Wireless communications have seen a remarkably fast technological evolution. Although separated by only a few years, each new generation of wireless devices has brought significant improvements in terms of link communication speed, device size, battery life, applications, etc. In recent years the technological evolution has reached a point where researchers have begun to develop wireless network architectures that depart from the traditional idea of communicating on an individual point-to-point basis with a central controlling base station. Such is the case with ad-hoc and wireless sensor networks, where the traditional hierarchy of a network has been relaxed to allow any node to help forward information from other nodes, thus establishing communication paths that involve multiple wireless hops. One of the most appealing ideas within these new research paths is the implicit recognition that, contrary to being a point-to-point link, the wireless channel is broadcast by nature. This implies that any wireless transmission from an end-user, rather than being considered as interference, can be received and processed at other nodes for a performance gain. This recognition facilitates the development of new concepts on distributed communications and networking via cooperation.

The technological progress seen with wireless communications follows that of many underlying technologies such as integrated circuits, energy storage, antennas, etc. Digital signal processing is one of these underlying technologies contributing to the progress of wireless communications. Perhaps one of the most important contributions to the progress in recent years has been the advent of MIMO (multiple-input multiple-output) technologies.

In this chapter, we present a cooperative protocol based on the relay-selection technique using the availability of the partial channel state information (CSI) at the source and the relays. The main objective of this scheme is to achieve higher bandwidth efficiency while guaranteeing the same diversity order as in a conventional cooperative scheme. Two cooperation scenarios are addressed: a single-relay scenario and a multi-relay scenario. In the single-relay scenario, the focus is to answer the question: “When to cooperate?” The rationale behind this protocol is that there is no need for the relay to forward the source's information if the direct link, between the source and destination, is of high quality. It turns out that an appropriate metric to represent the relay's ability to help is a modified version of the harmonic mean function of its source–relay and relay–destination instantaneous channel gains. The source decides when to cooperate by taking the ratio between the source–destination channel gain and the relay's metric and comparing it with a threshold, which is referred to as the cooperation threshold. If this ratio is greater than or equal to the cooperation threshold, then the source sends its information to the destination directly without the need for the relay. Otherwise, the source employs the relay in forwarding its information to the destination as in the conventional cooperative scheme.

The previous chapter studied the effects and use of cooperation on the multiple access channel. In this chapter we look further into using the properties of the source traffic to improve the efficiency of cooperative multiple access. Because the presentation in this chapter is highly dependent on the characteristics of the source, we will focus on the communication of packet speech. Nevertheless, the main underlying ideas can be extended to other types of sources.

Speech communication has a distinctive characteristic that differentiates it from data communication, which was the main focus of the previous chapter. Speech sources are characterized by periods of silence in between talk spurts. The speech talk–silence patterns could be exploited in statistical multiplexing-like schemes where silent users release their reserved channel resources, which can then be utilized to admit more users to the network. This comes at the cost of requiring a more sophisticated multiple access protocol. One well-known protocol that uses this approach for performance improvement is the packet reservation multiple access (PRMA) protocol [49], which can be viewed as a combination of TDMA and slotted ALOHA protocols. In PRMA, terminals in talk spurts contend for the channel in empty time slots. If a user contends succesfully, then the slot used for contention is reserved for the user. Users with reservations transmit their voice packets in their reserved slots.

In the previous chapters, the gains of cooperative diversity were established under the ideal model of negligible listening and computing power. In sensor networks, and depending on the type of motes used, the power consumed in receiving and processing may constitute a significant portion of the total consumed power. Cooperative diversity can provide gains in terms of savings in the required transmit power in order to achieve a certain performance requirement because of the spatial diversity it adds to the system. However, if one takes into account the extra processing and receiving power consumption at the relay and destination nodes required for cooperation, then there is obviously a tradeoff between the gains in the transmit power and the losses due to the receive and processing powers when applying cooperation. Hence, there is a tradeoff between the gains promised by cooperation, and this extra overhead in terms of the energy efficiency of the system should be taken into consideration in the design of the network.

In this chapter the gains of cooperation under this extra overhead are studied. Moreover, some practical system parameters, such as the power amplifier loss, the quality of service (QoS) required, the relay location, and the optimal number of relays, are considered. Two communications architectures are considered, direct transmission and cooperative transmission. The performance metric for comparison between the two architectures is the energy efficiency of the communication scheme.

In broadband communications, OFDM is an effective means to capture multipath energy, mitigate the intersymbol interference, and offer high spectral efficiency. OFDM is used in many communications systems, e.g., wireless local area networks (WLANs) and wireless personal area networks (WPANs). Recently, OFDM together with time–frequency interleaving across subbands, the so-called multiband OFDM [9], has been adopted in the ultra-wideband (UWB) standard for wireless personal area networks (WPANs).

