1 Introduction

The constant false alarm rate is among the most important indicators of radar signal processing devices [1]. It is desirable in modern radar systems to maintain CFAR while maximizing the probability of detection (Pd). To achieve this, the threshold value automatically adjusts itself to maintain the probability of constant false alarm rate (Pfa) [2]. The detection process is straightforward by comparing the signal to some threshold value [3]. Thresholding criteria can be categorized into two types: constant threshold and adaptive threshold [4]. Despite its simplicity of design, the constant threshold does not reduce the amount of false alarm rate and has a high rate of misdetection. Target identification is improved by the adaptive threshold, also known as CFAR, and the false alarm rate is better controlled [5]. Dense radar target scenarios [6, 7] become a challenge to existing target detection algorithms because nearby targets often raise the noise level and decrease the likelihood of discovery [8]. The threshold level of a CFAR detector should be set in accordance with the volume of the ambient noise [9], which is calculated using certain algorithm and is varied depending on the detecting environment. Different detection environments should be considered when evaluating target detection algorithms. There are two distinct classifications for the environment: homogeneous, which refers to a setting with either a solitary objective or multiple objectives that are similar, and non-homogeneous, which pertains to a scenario with several targets that are either in close proximity or are located near cluttered edges [10, 11]. In response to these complex settings, several CFAR detectors have been developed, including Cell Averaging CFAR (CA CFAR) [12, 13], Greatest Of CFAR (GO CFAR) [14], Smallest Of CFAR(SO CFAR) [15], and Ordered Statistics CFAR (OS CFAR) [16, 17]. Furthermore, many CFAR algorithms have been proposed by combining basic CFAR algorithms, such as Smallest of Cell Averaging CFAR (SOCA CFAR) [18], Trimmed Mean CFAR (TM CFAR) [19, 20], also, Order Statistics Greatest Of CFAR (OSGO CFAR) [21], Ordered Statistics Variability Index CFAR (OSVI CFAR) [22], weighted amplitude iteration CFAR (WA CFAR) [5], Clutter Map CFAR (CM CFAR) [23], furthermore Truncated Statistics CFAR (TS CFAR) [24], Censored Mean Level Detector (CMLD CFAR) [25], Fuzzy CFAR detectors [26, 27], fusion of different CFAR detectors such as (AND CFAR) and (OR CFAR) detector [28]. Table 1 illustrates the shortcomings of some of the CFAR detection techniques that are mentioned above [29]. To overcome the shortcomings of these techniques and to provide a simple and affordable detector, this research introduces the CM-CM CFAR algorithm to detect targets in various situations, which is meant to detect targets in various contexts based on the features of different CFAR types to progress to a higher Pd and a lower Pfa.

Table 1 A clear definition of the shortcomings of some CFAR algorithms
Full size table

2 Clutter statistical models

Modern high-resolution radar may not follow the Rayleigh model for clutter returns (sea clutter, weather clutter, or land clutter), as the amplitude, distribution develops a “larger” tail that may increase the false alarm rate. Compound Gaussian distributions have been investigated as an option to suit sea radar clutter [30]. The following lists some common distributions that are taken into account for CFAR detection of maritime targets.

2.1 Log-normal model

The characteristics of clutter in radar systems are described statistically by the log-normal model. It is based on the assumption that the clutter echoes can be represented by a log-normal distribution, which is a commonly used distribution in many fields of science and engineering [31].

$$\begin{aligned} f\left( x\right) =\frac{1}{x\sqrt{2\pi \sigma ^2}}*e^\frac{-{(\ln {x-\mu )}}^2}{2\sigma ^2} \end{aligned}$$
(1)

where \(\mu \) and \(\alpha \) are the median and the standard deviation of the random variable ln(x) respectively.

2.2 Weibull model

The Weibull model is particularly useful for modeling clutter from fabricated objects, such as buildings and vehicles. The model assumes that the clutter echoes are the result of multiple reflections and scattering from the surfaces of fabricated objects. The Weibull distribution [30] has two parameters: a shape parameter, denoted by a, and a scale parameter, denoted by b. The PDF of the Weibull distribution can be expressed as:

$$\begin{aligned} f\left( x\right) =\frac{ax^{a-1}}{b^a}*e^{\left( -\frac{x}{b}\right) ^a},\ \ a,b>0\ \ \end{aligned}$$
(2)

2.3 Pareto type II model

For data sets with a particularly heavy tail, such observations of sea clutter, the Pareto disturbance is taken into consideration as a potential model. The texture component must adhere to the inverse gamma law to produce the Pareto type II pdf. The latter explains how the tilting of the lighted region causes differences in the local reflected power. The probability density function has been used in [32] to characterize the statistics of a Pareto distributed random variable x.

$$\begin{aligned} f\left( x\right) =\frac{\alpha \beta ^\alpha }{\left( x+\beta \right) ^{\alpha +1}}\ \ \ \ \ \ \ \ \,x>0\ \ \ \ \ \end{aligned}$$
(3)

where \(\alpha \) is the shape parameter and \(\beta \) the scale parameter.

