Space-Time Adaptive Processing Using Sparse Arrays Michael Zatman 11 th Annual ASAP Workshop March 11 th -14 th 2003 This work was sponsored by the DARPA under Air Force Contract F19628-00-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author, and are not necessarily endorsed by the United States Government. 999999-1
Application: Space Based Radar Fast orbital velocity (Large aperture ~ GMTI performance) Long range to target (Large aperture ~ location accuracy) Launch cost ~low weight and size (folded) DARPA Erectorsat Program: Assembly of large radar apertures in space 999999-2
Outline Introduction Theory Performance Summary 999999-3
STAP Units 2 Vel. Vel. λ -Vel. λ2 Velocity Velocity Doppler (m/s) (Hz) 00 -Vel. λ2 v( θ ) = sin( θ ) D ( ) 2v sin θ = λ -2 Vel. -Vel. λ Azimuth ( o ) 999999-4
STAP Units 2 Vel. 0.5 λ Velocity Normalized Doppler Doppler (Hz) (Rel. PRF) -Vel. 0.25 λ 0 0 Vel. -0.25 λ D = ( ) 2v sin θ λ -2 Vel. -0.5 λ SIN (Azimuth) 999999-5
Doppler Ambiguous Clutter Vel. Beamwidth Normalized Doppler 2 PRF PRF 0 -PRF PRF Fast Platform Slow Platform Normalized Doppler SIN (Azimuth) β = 4v λprf -2 PRF SIN (Azimuth) -Vel. Main Beam Clutter Width 2v = λ L 4v L ( m/s) = ( Hz) 999999-6
Aperture and Doppler Limited Performance β=1 10 Pulses SINR Loss β=4 10 Pulses SINR Loss 0 # Elements # Elements -5 SINR Loss (db) 999999-7 Normalized Doppler Aperture limited limited performance is is reached if if the the array array travels travels more more than than one one aperture length length in in a CPI CPI Fast Fast moving platforms (e.g., (e.g., SBR) SBR) need need long long apertures to to achieve resolution limited limited performance for for typical typical CPI CPI lengths Large Large arrays arrays are are expensive Use. Dopp. Space Frac. Normalized Doppler β=1 Dopp. ltd β=4 Aper. ltd β=4 Dopp. ltd # Elements -10
Some Sparse Array Concepts Interferometer Useful Tx. Energy Mainlobe Tx+Rx Rx Even Spaced Equal Size Rx Tx+Rx Rx Uneven Spaced Equal Size Rx Tx+Rx Rx Response (db) Sidelobes Filled Sparse Angle ( o ) Grating lobes Sparse arrays trade mainlobe width against grating lobe height to find the optimum sparseness Rx 999999-8 Many Apertures Tx+Rx Rx Energy transferred from the mainlobe to the grating lobes is useless for Tx. Use a filled section of the sparse array for Tx. And form multiple Rx. beams
Sparse Array Issues Adaptive beamformer / STAP performance Narrower null due to increased aperture Losses due to grating lobes / nulls This Talk Angle estimation performance Improved accuracy due to narrower beamwidth (CRB) Non-local errors due to grating lobes (WWB, ZZB, AB, ) SAR performance Multiple spatial samples per pulse Tight PRF constraints Hardware and cost Sparse arrays require less hardware Cheaper & lighter 999999-9
Outline Introduction Theory Clutter Rank Waveforms SINR Loss Performance Summary 999999-10
Brennan s Rule & Ward s Rules* Brennan s Rule Rank = Total Synthetic Aperture Ward s Min Rank Rule Min Rank = N + M - 1 m = 1 m = 1 Time m = 2 m = M d o... Time m = 2 m = M d = β d o... Element Position N Element Position N fill Brennan s rule for filled arrays: r = N + β ( M 1) Ward s rules for sparse arrays: = N + M 1 r min r = Nfill + β ( M 1) max *J. Ward, Asilomar 1998 Element Position N = Number of elements, M = Number of pulses, β = 2 v T d -1 0, N fill = Number of elements in filled array 999999-11 Time m = 1 m = 2 m = M Ward s Max Rank Rule Max Rank = Total Synthetic Aperture... N fill
Additional Sparse Array Behavior N = 24, M = 10, β = 4 Example Length = 24 ele. Length = 50 ele. Length = 80 ele. Eigenvalue (db) 2 Subarrays 3 Subarrays 4 Subarrays 2 Subarrays 3 Subarrays 4 Subarrays 2 Subarrays 3 Subarrays 4 Subarrays Eigenvlaue Index Eigenvlaue Index Eigenvlaue Index Clutter Rank 2 Subarrays 3 Subarrays 4 Subarrays 999999-12 Aperture Length (Element Positions)
New (?) Rules for Sparse Arrays m = 1 Time m = 2 m = 3 m = 4 m = 5 Rank=min[6+1+4,6+2*1]=min[11,8]=8 Rank=min[6+2+4,6+2*2]=min[12,10]=10 Rank=min[6+3+4,6+2*3]=min[13,12]=12 Rank=min[6+4+4,6+2*4]=min[14,14]=14 m = 6 999999-13 Element Position For arrays which move less than the smallest subarray aperture during a pulse the rank is given by : min [ N + β ( M 1) + G, N + Sβ ( M 1) ] Jim Ward s r max Using each sub array independently Rank=min[6+5+4,6+2*5]=min[15,16]=15 For equal size subarrays a sparse array is no better than a single subarray if G > β( S 1)( M 1) I.e., The array is so sparse that there is no redundancy G = Sum gap sizes (element positions) S = Number of subarrays
