Hot-clutter cancellation using fast-time Space Time Adaptive Processing (STAP) can occur either pre or post range processing (RP) and to date, there has not been a direct comparison on which method offers the best results. This paper provides an analytic comparison which is verified with simulation and aims to provide insight into the location of the adaptive filter which would provide the best hot-clutter suppression. The covariance models are tested with signal models used in a multichannel Synthetic Aperture Radar (SAR)

Gray, D.

Rosenberg, L.

Trinkle, M.

Hot-clutter cancellation using fast-time Space Time Adaptive Processing (STAP) can occur either pre or post range processing (RP) and to date, there has not been a direct comparison on which method offers the best results. This paper provides an analytic comparison which is verified with simulation and aims to provide insight into the location of the adaptive filter which would provide the best hot-clutter suppression. The covariance models are tested with signal models used in a multichannel Synthetic Aperture Radar (SAR).Luke Rosenberg, Matthew Trinkle, Doug Gra

Adelaide Research & Scholarship

Fast-time STAP Performance in pre and post RangeProcessing Adaption as applied to Multichannel SARLuke Rosenberg∗†, Matthew Trinkle∗, Doug Gray∗∗University of Adelaide, Australia† Defence, Science and Technology Organisation, Australiae-mail: luker@eleceng.adelaide.edu.auAbstract: Hot-clutter cancellation using fast-time Space Time Adaptive Process-ing (STAP) can occur either pre or post range processing (RP) and to date, therehas not been a direct comparison on which method offers the best results. This pa-per provides an analytic comparison which is verified with simulation and aims toprovide insight into the location of the adaptive filter which would provide the besthot-clutter suppression. The covariance models are tested with signal models usedin a multichannel Synthetic Aperture Radar (SAR).1. IntroductionForming a SAR image in the presence of non-stationary hot-clutter will result in large regionsbeing distorted and unusable. Fast-time STAP has been shown to be an effective method forsuppressing the hot-clutter, while maintaining a coherent SAR image, [1]. The processingchain for a received SAR signal involves basebanding, sampling, RP and image formation.RP for SAR involves decoding the received signal with a Matched Filter (MF) to improve thetime/bandwidth product and hence achieve a finer range resolution.Previous studies on the performance of hot-clutter suppression algorithms have looked at usingan adaptive filter with no RP, [2] and also post RP, [3]. The former study derived an analyticalmodel for the pre RP covariance and tested its performance under different simulated topograph-ical conditions, while the latter study derived a post RP covariance model and used a simulatedscenario to compare element space and beam space approaches. The only study on fast-timeSTAP performance for SAR is by Klemm, [4] who looked at simulated data applied pre RPand concluded that firstly, fast-time filtering will degrade SAR resolution by broadening thepoint spread function mainlobe and increasing its sidelobes and secondly, as range resolutionimproved, sensitivity to filtering increased.This paper presents fast-time STAP models for pre and post RP adaptive filters and comparesthe relative adaptive performance as the number of fast-time taps is increased.2. Signal modelThe total received signal at the SAR, xn(·) includes the total ground return, interference fromthe direct-path and ground reflected path (hot-clutter) and receiver noise. The bistatic jammermodel is formed by the superposition of the direct path and K hot-clutter patches within a givenarea,zn(tl,u) =K∑k=0bkJ(tl − τ¯n,k(tl,u))exp[− jωcτ¯n,k(tl,u)]exp[− jωd,ktl] (1)where (tl,u) represents the lth fast-time sample within a pulse and the SAR position respectively,J(·) is the jamming signal waveform, τ¯n,k(·) is the bistatic delay for the kth patch, ωd,k is the fast-time doppler frequency and bk is the relative magnitude between the direct-path and hot-cluttersignals. The zero index refers to the direct-path with b0 = 1.Realisations of the jammer signal J(·) can be generated by an