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Feasibility of STAP for passive GSM-based radar

Xavier Neyt∗, Jacques Raout†, Mireille Kubica∗, Virginie Kubica∗,

Serge Roques‡, Marc Acheroy∗, Jacques G. Verly§

∗Electrical Engineering Dept., Royal Military Academy, Belgium, xavier.neyt@elec.rma.ac.be

†CREA, Ecole de l’Air, Salon de Provence, France, jraout@cr-ea.net

‡ONERA, Salon de Provence, France, Serge.Roques@onera.fr

§Dept. of Electrical Engineering and Computer Science, University of Li` ege, Belgium,

Jacques.Verly@ulg.ac.be

Abstract—In this paper, we examine the feasibility of applying

Space-Time Adaptive Processing (STAP) to bistatic passive radars

using illuminators of opportunity. The transmitters considered

are GSM base stations and are non-cooperative. Although STAP

has been extensively applied to signals from pulse-Doppler

radars, it was never applied to arbitrary signals arising from

illuminators of opportunity. We show that by computing the

appropriate mixing product, we essentially convert the signal of

opportunity to a pulse-Doppler like signal, hence making the ap-

plication of STAP to arbitrary signals straightforward. We finally

confirm these theoretical results by using real measurements.

I. INTRODUCTION

Radars using illuminators of opportunity are inherently

passive bistatic radars. The passivity of bistatic radars offers

definitive advantages [1] among which low cost, low weight

and enhanced radar cross-section for certain geometries. More-

over, stealth operations are possible since the receiver is totally

passive.

Radars using illuminators of opportunity have already been

studied. Signals provided by FM radio broadcast [2], satellites

[3], [4], digital video broadcast (DVB-T) [5], and Global

System for Mobile communications (GSM) base stations [6]

have been considered. Arguments for the selection of the

transmitter type include spatial and time coverage, power,

central-frequency and bandwidth of the emitted signal, and

shape of the ambiguity function. The bandwidth dictates the

achievable range-resolution and the shape of the ambiguity

function is decisive in determining the detection performance

of the radar. In particular, signals from digital modulation

(GSM, DVB) have much less range and Doppler ambiguities

than other modulations [7], which makes them more suit-

able for passive radar. In this paper, we will consider GSM

base stations as illuminators of opportunity. They have an

ubiquitous spatial coverage, are permanent in time and have

a thumbtack like ambiguity function due to the noise-like

behavior of the GMSK modulation used. The main drawback

of GSM base station signals is the small bandwidth [8] that

yields a range resolution of about 1.8 km. Thus a GSM-based

radar will only be usable to perform moving target detection.

The Doppler frequency resolution will only depend on the

coherent integration time (CIT). A CIT of a few tenths of a

second is easily achievable and yields a Doppler frequency

resolution of about a few Hz.

Space-Time Adaptive Processing (STAP) is typically used

to filter out (clutter-)interferences in GMTI radars in order

to detect slow-moving targets. STAP offers a benefit over

separate spatial and temporal processing when there is a

coupling between the clutter signal direction of arrival (DOA)

and its Doppler frequency. STAP consists in performing a joint

spatio-temporal optimum filtering of the signal in order to

reject interference (clutter) contributions [9], [10].

In the STAP literature, it is assumed that the available signal

is formed by the echoes from a pulse-Dopplerradar. This paper

shows how STAP can be applied to other types of signals and

in particular to the noise-like GSM signals. The acquisition of

a GSM signal and the signal itself are described in Section II.

Section III shows how noise-like signals must be handled in

order to make STAP processing feasible. Section IV details

the issues involved in the estimation of the covariance matrix

required to perform STAP processing and Section V shows

end-to-end results for real signals.

II. SIGNAL ACQUISITION AND PRE-PROCESSING

A block diagram of a passive GSM-based radar receiver

is depicted in Fig. 1. We use a two-channel receiver, the

two antennas being arranged to form an array. The array

is oriented such that the broadside direction is pointing to

the targets.After amplification by the low noise amplifier

LO

ejωIFt

D

A

A

D

ADC

LPF BPFLPF

ch1

ADC

LPFBPF LPF

ch2

LNA

LNA

Fig. 1.Block diagram of the receiver.

(LNA) and filtering by the band pass filter (BPF) to keep

only the GSM downlink band, the signal is down-converted

to intermediate frequency and sampled. Once sampled, the

received signal is further down-converted using digital down-

conversion (DDC). Performing the last down-conversion step

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numerically eliminates imbalances between the in-phase and

the in-quadrature channels.

To correct for possible asymmetry between the two chan-

nels, a calibration step is required. The calibration is also used

to measure the phase center of the antennas in order to extract

correct direction information from the measurements.

