Maximum Autocorrelation Sidelobe Research Articles

Constant Modulus MIMO Radar Waveform Design via Iterative Optimization Network Method

Constant modulus (CM) waveform design with good auto- and cross- correlation properties is the key issue in the multiple-input multiple-output (MEMO) radar systems. The problem is non-convex and NP-hard, due to the CM constraint and the nonconvex objective function. Most existing methods solve this problem by relaxation (relaxing CM costrint or the objective function) or directly designing phase, which degrade the performance or need huge computational cost. To address these issues, an unsupervised double Iterative Optimization Network (ION) method is proposed, by using the strong non-linear mapping ability of the deep learning network. The outer iteration updates the input waveform, and the inner iteration optimizes the waveform through the residual network. Compared with the existing methods, the proposed method has lower sidelobe in both the weighted maximum autocorrelation sidelobe (WMAS) and the weighted maximum crosscorrelation sidelobe (WMCS) with less computational cost.

Lower Bounds on the Hamming Auto- and Cross Correlations of Frequency-Hopping Sequences

Frequency hopping (FH) sequences have found wide applications in various modern FH spread-spectrum communications and radar systems. In FH spread-spectrum communications, the interference occurs when two distinct transmitters use the same frequency simultaneously. In order to evaluate the goodness of FH sequence design, the Hamming correlation function is used as an important measure. In this correspondence, by considering separately the maximum Hamming autocorrelation sidelobe H/sub a/, and the maximum Hamming cross correlation H/sub c/, several new lower bounds on the size p of the frequency slot set F, the sequence length L, the family size M, and correlation properties are established. The new periodic bounds include the known Lempel-Greenberger bounds as special case when M=2, and are tighter than the Seay bounds under certain conditions when M>2. Furthermore, the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the Lempel-Greenberger bounds and Seay bounds. Besides, the aperiodic FH bounds which have not yet been previously reported are also presented and discussed in this correspondence.

Generalised Sarwate bounds on the aperiodic correlation of sequences over complex roots of unity

General aperiodic correlation bounds named generalised Sarwate bounds are derived, for sequence sets over complex roots of unity with zero or low correlation zone (ZCZ/LCZ), with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum cross-correlation value and the zero or low correlation zone. It is shown that the existing aperiodic binary sequence bounds, such as Sarwate bounds, Welch bounds, Levenshtein bounds, Tang–Fan bounds and Peng–Fan bounds, are only special cases of the presented generalised Sarwate bounds. In addition, the new bounds are also, in general, stronger than the existing aperiodic binary sequence bounds, as well as Boztas aperiodic correlation bounds for normal complex roots-of-unity sequences.

Generalised Sarwate bounds on periodic autocorrelations and cross-correlations of binary sequences

A general periodic correlation bound named generalised Sarwate bound for binary zero or low correlation zone (ZCZ/LCZ) sequence set with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum cross-correlation value and the zero or low correlation zone, are derived. It is shown that all the previous periodic sequence bounds, such as Sarwate bound, Welch bound and Tang-Fan bound, are only special cases of the generalised Sarwate bound.

Aperiodic correlation constraints on large binary sequence sets

The existence of binary sequences with specific aperiodic autocorrelation and cross correlation properties is investigated. Relationships are determined among the size of a sequence set, the length of the sequences n, the maximum autocorrelation sidelobe magnitude \alpha , and the maximum cross correlation magnitude \beta . The principal result is the proof of the existence of sequence sets characterized by certain combinations of n, \alpha , and \beta . The proof makes use of a new lower bound to the expected size of sequence sets constructed according to an explicit random procedure. For large n , the sequence set size is controlled primarily by the cross correlation constraint \beta . Two consequences of the existence theorem are 1) a demonstration that large sequence sets exist for which the maximum autocorrelation sidelobe and cross correlation magnitudes vanish almost as fast as the inverse square root of the sequence length (l/\sqrt{n}); 2) a new proof of the Gilbert bound of coding theory.