[7] ATDIFeb. 2007, http://www.atdi.com/icstelecom.php.

[8] Chukkala, V., Leon, P. D., Horan, S., and Velusamy, V.Modeling the radio frequency environment of Mars forfuture wireless, networked rovers and sensor webs.In Proceedings of the IEEE Aerospace Conference, BigSky, MT, 2004.

[9] Anderson, F., Haldemann, A., Bridges, N., Golombek, M.,and Parker, T.Analysis of MOLA data for the Mars exploration roverlanding sites.Journal of Geophysical Research, 108, E12 (Dec. 2003).

[10] Kirk, R., Howington-Kraus, E., Redding, B., Galuszka, D.,Hare, T., Archinal, B., Soderblom, L., and Barrett, J.High-resolution topomapping of candidate MER landingsites with Mars orbiter camera narrow-angle images.Journal of Geophysical Research, 108, E12 (Dec. 2003).

[11] USGSJune 2006, http://webgis.wr.usgs.gov/mer/moc na topography.htm.

[12] Hufford, G., Longley, A., and Kissick, W.A guide to the use of the ITS irregular terrain model inthe area prediction mode.NTIA Report 82-100, Apr. 1982.

[13] Cummer, S., and Farrell, W.Radio atmospheric propagation on Mars and potentialremote sensing applications.Journal of Geophysical Research, (June 1999),104,14,149—14,157.

[14] Ho, C., Slobin, S., Sue, M., and Njoku, E.Mars background noise temperatures received byspacecraft antennas.The Interplanetary Network Progress Report, 42-149 (May2002).

[15] Hansen, D., Sue, M., Ho, C., Connally, M., Peng, T.,Cesarone, R., and Horne, W.Frequency bands for Mars in-situ communications.In Proceedings of the IEEE Aerospace Conference, BigSky, MT, 2001.

[16] IEEE Standard 802.11aIEEE Part 11: wireless LAN medium access control (MAC)and physical layer (PHY) specifications: High-speedphysical layer in the 5 GHz, Sept. 1999.

[17] Borah, D., Daga, A., Lovelace, G., and DeLeon, P.Performance evaluation of the IEEE 802.11a and bWLAN physical layer on the Martian surface.In Proceedings of the IEEE Aerospace Conference,Big Sky, MT, Mar. 2005.

[18] Pearson, B.A review of spread spectrum techniques for ISM bandsystems.Intersil Corp., Milpitas, CA, Application Note 9820, Oct.1998.

[19] Doufexi, A., Armour, S., Karlsson, P., Nix, A., and Bull, D.A comparison of HIPERLAN/2 and IEEE 802.11a.IEEE Communications Magazine, (May 2002).

Interference Mitigation in Aeronautical TelemetrySystems using Kalman Filter

In this correspondence we present a new method for

mitigating multipath and adjacent channel interference in

aeronautical telemetry systems. The proposed method uses a

linear equalizer that is derived using Kalman filtering theory,

which has been used successfully for channel equalization for

high-speed communication systems. We illustrate the proposed

method with numerical examples obtained from simulations that

show the improvement in bit error rate performance (BER) for

two modulation schemes using advanced range telemetry (ARTM)

tier-1 waveforms currently used in aeronautical telemetry

systems.

I. INTRODUCTION

Aeronautical telemetry is used by the aviationindustry to investigate the performance and safetyof aircraft during flight tests before the aircraft areput into active service, and uses radio signals to sendflight test data from transmitters on board the aircraftto ground stations for analysis. Modern aeronauticaltelemetry applications operate at data rates of theorder of 10—20 Mbit/s, and they must cope withmultipath interference (MPI) due to propagationthrough frequency selective radio channels [1], aswell as with adjacent channel interference (ACI) dueto the presence of multiple signals with potentiallyoverlapping spectra in the frequency bands allocatedfor aeronautical telemetry.We note that MPI and ACI have been treated as

two separate problems in the literature so far. For theformer, application of equalization techniques fromdigital communications, such as the constant modulusalgorithm (CMA) and the decision-feedback minimummean square error (DF-MMSE) algorithm, to mitigatethe effects of multipath propagation and reduce MPIwas investigated in [2]. For the latter, improveddigital modulation schemes such as Feher-patentedquadrature phase-shift keying (QPSK) (FQPSK) [3]and shaped-offset QPSK (SOQPSK) [4] have beenproposed for use in aeronautical telemetry. These are

Manuscript received December 10, 2006; revised August 4, 2007;released for publication September 12, 2007.

