frequency diversity in multi static radars_2008

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Frequency Diversity in Multistatic Radars

Byung Wook Jung1, Raviraj S. Adve2, and Joohwan Chun1

1Department of Electrical Engineering and Computer Science, KAIST

335 Gwahangno Yuseong-gu, 305-701, Daejeon, Korea

phone: + (82) 42-869-5457, fax: + (82) 42-869-8057 , {bwjung, chun}@sclab.kaist.ac.kr2Department of Electrical Engineering and Computer Science, University of Toronto

10 Kings College Road, Toronto, Canada

phone: + (1) 416-946-7350 , fax: + (1) 416-946-8765 , [email protected]

Abstract This paper presents the model and analysis ofa frequency-diverse radar system. Multistatic radar systemsprovide an inherent spatial diversity by processing signals fromdifferent platforms which view a potential target from differentaspect angles. By using different frequencies at each platform, anadditional diversity gain can be obtained on top of the advantagesof spatial diversity. Here, since platforms are distributed spatially,true time delay is used at each platform to align the samplelook point in time. The signal-to-interference-plus-noise ratio andprobability of detection are derived for the case for the frequencydiverse and the non-frequency diverse cases. Comparing thesetwo cases illustrates the significant benefits of frequency diversity.In addition, performances of optimum and suboptimum decen-tralized algorithms are compared.

I. INTRODUCTION

Multistatic radar systems have been an interesting research

area for some time now [1][5]. In spite of the added

complexity due to its distributed configuration, a system has

many advantages; for example, energy from a target echo

generated by one platform can be used by many platforms,

which reduces the energy necessary for the coverage of a

large surveillance volume. The observations from the different

aspect angles reduce the probability of miss yielding an anti-

stealth characteristic.

Most of the original work in radar focused on the simplest

case of a single transmitter and multiple receivers [3][6].Recently Fischler et al. proposed and analyzed a system with

multiple transmitters and multiple receivers [7]. In [8] the

authors generalize this configuration allowing for multiple co-

located antennas at each platform, i.e., an antenna array at each

transmitter/receiver. This paper focuses on this most general

configuration that includes the first and second configurations

as special cases. In this regard, a recent proposal has been

the use of frequency diversity to allow for the simultaneous

processing of multiple transmit-receive pairs [9]. A crucial

issue raised there is that joint processing requires true-time

delay to align, in time, the multiple transmit-receive pairs. The

system in [9] is a ground-based system with a single antenna

at each radar platform.A related track in radar signal processing is that of in-

terference suppression. Radar systems invariably deal with

strong interference. Space-time adaptive processing (STAP)

techniques promise to be the best means to detect weak targets

in severe, dynamic, interference scenarios including clutter and

jamming [10], [11]. STAP entails adaptive processing using

multiple antenna elements that coherently process multiple

pulses within a single coherent pulse interval (CPI). While

STAP was originally developed for monostatic radar, it has

been recently extended to bistatic [12], [13] and multistatic

configurations [8], [9], [14].

This paper models and develops space-time adaptive pro-

cessing for distributed radar systems on multiple airborne plat-

forms. The radar system potentially uses frequency diversity

to concurrently process multiple transmit-receive pairs. The

preliminary true-time delay model of [9] and the bistatic radar

model of [15], [16] is extended to airborne radar systems

with multiple antennas and the performance gains by using

frequency diversity, in conjunction with true-time delay, over

other forms of adaptive processing. The numerical simulations

illustrate the robustness provided by the spatial diversity

inherent in systems.

The remainder of this paper is organized as follows. Sec-

tion II presents the system model for the radar system under

consideration and develops the data model for both target and

interference. Section III-A presents performance analyses of

the frequency and non-frequency diverse cases based on the

data model developed here. The simulation results illustrate

the benefits of frequency and spatial diversity in radar systems.

This paper ends in Section IV after drawing some conclusionsand indicating potential avenues for future research.

I I . SYSTEM AND DATA MODEL

This section develops the system and data model for a radar

system with K distributed apertures potentially using jointprocessing of the received signals over all K platforms. Eachplatform uses an N-element, side-mounted, uniformly spaced,linear array and M coherent pulses within a single CPI. Allplatforms are assumed to use the same pulse repetition interval

(PRI) T. The entire system is used to detect the potentialpresence of a target in a specific region of space known as

the look point and at a specific velocity, the look velocity.

Each radar in the system transmits a pulse which reflects ofthe ground (causing clutter) and possibly a target. These pulses

are delayed on transmit at each platform to ensure that they

reach the look point simultaneously. Each radar can receive

the reflections due to its own transmissions and those of all

other K 1 radars.

