Multistatic adaptive CFAR detection in non-Gaussian clutter
- Riccardo Palamà^{1},
- Maria Greco^{1}Email authorView ORCID ID profile and
- Fulvio Gini^{1}
https://doi.org/10.1186/s13634-016-0408-1
© The Author(s). 2016
Received: 5 August 2016
Accepted: 4 October 2016
Published: 19 October 2016
Abstract
This work addresses the problem of target detection for multistatic radars. We propose an algorithm that is able to keep constant the false alarm rate, when the disturbance samples associated with each receiver-transmitter pair are distributed according to a compound Gaussian model. The performance of the proposed detection algorithm are analysed to assess the impact of clutter diversity on detection performance. The results show that clutter statistical diversity has a strong impact on detection performance. The performance of both single-channel and multichannel detection schemes are evaluated by processing real sea clutter data collected by the NetRAD nodes, in order to evaluate which of the two channels, i.e. the bistatic and monostatic channels, is more favourable for target detection. Furthermore, the gain achieved by using a multistatic detection algorithm is also analysed.
Keywords
1 Introduction
Sea clutter is typically non-Gaussian and non-stationary, which makes the design of proper detection algorithms a critical task. The development of radar detection algorithms in the presence of Gaussian or non-Gaussian disturbance has been widely addressed in literature and is still an active research field. In the case of non-Gaussian disturbance, one of the most used algorithms is the so-called normalized matched filter (NMF) [1–3]. Under the hypothesis of compound Gaussian clutter, this algorithm is able to keep constant the false alarm rate (FAR). This property is verified both when the clutter covariance matrix is a priori known and when it is unknown and estimated from the range cells surrounding the range cell under test (in this case, we use the adaptive version of the NMF, i.e. the normalized adaptive matched filter (NAMF) [4–6]). The fast temporal fluctuations of the clutter make its samples to be only partially correlated in short times and broaden the clutter spectrum. The correlation properties are described, from a statistical standpoint, by the clutter covariance matrix.
The use of multiple transmitters and receivers in a radar system aims at improving the target detection, tracking and recognition capabilities of a radar system [7–13]. Radar detection techniques for multistatic radars can be distinguished between centralized and decentralized ones. According to a centralized detection scheme, the signals associated with each transmitter-receiver pair are processed locally at each receiver node, which computes a local statistic, and then, all the local statistics are transmitted to a central processor, which in turn computes a global statistic [7, 9]. The hard decision is performed by comparing this global statistic with a threshold. An alternative detection rule is the decentralized one (see, e.g. [14–17]), according to which each node performs a hard decision, then transmits the resulting binary symbols to a central processor, that executes the final decision. One of the main limitations of a centralized detection technique is that it requires a large bandwidth of the communication link between the system nodes. If the communication bandwidth is not sufficiently large, the local statistics, transmitted by each node to the central processor, may be distorted [18]. For this reason, in real systems, the local statistics are quantized and then transmitted to the central processor; thus, a quantization noise is present. In this work, a centralized detection rule is considered, without accounting for the limitations associated with a communication link with finite bandwidth, as the aim of the work is to study the effect of clutter diversity on the detection performance of a multistatic radar system.
