UWB Relay With Physical Layer SecurityEnhancement

Xie XianzhongInstitute of Personal Communication

Chongqing University of Posts and TelecommunicationsChongqing 400065, ChinaEmail: xiexzh@cqupt.edu.cn

Gou NanTennessee Tech UniversityCookeville TN, USA

Email: nguo07974@yahoo.com

Abstract—Motivated by the demand for alternative ways toenhance wireless security, this paper proposes a technique toenhance wireless security at physical layer. It takes advantageof rich multipath environment to focus radio energy on somedesired spatial spot, while achieving nulling at other spots.This can be viewed as a physical-layer security enhancement.What makes spatial focusing and nulling possible is transmitwaveform optimization based on propagation environments. Theconcept and principle are studied in an ultra-wideband (UWB)relay network scenario. Using a matched filter receiver at testpoints, the optimization problem is actually the QuadraticallyConstrained Quadratic Program (QCQP) which is known as anNP-hard problem, thus the Semidefinite Program (SDP) as arelaxation technique is used to obtain suboptimal results. The fea-sibility is numerically validated using the UWB outdoor channelmodel. It is found that, by choosing a proper transmit waveform,the worst-case information leakage at unintended locations canbe significantly minimized, with acceptable attenuation at theintended location.Index Terms—UWB, relay network, physical-layer security,

QCQP, and SDP.

I. INTRODUCTIONStimulated by the FCC’s move that allows ultra-wideband

(UWB) waveforms to overlay over other systems’, UWBradio has received significant attention in the last decade[1]–[9]. Among many attractive features offered by UWBare high-resolution imaging, precise ranging and LPI/LPD(Low Probability of Interception/Low Probability of Detec-tion) communications. All of these are achieved directly fromthe nature of UWB radio’s low power spectral density (PSD).In fact, UWB as an enabling technology can be even morepromising. One unique feature offered by UWB is link securityenhancement at physical layer.The UWB channel impulse response (CIR) typically con-

tains a large number of resolvable multipath components.This fact indeed poses challenges for efficient signal re-ception. However, rich multipath propagation is not alwaystroublesome–they benefit sometimes. The multipath propa-gation can be utilized to focus a signal on an intendedlocation while minimizing signal strengths at other locations.This can be analogous to a situation of beamforming withnulling, where radio energy is focused as a beam pointing adesired direction. But in our case, by using a proper transmitwaveform, the energy can be focused and/or nulled on some

spatial spots. This very unique feature can be viewed asa location-based security enhancement mechanism with twoobvious advantages: (1) the “security key” is location-basedCIR which is not easy to for an interceptor (if any) to obtain;(2) no extra radio resources are consumed during transmission.

S

R 1

D

P 1

P L

P 2

R M

R 2 R 3

Information leaking

Information leaking

S: source D: destination R: relay node P: sensitive location

Scattering environment

Fig. 1. UWB relay network with awareness of information leakage.

An elegant application scenario is a UWB relay networkthat can take advantage of rich radio scattering to deliverinformation from a source to a destination with low signalleakage to the surrounding area (see Fig.1). The CIRs ofall involved radio links have to be known in prior, whichmeans channel measurement and handshaking are required atbeginning. This may be achieved by using a backward channelsounding according to the reciprocal principle [7]. In this paperfocus is put on transmit waveform design, with little touch inthe CIR preparation and other details.The rest of this paper is organized as follows. In next sec-

tion, the system to consider is introduced. Transmit waveformoptimization is discussed in section III. Numerical results areprovided in section IV, followed by some remarks in sectionV.

