Cognitive Radar Signal Processing€¦ · There are a Low Pulse Repetition Frequency (PRF) regime...

Cover

2014 Workshop on Mathematical Issues inInformation Sciences

Cognitive Radar Signal Processing

Antonio De Maio∗, July 7, 2014

∗Professor, University of Naples, Federico II, Fellow IEEE

A. De Maio (University of Naples) Cognitive Radar Signal Processing July 7, 2014 1 / 51

Introduction

Introduction

Cognition: Conscious mental activity that informs a person about his or herenvironment (US National Institute of Mental Health).

It requires:

perceiving, thinking, reasoning, judging,problem solving, and remembering;

being smart and agile in the interactionwith the environment.

J. R. Guerci, “Cognitive Radar:The Next Radar Wave?”, Microwave Journal, January 2011.S. Haykin, “Cognitive Radar: A Way to the Future”, IEEE Signal Processing Magazine, January 2006.


Introduction

Introduction

It is necessary to develop a mapping among the mentioned biological cognitive prop-erties and the corresponding activities in a cognitive radar.

What exactly are the potential benefits of a radar possessing cognitive capabilities?

Type of radar Type of mission OperativeEnvironment

During this presentation some benefits will be highlighted.

J. R. Guerci, “Cognitive Radar: The Knowledge-Aided Fully Adaptive Approach”, Artech House RemoteSensing Library.


The Cognitive Radar

Functional Elements and Characteristics of a Cognitive Radar Architecture

Let us consider the basic block diagram of a conventional adaptive radar.

Adaptivity is usually confined to the receiver and is based solely on the received datastream.

In general, there is not provision for learning over time, feedback to the transmitter, or theintegration of environmental exogenous sources such as Geographical Information Systems(GISs) or Digital Terrain Maps.


The Cognitive Radar


A cognitive radar architecture is characterized by the presence of an environmentaldynamic database and, remarkably, the possibility of transmitter adaptivity.

Otherwise stated, there are a number of advanced functionalities attempting to emulatethose in a biologically cognitive systems.


The Cognitive Radar


The Environmental Dynamic Database (EDDB)contains knowledge of the environment and/ortargets of interest gleaned from endogenous orexogenous information sources.

This component permits a Knowledge-AidedSignal Processing.

In addition to an adaptive receiver, thecognitive radar includes an adaptive transmitterbased on the feedback from the receive chainand the interactions with EDDB.

The multiple transmit degrees of freedom also give rise to the concept of Multiple InputMultiple Output (MIMO) radar.

The joint TX and RX adaptivity entails the developmentof innovative signal processing techniques.


Waveform Diversity

Waveform Diversity

Most radars have some forms of primitive transmit adaptivity, usually in the terms ofmode selection, as for instance:

medium range vs long range;

track vs search;

low resolution vs high resolution;

staggering.

Waveform diversity is already used by many echolocating mammals (bats, whales, anddolphins) as an inherent component of their normal behaviour.

On the radar side, there is an attempt to mimic what Mother Nature has realized duringthe evolution of many species.

Let us focus on the bats which exploit tongue clicking to produce waveforms with a varietyof modulations that are transmitted via bone and muscle tissue to form an illuminatingbeam.


Waveform Diversity Waveform Diversity in the Bat’s Signal

Waveform Diversity in the Bat’s Signal

Let us consider the signal emitted by a bat to understand how it uses diversity.

Observations: presence of spatial, temporal, and waveform diversity.

C. Baker, H. Griffiths, A. Balleri, “Biologically Inspired Waveform Diversity”, chapter 6 of the bookWaveform Design and Diversity for Advanced Radar Systems, IET 2012 (Editors: F. Gini, A. De Maio, L.Patton).




The signal emitted by the Eptesicus Nilssoni bat.

There are a Low Pulse Repetition Frequency (PRF) regime and a High PRF regime.

Moreover, the signal shape changes from pulse-to-pulse.




Approach phase Terminal phase

↑

The distance between the bat and the prey is low enough that evenslight trajectory changes would produce large Doppler errors

(hence large ranging errors) between consecutive pulses.



Avoiding Being Eaten by Bats: Countermeasures

Some insects have developed evasive behaviours inresponse to signals from bats.

For instance, arctiids might disturb bat biosonarin two ways:

by simulating multiple targets;

by interfering with range determination.