One of the first works dealing with the design of centralized detection for multistatic radar is Conte et al.’s paper [7] that proposes both optimum and suboptimum detection algorithms in the case of white Gaussian noise. In [8], the authors discuss again the optimum and suboptimum multistatic radar detection techniques in the cases that clutter and jamming are Gaussian and correlated with both time and space. A multichannel detection technique, under cross-correlated Gaussian channels, is proposed in [19], where a multichannel generalized likelihood ratio test (GLRT) is derived. More recently, the interest of the radar community towards Multi-Input Multi-Output (MIMO) radar systems has encouraged the research on multichannel detection techniques. MIMO radars can be distinguished, based on the location of their nodes, between collocated and not collocated (also known as widely separated MIMO). In a collocated MIMO radar [11], the transmitter and receiver antennas are in the same location; thus, the diversity is achieved by using antennas with a certain number of elements, each of them transmitting a different waveform. Hence, the diversity gain is guaranteed by the fact that each element of the receiver antenna looks at a different channel. In the case of widely separated radars, transmitter and receiver locations are not the same; thus, the signals associated with each transmitter-receiver pair—if combined together in a correct way—can provide a diversity gain, due to the spatial separation between channels [10, 13]. The optimum detection technique for MIMO radars in the cases of Gaussian and spatially uncorrelated clutter, called MIMO-Optimum Gaussian Detector (MIMO-OGD), has been discussed in [13]. In [20], the authors evaluate the performance of the MIMO-OGD, compared with a decentralized detection scheme. A detection algorithm for MIMO radar that utilizes space-time coded waveforms is derived and discussed in [12]. A MIMO-GLRT, based on a parametric approach, is proposed and validated in [21]. In [22], a MIMO-GLRT and Rao detector are derived in the case of non-Gaussian clutter, and their performance are evaluated in the case of known covariance matrix.
In this work, we consider a multichannel extension of the NMF, introduced with the name of MIMO-Generalized Likelihood Ratio Test-Linear Quadratic (MIMO-GLRT-LQ) in [23]. This detector is the MIMO version of the aforementioned NMF; thus, it can also be termed MIMO-NMF. It has been demonstrated to be able to keep constant the false alarm rate under different clutter distributions belonging to the compound Gaussian family, associated with each transmitter (TX) receiver (RX) pair. The mode of operation of the adopted detection rule is centralized.
In this work, we first discuss the received signal model for multistatic radar, where the target is observed in the presence of non-Gaussian disturbance. Then, two fundamental assumptions—uncorrelated channels and compound Gaussian disturbance—are introduced, in order to derive a suboptimum detection scheme, i.e. the multichannel NMF. First, the performance of the proposed detector are tested by processing simulated data. The adaptive version of the adopted detector, i.e. the MIMO-NAMF is also implemented, by estimating the clutter covariance matrix [5]. The performance of the single-channel NAMF is then evaluated on real sea clutter data, collected by the nodes of the multistatic radar system, NetRAD [24, 25], in order to evaluate the differences between the bistatic and monostatic sea clutter from a radar detection standpoint. NetRAD sea clutter data have been analysed in some recent papers, in order to highlight the differences in the statistics between monostatic and bistatic sea clutter, which have been defined as clutter diversity in [25]. Our performance analysis aims at assessing which of the two channels is the more favourable for target detection. At the same time, the performance of the multichannel NAMF are also analysed by processing real clutter data, with the aim of investigating whether and under which conditions a multistatic detector is able to provide a performance gain with respect to the single-channel detector. In synthesis, the novelty of this work consists of the evaluation of false alarm regulation and detection performance over the two channels, bistatic and monostatic, with different statistical properties. Performance analysis has been carried out by processing both simulated and real clutter data.
The rest of this paper is organized as follows. In Section 2, we summarize the single-channel NMF detector, describe the multistatic signal model and derive the multichannel detection scheme. In Section 3, the performance of the multichannel NAMF are analysed by processing simulated data. In Section 4, the performance of the single-channel and multichannel NAMF are analysed by processing real sea clutter data collected by the NetRAD system. Final remarks are drawn in Section 5.
2 Problem formulation
2.1 Single-channel detection
In the case of single-channel radar, the received signal model under the hypothesis H _{1} (target signal plus disturbance) is z = αp + w, whereas under the H _{0} hypothesis (disturbance only), is z = w ([1, 2]). The received signal samples, z(n), are stacked into the vector \( z={\left\{z(n)\right\}}_{n=0}^{L-1} \), where L is the number of coherently integrated pulses. The time duration of the coherent processing interval (CPI) is T _{CPI}; thus, L = T _{CPI} ⋅ PRF. Similarly, the vector w contains the disturbance samples. The target signal is modelled by the target complex amplitude α times the target steering vector \( p={\left\{p(n)\right\}}_{n=0}^{L-1} \), whose nth element is given by \( p(n)= \exp \kern.3em \left\{-j2\pi n{f}_{\mathrm{D}}/\mathrm{P}\mathrm{R}\mathrm{F}\right\} \), where f _{D} is the target Doppler frequency.