eigen-decomposition of the jam-mer auto-covariance, rJ(τ) = σ2J sinc(Bτ) with bandwidth, B and power level, σ2J . The relativescattering magnitude is determined by a physically based model for the multipath scattering,[5]. It uses a rough surface to define the scattering distribution between the SAR and an air-borne jammer. The coefficients, bk = ρBk for k > 1 are formed with a hot-clutter scaling factorρ, relative to the direct-path and a random amplitude Bk, determined from the scattering model.3. Fast-time STAPThe focussed output from the fast-time STAP filter is determined by the following convolutionover ˜L taps,xfs(tl,u) =l+ ˜L−1∑q=lHH(tl − tq,u)x(tq,u)= ˜HH(u)X(tl,u) (2)where ˜H(·) is the space/fast-time steering vector and X(·) is the fast-time received data vector.If there are N antenna elements, the received data signal can be stacked twice with the referenceantenna at the centre of the array to give,x(tl,u) =[x−(N−1)/2(tl,u), . . . ,x(N−1)/2(tl,u)]T∈ CN×1 (3)X(tl,u) =[xT (tl,u) ,xT (tl+1,u) , . . . ,xT (tl+ ˜L−1,u)]T ∈ C ˜LN×1 (4)with data components for the final ˜L taps set to zero. Fast-time STAP then involves substitutinga weight vector for the steering vector in Equation 2. The maximum SINR weight is given by,W(u) = γR−1Z (u) ˜H(u) (5)where γ is an arbitrary scaling factor and RZ(·) is the space/fast-time covariance. The formof the pre and post RP space/fast-time steering vectors are based on the spatial and temporalcomponents of the received SAR signal model. The spatial steering model for the nth channelis given by,sn(u) = exp[jωccdn sin [θ(u)]](6)where ωc is the carrier frequency, c is the speed of light, dn = nλc/2 is the antenna offset fromthe array phase centre with wavelength λc and θ(u) is the steering angle relative to the centreof the imaging patch. The spatial steering vector, s(u) is then formed similarly to Equation 3.The pre RP fast-time steering model is given by the SAR waveform which is a chirp. For thelth fast-time sample and qth fast-time tap,gpre,q(tl) = exp[− jBpi(tl − tq)+ jα(tl − tq)2] (7)where B is the bandwidth, 2α represents the chirp rate and the fast-time samples occur at tl =Ts +(l−1)∆t where Ts is the pulse collection starting time and ∆t is the fast-time sampling rate.As the steering vector is a chirp function, it can only provide a partially accurate representationof the target signal within ˜L fast-time taps. The pre RP temporal steering vector shows this,gpre =[1,exp[ jBpi∆t + jα∆2t ] , . . . ,exp[ jBpi( ˜L−1)∆t + jα(( ˜L−1)∆t)2]]T ∈ C ˜L×1 (8)and is now a function of the difference between time taps. After RP, the fast-time steering modelis represented by,gpost,q(tl) = sinc[B(tl − tq)] (9)which is a decaying function and can therefore be accurately represented by a small number oftaps as shown by the post RP temporal steering vector,gpost =[1,sinc [B∆t ] , . . . ,sinc[B( ˜L−1)∆t]]T∈ C˜L×1 (10)Consequently better signal detection results will be achieved in gpost as the signal energy ismore concentrated.The combined space/fast-time steering vector for each case is then formed by the Kroneckerproduct of the temporal and spatial components to give,˜Hpre(u) = gpre⊗ s(u) ∈ C˜LN×1, ˜Hpost(u) = gpost⊗ s(u) ∈ C˜LN×1 (11)4. Covariance ModelsThe pre and post interference covariance models are based on the estimated sample matrix form,ˆRZ(u) =1LtLt∑l=1Z(tl,u)ZH(tl,u) ∈ C˜LN× ˜LN (12)where Z(·) is the space/fast-time interference signal formed similarly to Equation 4. Also,as the instantaneous covariance models presented in [2]-[3] are fast-time dependent, the meanestimated covariance models will be used with a minor multiplicative bias determined by thenumber of averaged fast-time taps, Lt . Both models also assume that the broadband jammer isa stationary random process within the pulse interval, and therefore the received interferencesignal before, zn(·) and after RP, yn(·), can be similarly defined. The pre RP covariance is givenby,RZ,pre(u,ζ,n,n′) = E{1LtLt∑l=1zn(tl,u)zn′∗(tl +ζ,u)}= σ2J ∑k∑k′bkb∗k′ sinc[B(ζ+ τ¯n,k− τ¯n′,k′)]exp[− jωc(τ¯n,k− τ¯n′,k′)+ jωd,k′ζ]exp[− j∆ωk,k′(Ts +0.5(Lt −1)∆t)] sin[0.5∆ωk,k′Lt∆t]Lt sin[0.5∆ωk,k′∆t] (13)where ∆ωk,k′ = ωd,k −ωd,k′ and ζ is the delay between two fast-time taps. The post RP co-variance requires the range compression to be