To improve the performance of OFDM systems, the fundamental concept of cooperative diversity can be applied. Nevertheless, special modulations/cooperation strategies are needed to efficiently exploit the available multiple carriers.

In this chapter, we study an OFDM cooperative protocol that improves spectral efficiency over those based on fixed relaying protocols while achieving the same performance of full diversity. By exploiting limited feedback from the destination node, the described protocol allows each relay to help forward information of multiple sources in one OFDM symbol. We also describe a practical relay assignment scheme for implementing this cooperative protocol in OFDM networks.

System model

In this section, we describe the system model of a wireless network, in which we take into consideration the random users’ spatial distribution. The channel model, the signal model, and the performance measure in term of outage probability are discussed.

We consider an OFDM wireless network such as a WLAN or a WPAN with a circular cell of radius ρ. The cell contains one central node and multiple users, each communicating with the central node.

For practical implementation of cooperative communications in wireless networks, we need to develop protocols by which nodes are assigned to cooperate with each other. In most of the previous chapters on cooperation, the cooperating relays are assumed to exist and are already paired with the source nodes in the network. A deterministic network topology, i.e., deterministic channel gain variances between different nodes in the network, was also assumed. If the random users' spatial distribution, and the associated propagation path losses between different nodes in the network, are taken into consideration, then these assumptions, in general, are no longer valid.

Moreover, it is of great importance for service providers to improve the coverage area in wireless networks without the cost of more infrastructure and under the same quality of service requirements. This poses challenges for deployment of wireless networks because of the difficult and unpredictable nature of wireless channels.

In this chapter, we address the relay assignment problem for implementing cooperative diversity protocols to extend the coverage area in wireless networks. We study the problem under the knowledge of the users’ spatial distribution which determines the channel statistics, as the variance of the channel gain between any two nodes is a function of the distance between these two nodes. We consider an uplink scenario where a set of users are trying to communicate to a base station (BS) or access point (AP) and describe practical algorithms for relay assignment.

In broadband wireless communications, the channel exhibits frequency selectivity (delay spread), resulting in inter-symbol interference (ISI) that can cause serious performance degradation. A mature technique to mitigate the frequency selectivity is to use orthogonal frequency division multiplexing (OFDM), which eliminates the need for high complexity equalization and offers high spectral efficiency. In order to combine the advantages of both the MIMO systems and the OFDM, space–frequency (SF)-coded MIMO-OFDM systems, where two-dimensional coding is applied to distribute channel symbols across space (transmit antennas) and frequency (OFDM tones) within one OFDM block, can be developed to exploit the available spatial and frequency diversity.

If longer decoding delay and higher decoding complexity are allowable, one may consider coding over several OFDM block periods, resulting in space–time–frequency codes to exploit all of the spatial, temporal, and frequency diversity.

The chapter is organized as follows. First, we focus on SF-coded MIMO-OFDM systems in broadband scenario and introduce two systematic approaches to design SF codes to achieve full spatial and frequency diversity within each OFDM block. Then, we consider STF coding for MIMO-OFDM systems, where the coding is applied across multiple OFDM blocks to exploit the spatial, temporal, and frequency diversity available in broadband MIMO wireless communications.

Space–frequency diversity and coding

In this section, we focus on SF-coded MIMO-OFDM systems to achieve the spatial and frequency diversity in broadband wireless communications. First, we specify an SF-coded MIMO-OFDM system model and discuss design criteria for achieving the full spatial and frequency diversity.

Routing is the process of transferring data packets from one terminal to another. Routing aims to find the optimal path according to some criterion. Shortest-path routing is a common scheme used for routing in data networks. It depends on assigning a length to each link in the network. A path made up of a series of links will have a path length equal to the sum of the lengths of the links in the route. Then, it chooses the path between source and destination that has the shortest route. The shortest-path route can be implemented using one of two well-known techniques, namely, the Bellman–Ford algorithm or the Dijkstra's algorithm [11].

In mobile ad hoc networks (MANETs), data packet transmissions between source and destination nodes are done through relaying the data packets by intermediate nodes. Hence, the source needs to locate the destination and set up a path to reach it. There are two types of routing algorithms in MANETs, namely, table-based and on-demand algorithms. In table-based routing algorithms, each node in the network stores a routing table, which indicates the geographic locations of each node in the network. These routing tables are updated periodically, through a special HELLO message sent by every node. Table-based routing protocols for MANETs include the destination sequence distance vector routing protocol (DSDV), wireless routing protocol (WRP), and cluster-head gateway switch routing (CGSR). The periodical updating of the routing tables makes table-based routing algorithms inefficient.

