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The term "radar signal processing" encompasses the choice of transmit waveforms for various radars, detection theory, performance evaluation, and the circuitry between the antenna and the displays or data processing computers.
The relationship of signal processing to radar design is analogous to modulation theory in communication systems; both fields continually emphasize communicating a maximum of information in a specified bandwidth and minimize the effect of interference .
In radar systems signal processing tasks which may be performed either digitally or by analog circuits include:
1- Nonlinear processing to reject strong interfering signals.
2- Instantaneous adjustment of gain to avoid saturation in amplitude and to control false alarm.
3- Filtering and pulse compression, to select the pulse spectrum from wide band noise and ECM. (Electronic counter measurement)
4- Integration of successive pulses or samples in a pulse train.
5- MTI (Moving Target Indicator)
6- MTD (Moving Target Detection)
7- CFAR (constant false alarm rate) processing.
8- Estimation of target coordinates.
Perhaps the most striking recent development in radar technology has been the transition from analog to digital signal processing . Analog electronic circuits tend to suffer from the effects of temperature change and component aging. Regular monitoring and adjustment is needed to maintain complex analog systems at peak performance. By contrast, digital circuits and computers working on the binary principle, are remarkably stable and reliable. Another advantage of digital processing in the radar context is the flexibility. Not only elaborate signal processing schemes are quite feasible, but they may be selected and modified under computer control. Radar systems can be made adaptive. For example, they can continuously be adjusted to variations in the clutter environment. The use of digital computers also allows information from a number of radars to be stored, processed and combined for presentation to a radar operator.
Advances in microprocessors which are optimized for digital signal processing (â€ŽDSP) functions, analog to digital converters, and development tools associated with them boosted low-cost, high-speed, highly precise, flexible, and expandable implementation of radar systems. Furthermore, the digital signal processing (DSP) technology has shortened hardware and software development time requirements significantly .
In digital signal processing (DSP) based systems, since great percentage of the system functions is incorporated in the software section, algorithm tunings for the desired missions are provided and is the most important advantage of the flexibility for military applications.
The new digital hardware components are programmable logic devices so that most of the digital logic can be implemented in general-purpose very large scale integrated (VLSI) circuits. These devices are programmed with special tools which indeed provide a kind of software generation. When this software is compiled and loaded into the device, the device is now ready to implement the application specific circuit.
The detailed hardware of modern radar signal processors varies widely between different installations. However, certain key principles are now well established and widely implemented. These principles are the subject of the subsequent sections.
2.2 CLUTTER REDUCTION
Modern radar signal processing techniques can be highly effective against clutter. They may be split into two main categories; those which make use of the doppler shift produced by moving targets, and those which do not. The present section deals with a number of techniques in the latter category. Being relatively simple to implement, they are often found in inexpensive radar systems.
It is clear that clutter reduction is not exclusively the concern of radar signal processing. Prevention is often better than cure. In the case of ground-based or marine radar, several preventative measures have already been mentioned. They include :
The use of a small radar resolution cell
Careful siting of the antenna
Tilting the antenna beam
The use of more than one antenna beam
The use of circular polarization to reduce weather clutter.
Moving back to signal processing, different techniques for clutter reduction will be discussed.
2.2.1 Sensitivity Time Control (STC)
STC, also called swept gain, is a technique used to attenuate echoes from nearby targets and clutter without attenuating echoes from far away targets. This prevents very strong echoes produced by nearby clutter from saturating the display. With STC, the receiver gain (sensitivity) is programmed such that it is highly reduced after trigger pulse, then it increases with time (and therefore range) until the following pulse is transmitted. Fig. (2.1) shows the variation (in dB) of clutter power with range for land, sea and rain clutter, as well as the ideal STC functions for these types of clutter . Also Fig. (2.2) shows how STC prevents saturation of the display; it attenuates the video signal levels only at close range. So, the near target is now detected as well as the distant target.
