# The Radio Link—A tutorial

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What is involved in the engineering of a wireless system? When your mobile phone rings, a set of actions has already been put in motion to allow you to stay effortlessly connected to a vast communication network not dreamed of by your parents. Several disciplines, theoretical studies, technologies, and engineering developments have converged to create this wonder, and it starts with the invisible radio frequency (RF) link connecting your mobile phone to one of the ubiquitous base station towers around your town. To begin our study of wireless systems engineering, we first investigate RF links. The engineering of these connections will introduce the process of systems engineering that will take us through most of the physical system design.

Two fundamental and interrelated design considerations for a wireless communication system are:

• The distance, area, or volume over which the system must meet specified performance objectives, and

• The capacity of the system, as related to the number of users that can be served by the system and the uses to which the system will be put

Note that capacity may be expressed in a number of ways. It may be expressed as the number of simultaneous two-way conversations that can take place, the average data rate available to a user, the average throughput for data aggregated over all users, or in many other ways, each related to the nature of the information being communicated. It should become apparent in later discussions that area and capacity criteria are interdependent from both technical and economic viewpoints. For wireless systems, coverage area and capacity are intimately related to the attributes of the RF link (or, in cellular telephone terminology, the “air interface”), and thus we begin our study with an overview of this type of link.

Most people have experienced the degradation and eventual loss of a favorite broadcast radio station as they drive out of the station’s coverage area. This common experience clearly demonstrates that there are practical limits to the distance over which a signal can be reliably communicated. Intuition suggests that reliable reception depends on how strong a signal is at a receiver and that the strength of a signal decreases with distance. Reception also depends on the strength of the desired signal relative to competing phenomena such as noise and interference that might also be present at a receiver input. In fact, the robustness of a wireless system design strongly depends on the designers’ abilities to ensure an adequate ratio of signal to noise and interference over the entire coverage area. A successful design relies on the validity of the predictions and assumptions systems engineers make about how a signal propagates, the characteristics of the signal path, and the nature of the noise and interference that will be encountered.

Among the many environmental factors systems engineers must consider are how a signal varies with distance from a transmitter in the specific application environment, and the minimum signal level required for reliable communications. Consideration of these factors is a logical starting point for a system design. Therefore, to prepare for a meaningful discussion of system design, we must develop some understanding of how signals propagate and the environmental factors that influence them as they traverse a path between a transmitter and a receiver.

In this chapter we investigate how an RF signal varies with distance from a transmitter under ideal conditions and how the RF energy is processed in the early stages of the receiver. Specifically, we first introduce the concept of path loss or free-space loss, and we develop a simple model to predict the increase in path loss with propagation distance. Afterward, we investigate thermal noise in a receiver, which leads to the primary descriptor of signal quality in a receiver—the signal-to-noise ratio or SNR. This allows us to quantitatively describe the minimum signal level required for reliable communications. We end our discussion with examples of how quantitative analysis and design are accomplished for a basic RF link. In the next chapter we will discuss path loss in a real-world environment and describe other channel phenomena that may limit a receiver’s ability to reliably detect a signal or corrupt the information carried by an RF signal regardless of the signal level.

**Transmitting and Receiving Electromagnetic Waves**

Electromagnetic theory, encapsulated in Maxwell’s equations, provides a robust mathematical model of how time-varying electromagnetic fields behave. Although we won’t deal directly with Maxwell’s equations, our discussions are based on the behavior they predict. We begin by pointing out that electromagnetic waves propagate in free space, a perfect vacuum, at the speed of light c. The physical length of one cycle of a propagating wave, the wavelength ?, is inversely proportional to the frequency f of the wave, such that:

For example, visible light is an electromagnetic wave with a frequency of approximately 600 THz (1 THz = 10^{12} Hz), with a corresponding wavelength of 500 nm. Electric power in the United States operates at 60 Hz, and radiating waves would have a wavelength of 5000 km!

A typical wireless phone operating at 1.8 GHz emits a wavelength of 0.17 m. Obviously, the range of wavelengths and frequencies commonly dealt with in electromagnetic science and engineering is quite vast.

In earlier studies you learned how to use Kirchhoff’s laws to analyze the effects of arbitrary configurations of circuit elements on time-varying signals. A fundamental assumption underlying Kirchhoff’s laws is that the elements and their interconnections are very small relative to the wavelengths of the signals, so that the physical dimensions of a circuit are not important to consider. For this case, Maxwell’s equations reduce to the familiar rules governing the relationships among voltage, current, and impedance. This case, to which Kirchhoff’s laws apply, is commonly called lumped-element analysis. When the circuit elements and their interconnections are comparable in physical size to the signal wavelengths, however, distributed-element or transmission-line analysis must be employed. In such cases the position and size of the lumped elements are important, as are the lengths of the interconnecting wires. Interconnecting wires that are not small compared with a wavelength may in fact be modeled as possessing inductance, capacitance, and conductance on a per-length (distance) basis. This model allows the interconnections to be treated as a network of passive elements, fully possessing the properties of a passive circuit. It also explains the fact that any signal will be changed or distorted from its original form as it propagates through the interconnection in much the same way as any low-frequency signal is changed as it propagates through a lumped-element circuit such as a filter. Furthermore, when a circuit is comparable in size to a signal wavelength, some of the electromagnetic energy in the signal will radiate into the surroundings = unless some special precautions are employed. When such radiation is unintentional, it may cause interference to nearby devices. In some cases, however, such radiation may be a desired effect.