Since the bandwidth of the receiver is much larger than

that of one GSM channel, the signals from several GSM

base stations can be received at once. A typical spectrum of

the acquired signal is depicted in Fig. 2. The different GSM

−1000 −5000 500 1000

10

15

20

25

30

35

Frequency (kHz)

Amplitude (dB)

Fig. 2. Spectrum of the received signal

downlink channels are clearly visible. The two most powerful

channels, located around 0Hz and −600kHz, correspond to

two different base stations.

The received signal contains the direct signal coming from

the GSM base-station transmitter and the echoes of the GSM

base-station signal backscattered by the vegetation, buildings

and targets. To be able to perform the coherent processing, it

is fundamental to know the reference signal broadcast by the

GSM base-station. [11] describes a method able to blindly

extract the reference signal from an array of sensors. The

method uses adaptive beamforming. Indeed, to avoid artifacts,

it is essential that the reference signal does not contain any

echoes from any target. If the reference signal would contain

echoes from targets, the concerned targets would be attenuated

by the echo cancellation processing. In the remaining of this

paper, we will assume that the reference signal, denoted xref,

is available.

III. GENERALIZATION OF STAP TO NOISE-LIKE SIGNALS

The detection of targets in echo signals is typically per-

formed by using a matched filter. The matched filtering can

be generalized in the form of the range-Doppler diagram [12],

[13]

χ(νd,n) =

k

where x(k) are the samples of the signal containing echoes

from the potential target, the clutter, and the direct path signal;

?

x(k)x∗

ref(k − n)e−j2πνdk

(1)

n denotes the range at which the correlation is computed; and

νdis the reduced Doppler frequency. As noted in [13], [14],

this can be seen as the Fourier transform of the mixing product

xm(k) = x(k)x∗

ref(k − n).

(2)

This mixing can be seen as a generalization of the usual

heterodyne down-mixing. In this way, the random phase

variation of x(k) along k due to the emitted signal xref(k−n)

is removed. Further, this formulation is useful to implement

adaptive filtering instead of the classical Fourier-based filter

banks [11].

To perform STAP, measurements obtained from N different

channels are required. Let us denote by x(k) the vector

containing the N signal samples at time kTswhere Ts= 1/fs

is the temporal sampling interval and fs is the temporal

sampling frequency. Let the mixing product resulting from

mixing the signal from each channel with a time-delayed

version of the reference signal xref(k − n) be denoted by

xm(k;n) = x(k) ◦ (1 ⊗ xref(k − n))∗

where 1 is a N × 1 column vector with unit elements, ⊗

denotes the Kronecker product and ◦ the Hadamar (element-

wise) product. Since the targets of interest induce a Doppler

frequency that is much smaller than the sampling frequency

fs, the signal xm(k) can be low-pass filtered and subsampled

as suggested in [14]. Note that this subsampling does not affect

the range-resolution of the radar.

Let us denote by

(3)

xs(n) = [xT

m(0;n),xT

m(S;n),xT

m(2S;n),...,

xT

m((M − 1)S;n)]T

(4)

the lexically ordered subsampled signal, where S is the sub-

sampling factor. The number of temporal samples M depends

on the CIT and on the subsampling factor S. A typical value

is M = 256. The temporal Fourier transform processing that

was applied to single-channel signals in eq. (1) can also be

generalized to the spatial domain and applied to xsyielding

ym(νs,νd;n) = v†(νs,νd)xs(n)

(5)

where v is the spatio-temporal steering vector

v(νs,νd) = a(νs) ⊗ b(νd).

(6)

In the case of an uniform linear array (ULA), the spatial

steering vector is

a(νs) = [1,ej2πνs,...,ej2πνs(N−1)]T

(7)

where νs =

the inter-element spacing, λ the carrier wavelength and θ the

incidence angle. The temporal steering vector is given by

d

λsinθ is the reduced spatial frequency with d

b(νd) = [1,ej2πνd,...,ej2πνd(M−1)]T.

(8)

where νd=fDS

Doppler frequency of the target and fsthe sampling frequency

of the acquisition. The size of the spatio-temporal steering

vector depends on the number of channels N and on the

fs

is the reduced Doppler frequencywith fDthe

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number of temporal samples M considered in the subsampled

signal.

This is illustrated on Fig. 3, where the matched filter

νd

νs

−0.50 0.5

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0

2

4

6

8

10

Fig. 3.Matched filter output on a signal containing simulated targets.

output ym of a simulated signal is shown. The signal was

generated by adding simulated targets to real clutter mea-

surements. The spatial (direction) ambiguities results from the

use of a 2-elements antenna array with a distance of about

0.8λ between the two elements. The targets are simulated

by adding time-delayed and frequency-delayed versions of

the reference signal to the signals from the spatial chan-

nels. Targets all have the same amplitude except the last

one with half this amplitude and are located at (νs,νd) =

{(0.3,−0.4),(−0.2,0.2),(0.1,0.08)}. Note that in addition to

the targets, a relatively strong direct path signal is present at

(νs,νd) = (−0.2,0).