Sparse Aperture Waveforms Unambiguous Waveform Ambiguous Waveform Response (db) Doppler PRF Doppler Clutter Ridge D = 2 v sin (θ) λ -1 PRF Sparse Filled Sin (θ) Sin (θ) Ambiguous waveforms (e.g., pulse-doppler) and sparse (ambiguous) apertures lead to multiple clutter nulls 999999-14 Unambiguous waveforms preferable
Long Single Pulse Waveforms Pulse length: up to 20ms @ 3000 km Phase Encoded Waveform Amplitude Doppler 20 ms = 50 Hz Doppler Resolution = 0.75 m/s Velocity Resolution @ 10 GHz Waveform Code Range Time Single pulse means no range or Doppler ambiguities High chip rate sets Doppler ambiguities Must pulse compress each Doppler bin separately More computation than pulse-doppler waveforms 999999-15 Concern about strong sidelobe clutter > noise floor Wide bandwidth & narrow antenna beampatterns
Processing Long Single Pulse Waveform N Channels Digital Digital Digital Receiver Receiver Receiver Pulse Comp. Pulse Pulse Doppler Comp. Comp. Bin 1 Doppler Doppler Bin Bin 1 1 Pulse Comp. Pulse Pulse Doppler Comp. Comp. Bin 2 Doppler Doppler Bin Bin 2 2 Pulse Pulse Comp. Comp. Pulse Doppler Doppler Comp. Bin Bin Doppler Bin Pulse Pulse Comp. Comp. Pulse Doppler Doppler Comp. Bin Bin Doppler Bin M Inverse Fourier Transform M Pulses (Nyquist sampled for highest Doppler) Any STAP Algorithm Long single pulse radar can be made to appear like a regular pulse-doppler radar Looks like high PRF radar without the range ambiguities 999999-16
Space Time Adaptive Processing Response / Doppler Sparse / Filled Clutter ridge Normalized SINR (db) Sparse Filled Grating lobes lead to reduced detection performance at particular Doppler frequencies H H 2 GratingLobe Gain SINRLoss v v v e = 1 MainbeamGain Should not make the array too sparse For <3 db SINR loss grating lobe gain must be 3 db less than main lobe gain (Σ grating lobes for pulse-doppler waveforms?) 999999-17 Sin (Angle) Normalized Doppler
Outline Introduction Theory Performance Dependence on waveform SBR Design Example Summary 999999-18
Unambiguous vs. Ambiguous Waveforms Interferometer Example N = 8, M = 32, β = 1 N = 8, M = 8, β = 4 Gap (Element Positions) Single Sub. Perf. SINR Loss (db) Gap (Element Positions) Runs out of DOFs SINR Loss (db) Normalized Doppler (β=1 system) Normalized Doppler (β=1 system) Filled rank = 8+1(32-1) = 39 Max. sparse rank = 8+2(32-1) = 70 (reached with a 31 element gap) Filled rank = 8+4(8-1) = 36 Runs out of DOFs with a 27 element gap 8+27+2(32-1) = 63 Doppler unambiguous waveforms better preserve the available DOFs 999999-19
Unambiguous vs. Ambiguous Waveforms N = 8, M = 32, β = 1 N = 8, M = 8, β = 4 Gap (Element Positions) SINR Loss (db) Gap (Element Positions) SINR Loss (db) Normalized Doppler (β=4 system) Normalized Doppler (β=4 system) Grating lobes on Doppler ambiguous clutter Multiple grating lobes on Doppler ambiguous clutter Combination of of Doppler and and angle ambiguities leads to to poor SINR performance 999999-20
Space Based GMTI Radar Examples Parameters 32m x 2.5m filled aperture Scenarios 10 GHz operating frequency 1000 km orbit 7282 m/s orbital velocity 1 kw peak transmit power 200 MHz bandwidth Area of interest 0 o Rotation 60 o Rotation Unambiguous waveform -12 db const. γ clutter model 2500 km range 16.67ms CPI length Travel ~120m in a CPI Doppler SIN (Angle) Doppler SIN (Angle) 999999-21
Space Based Radar GMTI Designs Interferometer Array Even Spaced Equal Size Tx & Rx Rx Rx Tx & Rx Rx Uneven Spaced Equal Size Many Apertures Rx Tx & Rx Rx Rx Tx & Rx Rx Many possible array configurations Radar performance Ease of launch and assembly* Mechanical issues* * Issues being addressed by Aerospace Corporation 999999-22
0 o Rotation Scenario Interferometer Array Three Equal Arrays - Even Array Length (m) Array Length (m) 999999-23 50m 1.88 m/s Three Equal Arrays - Uneven 97m 1.13 m/s Velocity (m/s) 65m 1.58 m/s Many Unequal Apertures 242m 0.98 m/s Velocity (m/s) 3.23 m/s Many unequal apertures provides the longest array and best performance Normalized SINR (db) 0-2 -4-6 -8-10
