By Target detection is one of the most important and challenging tasks in a radar system. After transmitting a pulse, the radar receives echoed or reflected signals and begins processing them. A fundamental difficulty is that the received signal may originate from a genuine target, from static objects such as terrain or buildings, or from various noise and interference sources. The primary objective of radar signal processing is therefore to reliably distinguish true targets from these unwanted returns and to maximize the probability of detection.
Background
Figure 1 illustrates a typical radar detection chain. In a conventional RADAR receiver, the incoming RF or IF signal is first amplified and digitized. The digitized signal is then demodulated into its in-phase and quadrature components, commonly referred to as the I and Q signals. The signal power is subsequently computed from these components using a square-law detector. Finally, this power is compared against a detection threshold using an appropriate decision technique to determine the presence or absence of a target.
Fig 1: A typical RADAR detection chain
The output of the I/Q demodulation stage is a complex baseband signal of the form $I(t)+jQ(t)$. The phase information contained in this complex signal is exploited in earlier stages of radar signal processing, such as coherent integration, Doppler processing, clutter suppression, and angle estimation. These operations rely on the predictable phase behavior of target echoes and therefore must be performed prior to detection.
Detection Threshold
Once these processing steps are completed, target detection is based on signal energy rather than phase, and a square-law detector is applied. A square-law detector is a nonlinear device used in radar receivers to convert the complex received signal into a form suitable for detection. It computes the signal power by squaring and summing the in-phase and quadrature components.
Mathematically, if the complex baseband signal is
\[
x(t) = I(t) + jQ(t)
\]
the output of the square-law detector is given by
\[
y(t) = |x(t)|^2 = I^2(t) + Q^2(t)
\]
This operation removes the phase information and produces a non-negative output proportional to the instantaneous signal power. Since radar detection is fundamentally based on energy rather than phase, the square-law detector is well suited for target detection.
Constant Threshold
For deterministic signals, or in situations where the noise or interference level is known and remains constant, a fixed detection threshold can be used for target detection. In such cases, the threshold is selected based on the desired trade-off between the probability of detection and the probability of false alarm, and is set relative to the known noise level to achieve the specified operating point.
However, in practical radar systems, the received signals are not deterministic, and the level of noise and interference is generally unknown and time-varying. The interference power may be very low under some conditions and significantly higher under others due to factors such as environmental changes, clutter, or external interference. When a constant detection threshold is used under these conditions, variations in noise power can lead to incorrect detection decisions. If the interference level increases, noise fluctuations may exceed the fixed threshold, resulting in spurious detections, commonly referred to as false alarms.
Fig 2: Detection under nominal and higher noise interference (with constant threshold)
Figure 2 illustrates target detection under nominal and elevated noise interference conditions using a constant detection threshold. As the interference power increases, noise samples are more likely to exceed the threshold, producing false alarms even in the absence of a target.
Probability of Detection vs False Alarm
If a fixed detection threshold is used, variations in noise and clutter power would cause the probability of false alarm to fluctuate unpredictably. This would lead to excessive false alarms in high-clutter regions and overly conservative detection in low-noise regions. Lowering the detection threshold increases the likelihood that weak targets exceed the threshold, thereby improving the probability of detection. However, this also increases the chance that random noise or clutter fluctuations cross the threshold, resulting in a higher probability of false alarms. Conversely, raising the threshold reduces the false alarm rate but at the expense of missed detections. This inherent trade-off implies that detection performance cannot be improved without affecting false alarm behaviour.
Fig 3: Probability of Detection $P_d$ vs Probability of False Alarm $P_{fa}$
Figure 3 illustrates the fundamental trade-off between the probability of detection $P_d$ and the probability of false alarm $P_{fa}$. Each point on the curve corresponds to a specific detection threshold. While the operating point on the $P_d$–$P_{fa}$ curve is fixed by design, maintaining this operating point using a constant threshold becomes challenging when noise and clutter power vary with time and environment.
Fig 4: Probability of False Alarm vs Noise Power
Figure 4 illustrates the sensitivity of fixed-threshold detection to variations in noise or interference power for several design values of the false alarm probability. Each curve shows how the actual probability of false alarm increases as the interference power rises above the level assumed during threshold calculation.