3 Related CFAR algorithms

The CA CFAR, OS CFAR, MOSCA CFAR, CMLD CFAR, SW CFAR, and CM CFAR methods are introduced in this section. All CFAR processors have the same goal: to declare the target’s presence or absence by setting an adaptive threshold that is dynamically determined by the assessed background level and the desired false alarm rate. Radar target detection is usually modeled by binary hypothesis test. The observed signal y under the two hypotheses, H1 for target present and H0 for target absent (clutter only), is given by

$$\begin{aligned} e(y)= {\left\{ \begin{array}{ll}H 1, &{} C U T>Z \\ H 0, &{} C U T \le Z\end{array}\right. } \end{aligned}$$
(4)

Figure 1 displays a general CFAR processor for a range profile. The samples at the demodulator’s output are kept in a sliding window shift register that is separated into N leading and lagging reference cells, Guard Cells (GC), and the Cell under test (CUT). The associated value of the video stream and the cell itself are referred to together as CUTs.

Fig. 1
figure 1

Block diagram of the sliding window technique

Full size image

The CUT is often found in the window’s center, and it compares a cell’s value to an adaptive threshold (Z) to determine whether a target is present or absent. The guard cells do not have an impact on this estimate because they may contain echoes connected to a target that spans several resolution cells, but to determine the interference characteristics (T), the reference cells N are only used. The window slides are replacing the CUT with all of the cells in the surveillance area. The leading (T lead) and lagging (T lag) windows’ interference estimations are often calculated separately. The overall interference estimate T is produced by combining both utilizing operations that depend on the technique used, such as mean, lowest, highest. The constant \(\alpha \), which depends on both the Pfa and other particular characteristics, is chosen to guarantee a particular Pfa. The estimated variable interference T and the product of these define the threshold Z. Z is calculated, and a judgement is taken after comparing it to the CUT sample. The sliding window is then advanced by one cell, and the procedure is carried out for each cell.

3.1 Cell averaging CFAR

The mean power of the samples in the reference window is used to estimate the background level in the CA CFAR [13] detector as:

$$\begin{aligned} Z_{CA}=\alpha \times \frac{1}{N}\sum _{i=1}^{N}x_i \end{aligned}$$
(5)

where ZCA is the threshold, \(\alpha \) is the threshold factor, N is the length of the reference window, and xi is the sample in reference window.

3.2 Ordered statistic CFAR

Using a value rank-ordered process, the OS CFAR [16] approach chooses a sample with a specific order as the anticipated background level. Considering that, the series is in ascending order:

$$\begin{aligned} X_1<X_2<\ldots <X_N \end{aligned}$$
(6)

where X1 and XN are the min and max values throughout the reference window, respectively. To determine the representative average background level, a specific order k is chosen:

$$\begin{aligned} Z_{OS}=X_K\ \ \ \ \ \ \ K\in {1,2,\ldots ,N} \end{aligned}$$
(7)

where \(Z_{OS}\) is the threshold and xk is sample in the window with specific order k.

3.3 Mean order statistic cell averaging CFAR

MOSCA-CFAR combines OS and CA CFAR as shown in [1]; Eq. (7) establishes the threshold.

$$\begin{aligned} Z_\mathrm{{MOSCA}}=\alpha *\left( X_K+\frac{1}{2N}\sum _{i=\frac{N}{2}+1}^{N}x_i\right) \end{aligned}$$
(8)

where \(Z_\mathrm{{MOSCA}}\) is the threshold, and Xk is selected sample with specific order k.

3.4 Censored mean level detector CFAR

The CMLD CFAR technique [25], in contrast to conventional CFAR algorithms, censors or eliminates the strongest samples in the reference cells to lessen the impact of significant clutter or interference on the threshold estimation. This enhances the detection capabilities in multiple target situations.

$$\begin{aligned} Z_\mathrm{{CMLD}}=\frac{1}{K}\ \sum _{i=1}^{k}x_i \end{aligned}$$
(9)

where \(Z_\mathrm{{CMLD}}\) is the threshold, and K is selected sample to censors.

