J. Salmi and A. F. Molisch, “Propagation parameter estimation

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 11, NOVEMBER 2011 4257

Propagation Parameter Estimation, Modeling andMeasurements for Ultrawideband MIMO Radar

Jussi Salmi, Member, IEEE, and Andreas F. Molisch, Fellow, IEEE

Abstract—Ultrawideband (UWB) radar is a promising methodfor reliable remote monitoring of vital signs. The use of multipleantennas at transmitter and receiver (MIMO) allows not onlyimproved reliability, but also better accuracy in localization andtracking of humans and their various types of movement. Thispaper describes an experimental demonstration of localizing atest subject and tracking his breathing under ideal conditions.The UWB MIMO channel, which includes the test subject aswell as other objects, is modeled as a superposition of multipathcomponents (MPCs). From the measured data one can extract theparameters of the MPCs, including their directions and delays,which allows localization of the test subject as well as trackingthe breathing motion. Since the breathing pattern of the testsubject induces delay variations of the diaphragm-reected MPCthat are much smaller than the Fourier resolution limits, thehigh-resolution RIMAX algorithm (iterative maximum-likelihoodestimation scheme) is employed together with a path detectionscheme for determining and tracking the MPC parameters.Furthermore, it is illustrated that with a wideband array model,the requirements for antenna spacing are not as limited as forconventional narrowband array processing. Through controlledexperiments with a vector network analyzer and a virtual antennaarray observing both an articial “breathing” object as well as ahuman subject, it is shown that one can accurately estimate thesmall scale movement from human respiratory activity. This isachieved both for line-of-sight between transmitter, receiver, andobjects, as well as for non-line-of sight.

Index Terms—Array signal processing, multipath channels, pa-rameter estimation, position measurement, propagation measure-ments, ultrawideband antennas, ultrawideband radar, virtual an-tenna array.

I. INTRODUCTION

A S LIFE expectancy increases, the range of diseases thatcan be treated expands and tasks like care of the elderly

are becoming increasingly important. While medical advance-ments have dramatically improved the quality of care, the costof providing care has also signicantly increased. Dramatic re-duction in costs can be achieved by exploiting information tech-

Manuscript received December 09, 2010; revised March 15, 2011; acceptedApril 07, 2011. Date of publication August 12, 2011; date of current versionNovember 02, 2011. Part of this work was presented at the Asilomar Conferenceon Signals, Systems, and Computers 2010. This research was supported in partby the Academy of Finland. The work of J. Salmi was supported by the FinnishTechnology Promotion Foundation (TES) and the Walter Ahlström Foundation.J. Salmi was with the Department of Electrical Engineering, University of

Southern California, Los Angeles, CA. He is now with the Aalto UniversitySchool of Electrical Engineering, SMARADCoE, Espoo, Finland (e-mail: jussi.salmi@aalto.).A. F. Molisch is with the Department of Electrical Engineering, University of

Southern California, Los Angeles, CA 90089 USA (e-mail: [email protected]).Color versions of one or more of the gures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identier 10.1109/TAP.2011.2164214

nology, new sensing mechanisms, and automated data collec-tion. A particularly promising area is the continuous or quasi-continuous sensing of vital health signs, i.e., parameters that areindicative of a person’s health, such as breathing activity.While body-mounted sensors can provide these data with

great reliability, there are many situations where the inconve-nience of having to constantly wear such sensors renders itimpractical. Therefore, remote monitoring is highly desirable.Various methods for remote breathing monitoring have beenstudied at least since 1975, when [1] demonstrated the obser-vation of phase shifts of microwave chirp signals reected offthe chest of a rabbit. Relatively narrowband Doppler radars(see, e.g., [2], [3] and references therein) are by far the mostpopular method, as they require relatively small hardwareeffort. However, their drawback is that they do not allow thelocalization of the target; this also leads to increased dif-culty in separating multiple breathing objects and suppressinginterference. Further improvement can be achieved by usingmultiple antenna elements at transmitter and/or receiver. Forthe conventional Doppler radar case, [4] and [5] demonstratedthe ability to resolve multiple sources.Further performance improvements can be achieved by ul-

trawideband (UWB) radar. UWB provides high delay resolu-tion, and thus has the ability to determine the range to eitheractive or passive reectors with high accuracy [6], [7]. This al-lows to more accurately localize the breathing subject [8] andtrack the small movements of the diaphragm during breathing.A number of recent papers have provided system designs and/orexperimental results, such as [9]–[12]. These papers use a singletransmit and single receive antenna, usually a horn antenna thatis pointed towards the target. This is useful in controlled sce-narios where the location of the test subject is known.In this paper we investigate a scenario were the location of

the subject is not predetermined, but nding it is one of thegoals of the measurement. This can be achieved by combiningUWB signalling (providing high range resolution) with thedirectional resolution capability of multiple antenna elements.The underlying theoretical framework formulates a widebandantenna array model and employs the double-directional radiopropagation channel model [13] to characterize the UWBchannel as a superposition of plane waves (multipath compo-nents, MPCs). The characteristics of the MPCs form the basisfor the subject localization and the tracking of the breathing.We rst establish the model in a general form, applicable toarbitrary antenna array congurations and supporting alsopolarization aspects. We then give an example of a reducedmodel, applicable to the employed measurement setup. Thepaper also discusses modeling of wideband antenna arrays,along with a description of a virtual array model. The virtual

