A performance evaluation of SAR-GMTI missions for maritime applications

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 A Performance Evaluation of SAR-GMTI Missions for Maritime Applications Eduardo Makhoul, Student Member, IEEE, Antoni Broquetas, Member, IEEE, Josep Ruiz Rodon, Student Member, IEEE, Yu Zhan, Francisco Ceba Abstract—This paper proposes a new optimized multichannel synthetic aperture radar (SAR) configuration, based on receiving antennas with non-uniformly displaced phase centers, intended for ground moving target indication (GMTI) applications over maritime scenarios. This system is compared with current SAR missions, such as TerraSAR-X (TSX) or TanDEM-X (TDX). The GMTI capabilities of the different configurations are analyzed in a two-level performance approach. First, an intensive numerical simulation evaluation, based on Monte Carlo (MC) trials, is carried out in order to characterize the probabilities of detection under different system parameters as well as scenario conditions. Different GMTI techniques, displaced phase center antenna (DPCA), along-track interferometry (ATI) and extended displaced phase center antenna (EDPCA), are assessed. In a second step, synthetic simulated SAR data, obtained in a study case scenario, is used to demonstrate the potential improvement of the proposed multichannel configuration compared to current SAR missions, providing subclutter visibility for maritime surveillance of small and slowly moving boats. Index Terms—Synthetic aperture radar (SAR), ground moving target indication (GMTI), displaced phase center antenna (DPCA), along-track interferometry (ATI), extended DPCA (EDPCA), constant false alarm rate (CFAR) detector, Monte Carlo (MC) simulations, SAR raw data simulation. I. INTRODUCTION SYNTHETIC aperture radar (SAR) systems for remote sensing applications have been gaining special interest during the last decade, as demonstrated by the increased number of missions: TerraSAR-X (TSX), TanDEM-X (TDX), COSMO-SkyMed, RADARSAT-2 (RS2), Sentinel-1 and PAZ [1]-[4]. Some of them include an experimental mode that adds ground moving target indication (GMTI) capabilities from spaceborne platforms. This kind of missions will provide a powerful tool to globally monitor traffic, illegal ship movements, migration movement and piracy attacks, covering the requirements on the so called Situation Awareness, [5]-[8]. Single channel approaches, based on Doppler filtering, fail to detect slow moving targets, [9]. Moreover, an intrinsic Manuscript received Month Day, Year; revised Month Day, Year. This work has been supported by FPU Research Fellowship Program, Ministerio de Educaci´ on, contract AP2009-4590; by FPI-AGAUR Research Fellowship Program, Generalitat de Catalunya, contract 2010FI EM051757; by the Spanish Ministry of Science and Innovation (MICINN) under projects TEC2011-28201-C02-01 and CONSOLIDER CSD2008-00068; and by European Commission under FP7-SPACE Project SIMTISYS Ref. 263268. E. Makhoul, A. Broquetas, J. Rodon, Y. Zhan and F. Ceba are with the Department of Signal Theory and Communications, Universitat Polit` ecnica de Catalunya, Barcelona (Spain). Phone: +34 934017359, e-mail: {edumak,broquetas,josep.ruiz,yu.zhan,francisco.ceba}@tsc.upc.edu ambiguity between radial velocities and azimuth location in single SAR images exists, [9]. This ambiguity problem can be solved by means of multiple receiving channels, which provide improved detection capabilities thanks to the increased spatial diversity. Current SAR missions, as TSX, TDX and RS2, equipped with two receiving antennas, have limited capabilities to detect weak and slow moving targets, i.e. small boats in the sea. For this dual receive antenna (DRA) mode configurations, conventional SAR-GMTI processing techniques operating on the SAR images can be applied, based on either phase change detection, along-track interferometry (ATI) [10]- [11]; or clutter cancellation in the case of displaced phase center antenna (DPCA) [11]-[13]. In order to obtain adequate performance, by means of spacetime adaptive processing (STAP), more than two receiving antennas are required [9]. One way to obtain additional spatial diversity, without increasing the system complexity, is based on the use of suitable antenna switching and toggling modes [14]. These kinds of approaches imply an antenna effective area reduction, resulting in a degradation of the signal-to-noise ratio (SNR) and increased pulse repetition frequency (PRF) requirements to reduce the azimuth ambiguities, [14]. Alternative multichannel approaches are based on the deployment of coherently operating SAR constellations, which provide better performances (angular and Doppler resolutions) thanks to extended apertures [15], [16]. However, this kind of configurations suffer from a high number of grating lobes, creating numerous blind velocities. Moreover, the technological complexity and cost of maintaining a constellation of satellites is rather high. From these considerations, this manuscript proposes an optimized SAR mission that maximizes the GMTI performance, keeping low system complexity in terms of receiving channels and hence data volume to be downloaded. The novel architecture is based on a single monostatic multichannel satellite with non-uniformly spaced receiving antennas, as briefly discussed in [7] and [17]. The objective is to provide subclutter visibility for maritime surveillance of small slowly moving boats. This optimized multichannel configuration, in combination with the new optimum GMTI processing techniques as imaging STAP (ISTAP) and extended DPCA (EDPCA), is