This chapter provides an overview of the basic concepts of a radar system. The intent is to give the reader a fundamental understanding of these concepts and to identify the major issues in radar system design and analysis. Later chapters then expand on these concepts.

This chapter includes a discussion of several forms of the radar range equation, including those most often used in predicting radar performance. It begins with forecasting the power density at a distance R and extends to the two-way case for monostatic radar for targets, surface clutter, and volumetric clutter. Then radar receiver thermal noise power is determined, providing the SNR. Equivalent but specialized forms of the RRE are developed for a search radar and then for a tracking radar. Initially, an idealized approach is presented, limiting the introduction of terms to the ideal radar parameters. After the basic RRE is derived, nonideal effects are introduced. Specifically, the component, propagation, and signal processing losses are introduced, providing a more realistic value for the received target signal power.

Though radar systems have many specific applications, radars perform three general functions, with all the specific applications falling into one or more of these general functions. The three primary functions are search, track, and image. The radar search mode implies the process of target detection. Target tracking implies that the radar makes measurements of the target state in range, azimuth angle, elevation angle, and Doppler frequency offset. This is not to exclude the fact that a search radar will perform target measurements to provide a cue for another sensor, for example, or that a track radar will perform the detection process.

This chapter discusses the effects of the transmission medium on the propagation of electromagnetic waves traveling from a radar transmitter to a target and back to the receiver. Many factors can influence the propagating radar signal, such as the composition of the atmosphere, clouds, rain, insects, and obstacles. The wave will also be affected by the ground the wave passes over as well as other topological features, such as hills, valleys, and lakes. This chapter considers only how these topological features affect the propagating wave, while the radar return from these features, known as clutter, are discussed in the next chapter.

Radar clutter is a radar return from an object or objects that is of no interest to the radar mission. For example, the mission of many radar systems is the detection and tracking of targets such as aircraft, ships, or ground vehicles. To these systems, clutter is considered to be an interfering return from a natural object such as precipitation, vegetation, soil and rocks, or the sea. However, to radars designed for remote sensing such as synthetic aperture radar (SAR) imagers, these objects may be the primary targets of interest. For this chapter, it will be assumed that targets of interest are man-made while natural target returns are unwanted (i.e., clutter).

The basic motivation for this chapter is to describe a key link in the understanding of radar: how does a radar wave, more properly known as an electromagnetic (EM) wave, transmitted from some transmitter source, interact with a target to produce reflected energy at some receiver position? The goals for this chapter are as follows: 1. To understand what an electromagnetic wave is. 2. To understand its properties. 3. To describe a measure of the amount of reflected energy, a quantity known as radar cross section (RCS). 4. To understand basic scattering or reflectivity physics. 5. To focus on the typical microwave scattering mechanisms. 6. To understand how two or more scattering centers add and subtract. 7. To illustrate examples of high-frequency scattering from targets along with scattering center images.

A sample of radar data is composed of either interference alone or interference plus target echoes. The interference is, at a minimum, receiver noise and might also include clutter echoes, electromagnetic interference (EMI) from other transmitting sources (e.g., radars, television stations, cellular telephones), and hostile jamming. Most of these interfering signals are noise-like and are therefore modeled as random processes. Occasionally, a target echo will also be present in a particular sample of radar data. One of the major tasks of a radar system is to detect the presence of these targets when they occur. As was seen in Chapter 3, this is generally accomplished by threshold detection. In this chapter, common models for the statistics of target echoes are discussed, with an emphasis on the traditional Swerling models. The effect of these models on radar detection performance is considered in Chapter 15.

Many signal processing techniques used by modern radars take advantage of the differences in the Doppler frequency characteristics of targets, clutter, and noise to minimize the interference competing with the target signals, and thus to improve the probability of detection and the measurement accuracy. Consequently, it is useful to study the Doppler frequency characteristics of typical radar signals. The chapter begins by showing how the Doppler shift predicted by special relativity reduces to the very good standard approximation commonly used in radar, including in this book. The dependence on radial velocity is described. The principal focus of this chapter is on the Doppler spectrum of pulsed radar signals. The spectrum of the received signal for idealized stationary and moving point targets viewed with a finite pulse train waveform is developed step by step with key Fourier transform relationships introduced as required. These results are used to illustrate the concept of Doppler resolution. Attention then shifts to practical measurement of Doppler shift using finite pulse trains and Fourier analysis of the pulse-to-pulse phase shift. In doing so, the idea of coherent detection, first introduced in Chapter 1, is revisited. Finally, the contributions of noise, clutter, and moving targets are described to build an understanding of the range-Doppler or range-velocity distribution as viewed by stationary or moving (airborne or spaceborne) radars. The clutter foldover (ambiguity) effects on this distribution of range and velocity ambiguities are described and illustrated.

