The performance of conventional polyphase pulse compression codes such as the Frank, Frank-Zadoff-Chu (FZC), P1, P2, P3, P4, and Px codes will be compared with Oppermann codes. While the majority of the former code classes focus on radar applications, Oppermann codes have been discussed only within the context of code-division multiple-access (CDMA) systems. In this paper, we therefore consolidate findings on the conventional codes and extend the performance assessment to Oppermann codes by accounting for Doppler shifts as needed in radar applications. It is shown that Oppermann codes can conceptually support integrated radar and communication systems as compared to the P1, P2, P3, P4, and Px codes where this is not readily feasible. The numerical results given here illustrate that Oppermann codes outperform Px codes in the presence of Doppler shifts as supported by the ambiguity function.

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.

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.

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.

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.

The cross-ambiguity function (CAF) relates to the correlation processing of signals in radar, sonar, and communication systems in the presence of delays and Doppler shifts. It is a commonly used tool in the analysis of signals in these systems when both delay and Doppler shifts are present. In this chapter, we aim to tackle the CAF synthesization problem such that the synthesized CAF approximates a desired CAF. A CAF synthesization problem is addressed by jointly designing a pair of waveforms using a metaheuristic approach based on the echolocation of bats. Through four examples, it is shown that such an approach can be used as an effective tool in synthesizing different types of CAFs.