In real-world engineering problems, several conflicting objective functions have often to be optimized simultaneously. Typically, the objective functions of these problems are too complex to solve using derivative-based optimization methods. Integration of navigation and radar functionality with communication applications is such a problem. Designing sequences for these systems is a difficult task. This task is further complicated by the following factors: (i) conflicting requirements on autocorrelation and crosscorrelation characteristics; (ii) the associated cost functions might be irregular and may have several local minima. Traditional or gradient based optimization methods may face challenges or are unsuitable to solve such a complex problem. In this paper, we pose simultaneous optimization of autocorrelation and crosscorrelation characteristics of Oppermann sequences as a multiobjective problem. We compare the performance of prominent state-of-the-art multiobjective evolutionary meta-heuristic algorithms to design Oppermann sequences for integrated radar and communication systems. © 2017 IEEE.

Performance of polyphase sequences in radar applications can be evaluated using measures including autocorrelation function, integrated sidelobe ratio (ISLR), and peak-tosidelobe ratio (PSLR). In this paper, we adopt particle swarm optimization to find optimal parameters of Oppermann sequences such that sequences with optimal ISLR and PSLR are generated. This class of sequences has been chosen as it allows to design for a wide range of correlation characteristics by essentially controlling three parameters. A sequence design example is provided in order to illustrate that particle swarm optimization is indeed well-suited to produce optimal sequence designs with respect to the considered performance measures.

The cross-ambiguity function (CAF) is commonly used to analyze the delay-Doppler characteristics of signals in radar, sonar, and communication systems. Accordingly, a CAF relates to the correlation processing of signals in the presence of delays and Doppler shifts. In this paper, we use a metaheuristic approach to address the CAF synthesis problem by jointly designing a pair of waveforms. The CAF of waveforms designed in this way, approximates a desired pre-defined CAF. It turns out that the waveforms designed by this approach have the benefit of low peak-to-average power ratios. Numerical examples are presented to show that nature-inspired metaheuristic algorithms can be used as an effective tool to synthesize different types of CAFs.

A review of metaheuristic algorithms (MAs) is presented. Levy flights (LFs) in the context of global optimization, the Levy distribution, a method to generate random numbers within this distribution are discussed. Subsequently, diversification and intensification in global optimization based on LFs are discussed. Then, MAs using LFs as a search mechanism to solve global optimization problems are presented along with highlighting the differences and similarities of different MAs.

Modern engineering and scientific optimisation problems are becoming complicated. In order to cope with the increasing level of difficulty of these problems, optimisation methods are required to find more than one solution to these problems. The aim of this paper is to gain an insight into the ability of cuckoo search to locate more than one solution for multimodal problems. We also study the performance of this algorithm in the additive white Gaussian noise. Numerical results are presented to show that the cuckoo search algorithm can successfully locate multiple solutions in both non-noise and additive white Gaussian noise with relatively high degree of accuracy.

In this book chapter, we present a comprehensive collection of unconstrained optimization test problems that can be used as a benchmark function to validate and compare different optimization algorithms.

Integration of multiple functions such as navigation and radar tasks with communication applications has attracted substantial interest in recent years. In this chapter, we therefore focus on the waveform optimization for such integrated systems based on Oppermann sequences. These sequences are defined by a number of parameters that can be chosen to design sequence sets for a wide range of performance characteristics. It will be shown that meta-heuristic algorithms are well suited to find the optimal parameters for these sequences. The motivation behind the use of biologically inspired heuristic and/or meta-heuristic algorithms is due to their ability to solve large, complex, and dynamic problems.

The design of integrated radar and communication systems may be based on sets of polyphase sequences such as Oppermann sequences. In this paper, we derive an analytical expression for the cross-ambiguity function of weighted pulse trains with Oppermann sequences. Further, the auto-ambiguity function is deduced from this as a special case. Numerical examples are provided to illustrate the relationship between sequence parameters and performance characteristics.

In this paper, we consider properties of the autoambiguity and cross-ambiguity functions of weighted pulse trains with Oppermann sequences. Several properties are examined and proved which in turn allows for reducing the design space for optimization of a particular design. The insights gained from these properties are consolidated in a formal framework leading to procedures that can be used for a more structured waveform design. Numerical examples are provided to illustrate the relationship between sequence parameters and performance characteristics.

In this paper, we consider the design of integrated radar and communication systems that utilize weighted pulse trains with the elements of Oppermann sequences serving as complex-valued weights. An analytical expression of the ambiguity function for weighted pulse trains with Oppermann sequences is derived. Given a family of Oppermann sequences, it is shown that the related ambiguity function depends only on one sequence parameter. This property simplifies the design of the associated weighted pulse trains as it constrains the degrees of freedom. In contrast to the single polyphase pulse compression sequences that are typically deployed in radar applications, the families considered in this paper form sets of sequences. As such, they readily facilitate also multiple-access in communication systems. Numerical examples are provided that show the wide range of options offered by Oppermann sequences in the design of integrated radar and communication systems.