IEEE Log No. T-AES/43/4/914442.

Refereeing of this contribution was handled by P. K. Willett.

This work was presented in part at the 2006 IEEE MilitaryCommunications Conference (MILCOM 2006).

0018-9251/07/$25.00 c° 2007 IEEE

1624 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 43, NO. 4 OCTOBER 2007

known as advanced range telemetry (ARTM) tier-1waveforms and have increased spectral efficiency,which allows for more signals in a given frequencyband through closer spacing of their carriers. Inaddition, minimum carrier spacings have beenrecommended for telemetry signals to reduce ACI[5], and recently the use of interference cancellationtechniques has also been investigated for ACImitigation [6].We present a new approach that mitigates both

MPI and ACI in aeronautical telemetry systems.The proposed method uses a linear equalizer basedon Kalman filtering theory [7, 8] and improvesperformance in the presence of both MPI and ACIwithout requiring separate processing to equalizethe channel and remove ACI. This is different fromthe approach in [2] which employs equalizationtechniques to mitigate MPI only, as well as fromthe approach in [6] where interference cancellationmethods are used solely for ACI mitigation. Wenote that Kalman-based equalizers have long beenused in digital communication systems to improveperformance [9, 10], and are based on the idea ofminimizing the mean-squared error (MSE) betweenthe detected symbols at the receiver and a set ofknown symbols transmitted during a training period.The paper is organized as follows: in Section II

we discuss modulation formats proposed for currenthigh data rate aeronautical telemetry applications andbriefly describe the ARTM tier-1 waveforms (FQPSKand SOQPSK). We continue with a description of theproposed equalizer in Section III. In Section IV wepresent numerical results obtained from simulations,followed by final remarks and conclusions inSection V.

II. MODULATION FORMATS FOR AERONAUTICALTELEMETRY APPLICATIONS

Pulse coded modulation/frequency modulation(PCM/FM) has been the primary modulation formatused in aeronautical telemetry applications for over40 years. Although PCM/FM has many desirablefeatures, it cannot provide the bandwidth efficiencyrequired by the present day high data rate aeronauticaltelemetry applications. The FQPSK and SOQPSKmodulation formats (which are variations of QPSKmodulation schemes that encode 2 bits/symbol) havesuperior bandwidth efficiency at high data rates evenwhen used with nonlinear power amplifiers [11].They both have approximately the same bandwidthand bit error rate (BER) performance when a simpleoffset QPSK (symbol-by-symbol) detector is used atthe receiver [12], and we focus on these modulationformats here.

Fig. 1. Block diagram of symbol-by-symbol detector for ARTMtier-1 waveforms using FQPSK and SOQPSK modulation.

A. FQPSK Modulation

FQPSK modulation [3] is a variant of offsetQPSK modulation in which the inphase (I) andquadradure (Q) components of the modulatedwaveforms are cross correlated to produce a signalwith quasi-constant envelope. The complex basebandFQPSK waveform is expressed in terms of a set ofM = 16 baseband pulses Sm(t), m= 0, : : : ,M ¡ 1, and isrepresented as

f(t) =pEbXn

[Si(n)(t¡ nTs)+ jSq(n)(t¡ (n+0:5)Ts)]

(1)

where Eb represents the average bit energy and Tsis the symbol duration. During the symbol intervalnTs · t· (n+1)Ts the waveform Si(n)(t¡nTs) is used toperform amplitude modulation of the I component ofthe carrier, while during the interval (n+0:5)Ts · t·(n+1:5)Ts the waveform Sq(n)(t¡ (n+0:5)Ts) is usedto perform amplitude modulation of the Q componentof the carrier, and indices i(n),q(n) 2 f0, : : : ,M ¡ 1gare determined by the input data streams as describedin [13, Sec. 3.2]. The specific waveforms used forgenerating the I and Q components of the transmittedsignal are given in [13, p. 138], and the mappingfunction that assigns the particular baseband I andQ channel waveforms transmitted during a givensignaling interval is described in [13, p. 142].The optimal detector for FQPSK modulation

is a sequence detector that uses a trellis whichaccounts for all possible combinations of waveformsdetermined by the memory of the waveformmapper [13, Sec. 3.5]. However, in practice asymbol-by-symbol detector as shown in Fig. 1 is used,that performs integrate-and-dump detection wheng(t) = 1 for 0· t · Ts and 0 otherwise. This type ofdetector is also used for SOQPSK modulated signals,and its performance is very close to that of the trellisdetector.