4881-4244-1539-X/08/$25.00 2008 IEEE


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x = x + x + x

Down Conversion

freq = f0

1 11 12 13

Platform 1

Dow

nConv

ersion

freq

=f0

Plat

form2

x=

x+

x+

x

Down

Conversio

n

freq

=f0

KK1

K2

KK

Platf

orm

K

x =

x+x+x

2

21

22

2K

(a) Non-frequency diverse case, K = 3

freq = f2

11 12 1K

Platform 1

BPF and down

conversionfreq = ffreq = f

1

x x x

K

freq=f2 2K

22

21

Platform

2

BPFandd

own

conversio

n

freq=f

freq=f1

x

x

x

Kfr

eq=

f2

K1

K2

KK

Platfo

rmK

BPF

anddown

conversio

n

freq

=f

freq

=f1

x

x

x

K

(b) Frequency diverse case, K = 3

Fig. 1. Receiver structure with and without frequency diversity

We distinguish two forms of this system: in the non-

frequency diverse (NFD) case, all platforms use the samecenter frequency, f0, and individual transmissions cannotbe distinguished. In the frequency diverse (FD) case each

platform transmits at a different center frequency and hence

each transmission can be distinguished. Figure 1 illustrates the

workings of each of these forms of multistatic radar. In the

figure, xpq represents the signal created at platform p due to atransmission from platform q. Note that for convenience, thefigure presents only a single antenna at each element, though

each platform uses N antenna elements and M pulses, i.e.,xpq is a length-N M vector. In the FD case, using band-passfilters (BPF) allows each signal to be isolated and and each

receiver can process K independent signal sets.

A. True Time Delay on Receive

In order to probe the same look point from different angles

and distances the K radar apertures need to be synchronized.Furthermore, with potentially joint processing of the signals

received at the K arrays, the samples at the receiver, which

correspond to a specific range, need to be aligned in time.

While distributed synchronization is outside the scope of this

paper, the received samples are aligned using true time delays

in relation to the look point [9]. The sample corresponding to

the look point is therefore, effectively, sampled simultaneously

by all receivers. The time delay, before sampling, used by the

k-th platform is

Tk =maxk{Dk} Dk

c, (1)

where Dk is the distance between the look point and k-thplatform and c is the speed of light.

B. Signal Models

Because of the differences in resolvability of individual

signals, the FD and NFD cases require their own signal

models.

1) NFD Case : In the NFD case all platforms share

a single frequency. As illustrated in Fig. 1(a), signals from

individual platforms cannot be discriminated. For platform p,the received signal corresponding to the target-absent (H0) andtarget-present (H1) hypotheses are respectively

H0 : xp =K

q=1

cpq + np = cp + np,

H1 : xp =K

q=1

[pqgpq + cpq] + np,(2)

where cpq represents the interference (clutter and jamming)

vector at platform p due to the transmission from platform qand cp and np represent the overall clutter and additive white

Gaussian noise (AWGN) component at platform p respectively.Under the H1 hypothesis, pq and gpq represent the targetamplitude and space-time steering vector, corresponding to

the look point and look Doppler, at platform p due to thetransmission from platform q. Under the Swerling II model,pq follows a complex Gaussian distribution with zero mean

and variance 2

tpq .Note that since the entire system operatesat a single frequency, xp is a length-N M vector.

2) FD Case : In the FD case, platform q transmits ata center frequency of fq . We assume the frequency spacingis sufficient to eliminate any overlap between the K trans-missions. Each platform, therefore, is able to separate the

K signals due to the different platforms as illustrated in thereceiver structure in Fig. 1(b).

For platform p, the received signal corresponding to thesignal transmitted from platform q, at frequency fq , in thetarget-absent (H0) and target-present (H1) hypotheses arerespectively

H0

:x

pq =c

pq +n

pq,H1 : xpq = pqgpq + cpq + npq, (3)

where pq is the target amplitude, gpq is the target space-time steering vector corresponding to the look point and look

Doppler frequency, cpq is the clutter return and npq is the

AWGN component at platform p due to the transmission from

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platform q. Each of the K vectors, corresponding to the Ktransmitted frequencies, received at the p-th platform are oflength-N M.