Fig. 2.1 Variation of clutter power and STC functions (In dB, where 0 dB is taken as the power for 1 km range) 
STC can be implemented at the IF stage of a radar receiver or at the RF stage using variable attenuation microwave diodes. It may be also implemented in the baseband using a voltage controlled amplifier (VCA), as shown in Fig.(2.3). The control voltage is synchronized with the PRF. Each time a pulse is transmitted, the voltage gain is reset to the minimum, it then rises until a new pulse is transmitted. The voltage gain of the VCA is proportional to the control voltage. Therefore the amplifier power gain is proportional to the square of the control voltage.
b) With STC
a) Without STC
Fig. 2.2 Effect of STC on saturation of video signal
Output Video Signal
Input Video Signal
Synchronization Pulses (PRF)
STC Function Generator
Fig. 2.3 STC circuit using voltage-controlled amplifier 
2.2.2 Instantaneous Automatic Gain Control
One technique for reducing saturation is the instantaneous automatic gain control (IAGC). IAGC is a quick-acting automatic gain control that responds to variations of the mean clutter level over different range or angular regions, thus preventing receiver saturation. It works by temporally reducing the receiver gain whenever a long pulse is received. Echo pulses from point targets pass with little attenuation, but longer pulses such as those from extended clutter or electronic countermeasures (jamming) are attenuated.
However; Fig.(2.4) shows the effect of IAGC on pulses from point target and those from extended clutter.
Fig. 2.4 Effect of IAGC on pulses from point target and those from extended clutter 
IAGC attenuates all but the leading part of the clutter, reducing the saturation to a small area. This allows detection of the target. In the PPI display, rain clutter appears as patches of saturation. IAGC can significantly reduces the size of these patches allowing targets within the clutter to be detected. Fig. (2.5) shows how IAGC can be implemented. Whether implemented in the IF stage or in the video section of the receiver, the technique is based on negative feedback controlling the amplifier gain. The response time is set to make the automatic gain control act within a few pulse widths, that is, almost instantaneously.
a) In IF stage
b) In video stage
Fig. 2.5 Implementation of IAGC 
2.2.3 The Logarithmic Receiver
A receiver can be designed with a logarithmic input-output characteristic. This increases the dynamic range of the receiver and often permits the detection of targets in clutter. An IF filter followed by envelope detector, with a logarithmic characteristic, can be used. Also the detected video signal can be passed through logarithmic amplifier. In some radars, the logarithmic conversion is implemented in a digital computer.
Figure (2.6) shows the input-output characteristic of both a logarithmic and a linear receiver, and how these receivers react to input pulses of various amplitudes . The shown logarithmic receiver characteristic has a steeper slope at low input levels than the linear receiver. As a result, weak signals receive more amplification with the logarithmic receiver.
Weak signal is amplified considerably
receives no extra amplification
Output pulses from strong signals
have different amplitudes
Output pulses from strong signals
have equal amplitudes
a) Logarithmic receiver
b) Linear receiver
Fig. 2.6 Input-output characteristic of logarithmic and linear receivers 
At high input levels, the slope of the logarithmic characteristic is less than that of the linear characteristic. This causes the logarithmic receiver to reach saturation at higher input level later than the linear receiver. So, logarithmic receiver has a greater dynamic range and its output pulses from strong signals have different amplitudes while in case of the linear receiver they would have equal amplitudes due to saturation. This allows the logarithmic receiver to differentiate between clutter and a strong target echo signal, when the linear receiver cannot .
At very low levels, the characteristic of the logarithmic receiver has a linear portion. This is necessary because the logarithm of a voltage tends towards minus infinity as the voltage approaches zero.
The capability of MTI processor to suppress non-stationary clutter like rain is limited. For this reason, other techniques such as log. FTC are often used in conjunction with MTI when rain clutter is encountered to improve
signal - to - clutter ratio. The combination of log-FTC is more effective than when either is used separately
2.2.4 The Logarithmic Fast Time Constant (Log-FTC) Receiver
Another type of receiver which is very useful in the presence of rain clutter has a logarithmic input-output characteristic followed by a differentiator (high pass filter). Since a differentiator has a fast-time-constant (FTC), this is known as a log-FTC receiver. It can be implemented in the video section as shown in Fig. (2.7).
