Low Correlation Zone Research Articles

Effective and efficient gradient based methods for low-bit discrete-phase sequence designs

We devise effective and efficient gradient based methods to design low-bit, including binary (one-bit per sample, or 1b) and quaternary (two-bit per sample, or 2b), discrete-phase sequences without or with low correlation zone (LCZ) requirements. We determine proper step sizes needed by the gradient based algorithms to monotonically decrease the optimization metric via efficient line search techniques for aperiodic and periodic low-bit discrete-phase sequence designs. Moreover, we introduce approximate gradient based approaches to reduce the autocorrelation sidelobes when the desired LCZ is relatively large. Numerical examples are provided to show that the proposed gradient based algorithms can outperform the state-of-the-art algorithms for designing 1b and 2b sequences with good autocorrelation properties.

A Learning-Inspired Strategy to Design Binary Sequences With Good Correlation Properties: SISO and MIMO Radar Systems

In this paper, the design of binary sequences exhibiting low values of aperiodic/periodic correlation functions, in terms of Integrated Sidelobe Level (ISL), is pursued via a learning-inspired method. Specifically, the synthesis of either a single or a burst of codes is addressed, with reference to both Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) radar systems. Two optimization machines, referred to as two-layer and single-layer Binary Sequence Correlation Network (BiSCorN), able to learn actions to design binary sequences with small ISL/Complementary ISL (CISL) for SISO and MIMO systems are proposed. These two networks differ in terms of the capability to synthesize Low-Correlation-Zone (LCZ) sequences and computational cost. Numerical experiments show that proposed techniques can outperform state-of-the-art algorithms for the design of binary sequences and Complementary Sets of Sequences (CSS) in terms of ISL and, interestingly, of Peak Sidelobe Level (PSL).

On Properties of Periodic Binary Sequences in the Presence of System Non-Linearities

Phase-modulated continuous-wave (PMCW) radar systems possess inherent interference mitigation capabilities and can be useful for many civilian applications including autonomous driving. For PMCW radar systems, binary sequences with good autocorrelation properties are used as probing sequences due to their low cost to generate in practical hardware systems. However, the non-linearity (NL) suffered by practical PMCW radar systems can produce undesirable cross-products and distort the receiver matched filter outputs. The purpose of this paper is to investigate the properties of the well-known periodic binary almost perfect autocorrelation sequences (APAS) under NL conditions, including even-order and odd-order NL conditions. We also consider designing long binary periodic sequences with low autocorrelation sidelobes within a low correlation zone (LCZ) using a computational algorithm. The computationally optimized sequences (COS) do not suffer from sequence length restrictions and offer much higher diversity than their APAS counterparts. We compare COS with APAS under NL conditions. We show that both types of sequences can be used to avoid ghost peaks in the range profiles under NL conditions.

Quasi-Orthogonal Z-Complementary Pairs and Their Applications in Fully Polarimetric Radar Systems

One objective of this paper is to propose a novel class of sequence pairs, called “quasi-orthogonal Z-complementary pairs (QOZCPs)”, each depicting Z-complementary property for their aperiodic auto-correlation sums and also having a low correlation zone when their aperiodic cross-correlation is considered. Construction of QOZCPs based on Successively Distributed Algorithms under Majorization Minimization (SDAMM) is presented. Another objective of this paper is to apply the proposed QOZCPs in fully polarimetric radar systems and analyse the corresponding ambiguity functions. It turns out that QOZCP waveforms are much more Doppler resilient than the known Golay complementary waveforms.

A Tighter Correlation Lower Bound for Quasi-Complementary Sequence Sets with Low Correlation Zone

Inspired by an idea due to Levenshtein, we apply the low correlation zone constraint in the analysis of the weighted mean square aperiodic correlation. Then we derive a lower bound on the measure for quasi-complementary sequence sets with low correlation zone (LCZ-QCSS). We discuss the conditions of tightness for the proposed bound. It turns out that the proposed bound is tighter than Liu-Guan-Ng-Chen bound for LCZ-QCSS. We also derive a lower bound for QCSS, which improves the Liu-Guan-Mow bound in general.

Overcoming 5G PRACH Capacity Shortfall: Supersets of Zadoff–Chu Sequences With Low-Correlation Zone

5G physical random access channel (PRACH) will use new preamble formats based on short Zadoff-Chu (ZC) sequences to enable new use cases. These formats result however in a PRACH capacity shortfall where the number of sequences available for network planning may just be enough to support few cells without sequence reuse. To overcome this issue, two enlarged constant-amplitude sequence constructions that include ZC sequences, and thus being backward-compatible with the current 5G PRACH design, are presented. Both constructions feature a desirable subset structure from which follows a natural cellular network sequence allocation where each cell-specific sequence subset has a controllable low-correlation zone similar to ZC sequences, and thus enables a similar detection performance inside a cell. The two extensions are meanwhile structurally different and offer different network allocations, as for one, new sequences are distributed among all cells, while for the other, they are in separated cells. With both proposed supersets and the new 5G PRACH formats, hundred-times more cells without sequence reuse can be supported compared to ZC sequences for a moderately larger inter-cell correlation than intra-cell correlation. Simulation results confirm that using the proposed supersets instead of reusing sequences in the network can significantly improve detection performance.

