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Effective pathloss compensation model based on multipath exploitation for throughthewall radar imaging
EURASIP Journal on Advances in Signal Processing volumeÂ 2023, ArticleÂ number:Â 42 (2023)
Abstract
Throughthewall radar imaging (TWRI) has attracted a great deal of attention in several sensitive applications, including rescue missions and military operations. Notwithstanding its broad range of applications, TWRI suffers from pathloss because distant targets experience more attenuation of signal power than those closer to the transceiver. This challenge may lead to missed targets with important information necessary for analysis and informed decision making. Responding to the challenge, we have developed a signal model with an effective pathloss compensator incorporating a free space exponent. Furthermore, multipath exploitation and compressive sensing techniques were employed to develop an effective algorithm for isolating residual clutter that may corrupt real targets. The proposed signal model integrates contributions from the front wall, multipath returns, and pathloss. Compared with the stateoftheart model under the same experimental conditions, simulation results show that the proposed model achieves improved signaltoclutter ratio, relative clutter peak, and probability of detection by 13.1%, 17.4% and 33.6%, respectively, suggesting that our model can represent the scene more accurately.
1 Introduction
Throughthewall radar imaging (TWRI) is used to detect obstructed targets behind the walls. TWRI involves imaging the interior parts of a building to detect, identify, classify and track the whereabouts of humans and other desired targets. This technology may be useful in rescue missions (e.g., recovering people from fire and earthquake tragedies) and military operations [1,2,3,4]. Recently, there has been notable achievements in TWRI with authors establishing robust methods and techniques to advance the field [5,6,7,8,9,10,11,12,13,14,15,16].
TWRI suffers from multipath reflections and pathloss that cause poor accuracy in target detection [17,18,19,20,21]. The former factor originates from surrounding walls and near targets that tend to produce ghosts (replicas of the genuine targets) during image reconstruction. Multipath ghosts cause scene cluttering that reduces the probability for accurate target detection, classification, and localization [1, 22]. Pathloss describes the reduction in power density of the electromagnetic wave as it propagates from the transceiver to the desired target. This process occurs during imaging of the behindthewall scene. Since free space pathloss varies with frequency and distance travelled by the electromagnetic wave, distant targets undergo more pathloss than near targets. If not effectively mitigated, pathloss may have substantial impact on target detection, especially on distant targets with weaker reflectivities. Consequently, the scene may not be accurately represented [17, 18].
Reverberation from the front wall may be another serious challenge that negatively impacts reconstruction of scenes in TWRI. Consequently, ghosts become equally spaced along the downrange because of multiple reflections from outer and inner surfaces of the wall. Moreover, strong reflections within the wall cause near targets to be masked out [18, 22]. Many TWRI applications require highly resolved radar images, which can only be achieved with large apertures and wide bandwidths. These requirements present yet another challenge of bigger sensing measurements that pose computational complexities and increased processing time [23, 24].
Researchers have devised multiple methods to address the challenges in TWRI. To alleviate the effects of multipath reflections, scholars have developed techniques that broadly fall into two categories: aspectdependent based and multipathexploitation based. The former technique is based on the finding that, when a scene is interrogated from different radar locations, the corresponding ghostsâ€™ locations change while the true targets remain at the same pixels [1, 25]. The later technique exploits additional energy from multipath reflections by focusing the energy to the real targets. This technique requires complete knowledge of the reflective geometry of the scene, and can be used with compressed sensing (CS) [22] or without CS [26]. When used with CS, multipath exploitation suppresses the ghosts thoroughly by inverting the multipath model [22]. The front wall effects are counteracted using relevant mitigation methods, such as spatial filtering [27] and singular value decomposition [28]. To address the big data challenge, CS is usually employed to reconstruct a sparse signal using only a small fraction of linear projections of the original signal without compromising the image quality [24, 29,30,31]. Despite these noteworthy efforts, pathloss effects have not been adequately mitigated in TWRI.
Most works in TWRI assume that pathloss is absorbed into the complex reflectivity of the target. This assumption is unrealistic because pathloss stems from the physical effects of electromagnetic wave propagation. Alahmed et al. [17] considered pathloss and proposed a pathloss compensator that recouped the effect of free space pathloss to two targets in the presence of the front wall. However, multipath returns were not considered in their model. Kokumo et al. [18] extended the work of Alahmed et al. [17] by incorporating multipath returns in the design of the pathloss compensator. However, the model by Kokumo et al. resulted in highly cluttered images. Notwithstanding the limitation, and considering a category of methods pursued along the current research trajectory, this model remains the most recent one with promising performance. Therefore, we have used the Kokumo et al.â€™s model for benchmarking and comparison.