II. SYSTEM DESCRIPTIONConsider a UWB relay network with M amplify-and-

forward relay nodes in between a source node and a destinationnode. Assume all involved individual UWB channels remain

Proceedings of 2010 IEEE International Conference on Ultra-Wideband (ICUWB2010)

978-1-4244-5306-1/10/$26.00 ©2010 IEEE

Si Si

1/TS

w(t)

x(t)h(t, p) =

∑Mm=1 hm(t)

n(t)

r(t)

w∗(T0 − t)h∗(T0 − t, p)

Fig. 2. Analytical system model with joint Tx-Rx optimization.

static during a transmission burst. Each relay link consists ofa first half and second half segments connected through arelay node. Let hf,m(t) and hs,m(t) be the baseband CIRscorresponding to the two segments of the m-th link, andhm(t) = hf,m(t)⊗ hs,m(t) be the baseband CIR of that link,where ⊗ represents convolution operation. A cluster of relaylinks between the source and a receiver located at position p

can be virtually viewed as an aggregated multipath channelmodeled in a baseband CIR:

h(t, p) =

M∑m=1

hm(t) = hf,m(t)⊗ hs,m(t). (1)

To simplify out description, assume h(t, p) takes into accountfiltering impact caused by baseband shaping filters and allradio frequency (RF) frontends at the source, relay nodes anddestination. The transmitted signal is

x(t) =

∞∑i=−∞

Siw(t− iTS), (2)

where TS is the symbol duration, Si is the i-th transmittedsymbol, and w(t) is the symbol waveform. The received noise-polluted signal is

r(t, p)=x(t)⊗ h(t, p) + n(t)

=

∞∑i=−∞

Siw(t− iTS)⊗ h(t, p) + n(t), (3)

where n(t) is a zero-mean additive white Gaussian noise(AWGN). To focus on waveform design issue, it is assumedin this paper that TS is less than the support of h(t, p), sothat there would be no inter-symbol-interference (ISI). Giventhe transmit waveform and the channel, specified by w(t) andh(t, p), respectively, the best receiver in terms of signal-to-noise ratio (SNR) is the matched filter receiver with receivefilter fp(t) = w∗(T0 − t)⊗ h∗(T0 − t, p), where “*” refers toconjugate operation and T0 is a time constant to ensure thatfp(t) is causal. A analytical system model is shown in Fig.2.The aggregated impulse response measured at the matched

filter’s output is w(t) ⊗ h(t, p) ⊗ fp(t), and the peak wouldappear at the sampling time t = T0. Obviously, there isan optimal transmit waveform that leads to the maximumreceive SNR. The optimal waveform wopt(t) can be obtainedby solving the following homogeneous Fredholm integralequation [10]:

λnwn(t)=

∫ TS

0

κ(t− τ)wn(t)dτ (4)

κ(t)=h(t, p)⊗ h∗(T0 − t, p), (5)

where wn(t) is the n-th eigenfunctions and λn is the cor-responding eigenvalue. If λ0 is the largest eigenvalue, thenwe have wopt(t) = w0(t) (omit a scale). However, thisdesign may not be proper in terms of system informationsecurity. In practice, a radio signal transmitted to the des-tination would also reach some unintended areas, resultingin potential information leakage. Let p0 be the intendeddestination location, and assume there are L sensitive locationspl’s where received signal strengths have to be sufficiently low.To evaluate the performance, a matched filter receiver withreceive filter fpl

(t) = w∗(T0−t)⊗h∗(T0−t, pl) is employed tomeasure signal leakage at location pl. Of course, the measuredresult would be the worst-cases result, assuming both w(t)and h(t, pl) are known (though it is unlikely for a potentialinterceptor to know this information). A better waveformdesign should compromise the receive signal strengths at bothintended and unintended spots.

III. WAVEFORM OPTIMIZATION

Closed-form optimal results are not easily obtainable espe-cially with various constraints. We turn to use a numericalapproach and take advantage of the powerfulness of someexisting optimization tool. To formulate an optimization prob-lem in numerical format, denote by w = (w1, w2, w3, · · · )

T ,and hp = (h1,p, h2,p, h3,p, · · · )

T the discrete-time versionsof w(t) and h(t, p), respectively, assuming Nyquist samplingrate or higher. The received pure signal w(t)⊗ h(t, p) can berepresented in discrete-time as Hpw with Hp being a Toeplitzmatrix created from hp. Therefore, for the intended receiver,the peak of the overall discrete-time impulse response mea-sured at the matched filter’s output would be w

