A pulse Doppler radar is the result of combining Doppler sensing techniques with pulsed radar operation. Such radars offer the powerful scope for direct measurements of both target range and velocity, even in the face of large clutter returns and even in the presence of chaff or other interference. To radar, the measurement of a time delay is tantamount to range, whereas the measurement of a (Doppler) frequency shift is tantamount to velocity. Thus, one must consider the design of suitable waveforms in both the time and frequency domains. However, there is a complex interplay between the waveform parameters, particularly when it comes to the selection of the radar pulse repetition frequency (PRF). All too often, the requirements for the measurement of range clash with those for the measurement of velocity. The result is that multiple waveforms may be required which depend on the nature of the targets and clutter conditions. The study of pulse Doppler radar is thus inextricably bound up with issues of waveform design and their associated processing methods whilst always maintaining a watchful eye on the target scenario and radar environment. Before tackling these waveform and processing issues, it is necessary to establish several fundamental radar concepts, which are covered in the ensuing chapters.

This chapter consists of noise-limited radar range equation, detections in noise, minimum detectable signal, processing gain via pulse integration and radar cross section.

Pulsed radar entails the transmission of a succession of radio frequency (RF) pulses. As noted in Chapter 1, pulse modulation enables the range of a target to be measured. Pulsed modulation also permits a high-power transmitter to be used, which helps achieve a long detection range. High transmitted powers can be used if the sensitive receiver can be isolated from the transmitted signal during the pulse. This is easily achievable in pulsed radars since electronic switches can be thrown to isolate the receiver from any input signals during the transmitted pulse. Once the transmitted pulse has died down, the switches open the receiver path. Hence, when the transmitter is on, the receiver is off, and when the transmitter is off, the receiver is on. This alternation also means that no echo returns can be received during the transmitted pulse and consequently that the radar is blind to targets at certain ranges.

In this chapter the Doppler effect, Doppler discrimination, platform motion compensation, Doppler blindness, continuous wave radar, and application to pulsed radar are discussed.

In Section 3.9.3, the point was made that a radar receiver performs a cross-correlation between the received signal and a reference of the transmitted waveform. Furthermore, the received signal may differ from the transmitted signal on account of being time delayed and Doppler shifted. The design of a matched receiver usually entails designing the receiver to match the transmitted waveform and so may no longer match the received signal on account of the time and frequency displacements of the received signal over the transmitted one. Matched reception is tantamount to autocorrelation of the received signal at a particular time shift. In radar, it is most convenient to think of the particular time shift associated with a given range cell. While the autocorrelation function handles shifts in time, it offers no provision for handling shifts in frequency. The ambiguity function describes the response of a matched receiver to a finite duration signal. The use of the ambiguity function in ambiguity analysis considers the receiver to be matched to a signal received from a target at a given time delay (range cell) and frequency. The ambiguity function describes the matched receiver response as a function of any additional time delay and any additional Doppler frequency.

In this paper backscatter coefficient, surface clutter, airborne radar clutter, clutter decorrelation, low pulse repetition frequency radar response to clutter, clutter limited detection range and volume clutter are discussed.

The processing of pulse Doppler radar signals is commonly depicted as a sequence of stages known as the processing chain. Signal processing is applied to enhance the signal-to-noise ratio (SNR) to enhance detection performance, to discriminate between true targets and interference, clutter, or jamming, and to extract the desired information about targets that, at the very least, includes target range and velocity. While the exact order and processing operations differ from radar to radar, they are all likely to include the stages depicted in Figure 7-1.

This section describes two of the most important specifications concerning the microwave signals pertinent to pulse Doppler radars: coherency; and close-to-carrier noise. Also, an introduction will be provided to the devices that can be used as sources of microwave signals. Radars use microwave oscillators and synthesizers as a source of transmitted power or for providing low-power drive signals for amplification in a master oscillator power amplifier (MOPA) type transmitter. RF and microwave signals also act as local oscillators (LOs) within a superheterodyne receiver and provide digital clocking and timing signals. Most radar systems have one fundamental oscillator from which all other signals are derived. This ensures that any drift in the oscillator frequency, such as due to temperature changes, cause a compensating drift in all other signals such that all signals remain coherent with each other.

Pulsed radars that are not required to be Doppler sensing systems have traditionally employed low pulse repetition frequency (PRF) waveforms. A low PRF is defined as one which is sufficiently low so as to avoid range ambiguities. To avoid range ambiguity, the maximum detection range of the radar for all target and clutter returns is required not to exceed R_mu. This ensures that all returns are first-trace echoes, that is, that they fall within the first receiving period, and their range may be determined from a simple range delay timing method. Low PRF waveforms are typically low duty ratio waveforms and employ a large number of range cells matched to the range resolution of the radar distributed throughout the receiving period. Target range is therefore readily available from low PRF systems.