Similarly, we can apply an adaptive filter

y(νs,νd;n) = w†(νs,νd)xs(n)

(9)

where y is the output of the filter at these frequencies, and

the filter w that rejects the interferences and the noise in an

optimum way is given by [9], [15]

w(νs,νd) = R−1v(νs,νd)

(10)

where R is the covariance matrix of the interference-plus-noise

data and v the spatio-temporal steering vector (6).

IV. ESTIMATION OF THE COVARIANCE MATRIX

The interference covariance matrix R required to compute

the optimum filter (10) is defined as

R = E[xsi+nx†

si+n]

(11)

where xsi+n is the mixed, low-pass filtered, subsampled

and lexically ordered signal, containing only interference and

noise.

The expectation operator E is typically replaced by a sum

over data samples taken at different ranges [16], i.e. the sample

covariance matrix (SCM). The estimation obtained will be un-

biased only if the averaged data samples are independent and

identically distributed. In bistatic configurations, the clutter

power spectrum locus is known to exhibit a range-dependency.

Hence, independently of possible clutter inhomogeneities, the

conditions for unbiased estimation are typically not verified.

However, in the configuration considered here, i.e. a static

transmitter and a receiver located on the ground, it was shown

in [17] that the clutter power spectrum locus is independent

of the range. This means that in the considered configuration,

no geometry-induced range dependence of the clutter statistics

will be present.

To obtain a useful estimation, a relatively large number

of samples needs to be averaged [16]. Taking into account

an optimistic reach of about 20km and a range-resolution

of 2km, only 10 independent samples are available. Note

that this is an overly optimistic figure since it does not take

into account range inhomogeneities. To cope with the low

number of samples available, diagonal loading (DL) is typi-

cally performed, leading to the so-called SCM+DL estimation

method. The low-rank nature of R can be exploited to further

reduce the number of samples required to perform a useful

estimation. In particular, a method based on the extraction of

the principal components of R was proposed [18]. The method

was subsequently enhanced [18] by taking into account the

modeling of decorrelation effects due, for instance, to internal

clutter motion (ICM) using a covariance matrix taper (CMT).

This yields the PC+CMT+DL method. Although many other

estimation methods exist, a complete discussion of covariance

matrix estimation methods applicable in the current scenario is

outside the scope of this paper and we will limit ourself to the

methods described above. Figure 4 presents the performances

of the estimation methods discussed above in terms of SINR

loss [19]. These results were obtained by using real data (the

actual scenario considered is detailed in section V). The refer-

ence for comparison is a theoretical covariance matrix model

obtained by assuming a zero-Doppler clutter with a small

amount of ICM. As can be seen, the SINR loss corresponding

−0.50

νd

0.5

−30

−25

−20

−15

−10

−5

0

SINR Loss (dB)

Model

SCM+DL

PC+CMT+DL

Fig. 4.

estimation methods (cut at zero spatial frequency νs= 0).

Comparison of the performance of various covariance matrix

to the SCM+DL covariance matrix estimation is relatively high

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even at non-zero Doppler frequencies. This is due partly to

the low number of data samples available and partly to the

Doppler sidelobes of the ambiguity function inherent to the

noise-like signal used. Although the PC+CMT+DL estimation

method performs better, the increase in minimum detectable

velocity is only marginally better. It should further be noted

that while it is desirable to remove estimation artifacts due to

a low number of data samples, the effect of Doppler sidelobes

should be kept and will impact detection performance. Other

methods, such as CLEAN-based methods [11], [20] suffer less

from the sidelobes of the ambiguity function.

V. END-TO-END PERFORMANCE

End-to-end performance results are obtained by computing

y(νs,νd;n) for a particular range n and for all possible spatial

and temporal frequencies νsand νd.

A. Simulated data

In this section we present results based on simulated data.

The scenario considered is depicted in Fig. 5 and involves a

static GSM base station and a receiver moving at a speed of

10m/s. The receiving array is an λ/2-spaced 8-elements ULA

and is oriented to be forward-looking. The transmit and the

−0.1

0

0.1

0.2

0.3

0.4

−0.2

−0.1

0

0.1

0.2

0

0.01

0.02

x (km)

y (km)

z (km)

TX

RX

RX antenna

ref. Range

Fig. 5.

line.

Scenario considered with the isorange considered drawn as a solid

receive antennas have an omnidirectional radiation pattern to

exacerbate the influence of the clutter. In practice, the radiation

pattern of GSM base-stations is far from omnidirectional.