HHHp Hpw,

where the superscript represents Hermitian transpose opera-tion.Now the optimization problem can be formulated as the

Quadratic Constraint Quadratic Program (QCQP) problem[11]:

maxw

wHHH

p0Hp0

w

s.t. wHw ≤ P

wHHH

p1Hp1

w ≤ c1

· · ·

wHHH

pLHpL

w ≤ cL

(6)

where P is the maximum waveform power, andc1, c2, c3, · · · , cL are nulling levels associated with L

unintended locations. A QCQP problem is known as a NPhard problem and semi-definitive programming (SDP) can beused as a relaxation means to obtain a suboptimal solution

TABLE ICASE 1–WITHOUT NULLING CONSTRAINT

SDP based time reversalgain (dB) at intended location 28.3545, 27.9642, 28.7277 27.6582, 28.2109, 27.5636leakage (dB) at 1st unintended location -12.7677, -13.8283, -19.4994 -3.7997, -5.5677, -5.3708leakage (dB) at 2nd unintended location -10.3726, -3.3289, -7.3550 -3.8288, -6.2499, -4.3137

TABLE IICASE 2–SDP BASED OPTIMIZATION; NULLING CONSTRAINT AT ONE TESTING LOCATION.

normalized gain 0 -5.9244 -7.2624 -7.8287 -8.0217 -8.0842(dB) at intended 0 -1.9879 -2.4687 -2.6530 -2.7151 –location 0 -2.7886 -4.0569 -4.5974 -4.7854 -4.8467leakage (dB) at -12.7677 -42.4301 -61.0921 -80.5258 -100.3328 -120.27041st unintended -13.8283 -45.9763 -65.4955 -85.3113 -105.2492 –location -19.4994 -45.9391 -64.6708 -84.1303 -103.9423 -123.8812leakage (dB) at -10.3726 -7.6922 -6.6474 -6.4337 -6.3718 -6.35332nd unintended -3.3289 -5.3921 -5.0535 -4.9775 -4.9516 –location -7.3550 -5.1452 -5.4119 -5.7382 -5.8678 -5.9116

TABLE IIICASE 3–SDP BASED OPTIMIZATION; NULLING CONSTRAINT AT TWO TESTING LOCATIONS.

normalized gain 0 -10.6795 -21.2654 -30.0571 -34.8730 -43.9362(dB) at intended 0 -4.6929 -9.5973 -21.1257 -36.1660 -47.1353location 0 -6.0840 -17.6435 -25.6679 -38.5599 -54.8805leakage (dB) at -12.7677 -37.6750 -47.0891 -58.2974 -73.4816 -84.41831st unintended -13.8283 -43.2713 -58.3669 -66.8385 -71.7982 -81.9788location -19.4994 -42.6437 -51.0842 -63.0598 -70.1678 -73.8472leakage (dB) at -10.3726 -37.6750 -47.0891 -58.2974 -73.4816 -84.41832nd unintended -3.3289 -43.2713 -58.3669 -66.8385 -71.7982 -81.9788location -7.3550 -42.6437 -51.0842 -63.0598 -70.1678 -73.8472

[12], [13]. Let W = wwH , then the above optimization can

be translated into an SDP formulation:

maxW

trace(HHp0

Hp0W )

s.t. wHw ≤ P

trace(HHp1

Hp1W ) ≤ c1

· · ·

trace(HHpL

HpLW ) ≤ cL

W �= 0

(7)

where notation W �= 0 means that W is a semidefinitivematrix. Let WΔ be the solution to the above SDP problem.The dominated eigenvector of WΔ, denoted by wΔ, is theresultant transmit waveform (omit a scale). If the rank of WΔ

is one, then wΔ is actually the optimal solution to the originaloptimization (QCQP) problem (6).The above formulation can be extended to include multiple

transmit antennas. Consider a configuration with N transmitantennas and one receive antenna. Let H1,p,H2,p, · · · ,HN,p

be the channel Toeplitz matrices, and w1,w2, · · · ,wN thetransmit waveform vectors, corresponding to the N transmitantennas. The channel matrices and waveform vectors can befurther represented by