In this paper, we apply the multipath exploitation under the CS framework to develop a compensation model that recoups pathloss more efficiently. The proposed model effectively applies a free space pathloss as the fundamental component for the compensator. We factor in multipath returns and introduce a clutter isolation algorithm. These modifications and improvements ensure that all behindthewall targets are accurately detected. Our novelty seats on the proposed clutter isolation algorithm that considers the established compensation model to generate high quality images with little clutter. This algorithm opens promising research avenues to implement superior TWRI approaches into practical systems, an achievement that may save lives of people trapped in hazardous natural disasters. We should note that TWRI is still an evolving field with several prospects for realworld realization.
The remainder of this paper is organized as follows. In Sect.Â 2, the TWRI signal model is presented. SectionÂ 3 describes the proposed pathloss compensation model and Sect.Â 4presents the pathloss compensated received signal model. In Sect.Â 5, the simulation setup and results are presented. SectionÂ 6concludes the study.
2 TWRI signal model
TWRI scene interrogation requires a steppedfrequency radar to maintain high energy of the transmitted ultrawideband signal. This strategy improves the downrange resolution [1, 26, 32]. Furthermore, crossrange resolution increases with aperture length, and this improvement in resolution gives a reason why recent TWRI systems employ Synthetic Aperture Radar [27, 32]. Consider a stepped frequency signal, realized by N radar locations and a series of M monochromatic waves with uniform frequency spacing, used to image a scene in which front wall reflections, internal wall multipath, and interaction multipath exist [22]. FigureÂ 1 illustrates a scene model showing firstorder multipath returns while imaging a typical TWRI scene. Suppose that the scene is subdivided into \(N_x\times N_y\) pixels along crossrange and downrange, respectively. The received signal corresponding to the \(m^{th}\) frequency \((m=0, 1,\ldots , M1)\) and \(n^{th}\) transceiver location \((n=0, 1,\ldots , N1)\) is obtained by combining the front wall returns, \(y_w[m,n]\), target returns, \(y_t[m,n]\), target interactions, \(y_i[m,n]\), and ambient noise sample, \(\upsilon [m,n]\), and can be expressed as [18]
If specular reflection is assumed, and if the reflectivity of a target at the \(p^{th}\) pixel is \(\sigma _p\), where \(p=0, 1, 2, 3,\ldots , N_x N_y1\), the received signal is given as [4]
where R represents the number of target returns, \(\sigma _w\) and \(\sigma _p\) are wall and target reflectivities in relation to \(r_w^{th}\) and \(r^{th}\) returns, respectively. Also, \(t_{pn}\) is the roundtrip delay between \(p^{th}\) target and \(n^{th}\) receiver due to the \(r^{th}\) return. Similarly, \(t_{pqn}\) denotes the roundtrip delay between the targets, p and q, with respect to the \(n^{th}\) receiver for the \(r^{th}\) return, while \(t_w^{(r_w)}\) signifies delay from the front wall.
3 Proposed pathloss compensation model
This work proposes a pathloss compensation model that can more effectively recoup the pathloss effects. Contrary to the conventional twostep approach (Fig.Â 2a), the proposed model compensates pathloss attenuation in three steps (Fig.Â 2b): firstly, the uncompensated (intermediate) image is formed, followed by estimation of the possible locations of targets; secondly, using the estimated target location vector, the selective pixelwise pathloss compensation is performed; lastly, the final image is reconstructed from the compensated measurements. For the second step, our work presents a clutter isolation algorithm that facilitates the estimation of target locations and the construction of a selective compensation matrix.
One of the shortcomings of the existing models is that pathloss is compensated for every pixel, even for the pixels unoccupied by targets. This shortcoming suggests that contributions from clutter will also be amplified and, consequently, the final image will have low signaltoclutter ratio (SCR) and low relative clutter peak (RCP). In the current work, we propose a clutter isolation algorithm that addresses this shortcoming by ensuring that only a few selected pixels with presumed targets are compensated. Since the locations of targets are unknown, the intermediate image is used to estimate such locations.
The idea of estimating the locations originates from the premise of TWRI: returns from pixels occupied by targets are stronger because targets have higher reflectivities. During image formation, the intensity of each pixel is normalized to the maximum intensity. Therefore, targets are reasonably assumed to reside in pixels of highest values of normalized intensity.