The same dicothomy exists between Electronic-Counter-Measures (ECMs) and Electronic-Counter-Counter-Measures (ECCMs).

L. A. Miller and A. Surlykkej, “How Some Insects Detect and Avoid Being Eaten by Bats: Tactics andCountertactics of Prey and Predator”, BioScience, Vol. 51 No. 7, July 2001.



Limitations

Why transmit adaptivity is not yet used in radar?

Two fundamental reasons:

1 it requires advanced hardware (digital arbitrary waveform generators, solid statetransmitters, etc.);

2 it necessitates the availability of new transmit adaptation algorithms.

Next hardware generation and the recenttechnological progress in digital electronic.

Potential benefits achievable throughwaveform diversity to motivate this newradar functionality.

J. S. Bergin and P. M. Techau, “High-Fidelity Site-Specific Radar Simulation: KASSPER ’02 WorkshopDatacube”, ISL Technical Note, Vienna, May 2002.


Optimizing Fast-Time Modulation

Optimizing Fast-Time Modulation

Let us analyze the benefits of tailoring the transmit waveform (fast-time modulation)to account for a colored noise RF interference source.

The optimum waveform optimally redistributes the transmit energy in the frequencydomain so as to maximizing the Signal-to-Interference-plus-noise-Ratio (SINR).

Additional context-dependent constraintscan be also forced to the radar waveform.

This shaping technique can be also ex-ploited to control the impact of radar onother communication systems.

A. De Maio, S. De Nicola, Z.-Q. Luo and S. Zhang, “Design of Phase Codes for Radar PerformanceOptimization with a Similarity Constraint” , IEEE Transactions on Signal Processing, February 2009.


Cognitive Radar Waveform Design for Spectral Coexistence

Spectral Coexistence

Spectrally Crowded Environments

Coexistence among radar and telecommunication systems is currently becoming oneof the challenging research topics in both radar and communication communities.

Basic electromagnetic considerations, such as good foliage penetration, and low path lossattenuation, push some communication and radar systems to coexist in the same frequencyband (for instance VHF and UHF).

It is thus mandatory the development of advanced radar signals ensuring compatibilitywith the surrounding electromagnetic radiators, namely keeping acceptable the mutualinterference induced on frequency overlaid systems.

A. Aubry, A. De Maio, M. Piezzo, and A. Farina, “Radar Waveform Design in a Spectrally CrowdedEnvironment via Nonconvex Quadratic Optimization”, IEEE Transactions on Aerospace and ElectronicSystems, April 2014.



Signal Model

Let us consider a monostatic radar system transmitting a signal composed of N sub-pulses, and denote by

c = [c(1), . . . , c(N)]T ∈ CN

the N-dimensional fast-time radar code. Thus, the N-dimensional column vector v ∈ CN

of the observations, from the range-azimuth cell under test, can be expressed as:

v = αc + n.

α is a complex parameter accounting for channel propagation and backscatteringeffects from the target within the range-azimuth bin of interest;

n is the N-dimensional column vector containing the filtered disturbance echo sam-ples:

1 it accounts for both white internal thermal noise as well as interfering signals withsame frequencies as the radar of interest;

2 it is modeled as a complex, zero-mean, circular Gaussian random vector sharing thecovariance matrix M.



Cooperative Radiators & Produced Interference

As to the cooperative radiators coexisting with the radar of interest, let us assume thateach of them is working over a frequency band Ωk = [f k1 , f

k2 ].

To guarantee spectral compatibility with K overlayed radiators, the radar has to controlthe energy produced on the shared frequency bands, namely the transmitted waveformhas to comply with

c†RI c ≤ EI

RI =∑K

k=0 wkRkI ;

RkI (m, l) =

f k2 − f k1 m = l

e j2πfk

2 (m−l) − e j2πfk

1 (m−l)

j2π(m − l)m 6= l

(m, l) ∈ 1, . . . ,N2 ;

wk ≥ 0, k = 0, . . . ,K , are suitable weights related to the importance of a givenradiator;

EI is the amount of allowed interference level.



Cognitive Spectrum Awareness

Radio Environment Map (REM) represents the key to gain spectrum cognizance whichis at the base of an intelligent and agile spectrum management.