The non-adaptive version requires the prior knowledge of the speckle covariance matrix, R, whereas in the adaptive version, R is replaced by its estimate, \( \widehat{\mathbf{R}} \); in this case, the detector is called normalized adaptive matched filter (NAMF). This test has been demonstrated to be “texture-CFAR” and “covariance matrix-CFAR,” i.e. it keeps constant the false alarm rate with respect to the texture distribution and to the shape of the speckle covariance matrix, if a proper estimation technique is used [4, 5, 31]. The estimation of the speckle covariance matrix is a crucial operation in order to guarantee good performance of the NAMF detector. In the case of CG-distributed clutter, the fixed-point (FP) estimate of the covariance matrix has been demonstrated [4–6] to be asymptotically optimum. Other possible estimators are the sample covariance matrix (SCM) and the normalized sample covariance matrix (NSCM) [32, 33].
2.2 Multichannel received signal model
The target complex amplitudes can be stacked into the vector α, whose covariance matrix is C _{ α } = E{αα ^{ H }}, of size MNL × MNL, and is block-structured, similar to Σ, C and R. Hence, if the target returns are statistically independent across different channels, the matrix C _{ α } is block-diagonal. In addition, if a Swerling I target model is used, the target amplitude is constant within a CPI.
This approach is tantamount to consider the clutter as Gaussian distributed with unknown covariance. In the following, a multichannel GLRT is derived in both cases of perfectly known target signal and unknown target complex amplitude.
2.3 Multichannel detection
In the case that target signal is perfectly known, we have knowledge of the elements of the vector α containing the target complex amplitudes and of the target steering vectors p _{ mn }, for all the values of m and n, which in turn requires a perfect knowledge of the system geometry and of the target velocity v. Hence, the target signal, for the mnth pair, is s _{ m,n } = α _{ m,n } p _{ m,n }; thus, \( {q}_{m,n}^{(1)}\left({\mathbf{z}}_{m,n}\right)={\left({\mathbf{z}}_{m,n}-{\mathbf{s}}_{m,n}\right)}^H{\mathbf{R}}_{m,n}^{-1}\left({\mathbf{z}}_{m,n}-{\mathbf{s}}_{m,n}\right) \).
If P = 1 (one receiver and one transmitter), P _{FA} = λ ^{1-L }, which is the well-known expression of the probability of false alarm achieved by the single-channel NMF [1]. In [23], it is also shown that detector (28) outperforms the MIMO-Optimum Gaussian Detector (MIMO-OGD) in non-Gaussian clutter.
3 Performance analysis on simulated data
The performance of the multichannel NMF detector was analysed by simulating the target and clutter signals. Simulations were realized for both known and unknown covariance matrix. In the latter case, the adaptive version of the detector (28) was implemented, by replacing the covariance matrix with its estimates.
Clutter configurations
Clutter configuration | Statistical distribution | Parameters |
---|---|---|
1 | K | v _{1} = 0.1, v _{2} = 0.5 |
2 | K | v _{1} = 0.2, v _{2} = 0.9 |
3 | K-plus-noise | v _{1} = 0.2, v _{2} = 0.9 |
\( {p}_1^{(n)}={p}_2^{(n)}=0.1 \) | ||
CNR = 10 dB |
3.1 False alarm regulation
By evaluating the “P_{FA}-vs-threshold” plots, the values of the detection threshold λ can be set in order to achieve a desired value of the P _{FA}. As the values of λ depends on the technique used to estimate the covariance matrix, λ _{KC} indicates the value of the threshold in the case of known covariance matrix; λ _{NSCM} and λ _{FP} are the values of the threshold in the case of NSCM and FP estimates, respectively. The values of λ _{KC}, λ _{NSCM} and λ _{FP} to set in order to achieve P _{FA} values from 10^{−5} to 10^{−2} are shown in Table 3. These values will be used in evaluating the detection performance of the multichannel NAMF, by setting a desired P _{FA}.