C. Covariance Matrix

The goal of this paper is to develop adaptive process-

ing schemes for distributed apertures. The adaptive process

depends on the interference covariance matrix [10]. From

Eqns. (2) and (3), the covariance matrix for platform p, Rpq =E{xpqxHpq}. This covariance matrix has significantly differentbehavior depending on whether frequency diversity is used. In

the NFD case, the contributions from individual transmissions

cannot be distinguished and the covariance matrix is a single

N M N M matrix. In the FD case, the individual signalscan be distinguished and there are K such covariance matrix(or equivalently, one KM NKM N block diagonal matrix).For zero mean, Gaussian and independent xk, k = 1, . . ,K, thecovariance matrix of p-th platform in NFD case and FD casecan be expressed as

NFD case : Rp = Rp1 + Rp2 + . . . + RpK

FD case : Rp =

Rp1 0 . . . 00 Rp2 . . . 0...

.... . .

...

0 0 . . . RpK

(4)

III. PERFORMANCE ANALYSIS

This section presents performance analyses in terms of the

Signal to Interference Plus Noise Ratio (SINR) and probability

of detection (PD).

A. Signal to Interference Plus Noise Ratio

The output signal can be divided into target and

interference-plus-noise components [11]

z = zt + zu = wHg + wHu (5)

where is the complex target return, g is the target space-time steering vector, u is the space-time snapshot of unwantedsignal and w is the weight vector.

Let pt = E[zt2] and pu = E[zu

2]. The SINR is defined as

SINR =pt

pu=

2t|wHg|2wHRw

(6)

where 2 is the noise power per element, t is the targetsignal-to-noise ratio (SNR) on a single pulse for a single

array element and R = [uuH] is the interference-plus-noisecovariance matrix [11].

Therefore, assuming each platform has the same SNR, the

overall SINR of K platform radar system is

SINR = 2t

Kk=1

|wHk gk|2

Kk=1

wHk Rkwk

(7)

50 0 5050

40

30

20

10

0

10

20

30

40

50

Velocity X (m/s)

VelocityY(m/s)

SINR : MonoStatic

5

0

5

10

15

20

25

Fig. 2. SINR : Monostatic case

50 0 5050

40

30

20

10

0

10

20

30

40

50

Velocity X (m/s)

VelocityY(m/s)

SINR : MultiPlatform

0

5

10

15

20

25

30

Fig. 3. Overall SINR : NFD case

where wk, gk and Rk are the weight vector, target space-time

steering vector and covariance matrix of unwanted signal of

platform k, respectively.

Figure 2 plots the output SINR for a monostatic system

using platform 1 only. The parameters used in this simulation

are listed in Table I and II. The target is located at (20e3, 0, 0)with SNR=0dB. Since platform 1 is moving along the y-axis, the SINR of the monostatic system is independent of

the velocity in the y direction. It has a dip around 0m/s oftarget velocity in the x direction where the clutter ridge ispresent (stretching along y-axis).

Figures 3 and 4 show the overall SINR of NFD caseand FD case, respectively. Compared to single platform case

of platform 1, overall response shows the benefit of spatialdiversity. The SINR is low only within a narrow region at

the maximum clutter power. The figures also illustrate the

significantly improved performance using frequency diversity.

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TABLE I

COMMON PARAMETERS

Parameter Value

System Parameters

Frequency Offset 20Mhz

Element Spacing 0.1m

Peak Transmit Power 200KW

Instantaneous BW 4MHz

System Loss 4dB

PRF 1KHz

M 10

N 10

K 3

Clutter Parameters

Ground Reflectivity -3dB

Number of Clutter Patches 360

Clutter to Noise Ratio 70dB

As is clear from the two plots, the region of low SINR is

significantly smaller in the FD case than in the NFD case.

B. Probability of Detection

The traditional approach to integrating detection over mul-

tiple platforms is purely distributed detection (which uses an

independent target-detection test at each platform) and then

merging these binary decisions at a centralized processor [17].

Each platform may use an optimized threshold to maximize

the detection probability, PD, while maintaining a fixed falsealarm rate, PF A. This distributed approach is clearly sub-optimal and improved target detection could be achieved if

all platforms signals were processed jointly. While this would

place an enormous burden on the inter-platform communica-

tion, it also provides an upper bound on system performance.

In this section we develop the probabilities of detection,

PD, and probability of false alarm, PF A for the case ofboth distributed and joint processing of the signals at the Kplatforms. The test statistic of optimum centralized detector is

defined as [14]:

NFD case : z =K

p=1

wHp xp2

1/2tp + gH

p R1p gp

,

FD case : z =K

p=1

Kq=1

wHpqxpq

21/2tpq + g

HpqR

1pq gpq

,

(8)

where wp = R1p gp for the NFD case and wpq = R

1pq gpq for

the FD case. For the notational convenience, if we rearrange

the index j = p for the NFD case and j = p2 p + q + 1 for

50 0 5050

40

30

20

10

0

10

20

30

40

50

Velocity X (m/s)

