5 - Target Detection and Pulse Compression Techniques in Radar Systems
One of the fundamental tasks of radar systems is to reliably detect targets in a noisy environment. This process constitutes a critical part of the signal processing chain and directly affects radar performance. Target detection is performed in the signal processor block after the analog-to-digital converter, and the detection process is then completed in the main computer. In this article, we will examine in detail the target detection mechanisms, pulse integration methods, and pulse compression techniques.
Characterization of Noise
In radar systems, noise is characterized as a random process. Over time, the noise level fluctuates up and down; sometimes it takes high, sometimes low values. Therefore, it is not possible to characterize noise with a single number—instead, a probability distribution is used.
Typically, noise is characterized by a Gaussian distribution. It is called "white noise" because all frequencies exist with equal probability—just as all colors are present with equal probability in white light. Noise fluctuates around a mean power, and this mean value is critically important in system performance calculations.
Detection Threshold and Probabilities
Setting the threshold value in radar systems is the cornerstone of detection performance. When a threshold is set, signals above this threshold are considered as targets. However, noise can also occasionally exceed this threshold, and this situation is called a "false alarm."
The probability of false alarm (Pfa) is the probability that noise exceeds the set threshold. When the threshold is set too high, the probability of false alarm approaches zero, but weak targets may be missed. When the threshold is set too low, the number of false alarms increases. In a typical radar system, the probability of false alarm is kept around 10⁻⁶—because there are thousands of range cells and hundreds of azimuth cells.
The probability of detection (Pd) expresses the probability of detecting a real target. For a high probability of detection (for example, 90%), together with a 10⁻⁶ probability of false alarm, a signal-to-noise ratio (SNR) of approximately 13.2 dB is required for a stationary target. This value is an important reference point frequently used in radar system design.
Pulse Integration
Pulse integration increases target detection capability by combining echoes from different pulses. There are two main methods: coherent integration and non-coherent integration.
Coherent Integration
In coherent integration, both the amplitude and phase of the signal are preserved—no information is lost. The signal is separated into real (in-phase, I) and imaginary (quadrature, Q) components:
• Real component: A·cos(θ)
• Imaginary component: A·sin(θ)
The coherent integration gain is equal to the number of integrated pulses (n). When two pulses are integrated, a 3 dB gain is obtained; for ten pulses, a 10 dB gain is achieved. For this gain to be fully realized, the noise samples from pulse to pulse must be independent.
Non-Coherent Integration
In non-coherent integration, phase information is generally lost and only amplitude values are summed. This method is less efficient than coherent integration. The typical gain is on the order of √n—that is, for 10 pulses, a gain of about 3.16 (5 dB).
Types of non-coherent integration:
• Video integration: The amplitude of each pulse is calculated, summed, and thresholded
• Binary integration: Each pulse is thresholded separately, m detections are required out of n pulses
• Cumulative detection: At least one detection is sought in n scans
Target Fluctuation Models
Real targets do not have a constant cross-section like a sphere—their radar cross-sections fluctuate due to their complex structures. Over 50 years ago, Peter Swerling developed four different fluctuation models.
Swerling 1 and 2 models assume that the target consists of a large number of independent scatterers of equal magnitude. This leads to an exponential cross-section distribution:
p(σ) = (1/σ̄)·e^(-σ/σ̄)
Swerling 3 and 4 models, on the other hand, address the case where there is a dominant scatterer and the sum of the other scatterers equals this dominant scatterer.
In terms of temporal behavior: Swerling 1 and 3 models assume fluctuation from scan to scan, while Swerling 2 and 4 models assume fluctuation from pulse to pulse. Fluctuating targets require a higher SNR than stationary targets for the same probability of detection.
Adaptive Thresholding and CFAR
A fixed threshold value cannot provide optimal performance in changing noise environments. Adaptive thresholding or Constant False Alarm Rate (CFAR) techniques dynamically adjust the threshold according to the local noise level.
In the mean level CFAR method:
1. Guard cells around the test cell are determined
2. The average noise level of the reference cells beyond the guard cells is calculated
3. The threshold is set as a multiple of this average value
4. The test cell is compared with this threshold
The disadvantage of this approach is that it can cause excessive false alarms at sharp clutter boundaries. To solve this problem, "greatest mean" CFAR is used—the averages of the left and right halves are calculated and the larger value is used.
Pulse Compression Techniques
There is a fundamental contradiction in radar systems: high average power requires long pulses, but good resolution requires short pulses. Pulse compression techniques resolve this contradiction by enabling the simultaneous achievement of the energy of a long pulse and the resolution of a short pulse.
For a simple CW pulse:
• Bandwidth B = 1/τ (τ: pulse width)
• Range resolution ΔR = c/(2B) = cτ/2
The time-bandwidth product is 1 for simple pulses. With pulse compression, this product can be increased to values much greater than 1.
Binary Phase Coding
In binary phase coding, the pulse is divided into small subunits (chips), and the phase of each unit is set to 0 or π radians. The bandwidth becomes 1/τ_chip instead of 1/τ, which provides much better resolution.
For example, consider a 3-bit code (+ + -):
• The phase does not change for the first two chips
• The phase is rotated by 180° for the third chip
At the output of the matched filter, a time-shifted multiplication and summation (convolution) operation is applied. At the center point, all components add constructively and the peak value (n) is obtained. At the edge points, values close to zero are produced. In this way, range resolution improves by a factor of n.
Linear Frequency Modulation (LFM)
In the LFM waveform, the frequency changes linearly throughout the pulse—from low frequency to high frequency (or vice versa). The bandwidth is:
B = f₂ - f₁
The time-bandwidth product BT can be much greater than 1, which provides superior resolution. A disadvantage of LFM is that a coupling occurs between range and Doppler velocity measurements—a delayed echo also appears as a frequency shift.
Matched Filter Concept
The matched filter is the optimum receiver filter that maximizes the peak signal-to-average noise ratio. For a simple rectangular CW pulse, the matched filter is a bandpass filter with the same shape as the power spectrum of the transmitted pulse.
This is physically logical: if the filter bandwidth is wider than the signal bandwidth, extra noise leaks in. If the filter is narrower, some frequency components of the signal are lost. The optimum case is when the two match exactly.
In digital implementation, the matched filter is realized as a convolution operation between the reflected echo and the time-reversed transmitted pulse. This operation is efficiently implemented using digital signal processors in modern radar systems.
Conclusion
Target detection and pulse compression are the fundamental building blocks of modern radar systems. Coherent and non-coherent integration techniques significantly enhance detection performance. Swerling models characterize the fluctuation behavior of real targets and sguides system design. CFAR techniques provide a consistent false alarm rate in varying noise environments. Pulse compression—whether phase coding or LFM—makes it possible to achieve high average power and good range resolution simultaneously. Together, these techniques enable radar systems to reliably detect targets in challenging environments.