Wireless Device Identification in MIMO Channels

8/14/2019 Wireless Device Identification in MIMO Channels

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Wireless Device Identification in MIMO channelsMing-Wei Liu and John F. DohertyDepartment of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802.

Email: {muI168, jfd6}@psu.edu

Abstract-A data-aided ite rative a lgor ithm to est imate thenonlinearities of wireless emitters for Specific emitter Identificat ion (SEI) is presented. To achieve robust estimation, InterSymbol Interference (lSI) is removed by iteratively est imatingthe channel coefficients and nonlinear transmit symbols toachieve asymptotically unbiased estimation. The complexity ofthe i teration procedure is further reduced by increas ing thestep size of the i teration result . The algorithm is applicable tovarious communication systems where multiple amplitude levelschemes are used such as QAM, OFDM, and PAM in MultipleInput Multiple-Output (MIMO) channels. Numerical results areshown which achieve nonlinearity estimation and radio emitteridentification over empirical channel models using an OrthogonalFrequency Division Multiplexing (OFDM) MIMO system.

I. INTRODUCTIONSpecific Emitter Identification (SEI) systems discern wireless radio emitters of interest based only on the external signalfeature measurement. This identification capability leads to awide variety of applications such as cognitive radio, networkintrusion detection, battlefield management, electronic supportmeasurement system, and intelligence gathering.Current research on performing SEI is based on physicalcharacteristics such as carrier frequency, pulse width, pulseduration, pulse shape, pulse repetition interval, angle of arrival, amplitude, and radio signal transient, Radio Frequency

(RF) front-end nonlinearity, [1]-[6]. This paper representsan extension from our previous work, [6], in which theidentification of radio emitters relies on the estimation ofRF front-end nonlinearity, and the transmitter nonlinearitiesare unavoidable and unique due to alternative designs andfabrication variations.A challenging SEI problem is robust estimation of multipledigital signals transmitted over multipath channels. Unfortunately, most prior work on equalization or channel estimationalgorithms derive channel information by either sending training sequences [7] or using a known constellation structure,such as Constant Modulus Algorithm (CMA), MultimodulusAlgorithm (MMA), and Reduced Constellation Algorithm(RCA) [8]-[10]. As a result, the constellation structures usedin blind equalization algorithms or desired signal in data-aidedequalizations come from ideal linear transmission systems, andthe desired nonlinear characteristics might be lost because thenonlinearities are not considered in these methods. Since ouridentification depends on the nonlinearity features, applyingthese algorithms jeopardize the SEI process.In this paper, we propose a data-aided time domain algorithm to overcome the lSI problem for RF front-end nonlinearity estimation by iteratively estimating the transmitted symbol

values and the channel coefficients to achieve asymptoticallyunbiased estimation. The main features of our approach canbe summarized as follows. The algorithm is flexible to operateunder various communication systems when multiple amplitude level schemes are used such as QAM, OFDM, and PAM.The rest of the paper is organized as follows. In SectionII, we give a concise description of the SEI problem in theMIMO channel scenario. In Section III, an iterative estimationalgorithm is shown. In Section IV, numerical results usingan OFDM system and a practical indoor channel model arepresented. Section V summarizes the paper.

II . PROBLEM STATEMENTIn this paper, we consider a scenario that a single targetemitter with multiple transmit antennas, and since the RFfront-ends of all the antennas likely share the same design[11], [12], the nonlinear properties of the transmit antennasare assumed identical throughout this paper. The channel andthe nonlinearity properties are assumed the same during theestimation process.The notations (.) +, and 0 stand for transpose,pseudo-inverse, amplitude operator of a complex number, andzero matrix respectively.