B. SOQPSK Modulation

SOQPSK modulation [4] is a ternary continuousphase modulation (CPM) scheme with modulationindex equal to 1/2, for which the baseband SOQPSK

CORRESPONDENCE 1625

waveform is represented as

s(t) = ejÁ(t) (2)

with phase Á(t) given by

Á(t) = ¼Xk

®(k)g(t¡ kTb) (3)

where ®(k) 2 f¡1,0,+1g is the kth ternary symbol, Tbis the bit duration, and g(t) is a phase pulse that is thetime integral of a frequency pulse p(t) with area equalto 1/2. In the work presented here, we consider theSOQPSK-TG waveforms as defined in [4], for whichthe frequency pulse is a spectral raised cosine pulsewindowed by a temporal raised cosine function thatare expressed as

g(t) =Z t

¡1p(x)dx (4)

p(t) = Acosμ¼½Bt

2Tb

¶1¡ 4

μ½Bt

2Tb

¶2 £ sinμ¼Bt

2Tb

¶¼Bt

2Tb

£wn(t) (5)

wn(t) is the window function given by

wn(t) =

8>>>>>>><>>>>>>>:

1 0·¯t

2Tb

¯· T1

12+12cos·¼

T2

μt

2Tb¡T1

¶¸T1 ·

¯t

2Tb

¯· T2

0 T1 +T2 <¯t

2Tb

¯(6)

and the constant A is chosen such that the area of p(t)is equal to 1/2. The SOQPSK waveform parametersare: ½= 0:7, B = 1:25, T1 = 1:5, and T2 = 0:5. Thefrequency pulse is defined on the interval ¡2·t=(2Tb)· 2 and spans four signaling intervals, and themapping from bits to ternary symbols f¡1,0,+1g isdone according to [4].The use of a symbol-by-symbol detector as shown

in Fig. 1 for more general binary CPM systemswas investigated in [14], [15], and for SOQPSKwaveforms was discussed in [16].

III. KALMAN FILTER BASED INTERFERENCEMITIGATION

Let r(t) be the received baseband signalcorresponding to a desired transmitted ARTM signalthat employs FQPSK or SOQPSK modulation asdescribed in the previous section, and which isaffected by MPI and ACI. To mitigate the interferenceeffects on the received signal r(t) we propose the useof a linear N-tap delay line filter inspired from theKalman-filter based channel equalizer proposed byGodard in 1974 [10], that operates on the sampled

received baseband ARTM signal r(n). We denote thefilter tap weights vector by

c= [c0 ¢ ¢ ¢cN]T (7)

with the corresponding tap output vector denoted by

rn = [r(n) r(n¡ 1) ¢ ¢ ¢r(n¡N)]T: (8)

Then, the equalized signal is expressed as

yn = rTnc: (9)

The values of the equalizer taps are obtained during atraining stage in which a set of samples of the desiredsignal fang known at the receiver is transmitted.The optimal tap values must minimize the expectedmean-squared distortion en between the trainingsample and the output of the equalizer, that is

E = E[jan¡ yn| {z }en

j2] = E[jenj2]: (10)

According to [10], the optimum tap weight vector isgiven by

c¤ = B¡1b (11)

with B= E[rnrTn ] and b= E[anrn], and when c is

chosen to be equal to c¤ the mean-squared distortionis minimized and equal to E¤. We note that, evenwhen no noise is present, E¤ 6= 0 due to the fact thatthe equalizer has a finite impulse response, while aninfinite impulse response filter is necessary to equalizea finite impulse response channel. We denote thedistortion when the optimal tap weights are used bye¤n, and we write the training symbols as

an = rTnc¤+ e¤n (12)

with E[je¤nj2] = E¤. With random initialization of thetap weights vector, the dynamic evolution of theoptimal tap weights vector c during the training stageis described by the following state-space model:

cn = cn¡1

an = rTncn+ en

(13)

in which the state transition matrix is the identitymatrix I, and the noisy measurement equationexpresses the value of training sample an at timeinstant n in terms of the actual output of the equalizerrTncn at time instant n and the expected distortion en.The fact that the state transition matrix is equal to theidentity matrix implies that at steady state the value ofthe optimal tap weights vector does not change, and isessentially constant [10].The optimal tap weights are obtained by applying

the Kalman filtering algorithm as in [10], whichis different from [9] in which the Kalman filter isactually the equalizer. We recall that, for a generallinear system described by the state-space equations:

xn =An,n¡1xn¡1 +wn

yn =Cnxn+ vn(14)