3.2 Detection performance
The detection performance in the first clutter configuration is similar to the one in the second clutter configuration, whereas it decreases in the third clutter configuration. This is probably because the third clutter configuration includes the presence of a thermal noise component. The P _{D} values are, as expected, the highest in the case of known covariance matrix. Furthermore, the NSCM method shows slightly better performance than the FP, whereas the P _{D} values obtained through the SCM method are always lower than the one obtained by using the NSCM and FP methods. This is an expected result, because the SCM method is optimum only if the clutter is Gaussian.
It should be noted that the single-channel optimum detector has already shown (for many combinations of the values of P_{FA} and SCR) better detection performance with decreasing values of the K-distribution shape parameter, i.e. with increasing clutter spikiness [1, 33, 38–40]
Threshold values (simulated data)
P _{FA} | Known covariance | NSCM | FP |
---|---|---|---|
10^{−2} | 1.13 | 1.23 | 1.25 |
10^{−3} | 1.18 | 1.31 | 1.35 |
10^{−4} | 1.23 | 1.44 | 1.45 |
10^{−5} | 1.29 | 1.54 | 1.55 |
In recent works [25, 30], the statistical analysis of simultaneously collected bistatic and monostatic data of the shape parameter has highlighted that the monostatic shape parameter is almost constant with range, whereas the bistatic one shows large deviations, due to the geometry change. Hence, the detection performance, achieved by applying the multichannel NAMF to monostatic and bistatic data at different ranges, may be heavily influenced by this clutter diversity, especially by the behaviour of bistatic clutter.
4 Performance analysis on real data
4.1 Data overview
NetRAD radar parameters
Radar parameters | |
---|---|
Carrier frequency | 2.4 GHz |
Transmitted signal | Up/down chirp |
Bandwidth | 45 MHz |
Pulse duration | Variable |
Pulse repetition frequency | 1 kHz |
Range resolution | 3.33 m |
Sampling frequency | 100 MHz |
Polarization | HH, VV (separately) |
Half power beamwidth | 9° (el.) × 11° (az.) |
The analysed data were collected by the NetRAD system during a measurement campaign realized in October 2010 at Scarborough, Cape Town, by researchers from the University College London and University of Cape Town. Two nodes—a monostatic one and a bistatic one—were employed in the measurements and were located on the sea coast, at a short distance from the sea.
Measurements were made by varying the azimuth angle, polarization and baseline. For each range cell, the number of received pulses is N _{ p } = 130,000, corresponding to a total acquisition time of 130 s. In this work, we consider the datasets collected on October 21, 2010, with a baseline of 728 m and a bistatic angle (β) of 30° [25, 30].
In order to evaluate the performance of both single-channel and multichannel NAMF detectors on NetRAD data, a target was simulated and its signal superimposed on real clutter data. In particular, the target fluctuations were modelled according to the Swerling-I model, with a complex Gaussian target amplitude, completely correlated within a CPI. The signal-to-clutter ratio (SCR) was set similar to the case of simulated data, and the clutter power is directly computed from the data [30].
The texture cross-correlation coefficient shows a small periodicity for both HH and VV data. For VV data, there are two peaks at a time lag of about 5 and 22 s, whereas for HH data, there are peaks at about 3, 16 and 22 s. In general, VV data show higher peaks, separated by longer intervals, with respect to HH data.
The values of the speckle cross-correlation coefficient are very low for all the data, even if not null (with maximum values around 0.01), and show different behaviours, depending on polarization. For HH data, both r _{ s,QQ } and r _{ s,II } show an almost identical periodic behaviour, whose fluctuations decrease with increasing time lag. For VV data, both r _{ s,QQ } and r _{ s,II } show a slightly decreasing behaviour as a function of the time lag, with the values of r _{ s,II } lower than the values of r _{ s,QQ }.
In general, the analysis of the cross-correlation suggests that bistatic and monostatic data have a certain degree of correlation, which could influence the performance of the adopted detector.