A. Memoryless Nonlinear ModelThe input signal, of the nonlinear system is assumed arandom process, and then by applying the nonlinearity distortion analysis from [13], [14], [6], the memoryless nonlinearsystem could be described by its coefficients as:

= L = L a 2 i _ 1 d ~ i - 1where both d and are complex numbers with their normalized forms and The normalization is set to a referencestructure with standard deviation of and hence =

and J = In this paper is assumed the maximumnumber of nonlinearity coefficients.Assuming unknown attenuation during the propagation, andtherefore the linear gain, and rotation of the nonlinearsystem are not available. Under this assumption, a tractablesolution is to estimate the scaled and rotated form of (1) asfollowing= = L b 2 i _ 1 d ~ i - 1

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(8)Lets unfold (7) to equation:

r=Hx+n=Xh+nwhere is the complex Gaussian noise vector, H is a complexmatrix populated by channel coefficients, and X is populatedby transmit symbols, x = [Xl, X2, .. . , XnR ]T, correspondingto the composition of r. Here, Hk is assumed zero whenk =1= 0 rv L - 1 and the length of the training sequenceis Q. The LnTnR x 1 overall channel coefficient vector isstructured as h [hfl" .hfnrlhIl" . h I n ~ ...1hrRI" .hrRnr]Twhere rt = [ hrt[O] hrt hrt[L - Furthermore, thereceive signal vector is r = [r [ rr r ~ J where rr =[rr[O]rr[l] .. . rr[Q+L-2]]T is the received signal of antenna

To describe the details of generating matrices X and H,several definition should be assigned for convenience. First,the convolution matrix t is defined:

. (3)Xp

where b2i-l, i = 1, ... , (M - 1) /2 are the normalized nonlinearity coefficients in complex format, and b is set to 1 bydefinition.Since our proposed approaches are data-aided and thetraining sequence is known, the outcome of the nonlinearsystem is assumed finite. The finite input set of emitteris {Jl ,J2 , ,Jp }, is then one-to-one mapped to outputset {Xl ,X2, . .. ,xp}, where P is the number of total outcomes. Our approach will estimate the nonlinear coefficients{b3 ,bs , .. . ,b which are identical for all the RF front-endsthrough the estimation of {Xl ,X2, .. . ,xp}. The relationshipbetween the input and output can further be expressed as:V3 VMdl dl dlV3 VMd2 d2 d2

Or re-write in matrix format x = Once the transmitsymbols are estimated as X, the least-squared nonlinearitycoefficients can be derived as following t =

Xt[O]xt[l] Xt[O]xt[2] xt[l] Xt[O] (9)(4)

To ensure the uniqueness of pseudoinverse, the columns of Dhave to be linearly independent [15]MIMO Channel ModelThe propagation channel model addressed in this paper is alinear MIMO system with nT transmit antennas and nR receiveantennas. We assume a linear dispersive channel in a basebanddiscrete-time equivalent model, which can be represented as[16], [17]:

Xt XtXt =Xt

X= [ Xl X2 XnTJh+n=r.

xt[Q-l] (Q+L-l)xLwhere is the length of the training sequence. Then, withthe definition of r in (8) and previous discussion, the receivesignal vector be re-arranged in terms of linear combination as:

(5)I[i] = L Hk


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estimated h

estimated x

classificationestimated b

n=n+ lestimated x

This initial estimation is further combined with (8) toestimate the linear channel coefficients, h, called h-step. Thenunder the premise this newly estimated information is moreaccurate than the previous estimation, the new data can beutil ized to re-estimate the transmit symbols by applying (8),called x-step. The result can be again sent to h-step and thenx-step for a new iteration or stop to output the results. Theiterative approach is based on the assumption that the newestimation supports more accurate knowledge about the nonlinear channel than the previous one, and therefore improvesthe next estimation. When this premise holds, the accuracywill increase with the iteration procedure.A. h-step Fig. 1. Block diagram of the iterative algorithm.

This new estimation is then used to repeat the process to h-stepfor the next iteration n (n 1).