It can be observed that even modest increases in noise power result in dramatic increases in the false alarm rate, particularly when the radar is designed for very low false alarm probabilities. For example, a noise power increase of only a few decibels can cause the false alarm probability to rise by several orders of magnitude. This effect is most severe for systems designed with very small $P_{fa}$, where the detection threshold is set high and becomes extremely sensitive to interference power mismatch.
These results demonstrate that fixed detection thresholds are highly unstable in practical operating environments, where noise and clutter power are inherently time-varying. Small errors in noise power estimation or environmental changes can therefore lead to an unmanageable number of false alarms, severely degrading radar performance.
Constant False Alarm Rate (CFAR) Detection
Constant False Alarm Rate (CFAR) detection addresses this limitation by fixing the probability of false alarm rather than the detection threshold itself. The local noise or clutter level surrounding the cell under test is estimated, and the detection threshold is adaptively adjusted so that the probability of false alarm remains constant, regardless of background variations. By controlling the false alarm rate, CFAR ensures stable and predictable radar behavior while enabling detection performance to be evaluated and optimized under consistent operating conditions.
A variety of CFAR techniques have been proposed to address different operating environments and interference conditions. Each technique differs primarily in the manner in which the local noise or clutter level is estimated. In this article, however, the discussion is limited to two widely used and important CFAR techniques:
- Cell-Averaging CFAR (CA-CFAR)
- Ordered-Statistics CFAR (OS-CFAR)
Before introducing CFAR detection techniques, it is important to understand the concept of range cells and how they are formed in a radar system. Radar target detection is performed independently at discrete range locations, commonly referred to as range cells or range bins (shown in Figure 5 below). The radar divides its observation space into a sequence of discrete range cells. Each range cell corresponds to a specific time interval of the received echo and therefore to a specific range interval. The width of a range cell is determined by the radar range resolution, which depends on the transmitted signal bandwidth (or equivalently, the pulse duration), rather than the carrier frequency.
Radars with larger signal bandwidths achieve finer range resolution, resulting in smaller range cells, while radars with narrower bandwidths produce larger range cells. Each range cell may contain a target return, noise, clutter, or a combination of these components. Radar detection is performed independently within each range cell by analyzing the received signal power and comparing it against a detection threshold.
In CFAR processing, each range cell is treated as a potential target location and is tested individually against an adaptive threshold determined from surrounding cells. In CFAR detection, when a decision is required for a given range cell, commonly referred to as the Cell Under Test (CUT), the local noise or clutter power is estimated using neighboring range cells. Based on this estimate, the detection threshold T is defined as
\[
T = \alpha P_n
\]
where Pn denotes the estimated noise power and α is a scaling constant known as the threshold factor.
From this expression, it is evident that the detection threshold adapts to the local signal environment through the noise power estimate. By selecting an appropriate value of the threshold factor α, the probability of false alarm can be maintained at a predefined constant level, independent of variations in the background noise or clutter. As a result, CFAR detection provides stable and predictable performance in time-varying environments where fixed-threshold detection would fail.
Cell Averaging CFAR (CA-CFAR)
Figure 5 illustrates the range-cell structure used in CA-CFAR detection. Target detection is performed on a specific range cell known as the Cell Under Test (CUT). To avoid contamination of the noise estimate by the target signal itself, a number of guard cells are placed on either side of the CUT. These guard cells are excluded from noise power estimation and provide isolation between the CUT and the surrounding cells.
Fig 5: Cell Averaging CFAR (CA-CFAR)
Beyond the guard cells lie the training cells (also referred to as data or reference cells). These cells are assumed to contain only noise and clutter and are used to estimate the local interference level. In CA-CFAR, the average power of the training cells is computed and scaled by a constant factor to form an adaptive detection threshold. The power in the CUT is then compared against this threshold to determine the presence or absence of a target.
For the CA-CFAR detector, assuming that the input data corresponds to a single pulse (i.e., no pulse integration is performed) and that the reference cells contain independent exponentially distributed noise samples, the detection threshold can be expressed as a scaled version of the estimated noise power. The scaling factor, commonly referred to as the threshold factor, is given by:
\[
\alpha = N \left( P_{fa}^{-\frac{1}{N}} – 1 \right)
\]
where $P_{fa}$ is the desired probability of false alarm and $N$ is the number of training cells used to estimate the local noise or clutter level.