Prior information on the number of targets behind the wall may be known or unknown [1, 33]. When the number of targets, k, is known, the algorithm sorts the elements of the image vector in a descending order. This process retrieves k largest values of normalized intensity and their corresponding indices in the original image vector. The indices represent k pixels (locations) occupied by k targets. Let k and \(\hat{s}_i\) be the number of targets and the intermediate image vector, respectively. Then, the resulting target vector, h, can be expressed as \(h=[h_1, h_2, h_3,\ldots , h_k]^T\) where \(h_1, h_2, h_3,\ldots , h_k\) are the k largest elements of \(\hat{s}_i\) with \(h_k=\hat{s}_{ik}\). The target location vector that contains the assumed target locations corresponding to h is given by \(l=[l_1, l_2, l_3,\ldots , l_k ]^T\), where \(l_1, l_2, l_3,\ldots , l_k\in [1, 2, 3,\ldots , N_xN_y]\) and \(l_k\) is the index of \(h_k\) in \(\hat{s}_i\).
For the unknown number of targets, estimation can be done from the available parameters of the imaging system. Scholars have established that, assuming scene sparsity, the number of targets in high resolution images is small compared with the number of pixels [23]. Therefore, for a given pixel grid of size \(N_xN_y\), if a small constant, \(\gamma\), representing the fraction of pixels occupied by targets is selected such that \(k<<N_xN_y\), the maximum number of targets, k, becomes
Once k is obtained, the location of the assumed targets is calculated the same way as for the known number of targets. Next, the compensation matrix is constructed for strategic preprocessing of the measurements. Specifically, the matrix compensates pathloss to simultaneously achieve higher values of SCR and RCP in the final reconstructed image.
The free space pathloss is quantified as
where \(G_t\) and \(G_r\) denote transmit and receive antenna gains, respectively, f represents the signal frequency, and d is the distance between the transmitter and the receiver. The equation
derived from (3.2) is used to compute entries of the compensation matrix. L(m,Â n,Â p) represents pathloss experienced by the radar return for the \(m^{th}\) frequency at the \(n^{th}\) location by the \(p^{th}\) pixel. The derivation of (3.3) is shown in the Appendix. The algorithm to isolate clutter from compensation is summarized in AlgorithmÂ 1.
4 Pathloss compensated received signal model
Since our focus is to compensate pathloss for target returns, we assume that front wall contributions in (2.1) have already been suppressed using the techniques by Lagunas et al. [27] and Tivive et al. [28]. To compensate for pathloss, y[m,Â n] is multiplied by a compensator, g(m,Â n,Â p), for the \(m^{th}\) frequency, \(n^{th}\) radar location, and \(p^{th}\) pixel to yield a pathloss compensated return
With R multipath returns from interior walls, (4.1) becomes
For notational simplicity, we can reasonably vectorize (4.2) such that the MN measurements in y[m,Â n] are stacked to form a tall vector [22]
Similarly, the reflectivities are expressed in vector form as
The phase terms for target and interaction returns are represented by dictionary matrices \(\varvec{\varPhi }\) and \(\varvec{\psi }\), respectively, defined by
and
where \(z=0, 1,\ldots ,MN  1, m= i\mod M\) and \(n=\lfloor i/M \rfloor\). After obtaining the target location vector, \(\varvec{l}\), selective compensation is achieved by the matrix equation
As indicated in (4.7), the matrix compensates pathloss only if the pixel contains a target, otherwise, the corresponding return is not compensated. Consequently, clutter caused by allpixel compensation is suppressed.
Applying CS to the received compensated signal yields [23]
where \(\varvec{C}^{(r)}=\varvec{D}(\varvec{G}^{(r)}\circ \varvec{\varPhi }^{(r)})\), \(\varvec{C}_i=\varvec{D}(\varvec{G}^{(0)}\circ {\psi }^{(r)})\), \(\varvec{D}\in \left\{ 0, 1\right\} ^{J\times MN}\), and \(r=0, 1,\ldots R1\). Considering the first target in target interactions to be the perfect reflector [34], (4.8) can be rewritten as
with \(\varvec{C}=\varvec{C}^{(0)}+\varvec{C}^{(1)}+\ldots +\varvec{C}^{(R1)}+\varvec{C}_i\). Equation (4.9) is a basis pursuit denoising problem, which is solved using YALL1 [35] by mixed \(\ell _1/\ell _2\)norm regularization, to recover the unknown image vector \(\varvec{\hat{s}}\).