Other forms of modulation also increase the signal bandwidth and enable range to be measured. Phase and/or frequency modulation (FM) may be imparted onto a CW signal for the measurement of range. In much the same way as pulsed modulation allows the time delay between the transmission of the signal and the reception of a target return to be established, so, too, does the use of phase or frequency modulation. The most commonly used form of modulation is a linear frequency modulation (LFM), and it gives rise to FM ranging in CW systems and high pulse repetition frequency (PRF) pulsed radars.

A medium pulse repetition frequency (PRF) gives rise to ambiguities in both range and velocity. Medium PRF is the general case; special simplifying cases arise for low PRF, in which range is unambiguous, and high PRF, in which velocity is unambiguous.

Many factors influence the choice of exact values of pulse repetition frequencies (PRFs), the total number of PRFs used within a medium PRF schedule, N, and the minimum number of PRFs in which target data are required, M. Some factors are more important than others, and in some cases PRFs have been selected on the basis of one or two of the most important factors with little or no regard to factors of lower priority. It is fair to say that the design of the PRF schedule (selection of precise values of PRFs and the numbers N and M) is fundamental to many aspects of the performance of the radar. It is worth noting that the performance of a radar is dictated by the combination of the PRFs used; no individual PRF can be regarded as good or bad in its own right. The quality of any medium PRF schedule is an attribute of how all the PRFs work together. Some key factors influencing schedule design are discussed in the following sections of this chapter. These factors tend to place constraints and limitations that guide the selection of PRF values; they do not dictate precise values to be selected. Indeed, the selection of precise values of PRF is an area shrouded in mystery and is commonly perceived as something of a black art. Recent work, however, has brought solid engineering principles to bear on this problem.

This chapter addresses the selection of the numbers M and N and considers the ramifications of using schedules that depart from the norm. Longer schedules, N > 8, have been perceived as advantageous in heavy clutter situations but also cause complications and compromises in other aspects of the radar performance. Recent work has examined the performance of shorter schedules (M < 3, N < 8), and these have been found to have several advantages over longer schedules. The question of how best to use the limited beam dwell time arises and is also examined here.

Conventional medium pulse repetition frequency (PRF) processing applies a double thresholding system of detection. First, within each coherent processing interval (CPI), signals in each range/velocity cell within the unambiguous range and unambiguous velocity space are compared with a threshold level to declare whether a target is present. These target detections are ambiguously repeated across the range/velocity space of interest. This process is repeated for all N CPIs; each CPI operates on a different PRF. Second, each range/velocity cell is subjected to a binary integration process, which is looking for target detections in the same range/velocity cell in M out of the N CPIs. A target is declared if detected in a consistent range/velocity cell in at least M of the total of N CPIs.

A great deal can be done to enhance and optimize the operation of a radar through careful selection of, principally, its PRFs but also of other waveform parameters. Simplifying the method of PRF selection can give a workable solution, but far superior performance can be achieved if one is prepared to take on a more complex problem entailing fine PRF resolution and combinations of PRFs with other waveform and processing parameters. The more complex problems demand more complex methods of optimization. Modern methods described here have been used with great success in the design of radar waveforms supporting a wide range of modes such as high and medium PRF pulse Doppler and ground-moving target indication (GMTI) and applications such as airborne fire control and long-range early warning radars.

Airborne fire control radars (FCRs) on fast strike aircraft are the quintessential pulse Doppler radars. They must work in a wide variety of air-to-air and air-to-ground modes, they must be lightweight and compact, yet they have to achieve long detection ranges in the presence of extreme clutter scenes and be capable of tracking a large number of agile targets, all of which must be highly automated, especially for single seat aircraft, to minimize the workload on the aircrew.

Airborne early warning (AEW) radars provide long-range surveillance from an airborne platform. Their primary targets of interest are hostile aircraft. Long-range radar surveillance coverage can be limited by the range to the horizon; however, satisfactory range can be re-established by placing the surveillance radars at high altitude. The line of sight horizon is then a respectable distance away, the range to the horizon, Rh in kilometers, from a radar at an altitude of h meters is given approximately. The following sections give some example radar parameters for two hypothetical AEW radar systems: one used for fleet protection and the other for long-range airborne surveillance.

This chapter considers the case of a hypothetical, but realistic, medium-range air-to-air missile using a fully active pulse Doppler radar seeker for terminal phase guidance. To scope this application, this chapter starts with a short overview of guided weapons system employing radar-based seekers followed by a brief discussion on the interaction between the seeker and other aspects of the guided weapon that influence the seeker design.

This chapter closes with the description of a hypothetical short-range ground-based air surveillance radar, typical of the type used for target acquisition as part of a short-range air defense system. This type of radar is chosen because it differs quite considerably from the longer-range applications and is illustrative of the wide variety of pulse Doppler radars in military service.