expected to provide a substantial improvement in SAR-GMTI performance, [18]-[19]. This paper presents an exhaustive GMTI performance evaluation of the proposed multichannel configuration compared to current state-of-the-art SAR missions over maritime scenarios. The GMTI capabilities are analyzed and characterized in terms 0000–0000/00$00.00 c 2014 IEEE 2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING of probability of detection based mainly on intensive numerical simulations at image level. In Section II, the multichannel data model at SAR image level is described, specifying the different assumed hypotheses. The different GMTI techniques evaluated throughout the paper (DPCA, ATI and EDPCA) are briefly presented in Section III. Section IV analyzes comparatively the expected theoretical SAR-GMTI performance of the different X-band configurations. Section V shows the results of the intensive numerical simulation based on Monte Carlo trials, which are complemented with processed synthetic raw data, for a representative sea clutter scenario. Through the manuscript a Gaussian-like model for the sea clutter is assumed. For analysis completeness, additional processed synthetic raw data results are included when considering a non- Gaussian sea clutter based on the K-distribution, [20]. Both Gaussian and K-distributions have been observed analyzing real data from TSX dual- and quad-polarized modes, see [21]. A preliminary study on the impact of SAR imaging high-speed boats (with high induced vertical and horizontal accelerations) has been also carried out, considering a complete SARGMTI processing chain, which integrates a matched filter bank (MFB) based on an adaptive range-Doppler (RD) processor. The different theoretical and simulation performance evaluations prove the potential capabilities of the proposed SARGMTI mission compared to current state-of-the-art missions. II. DATA MODEL Consider a general multichannel SAR configuration, consisting of Mparallel receiving (RX) antennas collocated in the along-track direction x, which are displaced {dxm}M m=1 from the transmitting (TX) reference phase center. A flat Earth geometry is assumed in the modeling, such that the platform, orbiting at a constant height Horb, moves with an effective velocity ve, [22]. The detection of the moving target, whose multichannel signal is denoted by s(ϑt), can be understood as a hypothesis testing problem H1:x=s(ϑt) + c(ϑc) + n H0:x=c(ϑc) + n,(1) driven by the presence of interference q, which consists of background clutter c(ϑc)and thermal noise n.ϑt= vx, vz, R0, σ2 tand ϑc=vxc, vzc, R0, σ2 care parameter vectors of the moving target and clutter, respectively; where the first two elements of the vectors correspond to the along- and across-track velocities, with R0the slant range of closest approach and the related power levels indicated by the sigma terms. A. Signal The target, modeled as a collection of single-like point scatterers, moves on the ground plane (y= 0) with a uniformly accelerated movement in both along- (x) and across-track (z) directions, as generally assumed in the literature [11], [23]: x(t) = x0+vxt+ax 2t2 z(t) = z0+vzt+az 2t2,(2) where tstands for slow time (or azimuth time). At t= 0 the target is located at x0and z0, which corresponds to the along- and across-track coordinates, respectively. Target velocities and accelerations are, respectively, represented by vx,vz, and ax,az. The multichannel signal of the moving target, at resolution cell level, can be formulated using vectorial notation as: s(ϑt) = αt∆AT I (ϑt),(3) where the different SAR images have been properly coregistrated and balanced, [24]. It is well-known that the target radar cross section (RCS) varies with the aspect angle [25]. For the deterministic target model the different scattering centers are assumed to have a constant radar response during the integration time, such that for calibrated images, αtis directly related to the square root of the RCS. The term ∆AT I (ϑt) collects the along-track phase change for the different channels at the displaced image position of the moving target. As it is extendedly considered in literature [23]-[25], x0= 0 is assumed for simplicity in the mathematical notation without losing generality. Then, the interferometric phase component of the i-th channel can be expressed as [23] ∠[∆AT I (ϑt)]i=φi(ϑt) = πdxivr λ·1 ve −vx−ve v2 rel (ϑt),(4) where λis the carrier wavelength; vrrefers to the radial velocity, i.e. line-of-sight projection of the ground range velocity; and the relative velocity term vrel is expressed as: vrel (ϑt) = s(vx−ve)2+v2 z1−z2 0 R2 0+z0az.(5) A more realistic modeling, which accounts for the target’s random variability on the radar response, is a zero-mean complex Gaussian scattering center, [26], i.e. αt∈C∼ N0, σ2 t=RCS. Then, the multichannel target signal s(ϑt) is characterized by its covariance matrix Rt, where decorrelation effects induced either by the target motion itself or the internal clutter motion (ICM), [27], can be included through the target correlation coefficient between each pair (i,j) of channels ρti,j , similar to the sea clutter in (6). B. Interference GMTI processing intends to detect moving targets masked by the presence of interference, consisting of the background clutter c(ϑc)and the unavoidable thermal noise nof the receiver. The latter is generally modeled as a zero-mean complex Gaussian process, n∈C∼ N (0,Rn). The noise has neither a temporal nor a spatial structure, Rn=σ2 nI, where Istands for a diagonal unitary matrix. For calibrated SAR images the noise mean power is related