Doppler Sensitive Discrete-Phase Sequence Set Design for MIMO Radar

We consider the design of sets of discrete-phase, including binary/quaternary, sequences for phase-modulated continuous-wave multiple-input multiple-output radar in the presence of nonnegligible Doppler shift. We consider the peak sidelobes of auto- and cross-correlations in a desired interval of the Doppler shift as the performance metric of the design. Then, the design problem is formulated via imposing the discrete-phase constraint for each element of the sequences, with emphasis on binary as well as quaternary cases. This problem is nonconvex and hence hard to solve. We introduce a method based on the block coordinate descent framework to solve the optimization problem. We also modify the proposed method to efficiently update the subproblem associated with each iteration. Also, we extend it to account for only a low-correlation zone in the presence of Doppler shift. Numerical examples are provided to illustrate the effectiveness and performance of the proposed algorithm in comparison with the existing methods.

Binary Complementary Sequence Set With Low Correlation Zone

Recently, quasi-complementary sequence sets (QCSSs) including low correlation zone complementary sequence sets (LCZ-CSSs), and low correlation complementary sequence sets (LC-CSSs) have raised lots of concerns. According to the theoretical bounds, the set size of a QCSS is much larger than that of a traditional perfect complementary sequence set (PCSS). As a result, it is believed that QCSSs have potential applications in multi-carrier code-division multiple-access (MC-CDMA) systems to support more users. As binary sequences are desired in practice because of easier realization, we consider the design of binary QCSSs with large set size in this letter. A construction of aperiodic binary LCZ-CSSs is proposed, which leads to aperiodic binary LCZ-CSSs with asymptotically optimal parameters. Additional, aperiodic binary LC-CSSs with asymptotically optimal parameters can also be derived from the proposed construction.

Constructions of Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets

Mutually orthogonal complementary codes have found many practical applications in wireless communications owing to their perfect correlation properties. However, the set size of a mutually orthogonal complementary code set (MOCCS) is upper bounded by the number of constituent sequences in each complementary code. As a result, the number of users in the communication system is limited. To overcome this limitation, quasi-complementary sequence sets (QCSSs) were proposed, which include low correlation zone complementary sequence sets (LCZ-CSSs) and low correlation complementary sequence sets (LC-CSSs). In this paper, aperiodic quasi-complementary sequences are our main interest. Constructions of aperiodic LC-CSSs and aperiodic LCZ-CSSs over the complex roots of unity are proposed. With these constructions, asymptotically optimal aperiodic QCSSs can be obtained.

Bounds and constructions of optimal optical orthogonal codes with low correlation zone

Bounds and constructions of optimal optical orthogonal codes with low correlation zone

Millimeter-Wave Phase-Coded CW MIMO Radar Using Zero- and Low-Correlation-Zone Sequence Sets

A phase-coded continuous-wave multiple-input multiple-output (MIMO) radar based on code division multiplexing is presented. Zero-correlation-zone (ZCZ) and low-correlation-zone (LCZ) sequence sets are used to separate signals from multiple transmitters at the receivers. In particular, we investigate three different sequence set types: an equidistantly shifted almost-perfect autocorrelation sequence set, sequence sets based on mutually orthogonal Golay complementary sets, and a binary LCZ sequence set. The required sequence lengths are discussed according to the physical propagation behavior in a radar sensor scenario. Furthermore, we summarize the theoretical limitations of LCZ/ZCZ sequence sets and provide examples with regard to the chosen scenario. We present measurements carried out with a software-defined radar platform, which is equipped with 16 MIMO channels operating at a frequency of 77 GHz. We investigated the behavior of the sequence sets on real hardware in the range, cross-range, and range-Doppler domains.

New constructions of quaternary low correlation zone sequence sets

Sequence sets with low correlation have very important applications in modern communication systems. As in quasi-synchronous code-division multiple access (QS-CDMA) system, sequence sets with low correlation zone (LCZ) perform better than other well-known sequence sets. Furthermore, binary or quaternary sequence sets are preferred because of their easy implementation. In this paper, based on the inverse Gray mapping and special binary sequence pairs, new quaternary LCZ sequence sets were constructed. In the LCZ, the maximum of the nontrivial autocorrelation and crosscorrelation values is 1 which show that the QS-CDMA system used the new sequences sets can control the interference in a very low level.