1626 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 43, NO. 4 OCTOBER 2007

wherexn is the system state vector,An,n¡1 is the state transition matrix,wn is the state noise vector with covariance matrix

Qn,Cn is the measurement matrix,vn is the measurement noise vector with covariance

matrix Rn,and the discrete-time Kalman filtering equations [7]for estimation of state vector x are

1) predicted state or a priori estimate

x¡n =An,n¡1x+n¡1 (15)

2) predicted measurement equation

yn =Cnx¡n (16)

3) error covariance extrapolation

P¡n =An,n¡1P+n¡1A

Tn,n¡1 +Qn¡1 (17)

4) Kalman gain matrix equation

Kn = P¡nC

Tn (CnP

¡nC

Tn +Rn)

¡1 (18)

5) error covariance update equation

P+n = (I¡KnCTn )¡1P¡n (19)

6) state estimate update (a posteriori estimate)

x+n = x¡n +Kn(yn¡ yn): (20)

For the particular case of the linear system in(13) which describes the evolution of the optimal tapweights during the training stage, there is no statenoise, which implies that the corresponding noisecovariance matrix in (17) is Qn = 0. The measurementequation of the system in (13) is a scalar equationwith scalar noise, in which case the covariance Rn isalso scalar and is equal to the mean-squared distortionE[jenj2] between the training sample and the equalizeroutput. At steady state this is equal to Rn = E¤, themean-squared distortion when the optimal tap weightsare used. Thus, the discrete-time Kalman filteringequations (15)—(20) for the system (13) become

an = rTn cn¡1

Kn = Pn¡1rn(rTnPn¡1rn+ E¤)¡1

Pn = (I¡KnrTn )Pn¡1cn = cn¡1 +Kn(an¡ an)

(21)

and the steady-state value of cn is the optimal estimateof the tap weights vector. Since the value of E¤ cannotbe known a priori, an estimated value E¤ is used inpractice to compute the Kalman gain Kn. Accordingto [10] the initial value for E¤ has no influence on thesuccessive estimates of the tap weights, and is usuallytaken between 10¡3 and 10¡2. Additional details about

the Kalman filtering algorithm (21) are discussed in[17, sec. 11.4].After the training stage is completed and steady

state is reached, the steady-state value c is usedto equalize the received telemetry signal, and thetransmitted symbols are estimated using the equalizedsignal.

IV. SIMULATION RESULTS

We have performed simulation experimentsto evaluate the improvements in BER when theequalizer filter described in the previous section isused for mitigating MPI and ACI in aeronauticaltelemetry systems using FQPSK and SOQPSKmodulation. The data rate for both modulationschemes was taken 10 Mbit/s, and the received signalwas sampled at 10 samples/symbol similar to [2]. Thechannel considered in our experiments is a two-raypropagation channel model specific to aeronauticaltelemetry systems [1] that was also used in theequalization studies in [2]. The channel model consistsof a direct line-of-sight path and a ground reflectedpath, and is characterized by parameter ¡ representingthe relative gain of the ground reflected path to thedirect path, which is normalized to unit gain.The length of the training sequence and the

number of equalizer filter taps were selectedempirically based on the magnitude of the errorbetween the training and equalized sequences assuggested by [18]. In all the experiments performedwe used 1000 samples (corresponding to 100transmitted symbols) for equalizer training. Thetap length of the equalizers differs for FQPSK andSOQPSK modulations and depends also on the valueof the channel parameter ¡ , with more equalizertaps for larger values of ¡ . In our experiments weconsidered the values of ¡ = 0:3,0:5,0:7 for whichthe equalizer filters had N = 5,7,10 taps, respectively,for FQPSK signals, and N = 3,5,7 taps, respectively,for SOQPSK signals. In all experiments the equalizerfilter taps were initialized to one, and the initialvalues of the parameters needed to crank the Kalmanfilter iterations were chosen to be E¤ = 10¡3 andP0 = 10