to the noiseequivalent sigma zero (NESZ) and the ground resolution cell area. The clutter has specific temporal and spatial correlations, which account for both temporal and spatial variability of its radar returns. Since the scope of the paper is to demonstrate the improved capabilities of the proposed configuration against current state-of-the-art SAR-GMTI missions, the clutter is MAKHOUL et al.:A PERFORMANCE EVALUATION OF SAR-GMTI MISSIONS FOR MARITIME APPLICATIONS 3 assumed to have a stationary zero-mean complex Gaussian distribution c(ϑc)∈C∼ N (0,Rc), as it is extendedly considered in the literature [16], [18], [19]. This hypothesis breaks down when considering realistic scenarios that may contain highly heterogeneous terrains, such as urban or industrial areas [13]. In the maritime case, it has been assumed that a K- distribution (compound model) fits well the sea clutter returns [20]. In [21], a preliminary statistical analysis of the sea clutter using two TSX data takes (dual- and quad-polarized) has been conducted, showing a good fitting of the K-distribution to the magnitude. For incidence angles between 29.7 and 32.3 degrees, shape parameters vbetween 3-10 are observed (small values indicate spiky/highly heterogeneous returns). To complement the mission performance study, a K-distributed sea clutter has been also simulated for the synthetic raw data approach (section V-B) in order to understand the impact of non-Gaussian statistics. A way to provide a more realistic maritime scenario is twofold: account for specific clutter decorrelation between the different channels induced by the ICM and the inclusion of an ATI phase, which can be related to a mean surface velocity on the sea structure. In this sense, the covariance matrix of the clutter Rccollects those parameters as: Rc=Enc(ϑc)c(ϑc)Ho=    σ2 c1. . .ρc1,M pσ2 c1σ2 cMe∆φc1,M . . ..... . . ρc1,M pσ2 c1σ2 cMe −∆φc1,M . . . σ2 cM   ,(6) where σ2 cirefers to the clutter power for the i-th channel, which is related to the radar backscattering coefficient σ0 and the ground resolution cell area. For maritime scenarios, this coefficient can be obtained using the Naval Research Laboratory (NRL) model [28], given specific system parameters (frequency, polarization, incidence angle) and scenario conditions (sea state or wind velocity). The phase term ∆φci,j represents the ATI phase between the i-th and j-th channels due to the sea mean Doppler velocity, [29]. In (6), the correlation coefficient ρci,j between channels i and jtakes into account the temporal decorrelation induced by the ICM and is related to the (baseline) time-delay τi,j between those two channels (equivalent two-way phase centers). From [27] and under the assumption of Gaussian distributed clutter, ρci,j has a Gaussian-like shape: ρci,j = exp (−τi,j τc2)= exp      −   (dxi−dxj)·ve 2·v2 rel(ϑc) τc   2     , (7) where τcis the clutter correlation (coherence) time, which for an X-band system can vary between 10-60 ms, depending on the sea conditions and system resolution, [29]. As the radar measures range and velocity (Doppler) ambiguously, the moving target should compete also with the ambiguous clutter patches. Therefore, for the main non-ambiguous clutter patch, a grid of Nsurrounding ambiguous clutter responses should be also considered when modeling the clutter [14], [18], [25]. Assuming a homogeneous (stationary) complex Gaussian sea clutter surface and uncorrelated ambiguities, the interference covariance matrix can be expressed as: Rq=Rc0(ϑc) + N X k,l Rck,l (ϑc) + Rn,(k, l)∈Z2\ {0,0}, (8) where Rc0(ϑc)is the covariance matrix for the main1clutter patch, as expressed in (6); analogously, Rck,l (ϑc)is the covariance matrix for the k, l-th ambiguous patch. In (8), (k, l)∈Z2\ {0,0}denotes the set of those whole-numbered index pairs of admissible range-azimuth ambiguities except for k=l= 0, which refers to the non-ambiguous clutter patch of interest. For simplicity the main clutter and the related ambiguous patches are assumed to have equal backscattering coefficient σ0and correlation properties. In this case, the corresponding power of the k, l-th ambiguous patch for the i-th channel is defined by σ2 ck,l i=σ2 ci·CRAASRk,l,(9) where CRAASRk,l refers to the combined-range-azimuth- ambiguity-to-signal ratio for the k, l-th ambiguity, as defined in section IV-B, such that a SAR related figure of merit is incorporated into the GMTI performance by means of the covariance matrix modeling. The off-diagonal phase terms of Rck,l (ϑc)are modeled as ∆βk,l i,j = ∆φci,j −2π·l·PRF ·dxi−dxj·ve 2·v2 rel (ϑc),(10) accounting for the interferometric phase ∆φci,j induced by the clutter’s mean Doppler velocity and the residual phase term due to wrong channel coregistration on the ambiguities as pointed out in [19]. This spatial alignment (coregistration) is accomplished by time-shifting the signals of the different channels via interpolation, efficiently performed applying a phase ramp in the Doppler domain. Due to partial backfolding of the different Doppler ambiguities (modeled by the l-th order azimuth ambiguity), this phase ramp produces a residual constant phase error on these ambiguities, modeled by the second phase term in (10). This residual error vanishes when the DPCA condition holds, i.e. the satellite’s displacement between pulses is a multiple of the baseline separation between the involved channels. III. GMTI PROCESSING TECHNIQUES A. Displaced Phase Center Antenna (DPCA) DPCA is a motion compensation technique, such that the equivalent two-way phase centers of the two antennas (i-th and j-th) occupy the same spatial location but at different instants of time. Therefore, a simple complex subtraction between the two coregistrated channels allow canceling the clutter while the moving targets show up in the final DPCA image, [11]- [13]. Ideally, DPCA could completely remove the clutter down to noise floor, but actually, the clutter suppression is limited by 1From now on the subindex 0 refers always to the main clutter patch. 