In the preceding chapter, the surface wave band gap of EBG structures was used to enhance the performance of microstrip patch antennas. Another important property of EBG structures is the phase response to the plane wave illumination, where the reflection phase changes from 180° to −180° as the frequency increases. In this chapter, we utilize this property to improve the radiation efficiency of wire antennas near a ground plane. Consequently, a novel type of low profile antennas referred to as wire-EBG antennas is proposed [1–2]. A series of design examples are illustrated with diverse radiation characteristics.

Dipole antenna on EBG ground plane

Comparison of PEC, PMC, and EBG ground planes

In wireless communications, it is desirable for antennas to have a low profile configuration. In such a design, the overall height of the antenna structure is usually less than one tenth of the operating wavelength. A fundamental challenge in low profile wire antenna design is the coupling effect of a nearby ground plane.

To illustrate this effect, let's examine the performance of a simple dipole antenna near three different ground planes, namely, perfect electric conductor (PEC), perfect magnetic conductor (PMC), and electromagnetic band gap (EBG) ground planes, as shown in Fig. 6.1. The dipole is horizontally positioned in order to achieve a low profile configuration [3–4]. The dipole length is 0.40 λ12 GHz and its radius is 0.005 λ12 GHz, while λ12 GHz, the free space wavelength at 12 GHz, is used as a reference length to define the physical dimensions of the antenna, ground plane, and EBG structure.

After demonstrating some interesting characteristics of EBG structures, this chapter focuses on how to achieve these characteristics by properly designing the EBG structures. A parametric study on the mushroom-like EBG structure will be presented first. Then two popularly used planar EBG structures, mushroom-like EBG surface and uni-planar EBG surface, are compared with each other to develop some selection guidelines for potential applications. Novel EBG designs such as polarization-dependent EBG (PDEBG), compact spiral EBG, and stack EBG structures will also be studied. Furthermore, the particle swarm optimization (PSO) technique is implemented to design EBG surfaces. At the end of this chapter, some recent research trends are summarized, including space filling curve EBG surfaces, multi-band EBG designs and reconfigurable EBG structures.

Parametric study of a mushroom-like EBG structure

Electromagnetic properties of an EBG structure are determined by its physical dimensions. For a mushroom-like EBG structure shown in Fig. 4.1, there are four main parameters affecting its performance [1], namely, patch width W, gap width g, substrate thickness h, and substrate permittivity εr. In this section, the effects of these parameters are investigated one by one in order to obtain some engineering guidelines for EBG surface designs. Note that the vias' radius r has a trivial effect because it is very thin compared to the operating wavelength.

In this study, the FDTD/PBC technique [2–3] is used to characterize the reflection phase of the EBG structure. Normal incidence is considered here.

In recent years, electromagnetic band gap (EBG) structures have attracted increasing interests because of their desirable electromagnetic properties that cannot be observed in natural materials. In this respect, EBG structures are a subset of metamaterials. Diverse research activities on EBG structures are on the rise in the electromagnetics and antenna community, and a wide range of applications have been reported, such as low profile antennas, active phased arrays, TEM waveguides, and microwave filters. We believe that the time is right for a focused book reviewing the state of the art on electromagnetic band gap (EBG) structures and their important applications in antenna engineering.

The goal of this book is to provide scientists and engineers with an up-to-date knowledge on the theories, analyses, and applications of EBG structures. Specifically, this book will cover the following topics:

• a detailed overview of the EBG research history and important results;

• an advanced presentation on the unique features of EBG structures;

• an accurate and efficient numerical algorithm for EBG analysis and an evolutionary optimization technique for EBG design;

• a wealth of examples illustrating potential applications of EBG structures in antenna engineering.

The book is organized into seven chapters and one appendix. Chapter 1 introduces the background and basic properties of EBG structures. The EBG analysis methods and antenna applications are also summarized.

In Chapter 2, the finite difference time domain (FDTD) method is presented with a focus on periodic boundary conditions (PBC), which is used as an efficient computation engine for the analysis of periodic structures.

FDTD fundamentals

Introduction

A fundamental quest in electromagnetics and antenna engineering is to solve Maxwell's equations under various specific boundary conditions. In the last several decades, computational electromagnetics has progressed rapidly because of the increased popularity and enhanced capability of computers. Various numerical techniques have been proposed to solve Maxwell's equations [1]. Some of them deal with the integral form of Maxwell's equations while others handle the differential form. In addition, Maxwell's equations can be solved either in the frequency domain or time domain depending on the nature of applications. The success in computational electromagnetics has propelled modern antenna engineering developments.