The threshold factor α ensures that the probability of false alarm remains fixed at $P_{fa}$ by compensating for the statistical variability of the noise estimate obtained from a finite number of training cells.
Fig 6: CA-CFAR: Adaptive Threshold and Detection
Figure 6 demonstrates the operation of a Cell-Averaging CFAR detector in a time-varying interference environment. The received signal power exhibits significant fluctuations and a gradually increasing noise floor, representing a non-homogeneous background. The CA-CFAR threshold adapts to these variations by estimating the local noise power from neighboring training cells and scaling it by a threshold factor chosen to maintain a constant probability of false alarm.
As shown in the figure, the adaptive threshold closely follows the underlying interference level rather than remaining fixed. Consequently, spurious noise peaks that would otherwise exceed a fixed threshold are suppressed, while genuine target returns are still detected when they rise sufficiently above the local background. The marked detection points correspond to cells under test whose signal power exceeds the adaptive CA-CFAR threshold.
This figure illustrates the fundamental advantage of CA-CFAR: robust and stable detection performance in the presence of non-stationary noise or clutter, without requiring prior knowledge of the absolute interference level.
Before introducing OS-CFAR, it is necessary to examine how the performance of a CA-CFAR detector is influenced by the choice of its design parameters, namely the number of training cells and guard cells. These parameters directly affect the estimation of the local noise or clutter level and therefore play a critical role in determining detection performance.
Effect of Training Cells
Figures 7(a) and 7(b) illustrate the effect of the number of training cells on CA-CFAR performance. When a smaller number of training cells is used (here, 32 per side) (in figure 7(a)), the estimated noise power exhibits larger statistical fluctuations, resulting in a threshold that closely follows local variations in the received signal. This improves responsiveness but can lead to increased threshold jitter and sensitivity to noise spikes.
Fig 7(a): CA-CFAR (With training cells per side = 32)
Fig 7(b): CA-CFAR (With training cells per side = 128)
In contrast, using a larger number of training cells (here, 128 per side) (in figure 7(b)) produces a smoother and more stable threshold due to improved noise power estimation. While this enhances robustness against random fluctuations, it may reduce sensitivity to weak targets and degrade performance near rapidly changing clutter conditions.
Effect of Guard Cells
Figures 8(a) and 8(b) illustrate the effect of guard cell selection on CA-CFAR performance in the presence of extended and closely spaced targets. In both cases, the same received signal, number of training cells, and desired probability of false alarm are used; only the number of guard cells is varied.
Fig 8(a): CA-CFAR (With Guard cells per side = 2)
Fig 8(b): CA-CFAR (With Guard cells per side = 8)
In Fig. 8(a), a small guard region (G=2) is employed. Because the guard cells provide limited separation between the cell under test and the training cells, portions of the target energy leak into the training window. This leakage biases the noise power estimate upward, causing a local increase in the adaptive threshold in the vicinity of strong or extended targets. As a result, the threshold rises excessively near the target region, which can partially mask weaker target returns and reduce detection reliability.
In Fig. 8(b), a larger guard region (G=8) is used, providing improved isolation between the cell under test and the training cells. This reduces contamination of the noise estimate by target energy, leading to a more representative estimate of the background interference level. Consequently, the adaptive threshold remains lower and more stable near target locations, allowing reliable detection of extended and closely spaced targets.
This comparison demonstrates that the primary role of guard cells is to prevent target self-masking by isolating the noise estimation process from target returns. While guard cell size has minimal impact in homogeneous noise environments with isolated point targets, it becomes critical in scenarios involving extended targets or closely spaced targets.
Even with careful selection of guard and training cell parameters, CA-CFAR performance can degrade in complex multi-target or non-homogeneous environments, motivating the use of more robust CFAR variants such as OS-CFAR.