3.5 Sorting weighting CFAR

The SW CFAR [5] strategy combines the qualities of three separate CFAR techniques (CA, OSGO, and OSSO) to calculate the background level as:

$$\begin{aligned} Z_\mathrm{{sw}}=\alpha \times \mathrm{{max}}{\left( X_k,Y_k\right) }+\beta *\mathrm{{min}}{\left( X_k,Y_k\right) }\ \ \end{aligned}$$
(10)

where \(Z_\mathrm{{sw}}\) is the threshold; (\( \alpha \),\( \beta \) ) are the threshold factors and (Xk,Yk) are the samples in lagging and leading reference windows respectively with specific order k.

3.6 Clutter map CFAR

The received signal stored in each cell of the map can then be utilized to set a threshold for each cell, as illustrated in Fig. (2) [23]. The value of clutter in each cell is updated often by averaging over numerous scans. The threshold is determined by Eq. ( 11):

$$\begin{aligned}{} & {} Y_n\left( i\right) =\left( 1-F\right) Y_{n-1}\left( i\right) +FX_n(i) \end{aligned}$$
(11)
$$\begin{aligned}{} & {} Z_{CM}={\alpha \times \ Y}_{n-1}\left( i\right) \ \ \ \end{aligned}$$
(12)
$$\begin{aligned}{} & {} N_s=\frac{2-F}{F} \end{aligned}$$
(13)
$$\begin{aligned}{} & {} P_d=\prod _{m=0}^{M}{{(1+\alpha _dF{(1-F)}^m)}^{-1}\ \ \ \ }, \alpha _d=\frac{\alpha }{1+SNR} \end{aligned}$$
(14)
$$\begin{aligned}{} & {} P_{fa}=\prod _{m=0}^{M}{(1-\alpha F{(1-F)}^m)}^{-1} \end{aligned}$$
(15)

where ZCM is the threshold, Yn(i) is the present background estimation, \(\alpha \) is the threshold factor, Ns is the count of consecutive scans, F is the filter weight, which ranges from 0 to 1, M is the scan number, SNR is the signal-to-noise ratio, Yn-1(i) is the most recent background estimate, and Xi is current input.

Fig. 2
figure 2

Block diagram of clutter map CFAR

Full size image

4 The proposed technique of CM-CM CFAR

As it is known, no one of the basic CFAR detectors is most appropriate for different detection situations in different environments. The concept of the proposed CM-CM CFAR relies on constructing a CFAR detector out of a mixture of these basic CFAR detectors. Therefore, the CM-CM CFAR detector is expected to be capable of achieving good performance in the majority of detection settings.

Fig. 3
figure 3

The proposed CM-CM CFAR technique block diagram

Full size image

The proposed CM-CM CFAR algorithm is developed as a mix of qualities from the CMLD CFAR and CM CFAR. The architecture of the proposed algorithm is shown in Fig. 3. The concept of our algorithm is as follows: When the returned signal reaches the last cell in the leading window, the algorithm begins to estimate the current background value from the previous background estimation and the current input, as shown in Eq. (11). Pd and Pfa, which are related to some SNR, are computed using Eqs. (14) and (15). The content of the lagging and the leading windows is sorted. The threshold (ZCMCM) will be extracted as shown in Eq. (16) after weighting it by the threshold factor (\(\alpha \)), and then the decision can be made as Fig. 3 shows:

$$\begin{aligned} Z_\mathrm{{CMCM}}=\alpha \times \left( Y_{n-1}+\frac{1}{K}\ \sum _{i=1}^{k}x_i\right) \end{aligned}$$
(16)

where X(i) is the current input, Yn-1(i) is the previous background estimation, K is selected sample to censors, and \(Z_\mathrm{{CMCM}}\) is the threshold.

5 Experiments and results

In this section, the proposed CM-CM CFAR algorithm will be evaluated using several experiments to demonstrate its effectiveness in different environments. With a parameter value of 105, Monte Carlo trails replicate the radar signal and the Weibull model clutter signal. Insert a Swerling I target model in scenarios of multiple targets moving related to the radar scan it can be simulated as a compound Gaussian noise signal [33]. The length of the reference leading and lagging windows is 30, the guard cell size is three, and the desired false alarm rate is 10-6.

5.1 Received signal in multi environments

In this scenario, the radar signal’s amplitude is represented by N samples from range cells. The analog radar signal is overlaid with the interference. Figure 4 depicts the multi-targets at the range cells (100, 300, and 700) regarding the first environment. Figure 5 depicts the close multi-targets at range cells (100, 105, 300, 303, 307, and 800) pertaining to the second environment. Figure 6 depicts multi-targets at the clutter edge at range cells (100, 500, and 700) in relation to the third environment.