In this chapter the primary features of the antenna will be presented, and their effect on performance will be discussed. Operational and performance issues associated with the two most important classes of radar antennas, the reflector and phased array, will be described. Emphasis will not be on antenna design, which is widely covered in the literature, but on salient antenna features and characteristics that every radar engineer should understand.

The radar transmitter subsystem generates the radiofrequency (RF) energy required for the illumination of a remotely situated target of interest. Targets may include aircraft, ships, missiles and even weather phenomena such as rain, snow, and clouds. The radar transmitters described in this chapter includes three basic elements: (1) a radiofrequency oscillator or power amplifier, (PA); (2) a modulator (either analog or digital); and (3) a power supply that provides the high voltages (HVs) and currents typically required in modern radar transmitters. Depending on the specific application, the peak powers generated by the radar transmitter can range from milliwatts to gigawatts. The carrier frequency can range from 3 to 30 MHz (high-frequency [HF] over-the-horizon [OTH] radars) to frequencies as high as 94 GHz (millimeter wave [MMW] radars). However, the majority of today's civilian and military search-and-track radar systems operate in the frequency range from 300 MHz to 12 GHz and typically generate an average power ranging from tens to hundreds of kilowatts. Both thermionic tube-type transmitters and solid-state transmitters are used, depending on the application.

The receiver is an integral part of the radar system. As shown in Figure 11-1, it provides the necessary downconversion of the receive signal from the antenna and the inputs required to the signal and data processors. The advantages and disadvantages of component placement and configurations will be addressed in this chapter. Continuing advances in analog-to-digital converters (ADCs) and digital signal processing (DSP) technology are driving receiver development. As converters improve in speed and resolution, the digitization moves closer to the antenna. Improvements in DSP resolution, speed, and cost are pushing traditional analog receiver functions into the digital domain. While these will be detailed in Chapter 14, some of the main digitization components affecting receivers will be discussed in this chapter. Modern radar receivers are often required to perform a variety of tasks including change of frequency, bandwidth, and gain functions to support the radar modes. These more complex receivers often include digital control networks to select the appropriate receiver depending on the particular radar mode. In addition, these complex receivers often include built-in-test (BIT) functions to enable automated detection of receiver faults.

This chapter is unique in that most radar texts do not have material related to the design characteristics of the coherent radar exciter. Many of the design practices for stable and exciters are proprietary design practices held by the major radar contractors. The technical literature on the exciter technologies of, for example, low phase noise oscillators, low spurious signals, and low timing jitter is found primarily in such periodicals as IEEE Transactions on Microwave Techniques, IEEE Transactions on Aerospace and Electronic Systems, and Proceedings of the IEEE International Frequency Control Symposia.

The signal processor is the portion of the radar system responsible for extracting actionable information about the signal (target, clutter, and jamming) environment from raw radar signals. The signal processor is composed of two major elements: (1) the algorithms that analyze the radar data; and (2) the hardware on which those algorithms are hosted. In this chapter, common approaches to the architecture of radar signal processors are described, along with metrics for evaluating those architectures. The role of both the hardware and the software in determining the effectiveness of a processor is described.

Radar technology was first seriously developed during the 1930s and through World War II. Radar systems evolved to use a variety of signal processing techniques to extract useful information from raw radar echoes. Examples include moving target indication (MTI), signal integration to improve the signal-to-noise ratio (SNR), pulse compression for fine range resolution, and angle and delay estimation for range and angle tracking.