VelocityY(m/s)

SINR : MultiPlatform

10

15

20

25

30

35

Fig. 4. Overall SINR : FD case

the FD case, Eqn. (8) can be unified as

z =J

j=1

wHj xj2

1/2tj + gHj R

1j gj

, (9)

where J = K for NFD and J = K2

for FD case.Define 0j = g

Hj R

1j gj and j = 1/

2tj + 0j . For the

threshold false alarm rate (PF A) is

Pfa =J

j=1

Jl=1, l=j

(A0j A0l)1AJ1

0j e/A0j (10)

where A0j = 0j /j . A closed form of threshold can befound in limited situations. Alternatively, can be found viaa simple one dimensional search for a given PF A [14].

The probability of detection Pd can be obtained in thesimilar manner

Pd =

Jj=1

J

l=1, l=j

(A1j A1l)1AJ11j e/A1j , (11)

where A1j = 0j (1 + 0j 2tj )/j .

Figure 5 is the probability of detection (PD) seen byplatform 1 which probability of false alarm PF A = 10

6 with

SNR=15dB. Simulation parameters are shown in Tables I, II

and III. The direction of target is measured counter clock wise

from positive x-axis. The labels Pp-NFD and Pp-FD refer tothe NFD and FD case at p-th platform respectively. Ppq isthe monostatic or bistatic case of the signal from platform qto p. Pp-FD-OR is the case using OR processor combiningPD of each incoming signal.

As can be seen in this figure, it is the FD case thathas the highest PD among all. The PD of the monostaticconfiguration (P11) is unreliable as it varies more than that

of bistatic configuration (P12 and P13). In addition, P11

has a major effect on the shape of PD yielding a maximumand minimum point of PD of platform 1 be same as those

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TABLE II

PLATFORM PARAMETERS

Parameter Value

Platform 1

Operating Frequency(NFD & FD) 450MHz

Position (0,0,3e3)

Velocity 100m/s

Direction of motion (0,1,0)

Platform 2

Operating Frequency(NFD) 450MHz

Operating Frequency(FD) 430MHz

Position (20e3,16e3,3e3)

Velocity 100m/s

Direction of motion (1,0,0)

Platform 3

Operating Frequency(NFD) 450MHz

Operating Frequency(FD) 410MHz

Position (20e3,-24e3,3e3)

Velocity 100m/s

Direction of motion (-1,0,0)

TABLE III

TARGET PARAMETERS

Parameter Value

Position (20e3,0,0)

Speed 10m/s

Moving Direction (1, 3, 0)/10

of monostatic case. This is mainly because of the difference

of Doppler frequency of each case and PD suffers when thetarget is moving parallel to the platform. On the other hand, in

bistatic and multistatic configurations, the Doppler frequency

is dependent on the velocity of the both signal-transmitting

and signal-receiving platform in bistatic configuration. This

provides robustness since even though the target is moving

parallel to one platform, the other platform can still contribute

to the Doppler frequency. Therefore, the Doppler frequency

fluctuation between the maximum and minimum value is lessthan that of monostatic configuration. The reason why NFD

case has poor performance than FD case is because signals

from other platforms contribute interference in the NFD case,

even if this case has 1/K less noise than the FD case.Figure 6 plots the overall the PD of the system with target

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Direction of Target

PD

Probability of Detection

P1FD

P1NFD

P1FDOR

P11P12

P13

Fig. 5. Probability of Detection with PFA = 106, SNR = 15dB

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Direction of Target

Pd


MPFD

MPFDOR

MPNFD

MPNFDOR

P1

P2

P3

Mono Static

Fig. 6. Probability of Detection with PFA = 106, SNR = 0dB

SN R = 0dB. In this case, PF A = 106 and the target

velocity is 10m/s. The labels MP-NFD and MP-FD are theoptimum NFD and FD cases respectively using Eqn. (11).

MP-NFD-OR and MP-FD-OR are the output of the OR pro-

cessor based on the binary output of each platform. This figure

illustrates the gains due to spatial and frequency diversity in

this radar system. In both NFD and FD cases, the overall PDhave less fluctuation than the PD of a single platform. Thisis because directions of motion of each platform; different

minimum and maximum values of PD for each platformappear at different moving direction of the target. Therefore,

combining the data in an optimal way smoothes out the PDcurve, regardless the direction of target motion. Interestingly,

the OR case performance extremely close to the optimal joint

processing case.