Fig. 4
figure 4

Signal received at range cells (100, 300 and 700)

Full size image
Fig. 5
figure 5

Signal received at range cells (100, 105, 300, 303, 307 and 800)

Full size image
Fig. 6
figure 6

Signal received at range cells (100, 500 and 700)

Full size image

5.2 The performance of different CFAR algorithms

The resulting three considered environments under Pfa = 10-6 are shown in Figs. 7,  8, and 9 for different CFAR algorithms (CA CFAR, OS CFAR, MOSCA CFAR, CMLD CFAR, SW CFAR, CM CFAR, and CM-CM CFAR).

In the first environment, CA CFAR, OS CFAR, MOSCA CFAR, CMLD CFAR, SW CFAR, CM CFAR, and CM-CM CFAR can detect multiple targets marked as (A, B, and C) from Fig. 4, as shown in Fig. 7.

Fig. 7
figure 7

CFAR decision for first environment, result under Pfa = 10-6

Full size image
Fig. 8
figure 8

CFAR decision for second environment, result under Pfa = 10-6

Full size image

In the second environment, CM-CM CFAR, CMLD CFAR, and SW CFAR can detect most of the multiple close targets marked as (D, E, F, G, H, and I) from Fig. 5 in comparison with other CFAR algorithms, as shown in Fig. 8.

Fig. 9
figure 9

CFAR decision for third environment, result under Pfa = 10-6

Full size image

In the third environment, CM-CM CFAR can detect targets at the clutter edge marked as (J, K, and L) from Fig. 6 when compared to other CFAR algorithms, as demonstrated in Fig. 9. From the previous results, the CA CFAR detection performance degrades in multiple close targets situations and power transition regions. In both cases, there are too many false alarms, which results in poor behavior in nonhomogeneous conditions. The CMLD CFAR has high multi-targets detection capability but with low capacity to control false alarms. The MOSCA CFAR detector has a high multi-targets detection capability without maintaining a constant false alarm rate at the clutter edge. In a multiple-targets scenario, OS CFAR displays a comparatively strong detection performance, despite a significant CFAR loss. Although the CM CFAR detector is immune to clutter edge environments, a target-masking effect occurs. The SW CFAR detector was trying to avoid suppressing targets that are close together (target masking); when all of the interferers are situated in either the leading or the lagging cells, this detector determines the principal target in instances involving multiple targets. However, SW CFAR has undesired effects when conflicting targets are in both halves of the reference cells. In addition, its detection performance degrades if both contain interfering targets. The prior drawbacks can be overcome using CM-CM CFAR with a high probability of detection and low probability of false alarm.

5.3 Probability of detection for the different CFAR algorithms

The probability of detection with the signal-to-noise ratio at a constant false alarm rate in the three environments with the performance of some CFAR algorithms (CA CFAR, OS CFAR, MOSCA CFAR, CMLD CFAR, SW CFAR, CM CFAR, and CM-CM CFAR) is shown in Figs. 10, 11, and 12.

Fig. 10
figure 10

pd with SNR for first environment, result under Pfa = 10-6

Full size image
Fig. 11
figure 11

pd with SNR for second environment, result under Pfa = 10-6

Full size image
Fig. 12
figure 12

pd with SNR for third environment, result under Pfa = 10-6

Full size image
Fig. 13
figure 13

Average of pd with SNR for three environments, result under Pfa = 10-6

Full size image

Results show that (CA CFAR, OS CFAR, MOSCA CFAR, CMLD CFAR, SW CFAR, CM CFAR, and CM-CM CFAR) have almost the same performance in the first environment as demonstrated in Fig. 10. Compared to other types of CFAR, CM-CM maintains the fastest access to the highest probability of detection with a low signal-to-noise ratio, as demonstrated in Fig. 11. By examining the third environment, it is apparent that there is a low probability of finding CFAR algorithm to get the required results and that CM-CM CFAR has achieved the best results, shown in Fig. 12. In general, with different probabilities of significance levels, the proposed CM-CM CFAR obtains the best overall performance in detecting all targets, as shown in the average probability of detection for the three environments as demonstrated in Fig. 13. This provides more proof that the suggested method is accurate and efficient in practical settings.

5.4 The effectiveness of various CFAR algorithms in relation to actual data

The actual data deemed available in this section are those gathered by radar at Egypt’s Suez Canal, as seen in Fig. 14.