4.2 False alarm regulation
In the first analysis, we studied the behaviour of the probability of false alarm as a function of the detection threshold, for the single-channel NAMF, applied separately on simultaneous bistatic and monostatic data. This analysis was realized also for the multichannel NAMF, combining the bistatic and monostatic data. In order to evaluate the robustness of the adopted detectors against the time-varying clutter spectra [36], four different values of the normalized Doppler frequency were chosen, i.e. f _{D} = [−0.1, 0, 0.1, 0.2]. As shown in Fig. 5 for the datasets collected by the NetRAD on October 21, 2010, at a bistatic angle of 30°, the clutter power is low for f _{D} = −0.1, 0 and 0.2 (P _{C} < −35 dBm) and very high for f _{D} = 0.1 (P _{C} ≈ −10 dBm).
In the following, we analyse the false alarm regulation performance of the single-channel and multichannel NAMF on the HH polarized data, collected at a bistatic angle of 30°. The range cell under test is at 1400 m.
It should be noted that the total number of pulses is about 130,000 and that the number of integrated pulses (L) was set as 8. The P _{FA} was measured over bursts of L pulses, with 50 % overlap; thus, it cannot be accurately estimated for values lower than 10^{−2}.
From the examination of the clutter spectra, it is confirmed that the Doppler bins giving higher values of P _{FA} are included within the area where the sea clutter is more powerful and spikier. This phenomenon has been already observed and explained in [36]. For this reason, the values of P _{FA} are not constant over the entire range, and their spread is larger if the SCM estimate is used and reduced if either the NSCM or FP estimates are employed. The SCM estimate is not accurate in the case that the clutter is not Gaussian, whereas the NSCM and FP estimates are more accurate [5, 36].
Average threshold values for PFA = 10^{−2}, evaluated on NetRAD data
SCM | NSCM | FPE | |
---|---|---|---|
Bi | 0.79 | 0.84 | 0.83 |
Mono | 0.81 | 0.85 | 0.83 |
Mono and Bi | 1.35 | 1.42 | 1.38 |
In general, the FP and NSCM estimates guarantee a more stable behaviour of the P _{FA} values, fluctuating around the desired value of 10^{−2}. The behaviour of P _{FA} seems to be less stable for the multichannel detector with respect to the single-channel one. It seems that the P _{FA} values obtained by using the multichannel detector adapt themselves to the less favourable between the bistatic and monostatic channels, i.e. the channel that, for each Doppler bin, gives P _{FA} values farther from the desired value of 10^{−2}. By comparing the covariance estimation methods, the SCM is shown to give larger fluctuations of the P _{FA} with respect to the FP and NSCM ones.
4.3 Detection performance
In addition, the difference between the P _{D} values of bistatic and monostatic channels is higher for HH polarized data with respect to the VV ones. This difference could be due to the different behaviours of the shape parameter between HH and VV data, shown in [30], according to which the estimated values of the K + N shape parameters are lower in the bistatic data compared to the monostatic ones, for both polarizations (relative to the datasets collected at a bistatic angle of 30 and range cell of 1400 m).
The higher P _{D} values shown by the bistatic channel are consistent with the results shown in Section 3.2 for simulated data, which highlight that, for each covariance estimate, the lower the shape parameter, the higher the detection probability (this behaviour of the detection probability of the NMF detector has been shown also in [1]).
The multichannel NAMF provides a gain in performance over the single-channel NAMF. This gain is more evident for a higher value of the SCR (i.e. SCR = 5 dB). In terms of detection performance, analysed on a single Doppler bin, it is evident that, by jointly processing the signals associated with two different channels of the system, the multichannel NAMF adapts itself to the more favourable between the two channels.
The analysis of detection performance was deepened by studying the behaviour of the P _{D} values as a function of the SCR, for a normalized Doppler of 0.1 and P _{FA} of 10^{−2}; thus, the threshold values contained in Table 4 were utilized. As the NSCM estimator seems to give better performance, it was chosen for the comparison between single-channel and multichannel detectors.