4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING possible ICM, coregistration errors and channel imbalances. Based on a constant false alarm rate (CFAR) detector, the DPCA magnitude is compared against a threshold ξ, which can be determined from the desired probability of false alarm Pfa and the related residual interference probability density function (PDF), [12]. B. Along-track interferometry (ATI) The high sensitivity of the interferometric phase to slight variations in the scene allows exploiting the ATI to perform detection of slowly moving targets [10]-[13]. ATI, as DPCA, is a dual-channel antenna technique, where the formation of the interferogram allows both detection of the moving target and estimation of its radial velocity. As opposed to DPCA, in the ATI processing there is no clutter cancellation. Therefore, the presence of both clutter and noise produces a noise phase that can impair the detection and estimation of the targets radial velocity. The ATI signal is formed as the complex conjugate multiplication of the two coregistrated channels ATIi,j=1 n n X p [x]i,p [x]∗ j,p ,(11) where ncorresponds to the number of looks (or resolution cells). To evaluate the ATI performance, a CFAR detector exploiting the joint PDF of ATI magnitude ηand phase ψhas been selected since it can provide improved performance compared to the two-step detectors (phase and magnitude separately, [10]), as pointed out in [30]. C. Extended Displaced Phase Center Antenna (EDPCA) processing In [18], Cerutti et al. have proposed an optimized SARGMTI processing technique, ISTAP, which exploits a suboptimal post-Doppler STAP in combination with SAR processing, following a similar approach as in [9], [31]. Cerutti et al. have also proposed EDPCA [19], which is an adaptive DPCA technique for architectures with more than two receive channels. Clutter homogeneity plays an important role in the estimation of the interference covariance matrix performed by ISTAP and EDPCA, and so directly affects the GMTI performance. In this sense, the EDPCA processing is preferred over maritime scenarios since it operates at image level, allowing to select and process homogeneous patches. Moreover, the performance characterization of the ISTAP via MC simulations would require its evaluation in the range-Doppler domain leading to a much more computationally costly approach compared to the efficient one presented in section V-A, which operates at image level. Both ISTAP and EDPCA provide the same GMTI performance when the DPCA condition is fulfilled; otherwise, ISTAP gives improved results as pointed out in [18]. Assuming that the MSAR images have been properly coregistrated and SAR focused with the target parameters ϑt(except radial velocity shift compensation), the weighting vector that provides the optimal combination of the different channels in terms of SCNR maximization at the EDPCA processor’s output, y=wH(ϑt)x, is [32]: w(ϑt) = βR−1 cd(ϑt),(12) where d(ϑt)refers to the spatial beamformer adapted to the target parameters, such that the phase differences between the channels are compensated d(ϑt) = ∆AT I (ϑt).(13) In order to ensure a CFAR test statistics at the output of the EDPCA, the scalar term βin (12) is properly chosen as: β=1 qdH(ϑt)R−1 cd(ϑt) ,(14) ensuring a unitary power residual interference. Similar to DPCA, the magnitude at the output of EDPCA should be compared against a threshold for a given Pfa. IV. MISSION ANALYSIS A. Multichannel configurations The state-of-the-art SAR missions, as TSX, TDX or RS2, equipped with two receiving antennas, have limited GMTI capabilities to detect slowly moving targets, due to both, the reduced number of channels and to the short baselines (2.4 m one way for TSX), which determine the minimum detectable velocity. The deployment of coherently operating SAR constellations, as TDX, provides improved performance in terms of Doppler (velocity) and angular resolution, but at expense of a reduced range of unambiguous velocities (around 1.4 m/s), caused by the longer baselines (around 200 m). In the maritime scenarios, where the clutter correlation could reach tens of milliseconds [29], depending on the sea conditions, the channel coherence (for the longer baseline) could drop off dramatically, and so would the capability of clutter rejection. Therefore, a trade-off solution is to consider a monostatic multichannel configuration with non-uniformly spaced receivers, taking advantage of baseline diversity to ensure high sensitivity to slowly moving targets (with the largest baseline), and simultaneously alleviating the Doppler ambiguities (with the shorter ones); in a way that channel coherence can be kept high enough to ensure proper detection capabilities. From these considerations, a three-channel configuration is proposed (see Fig. 1(a)), where the two external antennas are deployed using a telescopic boom, as suggested in [7], [17], and as an unfolding system, respectively. The number of channels has been selected to limit system complexity and at the same time to fulfill the required degrees of freedom driven by the eigenvalue distribution of the interference covariance matrix, as discussed in section IV-B. The