included in the derivation. At baseband, the MFreference signal is given by p∗c(−t), where the SAR waveform is a chirp defined by pc(t) =b(t/Tp)exp[− jBpit + jαt2] with the chirp rate duration Tp defined by b(t), which is unity for0 ≤ t ≤ 1 and zero otherwise. This gives the post RP jammer signal model as,yn(tl,u) =∫∞−∞zn(t′,u)p∗c(t′− tl)dt ′ (14)The post RP covariance model is then given by,RZ,post(u,ζ,n,n′) = E{1LtLt∑l=1yn(tl,u)yn′∗(tl +ζ,u)}= σ2J ∑k∑k′bkb∗k′ sinc[Bζ′(1−ζ′/Tp)−∆ fk,k′(Tp−ζ′)]exp[− jωc(τ¯n,k− τ¯n′,k′)+ jωd,k′ζ′]exp[− j∆ωk,k′(Ts +0.5(Tp−ζ′+(Lt −1)∆t))] sin[0.5∆ωk,k′Lt∆t]Lt sin[0.5∆ωk,k′∆t] (15)where ζ′ = ζ− τ¯n,k + τ¯n′,k′ and ∆ fk,k′ = 0.5∆ωk,k′/pi. This model is very similar to the pre RPcase with the sinc function containing the relative temporal delays and the correlation variable.There are now however extra terms related to the pulse width and the differential doppler. Thesedifferences are also present in the two exponential terms and will cause only a very small dif-ference in the overall model. These models are used to form covariance matrices, RZ,pre andRZ,post by varying the spatial channel indices, n,n′ and the fast-time delay, ζ.5. Simulated ResultsThe SINR loss is a common method of comparing adaptive performance and is defined by SINRdivided by the interference free Signal to Noise Ratio (SNR) and is a metric between 0 and 1.LSINR(θ(u)) =˜HH(u) [RZ + I ˜LN]−1 (u) ˜H(u)˜HH(u) ˜H(u)(16)To compare the SINR loss, simulation of a single pulse was used to model the covariancematrix in Equation 12 and the same parameters used for the analytic forms in Equations 13and 15. The simulation is at X-band with fc = 10GHz, B = 0.3GHz, ∆t = 1/2B, Tp = 28µs,α = 3.3×1015rad/s, σ2J = 50dB and ρ = 0.5. There are N = 5 spatial channels, L = 200 rangebins, K = 100 hot-clutter patches and the covariance matrices are estimated over Lt = 3˜LN rangebins. Results are given in Figure 1 for three different fast-time taps where there is a noticeabledecrease in SINR loss of approximately 20dB due to the extra correlation between the hot-clutter scatterers. To analyse this scenario more closely, the minimum point of the SINR loss ismeasured as the number of fast-time taps is increased. Figure 2 shows a decrease in SINR lossof close to 24dB as more taps are used.−20 0 20−60−40−20No. fast-time taps, L˜ = 1 No. fast-time taps, L˜ = 6 No. fast-time taps, L˜ = 12SINRloss(dB)−20 0 20−40−30−20−10Steering angle (deg)Steering angle (deg) Steering angle (deg)−20 0 20−40−30−20−10Figure 1: SINR loss with varying θ(u) for: (—) simulated pre RP, (- -) pre RP, (-.-) post RP1 3 6 9 12−65−60−55−50−45−40No. of fast-time taps (L˜)SINRloss(dB)Figure 2: SINR loss with varying ˜L for: (—) simulated pre RP, (- -) pre RP, (-.-) post RP6. ConclusionIn summary, both pre and post RP adaptive filters perform equally well at suppressing hot-clutter. However, since the pre RP steering vector only matches a small part of the chirp withinthe received data and the post RP case matches it almost completely, the latter model is thepreferred choice for SAR signal detection.References:[1] L. Rosenberg and D. A. Gray. Fast-time filtering with multichannel SAR. In Adaptive Sensor Array ProcessingWorkshop, June 2005.[2] P. M. Techau, J. R. Guerci, T. H. Slocumb, and L. J. Griffiths. Performance bounds for hot and cold cluttermitigation. IEEE Transactions on Aerospace and Electronic Systems, 35(4):1253–1265, 1999.[3] R. L. Fante and J. A. Torres. Cancellation of diffuse jammer multipath by an airborne adaptive radar. IEEETransactions on Aerospace and Electronic Systems, 31(2):805–820, 1995.[4] R. Klemm. Principles of Space-Time Adaptive Processing. The Institution of Electrical Engineers, 2002.[5] P Beckman. The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon Press Ltd., 1963.

Fast-time STAP performance in pre and post range processing adaption as applied to multichannel SAR

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Fast-time STAP Performance in pre and post Range Processing Adaption as applied to Multichannel SAR

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Fast-time STAP performance in pre and post range processing adaption as applied to multichannel SAR

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