5 Results and discussions
For fair comparison, we maintained the room layout, simulation setup, and radar imaging parameters used in the recently proposed model [18]. The origin of the coordinate system is selected to be at the center of the array. The front wall is located parallel to the array at \(0.5~\textrm{m}\), and had a thickness of \(20~\textrm{cm}\) and a relative permittivity, \(\epsilon\), of 7.6632. The first sidewall (sidewall 1) is positioned at \(1.83~\textrm{m}\) and the second sidewall (sidewall 2) is positioned at \(4~\textrm{m}\), while the backwall stands at \(6.37~\textrm{m}\). Three point targets were randomly placed at \((0.31,3.60)~\textrm{m}\), \((0.62,5.20)~\textrm{m}\), and \((0.71,1.00)~\textrm{m}\) (Fig.Â 3).
The imaging parameters were set as follows: stepped frequency signal, \(f=1~\textrm{GHz}\) to \(3~ \textrm{GHz}\); \(M=101\) frequency bins; \(N=45\) transceiver locations with equalweighted multipath; \(R=4\). The scene is discretized into 45 \(\times\) 45 pixels. Additive White Gaussian Noise of SNR 0 dB was added to the measurements and the simulation results were obtained using MATLAB R2018a.
For proper benchmarking, the simulation was carried out using the DelayandSum Beamforming (DSBF) technique that utilizes all measurements [36]. Then, CS was used and only half of the frequency bins and half of the transceiver locations were randomly selected. CS sparse image reconstruction was done using YALL1 algorithm as recommended by AlBeladi and Muqaibel [37]. The simulation was performed with two and three targets to further validate the performance of our model. Moreover, simulation was done by considering scenarios with known and unknown number of targets.
The metrics that were used to quantify performance of the proposed model were probability of detection, PD (which is similar to recall rate [37] and matching rate [19]), SCR and RCP. In addition, the images obtained from simulating the models were evaluated through qualitative analysis.
5.1 Two targets scenario
FiguresÂ 4b through d show images formed using DSBF with full measurement scene data. The pathloss effect manifests itself in Fig.Â 4b where the far target appears with diminished intensity compared with the original scene depicted in Fig.Â 4a. The resulting images from the existing and the proposed models are shown in Figs.Â 4c and d, respectively. Evidently, the proposed model recouped pathloss effects more effectively. To quantify the improvement, PD, SCR and RCP were computed. PD refers to the ratio of the number of detected targets to the total number of targets. The PD against normalized intensity threshold is shown in Fig.Â 5. The intensity of one signifies that the target was perfectly reconstructed. Ideally, the PD should be 100% (all targets detected) across the entire intensity threshold range, (01). The line graph in Fig.Â 5 shows that, for the uncompensated case, the PD fell to 50% (one target detected) beyond 0.5 intensity threshold. The Figure further shows that, in the existing model, the PD dropped to 50% for values of intensity above 0.7, and that the proposed model yielded a PD of 100% till the 0.9 intensity, where it fell to 50%.
SCR values obtained were 27.92 dB, 28.09 dB, and 28.22 dB for uncompensated case, existing model, and proposed model, respectively. RCP values were 2.86 dB, 2.31 dB, and 0.67 dB for the uncompensated, existing, and proposed (compensated) cases, respectively. In DSBF, ghosts are not suppressed, thus degrading SCR and RCP of the image.
Simulations using CS with only 25% of the original data volume were performed in two scenarios, known and unknown number of targets. FigureÂ 6a shows the image obtained when pathloss was not compensated. In this case, the second target was not detected completely. The existing pathloss compensation model generated a highly cluttered image despite its encouraging attempt to detect the second target (Fig.Â 6b). Meanwhile, assuming known number of targets, the proposed model performed well by efficiently detecting all targets (Fig.Â 6c). Negligible clutter from our result may be originated from the algorithm for isolating clutter. Furthermore, using 100 Monte Carlo runs, SCR for existing and proposed models were 37.44 dB and 61.21 dB, respectively, whereas RCP for these models was 6.08 dB and 28.81 dB, respectively. From both metrics, we apparently recognize that the proposed model surpasses the existing model significantly.
FigureÂ 6d shows that the existing model detected all two targets (PD of 100%) until the intensity threshold increased above 0.5, where the model could not detect the second (farthest) target. The proposed model, however, maintained the PD of 100% up to the intensity threshold of 0.7, after which the PD degraded to 50%. In essence, the proposed model can attain an acceptable value of the detection probability to recover all targets with considerably higher intensity.