¡6IN .In a first experiment we simulated the use of

the proposed method for MPI mitigation only, inwhich case the algorithm performed essentiallychannel equalization, and results are presented inFig. 2 (for FQPSK modulation) and Fig. 3 (forSOQPSK modulation). In this case we note thatthe equalizer improves the BER performance byapproximately 1—5 dB for FQPSK signals and1—3 dB for SOQPSK signals, which is very similarto the performance improvements obtained withthe CMA equalizer reported in [2]. However, theperformance of the CMA equalizer is heavily

CORRESPONDENCE 1627

Fig. 2. BER performance for FQPSK signals with multipathchannel.

Fig. 3. BER performance for SOQPSK signals with multipathchannel.

dependent on its initialization [19] while that of theproposed Kalman-based equalizer is independent onits initalization [10]. We also note that performanceimprovement depends on the gain value ¡ , withsmaller improvement for smaller gains, and largerimprovement for larger gains.We have also simulated the use of the proposed

Kalman-based equalizer in the presence of both MPIand ACI, and observed comparable performanceimprovement. In this case, in addition to the two-raychannel model used in the previous experiment forpropagation of the desired signal, we included alsotwo ACI signals. The ACI signals were placed inneighboring frequency bands on each side of thedesired signal with the same power as the desiredsignal, and arrived through similar two-ray channelsat the receiver. We have simulated the system forcarrier spacing values of 1, respectively 0.7, and samevalues of the ¡ as in the previous experiment, andsimulation results are presented in Figs. 4 and 5 (forFQPSK modulation), and Figs. 6 and 7 (for SOQPSKmodulation). Performance improvement in this caseis similar to that noted in the previous experiment,

Fig. 4. BER performance for FQPSK with MPI and 2 ACIsignals with carrier spacing 1.

Fig. 5. BER performance for FQPSK with MPI and 2 ACIsignals with carrier spacing 0.7.

and shows that the proposed equalizer can be usedsuccessfully in the presence of both MPI and ACI,eliminating the need for additional processing toseparately equalize the channel and remove ACI. Wenote that all ACI signals were assumed synchronizedwith the desired signal, and that there is about 1—2 dBloss in performance when synchronization is nolonger assumed.

V. CONCLUSIONS

In this paper we presented a new method formitigating interference in aeronautical telemetrysystems using ARTM tier-1 waveforms with FQPSKand SOQPSK modulation. The proposed methoduses a linear filter which has been used for channelequalization for high-speed communication systems,and which is obtained by applying Kalman filteringtechniques. The use of this Kalman-based equalizerfilter improves BER performance in the presenceof both MPI and ACI and does not require

1628 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 43, NO. 4 OCTOBER 2007

Fig. 6. BER performance for SOQPSK with MPI and 2 ACIsignals with carrier spacing 1.

Fig. 7. BER performance for SOQPSK with MPI and 2 ACIsignals with carrier spacing 0.7.

separate processing to equalize the channel andremove ACI.

ACKNOWLEDGMENTS

The authors are grateful to the anonymousreviewers and to the Editor, Dr. Peter Willett, for theirconstructive comments on the paper.

OTILIA POPESCUMOHAMMAD SAQUIBDept. of Electrical EngineeringUniversity of Texas at Dallas2601 N. Floyd Rd.Richardson, TX 75083-0688

DIMITRIE C. POPESCUDept. of Electrical and Computer EngineeringOld Dominion University231 Kaufman HallNorfolk, VA 23529E-mail: (dimitrie.popescu@ieee.org)

MICHAEL D. RICEDept. of Electrical and Computer EngineeringBrigham Young UniversityProvo, UT 84602

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[18] Gu, Y., Tang, K., and Cui, H.Sufficient condition for tap-length gradient adaptation ofLMS algorithm.In Proceedings of the 2004 IEEE InternationalConference on Acoustics, Speech, and Signal Processing(ICASSP 2004), vol. II, Montreal, Canada, May 2004,II.461—II.464.

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1630 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 43, NO. 4 OCTOBER 2007