Fast algorithm for designing periodic/aperiodic sequences with good correlation and stopband properties

Abstract

Periodic/aperiodic sequences with low autocorrelation sidelobes are widely used in many fields, such as communication and radar systems. Besides the correlation property, the frequency stopband property is often considered in the sequence design when the systems work in a crowded electromagnetic environment. In this paper, we aim at designing periodic/aperiodic sequences with low autocorrelation sidelobes and arbitrary frequency stopbands, and propose an efficient algorithm named FFT (fast Fourier transform)-based conjugate gradient algorithm. To calculate the step size efficiently, a method based on Taylor series expansion is developed. By changing the number of FFT points, the proposed algorithm can be easily used to generate periodic/aperiodic sequences. Since the gradient and step size can be implemented by FFT operations and Hadamard product, the whole algorithm is computationally efficient and can be used to design very long sequences. Numerical experiments show that the proposed algorithm has better performance than the state-of-the-art algorithms in terms of the running time.

A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems

“…As an improvement to these cyclic algorithms, Steepest Descent based Cyclic Algorithm (SDCA) [33] has been proposed although it did only provided marginal speed improvement. In recent years, efficient algorithms aimed at generating unimodular sequences with desired spectral stopbands came into existence such as Lagrange Programming Neural Network (LPNN) [34], Alternating Direction Method of Multipliers (ADMM) [35], Gradient based algorithms [36], [37], Spectral-MISL [26], Fast Fourier Transform based Conjugate Gradient Algorithm (FCGA) [38], Stopband MISL-new (SMISLN) [39], where LPNN applies to periodic sequence design only. In the context of sequence design, there are also research on designing sequences based on binary constraint [40] ,Ambiguity Function [41], similarity [42], Peak to Average Power Ratio constraint [43] and Peak Sidelobe Level (PSL) [29], [44], [45].…”

“…The FCGA algorithm incorporates the Polak-Ribiere-Polyak Conjugate Gradient method and ensures the monotonic minimization of the objective function. In [38], the authors have also introduced a Taylor series expansion based method to deduce a highly accurate step length efficiently at every iteration. Since the phase gradient computation and step length calculation are based on Fast Fourier Transform operations, the overall convergence of the algorithm is quite fast.…”

“…FCGA is one of the state-of-art algorithms compared to other aforementioned contemporary methods. Interested readers may refer to [38] as for the comparison. Lately, a new algorithm Stopband MISL-New (SMISLN) has been proposed which solves the optimization problem via an alternate MM method for deeper suppression of the correlation sidelobes and spectral stopbands [39].…”

“…The few exceptions regarding step length selection are the first m iterations and the iterations where L-BFGS recursion yields an ascent search direction. In these few iterations, we take the standard steepest descent vector (i.e., the negative gradient) and we refer to the Taylor series expansion method in [38] to calculate the step length which is more efficient than the traditional searching methods. Since step length calculation is most often avoided and both the gradient and the step length are derived via Fast Fourier Transform (FFT) operations along with Hadamard products, the proposed LBSD algorithm turns out to be computationally efficient.…”

Frequency domain sequence design algorithm minimising weighted integrated sidelobe level

“…Later on, some computational methods such as evolutionary algorithms [2, 17, 18], heuristic search [19], and stochastic optimisation [20] have been utilised to design sequences with desirable properties. With the aim of generating longer transmit sequences with low‐ISL values; scientists have also been devising both analytic and computational methods [3–6, 9, 10, 17–29]. Since computational complexity of those techniques increases with the length of the designed sequence, computationally more efficient techniques such as cyclic algorithms [1, 6, 9, 28, 30] and majorisation minimisation (MM) methods [3–5, 10, 30] have lately been proposed.…”