Synthetic clutter samples were also generated, with similar statistical properties as the analysed real data. Clutter samples were generated according to the K-plus-noise distribution, whose parameters were estimated from real data through the Method of Moments [30]. For the HH data, shape parameter ν is 0.047 for bistatic data and 0.057 for monostatic data, whereas for VV data, ν = 0.064 for bistatic and ν = 0.091 for monostatic data.
The clutter autocorrelation was also estimated for each analysed dataset, where the symbol (.)* indicates the complex conjugate. The clutter samples were generated with the extracted correlation properties.
For the real data, Fig. 11a shows that, for a P _{D} of 0.8, the multichannel NAMF gives a SCR gain of about 1.5 and 6 dB over the single-channel NAMF applied on bistatic and monostatic data, respectively. The corresponding values for VV data (Fig. 11b) are 1 and 4 dB.
The behaviour of P _{D} is more flat for simulated data with respect to real ones, which means that the SCR has a higher impact when real clutter is processed. Relative to the single-channel detector, the gap between bistatic and monostatic data is similar to real and simulated data. On the other hand, we note a large deviation in the detection performance of the multichannel detector, between real and simulated data. In the case of real data, the P _{D} values achieved by the multichannel detector are not far from the ones obtained by using the single-channel detector on bistatic data. In the simulated data, a large gap is noticeable between the multichannel and the single-channel curves. In other words, the gain achieved by using a multichannel detection scheme is larger for simulated data with respect to real ones. One of the factors that could influence this different behaviour is that real bistatic and monostatic data show (Fig. 6) to be correlated, whereas simulated data are generated independently (i.e. they are uncorrelated). As the detection scheme is derived by assuming that the channels are uncorrelated, its performance is expected to be generally higher if this assumption is verified.
5 Conclusions
This work concerns suboptimum radar detection technique that combines the signal received by the nodes of a multistatic radar, in the case of non-Gaussian disturbance. The adopted multichannel detection scheme, called multichannel normalized adaptive matched filter, is able to keep constant the probability of false alarm, for different clutter conditions associated with the nodes of the system.
A derivation of the multichannel NAMF has been illustrated, as an alternative to the one already provided by authors in [23]. The performance of the multichannel NAMF has been evaluated, showing that clutter statistical diversity influences the detection performance. We have studied the behaviour of the P _{D} values as a function of the couple of shape parameters, associated with the two channels of the simulated system. The results have shown that, in the case of two channels, the contour plots of P _{D} as a function of the clutter shape parameters are similar to hyperbolas, meaning that the same value of P _{D} can be obtained for different couples of shape parameters. The performance analysis has been carried out also on real sea clutter data, combining the bistatic and monostatic clutter data collected by the nodes of the NetRAD system. The false alarm regulation performance of the multichannel NAMF seem to be slightly lower than the one of the single-channel NAMF, applied separately on bistatic and monostatic data. In particular, the behaviour of the P _{FA} values of the multichannel NAMF, for each Doppler bin, seems to adapt to the less favourable between the two system nodes. This behaviour is not desirable; thus, it should be better studied in future research steps.
The detection performance evaluation has shown that the multichannel NAMF gives a gain over the single-channel one, which is larger in the horizontally polarized data than in vertically polarized ones. If the multichannel detector is employed, the P _{D} values are higher in the case of simulated data with respect to real ones. A possible reason is that, in real data, the channels are not uncorrelated, whereas the multichannel NAMF has been derived from the assumption of independent channels. In future research steps, this assumption will be possibly removed, in order to derive a detection scheme that exploits the whole information carried on by the radar channels, by processing them jointly and not separately. In [37], the authors remove the aforementioned assumption and derive a detection scheme in the case of Gaussian clutter. It would be of interest to consider the case where the clutter samples are compound Gaussian distributed and correlated across channels.
It should be noted that another possible representation adopts MN × MN-sized blocks, whose total number is L ^{2}.
The P _{FA} versus threshold plots for the single-channel detector, applied separately to monostatic and bistatic data, are not shown for lack of space.
Declarations
Acknowledgements
The authors would like to thank the researchers of the University College London and University of Cape Town who provided the real clutter data and analysed this work.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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