First Cognitive Waveform Design Approach

Waveform Design: Objective Function & Constraints 1/2

Optimizing the detection performance, through the maximization of the Signal toInterference plus Noise Ratio (SINR),namely

SINR = |α|2c†Rc ,

where R = M−1.

Ensuring desirable radar features to the transmitted waveform forcing an energyconstraint and a similarity constraint with a prescribed waveform c0, namely

‖c‖2 = 1 ‖c − c0‖2 ≤ ε

(ε ruling the size of the similarity region, ‖c0‖ = 1), so as to indirectly control somerelevant characteristics of the waveform.

Providing a control on the interference energy produced on shared bands, in order toensure spectral coexistence with overlaid wireless networks, enforcing the constraint

c†RI c ≤ EI .



Code Design: Objective Function & Constraints 2/2

The waveform design problem can be formulated as the following optimization problem:

P1:QCQP

max

cc†Rc

s.t. c†c = 1c†RI c ≤ EI

‖c − c0‖2 ≤ ε

Problem P1 is a non-convex optimization Quadratically Constrained Quadratic Prob-lem (QCQP).



Code Design: Feasibility of the Optimization Problem

Not all the pairs (EI , ε) produce a feasible problem P1. As a consequence, it is manda-tory characterizing the feasibility of P1 as function of EI and ε, for any given similaritycode c0. This observation leads to the following definition of the so-called I/S achievableregion associated to the radar code c0:

F = (EI , ε) : EI ≥ λmin(R I ), 0 ≤ ε ≤ 2, problem P1 is feasible

By studying the set F , it is possible to show that:

1 the I/S achievable region is a convex set (from a practical point of view we cancontrol its accuracy description);

2 each point on its boundary region can be computed in a polynomial time.



Code Design: Solution to the Optimization Problem 1/3

Let us observe that an optimal solution to P1 can be obtained from an optimal solutionto the following non-convex Enlarged Quadratic Problem (EQP) P2:

P1:QCQP

max

cc†Rc


‖c − c0‖2 ≤ ε

Equivalent

P2:EQP

max

cc†Rc


c†c0c†0 c ≥ δε

where δε = (1− ε/2)2.




Exploiting the equivalent matrix formulation of P2 and neglecting the rank-one constraint,we obtain the following convex SDP Enlarged Quadratic Problem Relaxed (EQPR) P3:

P2:EQP

max

cc†Rc


c†c0c†0 c ≥ δε

Relaxation

P3:EQPR

max

Ctr (CR)

s.t. tr (C) = 1tr(C †RI

)≤ EI

tr(C †C0

)≥ δε

C 0

Problem P3 is solvable, since its feasible set is compact and its objective functionis continuous.

Problem P2 is hidden convex, namely the relaxation of P2 into P3 is tight.

It is possible to construct a rank-one optimal solution c c† to P3, starting from anarbitrary rank optimal solution C?.




Algorithm 1 summarizes the procedure leading to an optimal solution to P1.

The computational complex-ity connected with the imple-mentation of the algorithm ispolynomial as both the SDPproblem and the decompositioncan be performed in polynomialtime.



Code Design: Example 1/4

The radar designer can choose the pair (EI , ε) to suitably trade off spectral coexistence,desirable radar waveform characteristics and achievable SINR.


Extension of the Cognitive Waveform Design Approach

Extension: Energy Modulation

The previous design technique can be further improved through a suitable modulationof the transmitted waveform energy, which is no longer kept fixed.

The energy modulation can be accounted for through the constraint

1− η ≤ c†c ≤ 1

where η (0 ≤ η ≤ 1) is a design parameter which rules the maximum allowable de-crease of the radar transmit power (hence it can be set based on radar range equationargumentations or radar maximum operation range).

A. Aubry, A. De Maio, Y. Huang, M. Piezzo, and A. Farina, “A New Radar Waveform Design Algorithmwith Improved Feasibility for Spectral Coexistence”, accepted for publication on IEEE Transactions onAerospace and Electronic Systems.