Hp = (H1,p,H2,p, · · · ,HN,p) (8)

and

w =

⎛⎝

w1

...wN

⎞⎠ (9)

It is not difficult to prove that the pure receive signal vector isHpw and the overall impulse response peak measured at thematched filter output is w

HHHp Hpw. With N transmit an-

tenna and L unintended locations, the suboptimal waveformscan be obtained by solving

maxW

trace(HHp0

Hp0W )

s.t. wHw ≤ P

trace(HHp1

Hp1W ) ≤ c1

· · ·

trace(HHpL

HpLW ) ≤ cL

W �= 0

(10)

In general, introducing N transmit antennas does not have im-pact on the way of waveform design, but data size is increasedby N folds. Large scale optimization can be computationallydifficult, and this is the cost for performance improvement.Alternatively, time reversal (i.e., w(t) = h∗p(t0 − t) ) is arelatively simple waveform design strategy that simply uses atime-reversed version of the CIR as a transmit waveform [6]–[9], [14]. However, time reversal is not an optimal methodwhen a matched filter receiver is employed, and it is unableto offer sufficient nulling effect.

IV. PERFORMANCE EVALUATION

An IEEE802.15.4a outdoor NLOS (NonLine-Of-Sight)channel model has been used to produce numerical results.The IEEE802.15.4a standard is for low data rate UWB appli-cations, and its outdoor NLOS channel models are especiallysuitable for study of sensor and relay networks. Assume thereare 25 amplify-and-forward relay nodes of the same type, onedesired destination and two locations for signal leakage test.Three test cases are considered:• Case 1–maximizing the SNR at an intended location,without nulling constraint;

• Case 2–maximizing the SNR at an intended location, withnulling constraint at one testing location;

• Case 3–maximizing the SNR at an intended location, withnulling constraint at two testing locations.

Three parameters are tested: (transmission) gain at intendedlocation, (relative signal) leakage at first unintended locationand leakage at second unintended location, where the gain isdefined as a ratio of output symbol power to transmit symbolenergy, and the leakage is an output symbol power ratio ofunintended location to intended location. For each parameter,three sets of results are generated based on three independentchannel realization sets. Each channel realization set contains50 individual realizations that represent 25 pairs of first andsecond half CIRs. An optimization software tool called CVX[15] is used to solve the SDP problems. The spatial focusingand nulling results are summarized in Table I, II and III, whereeach column in Table II and III represents a trade-off betweenthe transmission gain (for the intended location) and the signalleakage (at two unintended locations).From the results we have the following observations. In

test case 1, waveform optimization seems not necessary sincetime reversal leads to similar results (surprising!). Whennulling is required, trade-off between transmission gain andsignal leakage can always be achieved through optimization.However, achieving nulling on two locations sacrifices moretransmission gain than nulling on just one location. Roughlyspeaking, a few dB loss in transmission gain can trade for 20dB reduction in signal leakage at one location. In contrast,to achieve the similar amount of leakage reduction on twolocations would sacrifice much more transmission gain.

V. REMARKS

Numerical results have supported our argument that spa-tial focusing on one spot and nulling at the same time onother spots via transmit waveform design is feasible. Thebenefit enjoyed here originates from the phenomenon of richmultipath propagation, and this phenomenon is enhanced byaggregating large number of relay notes. Because adding atransmit antenna is equivalent to introduce a certain numberof multipath components, it can be expected that multipletransmit antennas can be employed for sharp spatial focusingand nulling at the cost of increased complexity. Obtainingaccurate CIR is an essence and can be a great deal. A staticor quasi-static propagation environment is desired for good

channel estimation. Again, it should be pointed out that thenulling results are very conservative since they are worst-caseresults.

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