length of the boom has been selected to deliver a probability of detection (Pd) close to one for a 1 m2RCS target, whose ground range velocity is greater than 5.5 m/s when processing the three-channel data cube with EDPCA. The boom length is a multiple of the antenna length assuming a telescopic structure will be used for deployment. The system operates in X-band, equipped with a configurable 4.8 m MAKHOUL et al.:A PERFORMANCE EVALUATION OF SAR-GMTI MISSIONS FOR MARITIME APPLICATIONS 5 TX RX 4.8 m 14.4 m 4.8 m Unfolding Boom xx x 4.8 m (a) TX RX 4.8 m 200 m xxxx 4.8 m X-DRA (b) Fig. 1. Schematic representation of the different configurations to be analysed: (a) X-band Boom system and (b) Tandem system (including X- DRA satellite); transmitting (TX) phase center denoted by the solid circle, receiving (RX) by the triangle symbol and effective two-way (2-W) by the cross symbol. TABLE I RADAR SYSTEM PARAMETERS. Parameter Value Units Effective velocity (γ0= 33.17 deg) 7311.6 m/s TX/RX antenna height 0.7 m Carrier frequency 9.65 GHz Peak transmitted power 2.2 KW Polarization HH Noise factor 4.3 dB Transmitter (TX) / Receiver (RX) losses 2 / 2 dB phased-array antenna, with 32x12 transmit receive modules (TRMs). The main radar mission parameters, similar to TSX, are summarized in Table I. From now on, the proposed configuration will be referred as Boom system, and its SARGMTI performance will be compared against two different systems that emulate current state-of-the-art SAR missions: a 4.8 m length single satellite operating in dual receive antenna (DRA) mode (2.4 m per receiver), named as X-DRA; and a Tandem configuration, where two X-DRA fly in formation (only one TX) with a baseline of 200 m as schematically represented in Fig. 1(b). These systems are also characterized by the same radar parameters as in Table I. B. SAR-GMTI expected performance An orbital height of 514 Km has been selected to ensure an incidence range coverage from 14 to 60 degrees (swath ground extension of 640 Km), intended to be covered by 27 subswaths, whose extension is in the order of 30 Km. A proper PRF selection has been carried out taking the highest possible ones (according to the timing/diamond diagram) while keeping a trade-off between the azimuth and range ambiguities level. For the proposed system, and assuming uniform tapering on the TRMs, the NESZ is kept below -20 dB for the typical SAR incidence angles, 20-40 degrees. Instead, for low-grazing angles the noise contribution increases up to -17 dB. The optimization of the system’s NESZ is conservative due to power budget restrictions, keeping a nominal peak transmitted power of 2.2 KW. It must be noted that the system operates with a pulse bandwidth of 150 MHz for beams 1-10 (14- 38 degrees incidence angle) and 75 MHz for the rest of the subswaths. As modeled in section II-B, and noted in [14] and [25], the contribution of the ambiguous clutter returns should be taken into consideration as they could play an important role in the SAR-GMTI performance: the residual coregistration error on the ambiguities, as denoted by the second term in (10), when the DPCA condition does not hold, produces additional eigenvalues different from the noise floor, and therefore more RX channels are required to cancel out both unambiguous and ambiguous clutter patches, [19]. Moreover, temporal decorrelation of the sea clutter returns, present also in the ambiguous patches, could produce additional eigenvalues different from noise floor. These impacts depend in turn on the level of ambiguous returns with respect to (w.r.t.) the main clutter. The new combined-range-azimuth-ambiguity-to- signal ratio (CRAASR) metric is a helpful indicator: provides a single SAR performance metric that combines the definition of both the AASR as well as the RASR [33] for the grid of Nambiguities: CRAASR = N X k,l CRAASRk,l,(k, l)∈Z2\ {0,0} = N X k,l R3 0·sin(γ0)· |D2−w(θk,l, φk,l)|2 R3 k,l ·sin(γk,l)· |D2−w(θ0, φ0)|2 ·RBp/2 −Bp/2|P2−w(fd+l·PRF)|2df RBp/2 −Bp/2|P2−w(fd)|2df ,(15) where R0and Rk,l correspond to the slant range for the main and the k, l-th ambiguous clutter patches, respectively; γk,l refers to the incidence angle for the k, l-th ambiguous clutter patch. The impact of the two-way antenna patterns is accounted for in the D2−w(θk,l, φk,l)term, where θk,l and φk,l are the spherical angles in the antenna coordinate system for the specific ambiguous clutter patch. The term P2−w(fd) models the Doppler spectrum, including the antenna pattern and the azimuth window used in SAR focusing for a specific Bpprocessing bandwidth. Considering the first N=440 combined ambiguities, a Kaiser window (factor of 2.5) with processing bandwidths of 2.8 KHz in azimuth and the corresponding pulse bandwidth (subswath dependent) in range, the CRAASR for the Boom configuration is kept below -20 dB for the range of interest (20-40 degrees incidence angle). However, the ambiguities’ impact increases (up to -5 dB) for beams with high incidence angle (above 50 degrees), mainly due to range ambiguities. Nevertheless, assuming the ambiguous clutter returns have the same σ0as the main patch (close to the noise level for those incidence angles), the impact of the ambiguities gets masked by the noise floor. Fig. 2(a) and Fig. 2(b) show the eigenvalue distribution of Rqas a function of the incidence angle for the Boom and Tandem configurations, respectively. This kind of chart is a good indicator of the interference distribution as a function of the incidence angle and so of the predominant mechanism, against which moving targets should compete. A flat distribution of the eigenvalues (similar values) indicates that a predominant noise-like effect is expected, either due to the high contribution of noise or due to the possibly combined impact of high clutter decorrelation and ambiguities contribution. 