The algorithm use the previous transmit symbol estimationin 1)th iteration to re-estimate the channel coefficientvalues by applying (8):

x-stepSimilar to h-step, the estimated 6(n) is then used to fill in

matrix H to derive new transmit symbol estimation as:

where r is the received signal, and X+(n-l) is the pseudoinverse of X which is composed by the estimated channelcoefficients. For the first iteration, the estimated transmitsymbols are set to be linear, This new estimation is thenused to re-estimate the transmit symbols in x-step.

(16)(k) ,,(k) ("(k) - (k- l ) )+Jlwhere Jl is the step size. After the procedure, the estimatedresults are sent to h - step and continue the iteration process.

Convergence Rate ImprovementTo reduce the computation requirement and latency of theiterative algorithm, we modify the iterative estimation bypredicting the trajectory of the estimated feature on the featureplane. The algorithm first observes the previous trajectory andthen predicts the next estimated features. Therefore, instead ofwaiting for the next iteration, the algorithm simply moves tothe predicted result. The prediction is based on the fact that themaximum eigenvalue of the error transform matrix dominatesthe movement of the estimated features in each iteration, andhence the estimated features provide predictable behavior afterthe first few iterations. The the error vector evolution of eachiteration is analytically shown in [20].Suppose we start the next iteration from kth iteration, then-(k-l) ,,(k-l)set = and do the following estimation.

(13)

(14)(n ) = H+(n) . r.

6(n) = X+(n-l) . r,

C. step IV. SIMULATION RESULTSTo improve the convergence, an intermediate step couldbe used after h- and x-step. A natural augmentation is toconstraint the estimation result by utilizing our nonlinearitymodel in (3). The estimated symbols are over-fitted to themodel to reduce the error perpendicular to the solution planeand than they are re-projected back to the correspondingtransmit symbols. The estimated result is then sent to h-step

for the next iteration.If the user wishes to stop at this iteration, the estimatednonlinearity is derived by (4) as following(15)

Analytical result and other details of the algorithm includingthe convergence criteria and performance appear in [20].The algorithm can be depicted as a block diagram as shownin Fig. 1.

In the simulation, a practical example using an OFDMsystem, IEEE 802.11n draft, with the RF front-end devicemodels from [14] as transmitter 1, and [13] as transmitter 2,that were used in our previous research [6] will be shown.Here a 2 x 2 MIMO channel is used in this simulation, andthe training sequence in the simulation includes the 802.11a/glong training field and is further encoded over space and timeusing a orthogonal matrix [21].Here we apply an empirical indoor channel model, h[n] =

-1] 2], extracted fromexperimental result in [22]. This model is extended to a MIMOchannel with the channel correlation matrix obtained from[23].The output power is set 25 dBm for each emitter which is atypical average transmit power value in commercial marketproducts, and the nonlinearity coefficients are in TableThe degree of nonlinearity is -16dB Error Vector Magnitude



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----..... .... --- - - - - - - - - - -

o

co

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oc5z

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Fig. 2. The estimated nonlinearity feature, b3, using 0 and 1respectively at 35dB Eb/NO. Fig. 3. Convergence of estimated nonlinearity coefficients of transmitter 1 indifferent situations. The experiment uses 1 long training sequence in 35dBEb/NO environment.

b3 -0.0735 - 0.0114i -0.0910+0.1580ibs -0.0986 + 0.0590i 0.2503 + 0.0286ib7 -0.0547 - 0.0055i 0.0155 + 0.0025i

TABLE INONLINEARITY PARAMETERS OF TWO TRANSMITTERS

(EVM) satisfying the specification [24] when operating in 16QAM scheme. The parameters are extracted from a RF devicein [14] as transmitter 1 and a class A power amplifier in [13]as transmitter 2.

Fig. 2 shows the estimated features moving on each iteration. The figure demonstrates two estimation results usingthe original iterative estimation, Jl = 0, and the convergenceimprovement algorithm, Jl = 1 where Jl is the step size in(16). The convergence improvement algorithm initiates at the4th iteration and it is shown that the the improved versionachieve the same estimation result at the 14th iteration whilethe the original iterative estimation requires 24 iterations.

