with respect to the derived ambiguity lower bounds based on some algebraic tools such as characters over finite field and cyclic difference sets.

Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic and aperiodic LAZ sequence sets are asymptotically optimal with respect to the periodic and aperiodic lower AF bounds, respectively, which were proposed recently in [IEEE J. Sel. Areas Commun. 40 (6): 1809-1822]. Notably, the aperiodic LAZ sequence sets are the first such sequence sets in the literature that satisfy the bound. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

Low Ambiguity Zone (LAZ) sequences are essential in modern integrated sensing and communication (ISAC) systems. Recently, locally perfect nonlinear functions (LPNFs) have been employed to design LAZ sequences with flexible parameters. In this work, we propose three new classes of LPNFs and use them to construct LAZ sequences that offer additional flexible parameters. Notably, all the proposed LAZ sequences are asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang bounds derived in [IEEE J. Sel. Areas Commun. 40(6), pp. 1809-1822, 2022].

Enhancing Doppler Resilience for Integrated Sensing and Communication Systems through Low Ambiguity Zone Complementary Sequences

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called “oversampled low ambiguity zone (O-LAZ) sequences”. Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

Sequences with low ambiguity zone (LAZ) properties are employed in integrated sensing and communication (ISAC) systems. In this letter, we introduce a new class of LAZ sequence sets based on cubic sequences. The proposed LAZ sequence set is asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang (YZFLLT) bound when the sequence length is odd. Otherwise, it achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sqrt{2}$</tex-math></inline-formula> times of the YZFLLT bound. Furthermore, the sequence sets provide flexible choices for the sequence lengths, set size, and the LAZ region.