Ordered Statistics CFAR (OS-CFAR)
While Cell-Averaging CFAR provides effective and simple adaptive thresholding in homogeneous noise environments, its performance can degrade in the presence of non-homogeneous clutter, interfering targets, or closely spaced targets. In such scenarios, the assumption that all training cells contain noise samples drawn from the same distribution is violated. As demonstrated earlier, strong target returns or clutter edges within the training window can significantly bias the noise estimate, leading to excessive threshold inflation and missed detections.
Order Statistics CFAR (OS-CFAR) was introduced to address these limitations by modifying the manner in which the local noise or clutter level is estimated. Instead of averaging all training cells, OS-CFAR sorts the power values of the training cells and selects a specific ranked sample to represent the background interference level. This ranked value is then scaled to form the detection threshold.
Fig 9: Ordered Statistics CFAR (OS-CFAR)
In OS-CFAR, the power samples from the training cells are first sorted in ascending order according to their power levels obtained after square-law detection. From this ordered set, the k-th smallest sample, denoted by X(k), is selected as a representative estimate of the background noise or clutter level. This order statistic is then scaled by a threshold factor α to form the detection threshold.
\[
T = \alpha X(k)
\]
The power in the cell under test is compared against this threshold to determine the presence or absence of a target.
Fig 10: Ordered Statistics CFAR (OS-CFAR) demonstration
Figure 10 illustrates the operation of an Order-Statistics CFAR (OS-CFAR) detector applied to a range profile containing non-homogeneous interference and multiple strong outliers. The blue curve represents the received range profile after square-law detection, while the orange curve shows the adaptive OS-CFAR detection threshold.
A true target is present at the cell under test, whereas several strong interfering returns are deliberately placed within the training window. These interferers significantly increase the power of some training cells but do not represent the local noise background. In OS-CFAR, since the k-th smallest sample is selected to estimate the background level, the largest training-cell values, which correspond to interfering targets, are effectively ignored.
This behavior is clearly observed in the figure. Despite the presence of multiple high-power interferers in the training region, the OS-CFAR threshold remains relatively stable and does not rise excessively. Consequently, the true target exceeds the adaptive threshold and is correctly detected, while the threshold is not dominated by the interfering returns.
In CA-CFAR, the noise power is estimated by averaging the surrounding training cells. As a result, when two targets are closely spaced, the stronger echo can contaminate the training cells of the weaker one, causing the detection threshold to rise. This phenomenon, known as threshold masking, can prevent the weaker target from being detected. Consequently, CA-CFAR may struggle to resolve closely spaced targets, particularly in multi-target or non-homogeneous environments.
In contrast, OS-CFAR mitigates this problem by sorting the training-cell power samples and selecting a lower-ranked order statistic rather than averaging all samples. Since the largest samples typically caused by strong interfering returns are excluded from the noise estimate, their influence on the threshold is significantly reduced.
To illustrate this behavior, consider a simple example in which the power values from eight training cells are:
[0.9, 1.0, 1.1, 1.2, 0.95, 9.5, 11.0, 12.0].
Here, the values close to unity correspond to noise or clutter, while the larger values represent strong interfering returns within the training window.
After sorting the samples in ascending order, the ordered set becomes:
[0.9, 0.95, 1.0, 1.1, 1.2, 9.5, 11.0, 12.0]
Instead of averaging all samples, OS-CFAR selects a ranked value, for example the fourth smallest sample, as a representative estimate of the background level. By excluding the largest samples, which are dominated by interference, the resulting detection threshold remains representative of the true noise background and is not inflated by nearby strong targets.
As a result, OS-CFAR maintains a more stable threshold and enables reliable detection of closely spaced targets even in the presence of strong interference.
Concluding Remarks
In practice, the choice between CA-CFAR and OS-CFAR depends on the operating environment. CA-CFAR is well suited for scenarios with relatively homogeneous noise or clutter and isolated point targets, where its simplicity and computational efficiency are advantageous. OS-CFAR is preferred in complex environments characterized by non-homogeneous clutter, multiple closely spaced targets, or strong interference, where robustness to training-cell contamination is critical.
Overall, CFAR detection remains a cornerstone of modern radar signal processing. Understanding the strengths and limitations of different CFAR variants, along with careful selection of design parameters such as training cells, guard cells, and order-statistic rank, is essential for achieving reliable detection performance in real-world radar systems.