Simulations were also performed under the assumption of unavailable prior information on the number of targets. From the simulations, we empirically established that choosing \(\gamma\) between 0.5% and 1.0% produced more satisfactory results. This choice is fairly reasonable because sparsity of the scene is uncompromised. FigureÂ 7a shows a reconstructed image using the proposed model when the maximum number of targets was assumed to be only 0.5% of the pixelgrid size.
Comparing the images in Figs.Â 6b andÂ 7, the results apparently show that, even when the number of targets is unknown, the proposed model outperforms the existing one, especially when \(\gamma =0.5\%\) as its corresponding image contains relatively little clutter. SCR and RCP averaged over 100 Monte Carlo runs were, respectively, as follows: (37.44, 6.08) dB, existing model; (47.56, 21.79) dB at \(\gamma =1\%\) and (54.08, 23.64) dB at \(\gamma =0.5\%\), proposed model.
The PD line chart depicted by Fig.Â 8 shows that, for the existing model, the PD is maintained at 100% from intensity threshold of 0.0 up to 0.5, after which it falls to 50%. For the compensated model with \(\gamma =0.5\%\) and \(\gamma =1.0\%\), the PD was observed to coincide; the PD started at 100% and dropped to 50% above the 0.6 intensity threshold. Overall, the PD achieved by the proposed model was higher than the PD generated by the existing model.
5.2 Three targets scenario
Evaluating further the performance of our model, a threetarget scene was simulated. For benchmarking purposes, we firstly applied DSBF with full measurement set. The original scene is depicted in Fig.Â 9a. When pathloss was not compensated, the beamformed image appeared with two distant targets hardly visible (Fig.Â 9b). FigureÂ 9c presents results when the existing model was used to compensate pathloss. Apparently, results from this Figure show that the farthest target is hardly noticeable and that the middle target appears faint. This result suggests that the existing model did not adequately recoup the pathloss. However, the proposed model demonstrates its superiority by detecting all three targets with high intensity (Fig.Â 9d).
The PD line chart in Fig.Â 10 delineates the performance in detecting targets at different intensity thresholds. The uncompensated case shows poor performance as it was able to detect the three targets (PD=100%) only when the intensity was below 0.1. Between the intensity of 0.1 and 0.3, only two targets were detected (PD=66%) and above 0.3 intensity only one target was detected (PD=33%). This result explains why the two farthest targets in Fig.Â 9b are almost imperceptible visually. The existing model shows slight improvement by detecting all three targets below 0.3 intensity and by detecting two targets between 0.3 and 0.5 intensities. Nevertheless, beyond 0.5 intensity threshold, only one target was detected by the existing model. But the proposed model exhibited superior performance by maintaining the PD at 100% for all intensities below 0.9 intensity threshold.
With DSBF, SCR values obtained were 33.51 dB, 30.55 dB, and 26.59 dB for uncompensated case, existing model, and proposed model, respectively. RCP values were 6.58 dB, 6.02 dB, and 1.15 dB for the uncompensated, existing, and proposed model, respectively. Due to the presence of ghosts in the image, SCR and RCP did not improve for both existing and proposed models.
More simulations for the threetarget scenario were carried out using multipath exploitation with CS in two main categories: known and unknown number of targets. The same data compression ratio of 25% was maintained. The reconstructed images when the number of targets is known a priori are shown in Fig.Â 11a through c. FigureÂ 11a shows the image obtained when pathloss effects were ignored, resulting in the two farthest targets being barely visible. In Fig.Â 11b, the existing model generates visible targets but with highly cluttered image of low intensity caused by uniform compensation. FigureÂ 11c depicts a reconstructed image from the proposed model, in which the targets are clearly visible with unnoticeable clutter.
The PD trend is depicted in Fig.Â 11d. The PD for the existing model is 100% only for intensity thresholds below 0.1. In contrast, the proposed model maintains a PD of 100% up to 0.35 intensity threshold. Under this condition, the existing model detects only one target (PD=33%) whereas the proposed model detects two targets (PD=67%) until the intensity threshold of 0.5, beyond which only one target can be detected. The values of SCR for the existing and proposed models averaged over 100 Monte Carlo runs were 35.32 dB and 61.69 dB, respectively. Similarly, RCP values were 7.18 dB and 29.57 dB for the existing and the proposed model, respectively.