Fig. 2.7 Log-FTC circuit 
Since rain consists of a large number of drops which scatter the radar wave relatively uniformly, the amplitude of rain clutter in the unipolar video signal is a random value which tends to have a probability density function (pdf) of the Rayleigh type. This function has the property that the rms amplitude of the fluctuations about the mean ( standard deviation ) is proportional to the mean. When a random voltage whose standard deviation is proportional to the mean is applied to a logarithmic amplifier, the standard deviation of the output is constant, regardless of the input level (this can be shown mathematically in appendix (A) ). The differentiator removes the mean level from the video signal, leaving only the fluctuations due to rain clutter. When the resulting signal is applied to the threshold detector, the false alarm rate will be constant, since the amplitude of the fluctuations is constant. So, the log-FTC receiver, when used in the presence of rain clutter adapts itself to the clutter level and maintains a constant false alarm rate.
Since the logarithmic amplifier amplifies weak signals more than strong signals, it compresses the range of amplitudes in the video signal. This can be used an advantage in preventing saturation when the range of echo signal levels exceeds the dynamic range of the display. If this compression is not desired, however, it can be compensated by placing an antilogarithmic converter after the log.FTC circuit. The antilog converter characteristic is the inverse of the logarithmic characteristic.
2.3 MATCHED FILTERING AND PULSE COMPRESSION
Radar target echoes are generally contaminated by receiver noise or noise-like clutter. Before attempting to detect them using a threshold detector, it is important to improve the signal-to-noise ratio (S/N) as much as possible. The optimum filter for achieving this is known as the matched filter [6, 7].
c) Effect of matched filtering
a) Two rectangular echo pulses
b) Two rectangular echo pulses contaminated by random noise
Fig. 2.8 Improving signal-to-noise ratio by matched filtering 
The action of a matched filter is illustrated by Fig. (2.8). Part (a) shows two rectangular echo pulses. In part (b) they are contaminated by random noise. If this signal-plus-noise waveform is processed by a threshold detector, it is clear that occasional high noise peaks are likely to cause false alarms. Part (c) of the figure shows the effect of matched filtering. The peak output due to each signal is now considerably larger, compared with the noise, and a threshold level VT can be successfully employed
A matched filter is normally defined in terms of its impulse response, which always takes the form of a time-reversed version of the signal. Therefore such a filter is "matched" to a particular signal waveshape and not to others.
It may be shown that, when this waveshape is fed into the filter, the output takes the form of the signal's autocorrelation function. For this reason a matched filter is often referred to as a type of correlator. Appendix B describes such filtering in more details.
Matched filtering really comes into its own when pulse compression is used. Since pulse compression is increasingly specified for high-power radar systems. Transmitter pulses are stretched in time and specially coded. Received echoes are sharpened up, or compressed, by a matched filter prior to detection. The overall system therefore possesses the range resolution of a short pulse. A major advantage of the approach is that peak transmitter power may be greatly reduced, while maintaining average power. This is especially valuable in high-power, long-range, and high-resolution radar applications.
Figure (2.9) shows the pulse compression of the 'chirp' waveform and the pseudo-random binary sequence (PRBS) pulse code.
Fig. 2.9 (a) Pulse compression of a 'chirp waveform
(b) Pulse compression of the pulse code (PRBs) 
Although pulse compression offers excellent range resolution and reduced transmitter peak power requirements, it has the disadvantages of the time side lobes in the compressed pulse. Fortunately, a number of techniques have been devised for reducing time side lobes, including weighting of the received pulses in either the time or frequency domain
2.4 PULSE INTEGRATION
The noise that passes through the matched filter consist of random pulses whose average width is approximately the same as that of the signal pulse width. For high signal-to-noise ratio, the amplitudes of signal pulses will be generally greater than those of noise, but for low signal-to-noise ratio, a single signal pulse is virtually indistinguishable from a single noise pulse and target detection based on a single pulse is impossible.
The echo signal usually consists of a train of several to several hundreds pulses received from each target. Instead of considering each pulse separately to decide whether a signal is present, a number of pulses can be added together and the decision made on the basis of their sum. This process, called pulse integration, considerably improves the signal to noise ratio (S/N) and the accuracy of the decision. Since noise is a random phenomenon whereas an echo signal is not. Therefore, the sum of a number of pulses consisting of noise alone will be considerably different from the sum of a number of pulses containing a signal plus noise. Two techniques used for pulse integration:
More details about both techniques and effect of pulse integration on radar performance are discussed in appendix (C).