The considered waveform design problem can be formulated as the following non-convexoptimization Quadratically Constrained Quadratic Problem (QCQP) P1:

P1:QCQP

max

cc†Rc

s.t. 1− η ≤ c†c ≤ 1c†RI c ≤ EI

‖c − c0‖2 ≤ ε

Equivalent

P2:QCQP Reformulation

maxx

tr (Q0X )

s.t. 1− η ≤ tr (Q1X ) ≤ 1tr (Q2X ) ≤ EI

tr (Q3X ) ≥ 0tr (Q4X ) = 1X = xx†, x = [cT , t]T

where

Q0 =

[R 00 0

], Q1 =

[I 00 0

], Q2 =

[R I 00 0

],

Q3 =

[I −c0

−c†0 1− ε

], Q4 =

[0 00 1

]A. De Maio (University of Naples) Cognitive Radar Signal Processing July 7, 2014 29 / 51



Problem P2 can be relaxed into the following problem P3

P2:QCQP Reformulation

maxx

tr (Q0X )

s.t. 1− η ≤ tr (Q1X ) ≤ 1tr (Q2X ) ≤ EI

tr (Q3X ) ≥ 0tr (Q4X ) = 1X = xx†, x = [cT , t]T

Relaxation

P3:SDP Relaxation

maxX

tr (Q0X )

s.t. 1− η ≤ tr (Q1X ) ≤ 1tr (Q2X ) ≤ EI

tr (Q3X ) ≥ 0tr (Q4X ) = 1X 0

Problem P2 is hidden convex, namely the relaxation of P2 into P3 is tight.

An optimal solution c? to problem P1 can be obtained from an arbitrary rank op-timal solution X ? to problem P3.


Spectral Coexistence in Signal-Dependent Interference

Extension: Signal Dependent Interference

The previous design techniques can be further extended to the case of a radar operat-ing in a highly reverberating environment. The additional signal-dependent clutterenvironment disturbance contribution can be accounted for through the term

i =N−1∑

k=−N+1,k 6=0

αkJkc

which is the superposition of returns from the range cells adjacent that under test,with covariance matrix Σi (c), where Jk(l ,m) = 1 if l − m = k, 0 elsewhere, andαk ∼ CN (0, βk).

The covariance matrix of the clutter Σi (c) depends on the radar code c and them.s.v. of the clutter amplitude returns βk .

The radar system exploits a dynamic environmental database topredict the actual scattering scenario.

A. Aubry, A. De Maio, M. Piezzo, M. M. Naghsh, M. Soltanalian, and P. Stoica, “Cognitive RadarWaveform Design for Spectral Coexistence in Signal-Dependent Interference”, Proceedings of the 2014 IEEERadar Conference (RADARCON),Cincinnati, OH, USA, May 19-23 2014.



Signal Model

The N-dimensional column vector v ∈ CN of the fast-time observations, can be expressedas:

v = αc + i + n.

α is a complex parameter accounting for channel propagation and backscatteringeffects from the target within the range-azimuth bin of interest;

n ∼ CN (0,Mint) accounts for white internal thermal noise as well as interfering(licensed and unlicensed) radiators.

Hence, the SINR can be expressed as

SINR =|w†c |2

w† [Σi (c) + Mint] w



Problem Formulation

The main goal is to optimize the radar detection performance, through the maximiza-tion of the SINR, ensuring the spectral coexistence with overlaid licensed radiators.

The developed optimization procedure is based on the joint design of the radar codec and the receive filter w , which can be formulated as the following constrained opti-mization problem:

P

maxc,w

|w†c |2

w† [Σi (c) + Mint] ws.t. c†c = 1

c†RI c ≤ EI

‖c − c0‖2 ≤ ε

Problem P is a non-convex optimization problem, since the objective function is anon-convex function and the constraint ‖c‖2 = 1 defines a non-convex set.



SINR Sequential Optimization Procedure 1/2

Good Quality Solution to problem P1 Given w (n−1), we search for an admissible radar code c (n) at step n improving the

SINR corresponding to the receive filter w (n−1) and the transmitted signal c (n−1).

2 Whenever c (n) is found, we fix it and search for the filter w (n) which improves theSINR corresponding to the radar code c (n) and the receive filter w (n−1), and so on.

w (n) and c (n) are used as starting points at step n + 1. To trigger the procedure, theoptimal receive filter w (0), for an admissible code c (0), can be considered.