FigureÂ 12 shows images obtained when the proposed model was simulated under unknown number of targets. FigureÂ 12a shows an image from the proposed model with \(\gamma =0.5\%\) (the number of targets is 0.5% of the pixelgrid size). Likewise, Fig.Â 12b depicts a reconstructed image when \(\gamma =1\%\). Comparing Figs.Â 11b and 12, the proposed model exhibits a superior performance. Additionally, the image in Fig.Â 12a has less clutter than that of Fig.Â 12b, signifying that for this scenario, \(\gamma =0.5\%\) is a better estimation of the number of targets. SCR and RCP averaged over 100 Monte Carlo runs were, respectively, as follows: 35.32 dB and 7.18 dB, existing model; 39.54 dB and 7.96 dB (\(\gamma =1\%\)), proposed model; 39.96 dB and 8.43 dB (\(\gamma =0.5\%\)), proposed model. While the existing model managed to detect all targets below 0.1 intensity threshold, the proposed model performed much better (Fig.Â 13). With \(\gamma =1\%\), all targets were detected till 0.3 intensity threshold, whereas \(\gamma =0.5\%\) could maintain a PD of 100% until the intensity threshold reached 0.35.
6 Conclusion
This study has introduced a more effective pathloss compensation model in TWRI. The model contains two key components that facilitate generation of highly resolved images that can more accurately represent the scene of interest. The free space pathloss exponent incorporated into the compensation model ensures that targets are reconstructed with higher intensity. Furthermore, the proposed algorithm to isolate residual clutter when compensating pathloss guarantees high quality and almost clutterfree images. The overall outcome is that the probability of detecting targets is improved significantly. This outcome is beneficial for TWRI applications that require precise representation of the scene, including search and rescue operations. In addition, compelling features of our model may facilitate sensitive law enforcement operations. Results of the current study can be further extended by developing an experimental model to establish a suitable pathloss exponent for TWRI scenarios and by including other propagation effects, such as shadowing. Moreover, the method of estimating the number of targets behind the wall can be improved.
Availability of data and materials
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
Abbreviations
 CS:

Compressive sensing
 DSBF:

Delayandsum beamforming
 PD:

Probability of detection
 RCP:

Relative clutter peak
 SCR:

Signaltoclutter ratio
 TWRI:

Throughthewall radar imaging
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FM conceived the idea and wrote the first draft of the manuscript; ATAprovided technical concepts and guided the research; and, BM, IA, and AM finalized the manuscript writeup, proofread and checked technical correctness of the manuscript, and provided future perspectives of the research. All authors read and approved the final manuscript.
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Appendices
Appendix A: TWRI pathloss equation
Free space pathloss is expressed as the ratio of transmitted power to the received power, and is deduced from the Friis transmission Eq. (2.1). In multipath exploitation, target returns are calculated based on time delay. Since the distance covered by a signal is directly proportional to its propagation delay, the distance from the pixel to the transceiver can be expressed as
where \(t_{pn}\) is the propagation delay between the \(p^{th}\) pixel and the \(n^{th}\) transceiver, and c is the speed of light in free space. Because a stepped frequency radar is used to image the throughthewall scene, the frequency range is split into frequency bins. Substituting (A.1) into (2.1) yields
with
K is a constant and, since normalization is performed when reconstructing the image, (A.2) can be relaxed to
Equation (A.3) is used as a basis for computing pathloss during simulation.
Appendix B: Performance evaluation metrics
1.1 B.1 Signaltoclutter ratio (SCR)
SCR is defined as the ratio of maximum target amplitude to average amplitude in the clutter region. This metric is expressed in logarithmic notation by Leigsnering et al. [22] as
where \(A_t\) and \(A_c\) denote target and clutter areas, respectively, s(p) stands for the signal value corresponding to the \(p^{th}\) pixel and \(N_c\) is the number of clutter pixels.
1.2 B.2 Signaltoclutter peak (RCP)
RCP, calculated as
signifies how easily a target can be discerned amidst the surrounding clutter.
1.3 B.3 PD
Probability of Detection, expressed as
denotes the proportion of detected number of true targets with respect to the total number of true targets at a given intensity.
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Mkemwa, F., Abdalla, A.T., Maiseli, B. et al. Effective pathloss compensation model based on multipath exploitation for throughthewall radar imaging. EURASIP J. Adv. Signal Process. 2023, 42 (2023). https://doi.org/10.1186/s13634023010043
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DOI: https://doi.org/10.1186/s13634023010043