2.5 MOVING TARGET INDICATOR (MTI)
Targets moving with finite radial velocities produce Doppler shifted echoes. In MTI radar, this doppler information can be used to discriminate moving targets against fixed targets and clutter . The principles of MTI were well understood by the mid of 1950s, but its implementation with the available analog technology was difficult. Modern digital processing represents a major advance in this area of radar system design . Fig. (2.10) illustrates the classic Coho-Stalo method of extracting doppler phase shifts in a superhetrodyne radar receiver.
fc+ f1ï‚± fd
fc ï‚± fd
Fig. 2.10 Extracting Doppler information in a coho-stalo system 
A typical output from the phase sensitive detector (PSD), with a number of superimposed inter-pulse periods is illustrated in Fig. (2.11).
Fig. 2.11 Fixed and moving target echoes after phase-sensitive detection 
The difference between fixed and moving target echoes at the output of the phase-sensitive detection is clear. A fixed target produces the same PSD output on every pulse. But a moving target gives an output which fluctuates at doppler frequency. The fluctuations produce a "butterfly" effect when viewed on an oscilloscope. Such a video signal is not suitable for driving a radar display, because the fixed target echoes have not been eliminated.
A subtraction process is used to discriminate against them. Thus, if v(t) is subtracted from a version of itself which has been delayed by exactly one interpulse period, fixed target echoes will be canceled. While moving targets, which produce a different PSD output on each pulse, will remain. This technique of subtraction is known as delay line canceller.
More detailed information about the delay line cancellers and other MTI related items are discussed in Appendix D.
2.6 MOVING TARGET DETECTION (MTD)
During the early 1970s a new type of radar signal processor was developed at the Massachusetts institute of technology for airport surveillance radars in the United States. It was called the Moving Target Detector. There are two main differences between MTD-style processing and the traditional MTI techniques described in the previous section. Firstly, MTD makes extensive use of digital signal processing. This allows it to adapt continuously to the clutter environment, enhancing the visibility of moving targets at the expense of fixed and moving clutter. The second main difference is the way in which that doppler filtering is carried out . An MTD system performs a frequency analysis of incoming signals, using technique of discrete Fourier Transformation (DFT). This is most efficiently implemented using a fast Fourier Transform (FFT) algorithm. In effect, FFT analysis resolves the doppler signal into a number of separate spectral bands, and offers much greater processing flexibility. FFTs may, in principle, be implemented either in software or in hardware. However, the speed requirements of radar signal processing demand dedicated FFT hardware, and special-purpose integrated circuits are available. A radar FFT processor is often refereed to as a doppler filter bank.
The main components of a typical adaptive MTD system are as shown in Fig. (2.12). The output of filter 0 in the doppler filter bank is dominated by fixed clutter echoes having zero doppler shift. Avoiding using this output, fixed clutter may be suppressed. The suppression is not complete, however, because adjacent filters have significant sidelobes in the region of zero doppler frequency. To reduce such clutter "crosstalk", an MTI canceller is included at the input side of the FFT processor. This has the additional benefit of reducing the dynamic range of signals entering the filter bank.
FFT analysis is followed by frequency-domain weighting to reduce filter sidelobe levels, and the magnitude of the output in each spectral band is computed. A separate threshold level is applied to each filter output, to test for target echoes. The threshold is determined by the system noise level, and by any echoes appearing at the output of the same filter in a number of adjacent resolution cells. Thus, the threshold takes account of the average level of moving clutter (such as rain) in the vicinity of the cell under test. The use of such an adaptive video threshold for each doppler filter in each resolution cell provides constant-false-alarm-rate processing.
Weighing and magnitude
Doppler filter bank
Zero velocity Filter
I and Q Signals
Fig. 2.12 Block diagram of an adaptive MTD processor 
The function of the zero-velocity filter (ZVF) is to recover clutter echoes suppressed by the MTI canceller, using them to generate a clutter map. The map is build up over a number of antenna scans (typically between
6 and 20), and is continuously updated. It therefore adapts to slow changes in weather or ground clutter. The values stored in the map are used to establish thresholds for targets with zero radial velocity. In this way the problem of tangential fading suffered by traditional MTI cancellers is largely overcome. The technique is said to provide super-clutter-visibility.
