Cognitive MIMO Radar

Transcription

1 Cognitive MIMO Radar Joseph Tabriian Signal Processing Laboratory Department of Electrical and Computer Engineering Ben-Gurion University of the Negev Involved collaborators and Research Assistants: Prof. R. Shavit, Prof. H. Messer, Dr. I. Bili, I. Beerman, W. Huleihel, M. Teitel, N. Sharaga, O. Isaacs BGU Radar Symposium 2016

2 Outline MIMO radar at a glance Cognitive radar - introduction Cognitive MIMO radar for beamforming and detection Conclusion

3 MIMO Radar at a Glance Data model: XH( Θ) S W X S mn, in, - Rx signal at sensor m and time index n - Tx signal by element i and time index n H( Θ) - Tx-Rx channel matrix Θ - Unnown targets' parameters 1 RS SS N MIMO - R H s ci Phased array - ran( R )=1 s Tx elements Rx elements

4 MIMO Radar at a Glance Orthogonal Tx signals can be decomposed at the receiver, allowing adaptive beamforming of the Tx signals Virtual receiving elements: Tx elements Virtual Rx elements Single Tx element Rx element Rx element

5 MIMO Radar at a Glance Virtual receiving elements: Orthogonal Tx signals can be decomposed at the receiver, allowing adaptive beamforming of the Tx signals. Tx elements Virtual Rx elements Single Tx element Rx elements Rx elements Colocated (mono-static) MIMO radar: Beerman-Tabriian 2004 Distributed (multi-static) MIMO radar: Fishler et al. 2004

6 MIMO Radar Properties Array aperture extension: Receive elements Transmit elements Virtual elements Receive elements Transmit elements Virtual elements

7 MIMO Radar Properties Array aperture extension: Transmit/Receive elements Virtual elements

8 MIMO Radar Advantages More degrees of freedom due to the virtual sensors: Higher angular resolution. Higher number of targets/clutter in a given range-doppler cell, which can be detected and localized. Lower sidelobes by virtual spatial windowing. Digital beamforming of the Tx beams in addition to the Rx beams, and therefore avoid beam shape loss in cases that the target is not in the center of the beam. Decrease the spatial power density of the Tx signal spatial spread spectrum (SSS) which is critical for low probability of intercept radars (LPIR).

9 MIMO Radar Disadvantage Implementation Gain loss (omni-directional transmission) Not a real problem in search mode: omnidirectional coverage allows large time-on-target (requires quasi-stationarity or trac-before-detect). A real problem in trac/acquisition modes: If the target direction is nown with a given degree of accuracy, then MIMO radar wastes its energy towards undesired directions. Solution: Cognitive MIMO Radar

10 Cognitive Radar Proposed by Simon Hayin A cognitive radar employs adaptive Tx-Rx based on history observation and environmental information.

11 Cognitive Radar Why the term cognitive is used? NIH definition: Cognition: conscious mental activity that informs a person about his or her environment. Cognitive actions include perceiving, thining, reasoning, judging, problem solving and remembering. Biological Cognitive Properties versus Cognitive Radars Cognitive Property Perceiving Thining, Reasoning, Judging, Problem Solving Remembering [Guerci 2011] Cognitive Radar Equivalent Sensing Expert Systems, Adaptive Algorithms, and Computation Memory, Environmental Database

12 Cognitive MIMO Radar Data model at the th step: X H ( Θ) S W H ( Θ) - MIMO channel matrix, Θ - Target parameters Side Information Optimal Adaptive Waveform Design S H ( Θ) X Optimal Receiver/Processor Detection/ Estimation/ Tracing/ Classification noise Optimal processor: Detect/localize/trac/classify the target(s) based on available ( ) measurements, X [ X,, X ]. 1 Optimal adaptive waveform design: Design the transmit signal at the th pulse,, ( 1) based on the measurements during the previous pulses, X [ X to 1,, X 1] optimize a given criterion. S