Bistatic scenarios typically involve a geometry-induced

range-dependence of the clutter statistics. However, this par-

ticular case where the transmitter is static and the receiver is

located on the ground does not exhibit any geometry-induced

range-dependenceas shown in [17]. This is illustrated in Fig. 6

where the clutter power spectrum locus is depicted for different

ranges.

Figure 7 depicts the power spectrum of the mixed signal

xmat the range of interest. The clutter power spectrum locus

is plot as a thin line. The contribution of the clutter along the

clutter power spectrum locus is clearly visible.

We considered a modeled interference-plus-noisecovariance

matrix for the computation of the adapted matched filter.

The power spectrum of the considered covariance matrix

−0.5

0

0.5

−0.5

0

0.5

2

4

6

8

10

νs

νd

R (km)

Fig. 6. Clutter power spectrum locus in function of the range.

νd

νs

−0.50 0.5

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

−40

−35

−30

−25

−20

−15

−10

−5

0

5

10

Fig. 7. Matched filter output and clutter power spectrum locus.

is illustrated in Fig. 8. Again, the power spectrum of the

covariance matrix is located along the clutter power spectrum

locus.

The result y of the application of the optimum filter to the

mixed signal xm is illustrated in Fig. 9, the thin solid line

being the clutter power spectrum locus. As can be seen, the

clutter contribution is filtered out, leaving the target standing

out at (νs,νd) = (0.4,0.4).

B. Measured data

The results presented here correspond to real measurements.

The geometric configuration of the transmitter, receiver and

target is illustrated in Fig. 10. The receiving antenna array

is static and has 2 elements separated by about 0.8λ. The

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νd

νs

−0.4 −0.20 0.2 0.4

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

−70

−60

−50

−40

−30

−20

−10

0

10

20

Fig. 8.Covariance matrix power spectrum.

νd

νs

−0.50 0.5

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

−40

−35

−30

−25

−20

−15

−10

−5

0

Fig. 9. Adapted matched filter output and clutter power spectrum locus.

scenario involves a cooperative vehicle (a small van) approach-

ing the receiver and yielding a Doppler frequency of about

−40Hz. With this Doppler frequency and taking into account

the frequency resolution, the vehicle signature is buried in

the sidelobes of the (untapered) matched filter w = v.

A tapered matched filter yields the classical angle-Doppler

diagram of Fig. 11. By using the proposed STAP approach, the

contributions due to clutter (including both the static part and

the small ICM components) can be removed, leaving the target

echo standing out as can be seen at (νs,νd) = (0.4,−0.07)

in Fig. 12; the other signatures are due either to reflexions or

to other (uncooperative) targets. The adapted filter is obtained

from (10) using a modeled covariance matrix involving ICM.

Figure 13 presents a cut along νs= 0.4 in the angle-Doppler

diagrams presented in Fig. 11 and Fig. 12. As can be seen,

the effect of the adapted filter is essentially to remove the

components due to clutter, located around zero-Doppler. The

amplitude of the signature of the vehicle at νd = −0.07 is

smaller for the tapered matched filter than for the (untapered)

adapted filter. This is due to the tapering losses.

target

θ = 162.50

240m

Rx

Tx

Fig. 10.Geometric configuration for the real measurement.

νd

νs

−0.50 0.5

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

−10

−5

0

5

10

15

20

25

Fig. 11. Angle-Doppler diagram obtained by using a classical matched filter.

It should be noted that, since the transmitter and the receiver

are both static, the clutter angle-Doppler diagram does not

exhibit the classical coupling. Hence space-time processing is,

νd

νs

−0.50 0.5

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

−10

−5

0

5

10

15

20

25

30

Fig. 12. Angle-Doppler diagram obtained by using an adapted matched filter.

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−0.50

νd

0.5

−40

−30

−20

−10

0

10

20

30

Amplitude (dB)

AMF

MF

Fig. 13.

Fig. 12 comparing the behavior of the classical matched filter (MF) and the

proposed adapted matched filter (AMF).

Cut along νs= 0.4 in the angle-Doppler diagrams of Fig. 11 and

in this particular scenario, not really required and a temporal

processing would be sufficient. This can nevertheless be seen

as a degenerate case of joint space-time processing.

VI. CONCLUSION

In this paper, we propose a generalization of space-time

adaptive processing to noise-like signals. We show that the

estimation of the covariance matrix of the interference-plus-

noise samples is challenging due to the presence of range and

Doppler ambiguities. Finally, we show the applicability of this

generalization to a passive radar using GSM base stations as

illuminators of opportunity. The results obtained on real data

show that the proposed method effectively filters out the clutter

signal.

The computation of the optimum filter requires an estimate

of the interference plus noise covariance matrix. Obtaining

an accurate estimate of this matrix from noise-like signals is,

however, still challenging.

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UK: The