SINR Sequential Optimization Procedure 2/2

Pw(n): Filter Design max

w

∣∣∣w†c(n)∣∣∣2

w†[Σi

(c(n)

)+ Mint

]w

Pc(n): Code Design

max

c

|w (n−1)†c|2

w (n−1)† [Σi (c) + Mint] w (n−1)

s.t. ‖c‖2 = 1c†RI c ≤ EI

‖c − c0‖2 ≤ ε

Problem Pw(n) is solvable, and a closed form

optimal solution w (n) can be found for any c(n).

w (n) =

[Σi

(c(n)

)+ Mint

]−1c(n)

c(n)†[Σi

(c(n)

)+ Mint

]−1c(n)

Problem Pc(n) is a hidden-convex optimization

problem. Hence, an optimal solution can beobtained:

relaxing the problem into a fractional SDP;

applying the Charnes-Cooper transforma-tion to get an Equivalent SDP.

exploiting a suitable rank-one matrixdecomposition procedure to get an optimalsolution to the original non-convex opti-mization problem.


Target Classification

Target Classification

Let us denote by h1(n) and h2(n) theimpulsive responses of targets 1 and 2.

It is reported

|H1(v)− H2(v)|;

The modulus of the optimum pulsespectrum.

The optimal waveform places more energyin those spectral regions where the twofrequency responses (H1(ν) and H2(ν)) aresignificantly different.


Transmit Beamforming Diversity

Beamforming at the Transmitter end

While fast-time modulation has been used in the previous example, other degrees offreedom can also be exploited at the transmitter end:

1 transmitting azimuth andelevation beampattern;

2 polarization;

3 slow-time coding.

Transmit beampattern can be optimized to reduce as much as possible the effectsof strong sidelobe unwanted targets or clutter discretes.

Note the presence of nulls in transmit pattern along directions of competing tar-gets/discrete clutter elements.


Knowledge-Aided (KA) Radar Signal Processing


Real-time exploitation of the a-priori knowledge about the radaroperating environment.

KA Phylosophy:

The radar knows what it sees

The environmental context isthe key to an efficient adaptivity.

Many different knowledge sourcescan be available.



A-Priori Information and GIS Representation

Geographic map of the experiment site.

Intensity of clutter returns: strongest returns are represented in red, weakestreturns are in blue.

GIS representation of the considered dataset: blue cells indicate sea, orange cellsindicate land, red cells transition interfaces land-sea.

A. De Maio, A. Farina, G. Foglia, “Design and experimental validation of knowledge-based constant falsealarm rate detectors”, IET Radar Sonar & Navigation, 2007.



Cell Averaging CFAR (CA-CFAR)

621 false alarms over 122400 tests.

Only one target is over the threshold.

Decision Rule

|rcut |2∑Ki=1 |ri |2

H1><H0

TCA



Knowledge-Aided CFAR System

82 false alarms over 122400 tests.

All the targets are over the threshold.

Decision Rule

Knowledge-Aided Training Data Selectionplus CA-CFAR


Knowledge-Aided Techniques for Covariance Matrix Estimation


Conventional adaptive detectors require an estimation of the interference covariancematrix.

They achieve satisfactory detection performance when the size K of the homogeneoussample support complies with K ≥ 2N.

In real environments the numberof data where the interference ishomogeneous is very limited.

Indirect Approach: indirect exploitation of prior knowledge sources (for instancesecondary data selection)

Direct Approach: a-priori information used directly in the adaptive receiver designprocess.



Knowledge-Aided STAP: Indirect Approach

The data selector chooses secondary range-Doppler cells that have the same terrain asthe test clutter cell. National Land Cover Data (NLCD) are used to classify the groundenvironment illuminated by the radar.

Terrain map for MCARM flight 5,acquisition 151.

Conventional Adaptive Processing

Knowledge-Aided Processing

C. T. Capraro, G. T. Capraro, A. De Maio, A. Farina, and M. Wicks, “Demonstration of knowledge-aidedspace-time adaptive processing using measured airborne data”, IEE Proceedings Radar, Sonar & Navigation,Vol 153, Issue 6, 2006.



Multiple Models Exploitation: Direct Approach

Resorting to reflectivity/spectral clutter models, meteorological data, and previousscans/experiences, multiple models for the interference covariance matrix can beconceived.