13 Cognitive MIMO Radar Data model at the th step: X H ( Θ) S W H ( Θ) - MIMO channel matrix, Θ - Target parameters Side Information Optimal Adaptive Waveform Design S H ( Θ) X Optimal Receiver/Processor Detection/ Estimation/ Tracing/ Classification noise C S arg max C( S, X ) ( opt) ( 1) S s.t. Tx power constraint ( 1) ( S, X ) - Criterion for perofrmance optimization

14 Cognitive Beamforming Criterion for estimation accuracy: performance bound on the meansquared-error (MSE): Bayesian Cramér-Rao bound (BCRB): Simple, but not tight. Bobrovsi-Zaai, Reuven-Messer, or Weiss-Weinstein bounds: High computational complexity, but tighter. It can be shown that with Gaussian noise, the bounds depend on the Tx auto-correlation matrix: Power constraint: or R S P / N, 1,, T n N nn, S 2 F tr R R S S T 1 SS N P H

15 Cognitive Beamforming For single unnown parameter, θ, with total Tx power constraint, and zero-mean Gaussian noise with cov. : R u ( opt) S Pu u H - eigenvector corresponding to the maximum eigenvalue of Γ ( X ) E H ( ) R H ( ) X ( 1) H 1 ( 1) v R v Q Vector parameter case, Θ - weighted BCRB: Convex optimization problems, and thus can be solved efficiently (Boyd and Vandenberghe (2004)).

16 Example Cognitive Beamforming Scenario : Uniform linear array of transceivers N N with /2 inter-element spacing. 2 AWGN with covariance R IN. 2 2 NPNR ASNR / 6dB. R R T 7 elements

17 Example Cognitive Beamforming T * Posterior pdf s versus transmit beampatterns P ( ) a ( ) R a ( ). T S T Auto-focusing effect: Automatic beamforming before detection/estimation.

18 Example Cognitive Beamforming Single target direction estimation accuracy, 7 transceivers

19 Example Cognitive Beamforming Probability of resolution compared to space-reversal method. Two targets SNR=-2 db, =10, 7 transceivers.

20 Cognitive Detection Sequential Hypothesis Testing (SHT): H H 1, l l,, l, l 0 : x H ( Θ) s w : x w l, l,, 1,2,, l 1,, L, Goal: Minimize Average Sample Number (ASN) to achieve given error probabilities: 1 P, P. Decide H Decide H 1 if: if: log log D FA ( ) f ( )( X H ) P X 1 D ( ) f ( )( X H0) 1 P X D X 0 ( ) ( ) f ( )( X H ) 1 P f ( X H ) P X ( ) 1 0 FA FA

21 Cognitive Detection Two hypotheses: Optimal signal design: S, opt log(1 PD ) log P FA ASN max,. KLD( H1 H0) KLD( H0 H1) ( 1) CS, X log(1 PD ) log P FA arg min max,. S KLD( H1 H0) KLD( H0 H1) KLD H ( 1) ( m Hn) - conditional Kullbac-Leibler Divergence given X.

22 Cognitive Detection S L H H 1 ( 1), opt arg mins, l E H, l ( Θ) Rv H, l ( Θ) X s, l S l1 s.t. L l1 s l, 2 P u max H 2 j l T j DT T, ( Θ) e ar( ) at( ) e, 1,2,, l 1, L, l * ( 1) E ( ) T at at( ) X. R Pu u H s, opt max max - Eigenvector corresponding to the maximal eigenvalue of the matrix

23 Example - Cognitive Detection 4Tx, 16 Rx /2 inter-element spacing NF 7dB RCS 1m 2 Range=50m Azimuth=30

24 Example - Cognitive Detection 2 4Tx, 16 Rx, NF 7dB, RCS 1m, range=50m, azimuth=30

25 Conclusions and Future Research MIMO radar offers great advantages but needs to be used with care. In cognitive MIMO radar, Tx signal auto-correlation matrix is adaptively optimized. The optimized signal is not necessarily orthogonal (MIMO) or fully correlated (phased array). Two new cognitive Tx beamforming approaches were presented to optimize: localization accuracy and detection performance This approach provides an automatic focusing array: beamforming before detectionqestimation. Future research: Considering other criteria, such as probability of resolution, or target classification performance.

26 Than you!