A Coordinate-Descent Framework to Design Low PSL/ISL Sequences (1612.05880v1)

Abstract: This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). The problem is formulated as a bi-objective Pareto optimization forcing either a continuous or a discrete phase constraint at the design stage. An iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems which are non-convex and NP-hard in general. Each iteration of the devised method requires the solution of a non-convex min-max problem. It is handled either through a novel bisection or an FFT-based method for the continuous and the discrete phase constraint, respectively. Additionally, a heuristic approach to initialize the procedures employing the lp-norm minimization technique is proposed. Simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase/binary case.

• The paper introduces a coordinate descent framework that minimizes PSL and ISL through a bi-objective Pareto optimization approach.
• It applies novel polynomial-time bisection and FFT-based methods to address continuous and discrete phase constraints in non-convex min-max problems.
• Simulation results show the framework outperforms existing techniques, producing near-optimal binary sequences for favorable autocorrelation properties.

A Coordinate-Descent Framework to Design Low PSL/ISL Sequences

The paper "A Coordinate-Descent Framework to Design Low PSL/ISL Sequences" presents a sophisticated algorithmic framework for the design of phase sequences with favorable autocorrelation properties quantified by Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). This research contributes to the field by addressing the synthesis of constant-modulus sequences within the broader context of waveforms used in communications, radar systems, and electronic warfare applications.

Technical Overview

The authors propose a bi-objective Pareto optimization approach that simultaneously minimizes PSL and ISL metrics. The optimization problem is further divided into continuous and discrete phase constraints, considering the non-convex and NP-hard nature of the resulting problems. To solve these, the paper introduces an advanced algorithm based on the Coordinate Descent (CD) method, which iteratively tackles these optimization problems by solving a sequence of non-convex min-max problems. These problems involve quartic functions, addressed through novel techniques: a polynomial-time bisection method for the continuous phase scenario and an FFT-based method for the discrete phase scenario.

Notably, the paper details a heuristic initialization using an $l_p$-norm minimization method to generate promising starting points for the iterative CD framework. This component enhances convergence to high-quality solutions by intelligently navigating the complex landscape of possible sequences.

Numerical Results and Implications

Simulation results demonstrate that the proposed methodologies can outperform existing techniques, specifically in scenarios involving discrete phase/binary cases. The CD approach is shown to produce sequences with lower PSL and ISL when compared to existing cyclic optimization algorithms and heuristic techniques documented in the literature.

Key numerical evidence underscores the advantages of this approach for generating phase sequences adaptable to diverse operational environments, independent of the signal alphabet size. This is especially pronounced in the discrete phase case, where methodologies like CAN(D) and ITROX were benchmarked. In particular, for binary sequences, the framework achieves PSL values close to the theoretically optimal MPS sequences without exhaustive search, providing practical solutions for codes of longer lengths.

Practical and Theoretical Implications

From a practical standpoint, the research advances the design of waveforms with enhanced autocorrelation characteristics, which are critical in radar waveform design, code-division communication systems, and electronic countermeasures. The versatility and efficiency of the suggested framework for producing sequences with controlled PSL and ISL make it a valuable asset in applications requiring high-resolution range measurements and robust electronic protection.

Theoretically, the work proposes and validates new algorithmic primitives for non-convex optimization, which contribute to ongoing efforts in optimizing phase-coded sequences under computational constraints. It expands existing methodologies by offering a feasible solution with guaranteed convergence properties, especially for PSL minimization, which traditional methods struggle to address due to its non-differentiability and complexity.

Future Directions

Further exploration could examine the Doppler resilience of the synthesized sequences, potentially incorporating ambiguity function considerations. Additionally, constraints such as Peak-to-Average Ratio (PAR) can be integrated into the optimization problem, accommodating requirements specific to power-efficient waveform generation.

Overall, this paper makes a substantial contribution to the waveforms design literature by presenting a comprehensive and adaptable technique for synthesizing phase sequences with improved autocorrelation metrics, serving as a critical foundation for future developments in radar and communication waveform optimization.