The basic concept of threshold detection was discussed in Chapter 3. Chapter 7 described common statistical models for the target echo power, including both probability distributions and pulse-to-pulse decorrelation models. Chapters 3 and 8 discussed coherent and noncoherent integration of data to improve the signal-to-noise ratio (SNR). In this chapter, these topics are brought together to provide a more detailed look at the optimal detection of fluctuating targets in noise. The analysis shows how the idea of threshold detection arises. The strategy for determining threshold levels and predicting detection and false alarm performance is demonstrated, and specific results are developed for the common Swerling target models. Also discussed are Albersheim's equation (first mentioned in Chapter 3) and Shnidman's equation, both very simple but useful analytical tools for estimating detection performance.

The process of detecting a target begins with comparing a radar measurement with a threshold. Measurements exceeding the threshold are associated with returns from a target, and measurements below the threshold are associated with thermal noise or other interference sources including intentional jamming and background returns from terrain and bodies of water. The detector threshold is selected to achieve the highest possible probability of detection for a given signal-to-noise ratio (SNR) and probability of false alarm. A false alarm occurs when, in the absence of a target, a source of interference produces a measured value that exceeds the detection threshold. A radar system is designed to achieve and maintain a specified probability of false alarm. False alarms drain radar resources by appearing as valid target detections requiring subsequent radar actions and thus degrade system performance. If the statistics of the interference are known a priori, a threshold may be selected to achieve a specific probability of false alarm. In many cases, the form of the probability density function (PDF) associated with the interference is known, but the parameters of the distribution are either unknown or change temporally or spatially. Constant false alarm rate (CFAR) detectors are designed to track changes in the interference and to adjust the detection threshold to maintain a constant probability of false alarm.

Doppler processing refers to the use of Doppler shift information to achieve one or both of two goals. The first is to enable detection of targets in environments where clutter is the dominant interference. The second is to measure Doppler shift, and thus radial velocity, of targets. In this chapter, two general classes of Doppler processing will be discussed: moving target indication (MTI) and pulse-Doppler processing. MTI processing addresses the first goal; pulse-Doppler processing addresses both.

A radar is designed to transmit electromagnetic energy in a format that permits the extraction of information about the target from its echo. Once a target is detected, the next goal is often to precisely locate that target in three-dimensional space, which requires accurate measurements of the distance and angle (both azimuth and elevation) to the target. In addition, it is often desirable to estimate the radar cross section (RCS) and radial velocity of the target as well. In this chapter, some of the common techniques for radar measurements are described, along with factors determining their accuracy and precision. Space limitations preclude considering additional techniques and error sources.

When radar systems are discussed in the literature or the remainder of this text, it is in the context of a sensor providing observations of the environment. While some of those measurements are responses from coherent waveforms of finite duration, the environment is treated as stationary with at most linear motion on the targets. Target tracking addresses the integration of measurements into a longer-term picture as illustrated in Figure 19-1. Target tracking is separated into two parts: track filtering and measurement-to-track data association.

A radar system employing a continuous wave (CW) pulse exhibits a range resolution and signal-to-noise ratio (SNR) that are both proportional to pulse width. SNR drives detection performance and measurement accuracy and is a function of the energy in the pulse. Energy and SNR are increased by lengthening the pulse. Range resolution defines a radar's ability to separate returns in range and is improved by decreasing the pulse width. An undesired relationship, coupled through the pulse width, exists between the energy in a CW pulse and the pulse's range resolution. Near the end of World War II, radar engineers applied intrapulse modulation to decouple the two quantities. Range resolution was shown to be inversely proportional to bandwidth. A waveform's bandwidth could be increased via modulation, achieving finer range resolution without shortening the pulse. Waveforms that decouple resolution and energy via intrapulse or interpulse modulation are termed pulse compression waveforms.

Synthetic aperture radar (SAR) is a combination of radar hardware, waveforms, signal processing, and relative motion that creates photograph-like renderings of stationary targets and scenes of interest. The principal product of any basic SAR implementation is a fine-resolution two-dimensional intensity image of the illuminated scene. SAR is widely employed by the remote sensing community for mapping and land-use surveying and by the military for detection, location, identification, and assessment of fixed targets.

The behavior of electromagnetic (EM) waves is governed by the four laws, or equations, of electromagnetism known collectively as Maxwell's equations. Before stating Maxwell's equations mathematically, it is useful to describe them more heuristically.