Sequence Design to Minimize the Weighted Integrated and Peak Sidelobe Levels

Sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems. In this paper, we consider the problem of minimizing the weighted integrated sidelobe level (WISL), which can be used to design sequences with impulse-like autocorrelation and zero (or low) correlation zone. Two algorithms based on the general majorization-minimization method are developed to tackle the WISL minimization problem and the convergence to a stationary point is guaranteed. In addition, the proposed algorithms can be implemented via fast Fourier transform (FFT) operations and thus are computationally efficient, and an acceleration scheme has been considered to further accelerate the algorithms. Moreover, the proposed methods are extended to optimize the $\ell_{p}$-norm of the autocorrelation sidelobes, which lead to a way to minimize the peak sidelobe level (PSL) criterion. Numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller PSL compared with some well known analytical sequences.

2-Adic complexity of binary sequences with interleaved structure

In this paper, 2-adic complexity of some binary sequences with interleaved structure is investigated. Firstly, 2-adic complexity of low correlation zone (LCZ) sequences constructed by Zhou et al. [23] is completely determined. We show that their 2-adic complexity could attain the maximum if suitable parameters are chosen. Secondly, we also determine 2-adic complexity of optimal autocorrelation sequences constructed by Tang and Ding [16]. Results show that they have the maximum 2-adic complexity.

Linear complexity of binary sequences with interleaved structure

In this study, the minimal polynomials and the linear complexity of interleaved binary sequences are investigated. Both the linear complexity and the minimal polynomials of low correlation zone sequences constructed by Zhou et al. are completely determined. Besides, an open problem proposed by Li and Tang is discussed. At last, a sufficient condition and a necessary condition are presented about when the linear complexity of the interleaved sequences constructed by Tang et al. attains the maximum.

A generic construction of low correlation zone sequences based on interleaved technique

Low correlation zone (LCZ) sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, a generic construction of LCZ sequences based on interleaved technique is investigated. Firstly, the shift sequence is shown to correspond to two-tuple balanced d -form function essentially, which results in new shift sequence. Secondly, an optimal design of p 2 -ary sequences over the integer residue class ring Z p 2 is proposed, which improves the previous construction when p is an odd prime.

A New Method for Constructing Quaternary Sequence Sets with Low Correlation Zone

A method of constructing multiple quaternary low correlation zone (LCZ) sequence sets with the same parameters is proposed. Two mappings which can map two binary variables to a quaternary one are presented. Based on different mappings, new quaternary LCZ sequence sets are constructed. Furthermore, based on the same mapping, the parameters of shift sequences are changed to extend the number of LCZ sequence sets and there is only one shift equivalent sequence from different sets. The parameters of the LCZ sequence sets can be flexibly chosen. Compared with previous methods, the proposed construction extends the number of quaternary LCZ sequence sets. As a result, more spreading sequences are provided for multi-cell quasi-synchronous code-division multiple-access systems.

New construction of perfect sequence set and low correlation zone sequence set

For a given binary ideal autocorrelation sequence, we construct a perfect sequence set by changing a few bits of the sequence. The set has a large size with respect to the period of its sequences. Based on the constructed perfect sequence set, a new class of low correlation zone sequence sets whose low correlation zone length can be chosen flexibly is obtained. Moreover, the new constructed low correlation zone sequence sets can attain Tang-Fan-Matsufuji’s bound with suitably chosen parameters.

Construction of Shift Distinct Sequence Sets with Zero or Low Correlation Zone

A construction of shift sequence sets is proposed. Multiple distinct shift sequence sets are obtained by changing the parameters of the shift sequences. The shift sequences satisfy the conditions that P|L and P ≥ 2, where P is the length of the shift sequences, L is the length of the zero-correlation zone or low-correlation zone (ZCZ/LCZ). Then based on these shift sequence sets, many shift distinct ZCZ/LCZ sequence sets are constructed by using interleaving technique and complex Hadamard matrices. Furthermore, the new construction is optimal under the conditions proposed in this paper. Compared with previous constructions, the proposed construction extends the number of shift distinct ZCZ/LCZ sequence sets, so that more sequence sets are obtained for multi-cell quasi-synchronous code-division multiple access (QS-CDMA) systems.

Computational Design of Sequences With Good Correlation Properties

In this paper, we introduce a computational framework based on an iterative twisted approximation (ITROX) and a set of associated algorithms for various sequence design problems. The proposed computational framework can be used to obtain sequences (or complementary sets of sequences) possessing good periodic or aperiodic correlation properties and, in an extended form, to construct zero (or low) correlation zone sequences. Furthermore, as constrained (e.g., finite) alphabets are of interest in many applications, we introduce a modified version of our general framework that can be useful in these cases. Several applications of ITROX are studied and numerical examples (focusing on the construction of real-valued and binary sequences) are provided to illustrate the performance of ITROX for each application.