6 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING Eigenvalue distribution 1 2 3 Eigenvalues 14 26 38 49 61 Incidence angle [deg] -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 [dB] (a) Eigenvalue distribution 1 2 3 4 Eigenvalues 14 26 38 49 61 Incidence angle [deg] -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 [dB] (b) Fig. 2. Eigenvalue distribution for a 10 ms clutter coherence time with sea state 4 versus incidence angle: (a) Boom and (b) Tandem. SCNR EDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 Incidence angle [deg] -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 [dB] (a) SCNR (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] -5 0 5 10 15 20 [dB] X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch (b) Fig. 3. Boom system SAR-GMTI theoretical performance for a deterministic target (RCS of 0 dBm2) and a sea state 4 (Gaussian) clutter with 10 ms coherence time: (a) EDPCA-SCNR versus incidence angle and ground range velocity; (b) SCNR system-technique comparison at beam center of subswath 8 with 33.17 degrees of incidence angle (in legend X refers to X-DRA system, T and B to Tandem and Boom configurations, respectively). For Boom configuration, Fig. 2(a), and incidence angles between 14 and 40 degrees, there is a predominant eigenvalue, such that two receive channels are sufficient to cancel out the clutter and its ambiguities. For higher incidence angles, noise contribution masks clutter response (the three eigenvalues are similar). Comparatively, for Tandem, Fig. 2(b), two predominant eigenvalues are present due to the major impact of clutter decorrelation, [32], induced by the longer baseline configuration: SAR-GMTI techniques at image level require channel coregistration, by means of a time-shift related to the baseline time-delay τi,j, such that they observe the scene from the same position but at different instants of time. During this time frame sea has evolved, and so clutter returns have decorrelated from a statistical standpoint. For the longest baseline separation and 10 ms coherence time, sea clutter coherence drops off to values around 0.15 according to (7). This is directly translated into a GMTI performance degradation, as pointed out by the theoretical and simulation results. In Fig. 3(a) EDPCA SCNR for the Boom system is plotted as a function of the incidence angle (beam) and ground range velocity2. For incidence angles below 38 degrees, a notch around the zero-radial velocity can be recognized, which for higher incidence angles is not present as the thermal noise starts to be the dominant interference contributor, in accordance to the eigenvalue distribution in Fig. 2(a). Fig. 3(b) shows the SCNR cuts as a function of ground range velocity and at beam center of subswath 8 for different combination of system-techniques. From now on the comparative performance analysis is considered for a given set of system-technique combinations: classical (2-channel) GMTI techniques, such as DPCA and ATI, are presented only for X- 2The edge-like effects along the incidence angle are related to beam transitions (superposition between beams is not represented). MAKHOUL et al.:A PERFORMANCE EVALUATION OF SAR-GMTI MISSIONS FOR MARITIME APPLICATIONS 7 SCNR (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 5 10 15 20 [dB] Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Fig. 4. SCNR cut as a function of ground range velocity (at center of subswath 8) for EDPCA technique considering different variants of the Boom configuration, assuming a deterministic target (RCS of 0 dBm2) and a sea state 4 (Gaussian) clutter with 10 ms coherence time; XDB corresponds to a Boom configuration where the two first channels are X-DRA like (2.4 m separation with no unfolding) and the third one (2.4 m antenna length) is located on a 14.4 m mast. DRA system, showing the available capabilities for the current state-of-the-art SAR-GMTI missions with two RX channels; the optimum (>two RXs) EDPCA technique is considered for Boom and Tandem configurations to demonstrate the potentiality of oncoming SAR-GMTI architectures. Processing with EDPCA the data cube of the proposed Boom system (dash red line) provides improved SCNR when compared to DPCA and EDPCA techniques applied to the X-DRA system, dash-dot-dot green lines with and without square markers, respectively. The proposed Boom system proves improved detection capabilities, being more robust to clutter induced decorrelation effects, compared to Tandem system. The corresponding EDPCA SCNR (solid blue line) has a similar trend as X-DRA but with a mean SCNR 3 dB higher thanks to the two additional spatial degrees of freedom (DoF). At this point it must be also noted that for vz= 0 m/s and Tandem configuration the EDPCA SCNR improvement factor (IF) with respect to the single channel case (denoted by the blue circle markers) is around 3 dB and better when compared to the Boom configuration case. It can be theoretically demonstrated that for vz= 0 m/s and in the limit of zero clutter coherence between the different channels, IF tends to the number of channels M, since in this case clutter has no spatial structure and behaves like noise. As the worst clutter coherence is 0.15 according to (7) for the longest baseline and a 10 ms clutter coherence time, IF is expected to be lower than M. To complement the theoretical analysis, the