To represent the accuracy of our nonlinearity estimation, theNormalized Mean Squared Error (NMSE) of nth iteration isintroduced as the following2NMSE of 1010g 2 (dB). (17)

As shown in Fig. 3, the effect of different Jl to the convergencerate and result is presented. The algorithm converges fasterwith higher Jl and the final NMSE is similar to the originalalgorithm. In this example, the required number of iterationsfor original iterative algorithm is about 150 while it takes 60iterations to achieve similar NMSE when Jl equals 1.Furthermore, the effect of different number of headers usedwhen Jl equals 1 is demonstrated in Fig. 4. The result indicatesthat the performance improved when the number of headersused increases.

, , ~ -- -- -- - - -

----.

co

()

.

. CcCJ)z

As indicated in Fig. 4, the estimation is more accuratewhen more information is used. Fig. 5 depicts this situationin different Eb/NO scenarios. The result shows that when thesignal power increases, the NMSE decreases as expected. Inour simulation, the system is assumed 16QAM and a typicaloperation environment is 12dB to 16dB for 16QAM scheme[25].The classification rate depends on the accuracy of estimationand the knowledge of transmitters The misclassification rateis shown in Fig. 6 where minimum distance algorithm ischosen as the discriminating function. Here we consider atwo-class case, where the the nonlinearities of transmitter 1and 2 are known, and the probability of the observed datafrom transmitter 1 and 2 are equal.

Fig. 4. The nonlinearity estimation convergence of transmitter 1 usingdifferent number of long training sequence headers. and Eb/NO is 1 and35dB in this experiment.

Transmitter 2ransmitter 1



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August 2002.[2] L. E. Langley, "Specific emitter identification (SEI) and classical parameter fusion technology," in WESCON'93, Sept 1993, pp. 377-381.[3] K. A. Remeley, C. A. Grosvenor, R. T. Johnk, D. R. Novotny, P. D.Hale, and M. D. McKinley, "Electromagnetic signatures of WLANcards and network security," in IEEE International Symposium on SignalProcessing and Information Technology, Dec 2005, pp. 484-488.[4] A. Kawalec and R. Owczarek, "Specific emitter identification usingintrapulse data," in European Radar Conference, 2004, pp. 249-252.[5] K. B. Rasmussen and S. Capkun, "Implications of radio fingerprinting onthe security of sensor networks," in Proceedings of IEEE SecureComm,2007.[6] M.-W. Liu and J. F. Doherty, "Specific emitter identification usingnonlinearity device estimation," in IEEE 2008 Sarnoff Symposium,Princeton, NJ, 28-30 April 2008.[7] S. Haykin, Adaptive Filter Theory. New Jersey: Prentice Hall, 2002.[8] D. N. Godard, "Self-recovering equalization and carrier tracking intwo-dimensional data communication system," IEEE Trans. Commun.,vol. 28, no. 11, pp. 1867-1875, Nov 1980.[9] J. Yang, J.-J. Werner, and G. A. Dumont, "The multimodulus blindequalization and its generalized algorithms," IEEE Sel. Areas Commun., vol. 20, no. 6, pp. 997-1015, Jun 2002.[10] Y. Sato, "A method of self-recovering equalization for multilevelamplitude-modulation systems," IEEE Trans. Commun., vol. 23, pp.679-682, June 1975.[11] Y. Palaska, A. Ravi, S. Pellerano, B. R. Carlton, M. A. Elmala,R. Bishop, G. Banerjee, R. B. Nicholls, S. K. Ling, N. Dinur, S. Taylor,and K. Soumyanath, "A5-GHz 108-Mb/s 2 x 2 MIMO transceiver RFICwith fully integrated 20.5-dbm PidB power amplifiers in 90-nm cmos,"IEEE Solid-State Circuits, vol. 41, no. 12, pp. 2746-2756, December2006.[12] D. G. Rahn, M. S. Cavin, F. F. Dai, N. H. W. Fong, R. Griffith,J. Macedo, J. W. M. R. A. D. Moore, and M. Toner, "A fully integrated multiband MIMO WLAN transceiver RFIC," IEEE Sol id-StateCircuits, vol. 40, no. 8, pp. 1629-1641, August 2005.[13] P. B. Kenington, High-Linearity RF amplifier design. Boston: ArtechHouse, 2000.[14] K. G. Gard, L. E. Larson, and M. B. Steer, "The impact of RF frontend characteristics on the spectral regrowth of communications signals,"IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 2179-2186, June2005.[15] G. Strang, Linear Algebra and Its Applications. California: ThomsonHigher Education, 2006.[16] K. I. Pedersen, B. Andersen, J. P. Kermoal, and P. Mogensen, "A stocastic multiple-input-multiple-output radio channel model for evaluationof space-time coding algorithms," in Vehicular Technology Conference,vol. 2, Boston, September 2000, pp. 893-897.[17] S. Glisic, Advanced Wireless Communications: 4G Technologies. WestSussex: John wiley, 2004.[18] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, andF. Frederiksen, "A stochastic MIMO radio channel model with experimental validation," IEEE Sel. Areas Commun., vol. 20, no. 6, pp.1211-2002, August 2002.[19] Y. Gong and K. B. Letaief, "Performance evaluation and analysis ofspace-time coding in unequalized multipath fading links," IEEE Trans.Commun., vol. 48, no. 11, pp. 1778- 1782, November 2000.[20] M.-W. Liu and J. F. Doherty, "Specific emitter identification in multipathchannels," IEEE Trans. Commun., submitted for publication.[21] T. Paul and T. Ogunfunmi, "Wireless LAN comes of age: Understandingthe IEEE 802.11n amendment," IEEE Circuits Syst. Mag., vol. 8, pp.25-54, 2008.