An antenna is a device specifically designed to enhance the radiation phenomenon. A transmitting antenna is a device or transducer that is designed to efficiently transform a signal incident on its circuit terminals into an electromagnetic wave that propagates into the surrounding environment. Similarly, a receiving antenna captures an electromagnetic wave incident upon it and transforms the wave into a voltage or current signal at its circuit terminals.

Maxwell’s equations suggest that for an antenna to radiate efficiently its dimensions must be comparable to a signal wavelength (usually 0.1? or greater). For example, a 1 MHz signal has a wavelength of 300 m (almost 1000 feet). Thus an antenna with dimensions appropriate for efficient radiation at that frequency would be impractical for many wireless applications.

In contrast, a 1 GHz signal has a wavelength of 0.1 m (less than 1 foot). This leads to a practical constraint on any personal communication system; that is, it must operate in a frequency band high enough to allow the efficient transmission and reception of electromagnetic waves using antennas of manageable size.

An electromagnetic wave of a specific frequency provides the link or channel between transmitting and receiving antennas located at the endpoints, over which information will be conveyed. This electromagnetic wave is called a carrier, and as discussed in Chapter 1, information is conveyed by modulating the carrier using a signal that represents the information.

**Isotropic Radiation**

Development of the range equation is greatly facilitated by considering how a signal propagates in free space. By “free space” we mean a perfect vacuum with the closest object being infinitely far away. This ensures that the signal is not affected by resistive losses of the medium or objects that might otherwise reflect, refract, diffract, or absorb the signal. Although describing the propagation environment as free space may not be realistic, it does provide a useful model for understanding the fundamental properties of a radiated signal.

To begin, consider a transmitting antenna with power level Pt at its input terminals and a receiving antenna located at an arbitrary distance d from the transmitting antenna as shown in Figure 2.1. In keeping with our free-space simplification we consider that the transmitter and receiver have a negligible physical extent and, therefore, do not influence the propagating wave. We further assume that the transmitting antenna radiates power uniformly in all directions. Such an antenna is known as an isotropic antenna. (Note that an isotropic antenna is an idealization and is not physically realizable. Neither is an antenna that radiates energy only in a single direction.)

Imagine flux lines emanating from the transmitting antenna, where every flux line represents some fraction of the transmitted power Pt. Since radiation is uniform in all directions, the flux lines must be uniformly distributed around the transmitting antenna, as is suggested by Figure 2.2. If we surround the transmitting antenna by a sphere of arbitrary radius d, the number of flux lines per unit area crossing the surface of the sphere must be uniform everywhere on the surface. Thus, the power density p measured at any point on the surface of the sphere must also be uniform and constant.

Assuming no loss of power due to absorption by the propagation medium, conservation of energy requires that the total of all the power crossing the surface of the sphere must equal Pt, the power being radiated by the transmitter. This total power must be the same for all concentric spheres regardless of radius, although the power density becomes smaller as the radius of the sphere becomes larger. We can write the power density on the surface of a sphere of radius d as (2.2) where p is measured in watts per square meter.

**Example**

Suppose the isotropic radiator of Figure 2.2 is emitting a total radiated power of 1 W. Compare the power densities at ranges of 1, 10, and 100 km.

**Solution**

The calculation is a straightforward application of Equation (2.2), giving the results p = 80 × 10-9 W/m2, 800 × 10-12 W/m2, and 8 × 10-12 W/m2, respectively. There are two things to note from these results. First, the power density numbers are very small. Second, the power density falls off as 1/d2, as expected from Equation (2.2). Obviously transmission range is a very important factor in the design of any communication link.

A receiving antenna located in the path of an electromagnetic wave captures some of its power and delivers it to a load at its output terminals. The amount of power an antenna captures and delivers to its output terminals depends on its effective aperture (area) Ae, a parameter related to its physical area, its specific structure, and other parameters. Given this characterization of the antenna, the power intercepted by the receiver antenna may be written as:

where the r subscript on the antenna aperture term refers to the receiving antenna.

At this point we understand that received power varies inversely as the square of the distance between the transmitter and receiver. Our formulation assumes an isotropic transmitter antenna, an idealization that models transmitted power as being radiated equally in all directions.

For most practical applications, however, the position of a receiver relative to a transmitter is much more constrained, and we seek to direct as much of the power as possible toward the intended receiver. We will learn about “directive” antennas in the next section. Although the design of antennas is a subject for experts, a systems engineer must be able to express the characteristics of antennas needed for specific applications in terms that are meaningful to an antenna designer. Therefore, we discuss some of the concepts, terms, and parameters by which antennas can be described before continuing with our development of the range equation.

**Next: Antenna Radiation Patterns**

Introduction to Wireless Systems By Bruce A. Black, Philip S. DiPiazza, Bruce A. Ferguson, David R. Voltmer, Frederick C. Berry, Published Jun 7, 2011 by Prentice Hall, is reprinted with permission by Pearson Publishing.