As the antenna scans past any one target, there may be threshold crossings at one or more filter outputs, in several or many interpulse periods, and perhaps in adjacent resolution cells. The function of the hit processor is to correlate all threshold crossings, grouping together those which appear to come from the same target. At this stage, signal amplitude and shift information is used to eliminate very weak echoes, or those judged to come from moving clutter or angels. The hit processor generates target reports comprising range, azimuth, amplitude and radial velocity information, on all validated targets. It may also produce a reconstituted (synthetic) video signal for presentation on radar displays.
The block diagram of Fig. (2.12) does little to suggest the enormous amount of digital storage and signal processing involved in such a scheme. A typical system may divide each interpulse period into a thousand or more range intervals, and use several hundred azimuth intervals. Data from 10:20 successive interpulse periods must be stored, and presented, one resolution cell at a time, to the doppler filter bank. The overall radar output is therefore divided into millions of individual range-azimuth- doppler cells, each of which has its own adaptive threshold. The clutter map may have 100000 or more range-azimuth cells, and is continuously updated.
The main practical advantages of FFT processing of radar signals may be summarized as follows :
Dividing the doppler frequency domain into N separate bands offers a very flexible approach towards discriminating against fixed and moving clutter. If moving clutter (such as that from weather or birds) appears with a non-zero mean shift, the thresholds at the outputs of the various Doppler filter may be raised accordingly. The system can therefore be made adaptive to the clutter environment, rejecting clutter which would be passed by the usual type of delay-line canceller.
Although the filter centered at zero frequency (and at the PRF and its harmonies) has no clutter-rejection capability, it may be used to generate a clutter map. This offers a valuable method for detecting targets moving tangentially to the radar.
2.7. CONSTANT FALSE ALARM RATE (CFAR) PROCESSING
CFAR processing aims to produce a constant and acceptable mean rate of false alarms, regardless of the levels of noise and clutter . When a radar signal is viewed on a conventional analog display, false alarms caused by noise or clutter appear directly as unwanted "blips" on the screen. The detection threshold is effectively the signal level which just causes the screen phosphor to brighten. An experienced operator becomes skilful at recognizing true targets. But in case of confused by too many false alarms, the gain control on the display can be turned down. In a sense, the operator provides his own CFAR processing which cannot, of course, compensate for rapid clutter fluctuations.
The modern trend is towards digital techniques where the radar signals are processed digitally and presented on digital displays. This provides automatic detection and tracking (ADT); Decisions about the presence of targets are done automatically without human operator. Radar information are presented with "clean" displays, driven by synthetic computer-generated signals. In such cases CFAR is essential, because the ADT computer can easily become overwhelmed by too many false alarms . The detection threshold must adapt automatically to both short-term and long-term changes in clutter and noise levels.
Because CFAR is an essential signal processing technique which provide automatic detection and tracking (ADT) in modern trends in radar, It'll be discussed in more details in the next chapter.
2.8 NEW TRENDS IN RADAR SIGNAL PROCESSING
The basic signal processing and related tasks are heavily performed by the digital signal processing (DSP) processors. The real-time requirements and computation-intensive tasks necessitate parallel processing of several (DSP) processors. All these bring the concept of multiprocessing. In addition to this concept, sharing of system missions may impose several tasks to be run concurrently on a single (DSP) processor. This now brings the concept of multitasking. Multiprocessing and multitasking require a special software architecture where asynchronous external world events can occur and processors must switch between tasks upon these events and/or other
periodic or scheduled tasks. This architecture must be real-time and
especially robust .
Nowadays, an important feature of software based design is the availability of efficient operating systems optimized for (DSP) processors. These operating systems provide a framework for multitasking and also multiprocessing operation of the (DSP) processors. Each algorithm and function can run as a separate independent software task. The scheduling and timing of the tasks and system resource (hardware and software) allocation are automatically managed by the operating system. Accordingly, an expandable system structure can be developed so that new system mission based tasks can be embedded into the existing high-performance parallel processing system in a performance-safe manner.
The combination of flexible (DSP) hardware with the existence of effective software frameworks for parallel processing real-time systems, makes it possible to build a high-performance and expandable radar systems. Accordingly, user requests and performance tunings can be implemented in shorter development times. Another gain from software is that, software in a system can easily be downloaded in the field without any mechanical operation and system expert supervision. This also provides time and cost savings.
A radar designed through the modern technologies can provide:
Improved target detection
Automatic target classification.
Ground and sea surveillance features implemented in the same system.
Open structure for new system applications.