60 o Rotation Scenario Interferometer Array Three Equal Arrays - Even Array Length (m) Array Length (m) 999999-24 50m 1.2 m/s Three Equal Arrays - Uneven 97m 72m 1.05 m/s Velocity (m/s) Array Length (m) Array Length (m) 65m 0.98 m/s Many Unequal Apertures 224m 0.9 m/s Velocity (m/s) 1.8 m/s Better overall MDV, but reduced total baseline in some cases Normalized SINR (db) 0-2 -4-6 -8-10
-3 db MDV vs. Array Length 0 o Rotation 60 o Rotation MDV (m/s) Lower variance of the subarray positions of the many unequal config. MDV (m/s) Interferometer 3 Equal Even 3 Equal Uneven Many Unequal Array Length (m) Array Length (m) Many unequal subarrays configuration needs a larger baseline to obtain the same performance as the other configurations, but ultimately provides the best MDV 165m aperture optimizes MDV for 2500 km range Longer apertures improve angle metrics 999999-25
Summary Sparse arrays potentially improve the minimum detectable performance of space-based radars Approach the MDV performance of a large filled aperture much with lower size, weight and cost Sparse arrays and sparse (pulse-doppler) waveforms do not mix well Sparse arrays perform well with Doppler unambiguous waveforms Sparse waveforms (pulse-doppler) perform well with filled arrays Long single-pulse waveforms provide range and Doppler unambiguous operation and are compatible with current STAP algorithms Sparse arrays with many unevenly sized unevenly spaced subarrays provide the best GMTI performance 999999-26
Backup Viewgraphs 999999-27
Interferometer Array Grating Lobes Untapered Apertures 40 db Taylor Apertures Gratinglobe Level (db) 10 4 3 2 1 Gratinglobe Level (db) 10 5 4 3 2 1 Fill Fraction Fill Fraction = Filled Aperture Total Aperture Fill Fraction Grating lobes quickly appear for interferometer array ~ 2 / 3 fill fraction -3 db grating lobes untapered apertures 999999-28
Grating Lobe Distributions 3 Equal Arrays Peak Gratinglobe (db) Gap Ratio Interf. 1:1 2:1 3:1 4:1 5:1 Number GLs > -3 db Gap Ratio Interf. 1:1 2:1 3:1 4:1 5:1 Fill Fraction Fill Fraction Gap Ratio = Big Gap : Small Gap Small Gap Big Gap Lower grating lobes than interferometer 999999-29 Higher gap ratios lead to lower grating lobes Also poorer MDV performance
Grating Lobe Distributions Unequal Arrays Peak Gratinglobe (db) Gap Ratio Interf. 3 Equal 1:1 3 Unequal 2:1 5 Unequal 7 Unequal 9 Unequal Number GLs > -3 db Gap Ratio Interf. 3 Equal 1:1 3 Unequal 2:1 5 Unequal 7 Unequal 9 Unequal Fill Fraction Fill Fraction 50% filled aperture in center subarray Multiple unequal arrays have the best grating lobe performance 999999-30
0 o Rotation Scenario Interferometer Array Three Equal Arrays - Even Array Length (m) Array Length (m) 50m Three Equal Arrays - Uneven 97m Normalized Doppler Array Length (m) Array Length (m) 65m Normalized Doppler Many Unequal Apertures 242m Normalized SINR (db) 0-2 -4-6 -8-10 Normalized Doppler Normalized Doppler 999999-31
Three Equal Apertures Target Location Gap (m) Peak Grating Lobe -3 db Contour -6 db Contour Grating Lobe Level (db) Threshold SNR (db) Weiss Weinstein Bound Gap Ratio 1:1 1:2 1:4 1:5 Gap (m) Aperture (m) 96 m aperture largest possible without increasing the threshold SNR Provides 89 m rms error at 6 o grazing 82 m gives 107 m rms error 999999-32
Three Unequal Apertures Target Location Gap (m) Peak Grating Lobe -3 db Contour -6 db Contour Grating Lobe Level (db) Threshold SNR (db) Weiss Weinstein Bound Gap Ratio 1:1 1:2 1:3 1:4 1:5 Gap (m) Aperture (m) 72 m aperture largest possible without increasing the threshold SNR 72m aperture Provides 119m rms error at 6 o grazing 999999-33
SINR Loss Due To Grating Lobe (Spatial Only Example) 20 Element Array Example Normalized Gain Gap Size 5 ele 10 ele 20 ele 0.193 0.697 0.445 0.242 SINR Loss (db) -0.93 db -1.2 db -2.56 B -5.1 db SIN (Angle) SIN (Angle) Under the high INR assumption: SINR Loss H H v v v e = 1 2 Grating Lobe Gain Mainbeam Gain i.e., for 3 db loss grating lobe gain (sum grating lobes for pulse-doppler?) must be 3 db less than main lobe gain 999999-34