EDPCA SCNR for different variations of the proposed Boom configuration is reported in Fig. 4 as a function of the across-track ground velocity. Apart from the considered Boom architecture (solid red line), three alternatives are analyzed: the first two (blue asterisk and green diamond solid lines) have the same configuration as the Boom system but with a mast length of 28.8 m and 57.6 m, respectively; while the third system (black circles solid line), referred as XDB, is a Boom configuration, where the two first channels are X-DRA like (2.4 m separation and no unfolding) and the third antenna is deployed with a mast of TABLE II MONTE CARLO (MC) SIMULATION PARAMETERS. Parameter Value Units RCS (step of 1 dBm2) -10 to 20 dBm2 vz(step of 0.25 m/s) 0 to 50 m/s Target type Deterministic/Gaussian Sea state 4 Clutter correlation ∞/10 ms MC trials 5·106 Pfa 10−5 Window type Kaiser (factor 2.5) Azimuth/Range processing bandwidth 2.8e3/150e6 Hz 14.4 m. The proposed configuration (red solid line) provides an overall improved SCNR compared to the rest of systems. Increasing the mast separation allows a slightly narrower notch response (around zero velocity), at the expense of additional steeper secondary notches (“blind” velocities). Moreover, there is a progressive degradation in the SCNR peaks due to clutter decorrelation higher impact. For XDB a generally reduced SCNR is observed since the antenna dimensions are half of the Boom architecture. Secondary notches, much steeper, are located at slightly higher velocities because of effective shorter baselines. V. SIMULATION RESULTS:PERFORMANCE EVALUATION A. Monte Carlo approach The detection capabilities of any GMTI system can be statistically quantified through the probability of detection Pd. In this sense, MC simulations provide a very useful tool to asymptotically characterize this probability for specific system and scenario conditions. A flexible SAR-GMTI performance simulator tool, based on MC simulations at image level, has been implemented to provide statistical metrics in terms of Pd and Pfa. This simulator avoids generating and processing iteratively synthetic raw data for a given system/scenario to characterize the Pd, which could otherwise be time-consuming. In the MC simulations presented in this section some hypotheses have been assumed: (i) the clutter is a zero-mean complex Gaussian process with given spatial (along different channels) correlation properties; (ii) SAR processing has been adapted to the target kinematic parameters3; (iii) the residual phase error (due to coregistration mismatch) defined by the second term of (10) has been included for the first 440 combined ambiguities; (iv) theoretical covariance matrix in EDPCA processing is used; and (v) the target (either deterministic or Gaussian) is correlated from look to look, while clutter has been assumed uncorrelated. Table II summarizes the different parameters of the MC simulations considering the center of subswath 8 with an incidence angle of 33.17 degrees. Fig. 5 shows probability of detection maps as a function of the RCS and ground range velocity for X-DRA system with ATI processing and Boom configuration with EDPCA technique, when considering a deterministic target and 10 ms clutter coherence time (no multilook processing). Boom 3Discussion about SAR focusing mismatch on fast moving boats is considered in section V-B. 8 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING X-DRA ATI -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.0 (a) Boom EDPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.0 (b) Fig. 5. Probability of detection maps (versus RCS and ground range velocity) obtained from MC simulations for different system-technique configurations: (a) ATI X-DRA and (b) EDPCA Boom (deterministic target, complex Gaussian clutter with 10 ms coherence time, no multilook and CFAR detectors with Pfa of 10−5). system in combination with EDPCA, Fig. 5(b), provides improved performance compared to the other system-technique combinations, especially in the region of slow and low reflectivity moving targets. DPCA technique applied to X-DRA data provides the worst Pdin this region. However, the joint 2D phase-magnitude ATI detector on the X-DRA system, Fig. 5(a), gives comparatively a better performance, close to the EDPCA applied to Tandem system, where the induced higher clutter decorrelation is the driven parameter; but still EDPCA on Tandem has a threshold RCS, approximately 5 dB below the ATI case. In Fig. 5(b), the secondary notch around 20 m/s for RCS is related to the degradation on SCNR, as observed from Fig. 3(b), caused by the presence of a blind velocity associated to the longer baseline. Fig. 6(a) and Fig. 6(b) show cuts of the Pdfor the different system-technique combinations as a function of across-track ground velocity (for a RCS of -5 dBm2) and versus RCS (for vz= 1 m/s), respectively. Two sea clutter coherence times (∞and 10 ms) are reported for each system-technique combination to illustrate the impact of clutter decorrelation. For a completely correlated sea clutter the Tandem configuration with EDPCA processing (solid blue line) provides the highest sensitivity to slowly moving targets, at the expense of a reduced unambiguous range of velocities. However, for realistic scenario operations clutter decorrelation impairs especially the performance of the Tandem system (solid blue line with asterisk); while Boom configuration (with 14.4 m mast) shows a robust behavior (comparing red dashed lines with and without asterisk markers), providing the best detection capabilities as a function of