These a-priori models can be used to devise KA detection algorithms, where slow-time covariance estimation is performed forcing the inverse interference covariance Xto belong to the uncertainty set

A =

X 0 : X =

H∑i=0

tiX i , X Iσ2, ti ∈ R, i = 0, . . . ,H

,

with X i , i = 0, . . . ,H the inverse of the a-priori models.A. De Maio (University of Naples) Cognitive Radar Signal Processing July 7, 2014 44 / 51


Multiple Models Exploitation

The constrained Generalized Likelihood Ratio Test (GLRT) shares the form

maxα∈C,X∈A

[det(X )]K+1 exp− tr

[X(

(r − αp)(r − αp)† + RR†) ]

maxX∈A

[det(X )]K+1 exp− tr

[X(rr† + RR†

) ] H1><H0

η

r ∈ CN primary data (data from the cell under test).R = [r 1, . . . , rK ] ∈ CN,K secondary data matrix.p unitary norm steering vector.α unknown parameter accounting for target response.A covariance matrix uncertainty set: the inverse covariance matrix is expressed aslinear combination of the inverse of the available a-priori models, also accounting fora lower bound on the power of the white disturbance term.

The unknown parameters appearing in optimal decision statistics are replaced withtheir constrained Maximum Likelihood (ML) estimates under each hypothesis.

A. Aubry, V. Carotenuto, A. De Maio, G. Foglia, “Exploiting Multiple A-Priori Spectral Models forAdaptive Radar Detection”, IET Radar Sonar & Navigation, 2014.




The constrained ML estimates of the unknown parameters under the hypotheses H0 andH1 are optimal solutions to optimization problems P(SH0 ) and P(SH1 )

P(SHk)

minα,X

tr[XSHk

]− log det(X )

subject to X ∈ A

α ∈ ΘHk

k = 0, 1

ΘH0= 0.

ΘH1= C.

SH0= 1

K+1(rr†+RR†).

SH1= 1

K+1(Rα+RR†).

Rα = (r−αp)(r−αp)†.

Under H0

The ML estimate XMLH0

of X , under H0, is the optimal solution to P(SH0) and can be efficiently

computer in polynomial time using interior point methods.




Under H1

The ML estimates αML of α and XMLH1

of X , under H1, are obtainedresorting to the following alternating optimization procedure:

1 Initialize the algorithm considering α(0) =p†r‖p‖2 , ML(0) = 0,

and Rα(0) =(r − α(0)p

) (r − α(0)p

)†2 set n = n + 1

3 estimate X (n)H1

solving the MAXDET problem P(S(n−1)H1

)

4 estimate the target complex amplitude α(n) =p†X (n)

H1r

p†X (n)

H1p

5 compute Rα(n) =(r − α(n)p

) (r − α(n)p

)†6 compute ML(n) = [det(X (n)

H1)]K+1 exp

−tr

[X (n)

H1

(R

α(n) + KS)]

7 if (|ML(n) −ML(n−1)| ≤ ζ), set αML = α(n) and XMLH1

= X (n)H1

else, return to the step 2.

f (α,X )

maximize overX given α(n−1)

maximize over

α given X (n)

X (n) α(n)




Results for H = 20 Gaussian shaped a-priori models and a bimodal, exponentialshaped, interference PSD.

SINR values achieving Pd = 0.9

GLRT-1 GLRT-2 Optimum AMF Kelly’s GLRT

K = 10, H = 20 11.38 11.78 9.68 − −

K = 20, H = 20 10.39 11.65 9.60 13.31 13.41




Black curve: Actual PSD; Red curve: PSD using the proposed constrained covariancematrix estimator; Magenta curve: PSD using the sample covariance matrix.

Also with very small training data size (K = 1) the proposed algorithm is able totrack the actual PSD.

The estimation accuracy is better and better as the sample support increases.


Conclusions

Conclusions

The cognitive radar concept has been discussed based on two fundamental ingredients:

1 transmit diversity;

2 Knowledge-Aided signal processing.

Understanding how and why biological systems exploit diversity is the key to improvesensing in synthetic systems.

Even though the presentation is focused on radar, other sensors and communicationsystems could benefit of the cognitive paradigm.


End

THANK YOU FOR THE KIND ATTENTION

[email protected]


Cognitive Radar Signal Processing€¦ · There are a Low Pulse Repetition Frequency (PRF) regime...

Documents

Transcript of Cognitive Radar Signal Processing€¦ · There are a Low Pulse Repetition Frequency (PRF) regime...