[22] H. Hashemi, "The indoor radio propagation channel," in Proceeding ofthe IEEE, vol. 81, no. 7, July 1993, pp. 943-968.[23] WiMAX Forum Mobile Release 1.0 Channel Model. WiMAX Forum,2008.[24] IEEE Std 802.11a-1999: Wireless LAN MAC and PHY SpecificationHigh-Speed Physical Layer in the 5GHz Band. IEEE, 2000.[25] J. Thomson, B. Baas, E. M. Cooper, J. M. Gilbert, G. Hsieh, P. Husted,A. Lokanathan, J. S. Kuskin, D. McCracken, B. McFarland, T. H. Meng,D. Nakahira, S. Ng, M. Rattehalli, J. L. Smith, R. Subramanian, Y.-H. W.L. Thon, R. Yu, and X. Zhang, "An integrated 802.11a baseband andMAC processor," in IEEE International Solid-State Circuits Conference,vol. 1, Feb 2002, p. 126.

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Fig. 6. The misclassification rate of transmitter 1 and 2.

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[1] C.-S. Shieh and C.-T. Lin, "A vector neural network for emitter identification," IEEE Trans. Antennas Propag., vol. 50, no. 8, pp. 1120-1127,

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REFERENCES

0 . 1 5 ~ .. .. " ' : . : - " - ~ .. .. .. ~ . : . ; ; . : . -I()00C3 0.1 , ~ -I

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Fig. 5. The average minimum nonlinearity coefficient NMSE of transmitter1 and 2 using alternative number of headers.

CONCLUSIONIn this work, we have proposed a RF front-end nonlinearity estimator for SEI systems when multilevel modulationschemes are used. Our method overcomes the lSI effect inMIMO environments and provides reliable identification. Thealgorithm iteratively estimate the channel coefficients andnonlinear transmit symbols and the estimation then over-fitsto the memoryless nonlinearity model. Furthermore, the complexity of the iteration is reduced by increasing the estimationstep through the prediction of the next iteration result. Thenumerical result shows that our algorithm differentiate twoalternative nonlinear RF front-end in a commercial OFDMMIMO system.

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Wireless Device Identification in MIMO Channels

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