Figure 15 illustrates how the various CFAR algorithm types are able to detect targets using publicly available real data. With the exception of the first scan, it was observed that CM CFAR detects targets well. In CA, SW, and CMLD, false alarms frequently manifest. With a low false alarm rate, MOSCA CFAR finds almost all targets. The proposed CFAR algorithm has a better chance of being detected and is stable enough to sustain false alarms.

Fig. 14
figure 14

Practical radar data

Full size image
Fig. 15
figure 15

CFAR decision for real data

Full size image

The Pd vs. Pfa for various CFAR methods and CM-CM CFAR is displayed in Fig. 16. A few things can be made clearer, specifically:

  • The likelihood of detection for the CA, OS, and CMLD approaches is good in the real world, but as the figure illustrates, there is a significant flaw that prevents a constant false alarm rate from being achieved. In the actual data, there is a low false alarm rate and a good probability of detection for both SW and OS approaches.

  • CM CFAR does not have the best acceptable PD performance, but it has good performance to achieve continuous false alarm.

  • As the outcome was in the simulation 97.5% and with the real environment 96%, detection advanced in both the virtual and real worlds with a reasonable probability of detection.

Fig. 16
figure 16

pd versus Pfa for actual data

Full size image
Fig. 17
figure 17

FPGA schematic design

Full size image

6 FPGA schematic design implementation

Due to the creation of specialized hardware multipliers in these components, FPGAs are currently in competition with general-purpose programmable DSPs for signal processing tasks in many DSP applications [34]. The suggested architecture for implementing the CM-CM CFAR algorithms and report utilization is shown in Fig. 17 and Table 2. The VHDL, Verilog, and Xilinx Vivado Design Suite 2018 hardware description languages were used to design, synthesize, and simulate this architecture.

The suggested structure was developed for the Artix7-xc7a100t-2csg324 development platform at the register transfer level (RTL).

Table 2 Report utilization
Full size table

  • The samples of the input radar signal are fed into a circuit that selects the maximum sample in each range gate as a 8-bit digital word (under the control of the range gate, the analog-to-digital converter was turned on for the duration of the time interval equal to the transmitted pulse width).

  • A serial shift register is used in the shifting circuit to organize the CUT, remove the old cell, and add the new cell in order to create a moving window.

  • The CMLD CFAR uses sorting circuit to arrange the data from the leading and trailing windows and determine the censored mean threshold.

  • The most recent background estimate is saved by the clutter map circuit using a distributed memory generator with a 15-bit address, which helps it decide the clutter map threshold.

  • The CMLD CFAR circuit and clutter map circuit determine the CM-CM threshold, and the target’s presence or absence is checked using the threshold by the comparator circuit with the tested cell.

Table 3 Results of the CM-CM CFAR processor are compared with those of the earlier implementations
Full size table

A comparison of the outcomes between the suggested approach and the alternative CFAR processors in [35,36,37,38] is presented in Table 3. In [35, 36], an approach based on the Automatic Censored Ordered Statistics Detector (ACOSD) CFAR was applied in the scenario where the background distribution is log-normal. Although the CFAR processors are simple, they cannot be used in a variety of settings. A CFAR processor was presented [37] that can be used with both the Rayleigh distribution and the no-Rayleigh distribution by applying mean level CFAR. On the other hand, its high hardware complexity is a drawback. For multi-target environments, the automatic censored cell averaging detector based on ordered data variability (ACCA-ODV) CFAR processor was proposed [38]; however, it has extremely complex hardware. Furthermore, its limited compatibility with the ACCA-ODV algorithm makes it challenging to use in a variety of settings. When employing CM-CM CFAR with the suggested decision criteria, the suggested CFAR processor can offer better performance for both homogeneous and non-homogeneous environments when compared to earlier implementation results. Furthermore, despite the fact that the suggested CFAR processor is capable of supporting both CM and CMLD algorithms, the effective hardware architecture described in Sect. 6 allows for extremely low hardware complexity and fast operation.

7 Conclusion

A new CFAR technique based on combining various types of CFAR detectors has been developed to overcome changes in environments and multiple targets situations. Simulation results indicate that the Censored Mean Clutter Map CFAR (CM-CM CFAR) algorithm can greatly increase the probability of detection while preserving a fixed false alarm rate of less than \(10^{-6}\) compared to other CFAR algorithms, which makes this algorithm more effective for multiple environmental conditions. As a result, the approach is especially well suited for real-time implementation and requires little in the way of FPGA resources to be completed. As a result, it is envisaged that it will be ideal for systems like drone radar systems that must adjust to clutter and be able to recognize many targets.