Among various numerical techniques, the finite difference time domain (FDTD) method has demonstrated desirable and unique features for analysis of electromagnetic structures [2]. It simply discretizes Maxwell's equations in the time and space domains, and electromagnetics behavior is obtained through a time evolving process. A significant advantage of the FDTD method is the versatility to solve a wide range of microwave and antenna problems. It is flexible enough to model various media, such as conductors, dielectrics, lumped elements, active devices, and dispersive materials. Another advantage of the FDTD method is the capability to provide a broad band characterization in one single simulation. Since this method is carried out in the time domain, a wide frequency band response can be obtained through the Fourier transformation of the transient data.

Because of these advantages, the FDTD method has been widely used in many electromagnetic applications.

Background

Antenna designs have experienced enormous advances in the past several decades and they are still undergoing monumental developments. Many new technologies have emerged in the modern antenna design arena and one exciting breakthrough is the discovery/development of electromagnetic band gap (EBG) structures. The applications of EBG structures in antenna designs have become a thrilling topic for antenna scientists and engineers. This is the central focus of this book.

The recent explosion in antenna developments has been fueled by the increasing popularity of wireless communication systems and devices. From the traditional radio and TV broadcast systems to the advanced satellite system and wireless local area networks, wireless communications have evolved into an indispensable part of people's daily lives. Antennas play a paramount role in the development of modern wireless communication devices, ranging from cell phones to portable GPS navigators, and from the network cards of laptops to the receivers of satellite TVs. A series of design requirements, such as low profile, compact size, broad bandwidth, and multiple functionalities, keep on challenging antenna researchers and propelling the development of new antennas.

Progress in computational electromagnetics, as another important driving force, has substantially contributed to the rapid development of novel antenna designs. It has greatly expanded the antenna researchers' capabilities in improving and optimizing their designs efficiently. Various numerical techniques, such as the method of moments (MoM), finite element method (FEM), and the finite difference time domain (FDTD) method, have been well developed over the years.

Over the last decade, diversified and novel electromagnetic band gap (EBG) structures have appeared in the literature. They exhibit interesting electromagnetic properties, which are not readily available in natural materials. In this chapter, we illustrate these interesting properties of EBG structures. A classification of various EBG structures is also provided.

Resonant circuit models for EBG structures

To more readily understand the operation mechanism of EBG structures, some circuit models have been proposed. Let's start with a simple two-dimensional planar electromagnetic band gap (EBG) structure, as shown in Fig. 3.1. This structure was originally proposed in [1]. The EBG structure consists of four parts: a metal ground plane, a dielectric substrate, periodic metal patches on top of the substrate, and vertical vias connecting the patches to the ground plane. The geometry is similar to the shape of a mushroom.

Effective medium model with lumped LC elements

The parameters of the EBG structure are labeled in Fig. 3.2a as patch width W, gap width g, substrate thickness h, dielectric constant εr, and vias radius r. When the periodicity (W + g) is small compared to the operating wavelength, the operation mechanism of this EBG structure can be explained using an effective medium model with equivalent lumped LC elements, as shown in Fig. 3.2b [2]. The capacitor results from the gap between the patches and the inductor results from the current along adjacent patches.

The concept of surface wave antennas (SWA) was initiated in the 1950s [1–2] and numerous theoretical and experimental investigations have been reported in the literature [3–10]. To support the propagation of surface waves, a commonly used structure in SWA designs is a corrugated metal surface. However, the corrugated structure is thick, heavy, and costly, which may limit the applications of surface wave antennas in wireless communication systems.

In this chapter, novel surface wave antennas are presented. Compared to traditional SWA designs, surface waves are now guided along a thin grounded slab loaded with periodic patches, resulting in a low profile conformal geometry. In contrast to the previous wire-EBG antennas or patch antennas that radiate to the broadside direction, the proposed SWA achieve a monopole-like radiation pattern with a null in the broadside direction. The low profile SWA is more attractive than a traditional monopole antenna that is a quarter-wavelength high.

A grounded slab loaded with periodic patches

Comparison of two artificial ground planes

We start with analyzing a complex artificial ground plane, which will be subsequently used in surface wave antenna designs. Figure 7.1 shows two artificial surfaces: a mushroom-like EBG surface and a grounded dielectric slab loaded with periodic patches. In the latter structure vertical vias are removed, which results in different surface wave properties in the two ground planes.

To compare the electromagnetic properties of these two structures, the finite difference time domain (FDTD) method is used to simulate their performance [11–12].