Figures 7 and 8 are the PD with target parameter shownin Table III. In these figures, it can be seen that FD case

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30 20 10 0 10 20 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR(dB)

PD


P1FD

P1NFD

P1FDOR

P11

P12

P13

Fig. 7. Probability of Detection with PFA = 106

30 20 10 0 10 20 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

SNR

PD


MPFD

MPFDOR

MPNFD

MPNFDOR

P1FD

P2FD

P3FD

P11

Fig. 8. Probability of Detection with PFA = 106

has always higher PD than NFD case in both overall andsingle-platform case. Again, the OR processor can achieves

performance very close to the fully optimum case.

IV. CONCLUSION

This paper provided a data model and analysis for adaptive

processing in frequency diverse, distributed radar apertures.

The analysis is based on the probability of detection and

signal-to-interference-plus-ratio. As is clear from the results,

the benefits of using frequency and spatial diversity are

significant. Previous work has largely focused on spatial

diversity exclusively. However, by not considering frequency

diversity, signals from other platform contribute to undesiredinterference at each platform, significantly worsening perfor-

mance below even the monostatic case. Frequency diversity

allows for the discrimination of signals from different platform

and alleviates this situation. We also investigated the use of

suboptimum decentralized algorithms, such as the OR case,

and showed that with frequency diversity, the performance

of such algorithms are extremely close the optimum joint

processing scheme.

V. ACKNOWLEDGEMENT

This work was supported in part by Brain Korea 21 Project,

the School of Information Technology, KAIST in 2007 and

also supported in part by Korea Electronics Technology In-

stitute under System Integrated Semiconductor Technology

Development Project fund of South Korea

REFERENCES

[1] V. S. Chernyak, Fundamentals of Multisite Radar Systems : MultistaticRadars and Multiradar Systems, 1st ed. London: CRC Press, 1998.

[2] E. Hanle, Survey of bistatic and multistatic radar, IEE Proceedings,vol. 133, no. 7, pp. 587595, December 1986.

[3] E. Conte, E. DAddio, A. Farina, and M. Longo, Multistatic radardetection : synthesis and comparison of optimum and suboptimumreceivers, IEE Proceedings, vol. 130, no. 6, pp. 484494, Oct. 1983.

[4] E. DAddio and A. Farina, Overview of detection theory in multistaticradar, IEE Proceedings, vol. 133, no. 7, pp. 587595, Dec. 1986.

[5] A. Mrstik, Multistatic-radar binomial detection, IEEE Trans. onAerospace and Electronic Systems, vol. 14, no. 1, pp. 103108, Jan.1978.

[6] I. Bradaric, G. Capraro, D. Weiner, and M. Wicks, Multistatic radarsystems signal processing, in IEEE Conference on Radar, Apr. 2006,pp. 106113.

[7] E. Fishler, A. Haimovich, R. Blum, L. C. Jr., D. Chizhik, and R. Valen-zuela, Spatial diversity in radars-models and detection performance,

IEEE Trans. on Signal Processing, vol. 54, no. 3, pp. 823838, Mar.2006.

[8] D. Bruyere and N. Goodman, Performance of multistatic space-timeadaptive processing, in IEEE Radar Conference, Apr. 2006, pp. 533538.

[9] R. Adve, R. Schneible, M. Wicks, and R. McMillan, Space-timeadaptive processing for distributed aperture radars, in 1st IEE Waveform

Diversity Conference, Nov. 2004.[10] R. Klemm, Principles of Space-Time Adaptive Processing, 2nd ed.

London: IEE Press, 2002.[11] J. Ward, Space-time adaptive processing for airborne radar, 1st ed.

Cambridge, MA: MIT Linclon Laboratory, 1994.[12] W. Melvin, M. Callahan, and M. Wicks, Bistatic stap : application to

airborne radar, in Proc. of IEEE Radar Conference, Apr. 2002, pp.6065.

[13] B. Himed, J. Michels, and Y. Zhang, Bistatic stap performance analysisin radar applications, in Proc. of IEEE Radar Conference, Apr. 2001,

pp. 6065.[14] N. Goodman and D. Bruyere, Optimum and decentralized detection

for multistatic stap, IEEE Trans. on Aerospace and Electronic Systems,vol. 43, no. 2, pp. 806813, Apr. 2007.

[15] M. Jackson, The geometry of bistatic radar systems, IEE Proceedings,vol. 133, no. 7, pp. 604612, Dec. 1986.

[16] Y. Zhang, Bistatic space-time adaptive processing(stap) for air-borne/spaceborne application, Air Force Research Laboratory, Tech.Rep. F30602-98-C-0125, 1999, Final report by Stiefvater Consultants.

[17] P. Varshney, Distributed Detection and Data Fusion. New York:Springer-Verlang, 1996.

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frequency diversity in multi static radars_2008

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