the across-track velocity for a small target. ATI (dotted black line) and DPCA (dash-dot-dot green line) for X-DRA prove to have very limited capabilities to detect boats with reduced reflectivity (-5 dBm2), being almost insensitive to clutter decorrelation since X-DRA has the smallest baseline, 2.4 m. When considering the performance as a function of the RCS for slow moving boats, DPCA technique for X-DRA provides the worst results, being unable to detect targets even with moderate to high reflectivity. For the same configuration, ATI 2D detector gives much better results, and gets closer to the Boom-EDPCA, which still requires lower RCS to obtain the same Pd. In this regard, and even for a 10 ms coherence time, Tandem configuration provides the lowest threshold RCS value, since the boat velocity is still in the range of vz=±1.5m/s, where as already observed in Fig. 3(b) the Tandem SCNR is around 3 dB higher. Analogously, Fig. 7 shows the same Pdcuts but for a worse case scenario, where the target has been modeled as complex Gaussian process (completely correlated from channel to channel). Comparing both situations, Fig. 6 and Fig. 7, target randomness provides in average a smaller Pdas a function of vz, smoothing the trend of Pdas a function of the RCS. For the Gaussian target and for Pdbelow a threshold level of 0.3, improved performance is obtained w.r.t. deterministic case, whereas for values above this value there is a global degradation. Additionally, the impact of data averaging (multilook processing) on Pdhas been also evaluated (not reported here due to space limitations), showing an improvement on Pdas the number of looks (boxcar size) increases, whenever the target occupies a sufficient number of single-look resolution cells to avoid degradation on the effective SCNR after multilook, see [13]. B. SAR data approach To complement the MC simulations, synthetic multichannel data is generated using a flexible SAR-GMTI simulator tool, where different systems, modes of operation and scenarios can be easily configured [5], [7], [8]. In order to provide an analogous metric to the probability of detection, several raw data simulations (20 trials) have been carried out, such that a frequency of detection can be MAKHOUL et al.:A PERFORMANCE EVALUATION OF SAR-GMTI MISSIONS FOR MARITIME APPLICATIONS 9 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (a) -10 -5 0 5 10 15 20 RCS [dB] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (b) Fig. 6. System-technique comparison of the probability of detection obtained from MC simulations assuming a deterministic target and for different clutter correlations (τc= inf and 10 ms): (a) cut at RCS of -5 dBm2as a function of ground velocity and (b) cut at vz= 1 m/s as a function of RCS; no multilook processing is considered (in legend X refers to X-DRA system, T and B to Tandem and Boom configurations, respectively). 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (a) -10 -5 0 5 10 15 20 RCS [dB] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (b) Fig. 7. System-technique comparison of the probability of detection obtained from MC simulations assuming a complex Gaussian target and for different clutter correlations (τc= inf and 10 ms): (a) cut at RCS of -5 dBm2as a function of ground velocity and (b) cut at vz= 1 m/s as a function of RCS; no multilook processing is considered (in legend X refers to X-DRA system, T and B to Tandem and Boom configurations, respectively). TABLE III TARGET PARAMETERS. Target Type Scatterers mean RCS [dBm2] max. RCS [dBm2]vx[m/s] vz[m/s] ax[m/s2]ay[m/s2]az[m/s2] T1 Ramshackle 53 4.5 17 -1.12 6.25 -0.69 0.0 -0.30 T2 Civil cargo 102 28.2 40 -6.73 3.0 -0.22 0.0 -0.29 T3 Point-like target 1 -5 -5 0 5 -0.69 0.0 -0.4 T4 Point-like target 1 0 0 0 2.5 -0.69 0.0 -0.4 T5 Point-like target 1 5 5 20.6 0.0 2.45 3.43 0.0 T6 Point-like target 1 5 5 0.0 20.6 0.0 3.43 2.45 extracted. A complete processing chain has been implemented integrating a MFB (based on a RD processor) with the different GMTI techniques, similar to [19], [34]. Each filter performs an adaptive SAR processing, at both range cell migration correction (RCMC) and azimuth focusing steps, for a specific set of kinematic parameters (vz,azand vx), trying to recover a well focused moving object. No compensation of the Doppler shift (azimuth shift) is carried out, since, otherwise, the target will appear at different azimuth positions for different vzof the filter bank, posing difficulties to efficiently compare the outputs of the bank of filters. As in the MC simulations, a Kaiser window (factor 2.5) has been used in range and azimuth with processing bandwidths of 2.8 KHz and 150 MHz, respectively. A 1 Km by 1 Km scene extension (in ground) centered at γ0= 33.17 degrees has been simulated, considering a sea state 4 (-15.1 dB normalized reflectivity) with 10 ms coherence time. In a first approach, a zero-mean complex Gaussian reflectivity for sea clutter has been assumed, in a downwind acquisition. To complement these results, and for the same sea conditions, a K-distributed clutter has been also considered, trying to emulate more realistic maritime scenarios. Six deterministic moving targets are included in the scenario as indicated in Table III, where two different type of vessels (Ramshackle T1 and a Civil cargo T2) have been modeled as a collection of point-like targets. The electromagnetic modeling and RCS extraction of these vessels have been carried out by Telespazio Vega UK company, in the cooperation frame of the European Commission FP7 funded Project SIMTISYS, [8]. In a first approximation, the targets