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4258 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 11, NOVEMBER 2011

array is similar to synthetic aperture radar (SAR), employedrecently in through-the-wall imaging, see e.g., [14], [15]. How-ever, the virtual array differs from SAR imaging by relying onthe MPC model, which describes the radio channel as planewaves observed at a single point in space, namely the arrayphase center. This also limits the total size of the array, as theMPC should originate in the far eld of the array.The processing of the measurement data requires the decom-

position of the observed channel response into a superpositionof MPCs. For this purpose, we formulate a Maximum Likeli-hood (ML) based path detection framework, and jointly estimatethe MPCs using a modication of the RIMAX [16] algorithm.This approach allows to overcome the Fourier limit of the delayresolution, which in our case is about 5 cm and thus insufcientfor identication of the movement from breathing.The multi-antenna, UWB impulse responses are measured

by a vector network analyzer (VNA) combined with a vir-tual antenna array. This approach does not provide real-timecapabilities, and would have to be replaced by a faster ex-citation combined with real or switched antenna arrays foran actual deployment. However, it is eminently suitable fora proof-of-concept, and shows advantages due to better cal-ibration of the underlying signals. For the same reason, thisapproach for measuring MIMO-UWB channels is in generaluse for channel sounding [17], although real-time imple-mentations exist as well [18]. We show experimental results,both line-of-sight (LOS) and non-line-of-sight (NLOS), fromanechoic chamber measurement for detecting small scale

movement of both a passive, articial target, aswell as a human holding his breath with empty and full lungs,respectively. This information, together with the estimates ofthe absolute delays and angles of the corresponding MPCs, canbe further utilized for passive localization and surveillance ofhumans or animals. Part of this work was presented in [19],where the discussion was limited to LOS measurement of anarticial object.The paper is structured as follows. Section II introduces the

system model, including virtual antenna array model and thedouble directional MPC model. Section III describes the ex-periments conducted in an anechoic chamber. Section IV intro-duces the parameter estimation framework, that is applicable tothe performed measurements. Section V illustrates the resultsfrom the measurements and concluding remarks are given inSection VI.The following notational conventions are used throughout the

paper.• Boldface upper case letters (Roman or Greek ) denotematrices and lower case denote column vectors. Cal-ligraphic uppercase letters denote higher dimensionaltensors.

• The vector denotes the th column of a matrixand the scalar denotes the th element of a

vector .• Non-boldface upper case letters denote constants, andlower case denote scalar variables.

• Superscripts , and denote matrix transpose, and Her-mitian (complex conjugate) transpose, respectively.

• Operator denotes Khatri-Rao (column-wise Kronecker)product.

Fig. 1. MIMO channel modeling concept. (a) The channel tensor is de-ned as the transfer function between all the Tx/Rx antenna port pairs. (b) Theparameters of the double directional propagation path model are dened w.r.t.two points in space, namely the array phase centers.

• Symbol denotes an estimate of the vector .• Operation stacks all the elements of the input tensorinto a column vector.

• Operation transforms a given entity, typi-

cally a vector, into an -dimensional tensor, see also [20].• Operation permutes the order of tensor dimen-

sions, e.g., , see also [20].

II. SYSTEM MODEL

The considered system is based on measuring and charac-terizing the UWB radio propagation channel between two an-tenna arrays, one transmitting and the other receiving

. Measurements provide the transfer function betweenall Tx/Rx antenna port pairs, as illustrated in Fig. 1(a). However,the double-directional propagation channel model, illustrated inFig. 1(b), is dened between two points in space, namely thearray phase centers. Hence, the complete channel model is com-prised of two main components: i) The mapping of the MPCsonto the antenna ports, i.e., the antenna array model, and ii) thedouble-directional radio wave propagation model. In the fol-lowing description it is further assumed that the MPCs of in-terest interact in the far eld of the antenna arrays, i.e., the indi-vidual paths can be modeled as plane waves.

A. Antenna Array Model

The antenna array model describes the angular and frequencydependency of the array transfer function. The transfer functionof a Tx/Rx antenna array with ports, sampled at xedfrequency points, angles, and for the (horizontal) or (ver-tical) orthogonal polarization component for a far eld planewave signal, is dened as a three dimensional complex-valuedtensor

(1)

SALMI AND MOLISCH: PROPAGATION PARAMETER ESTIMATION, MODELING AND MEASUREMENTS FOR ULTRAWIDEBAND MIMO RADAR 4259

The two vectors andcontain angles for azimuth and eleva-

tion, respectively. The antenna array description (1) can beobtained, e.g., through a calibration measurement, wherethe whole antenna array is rotated w.r.t. a dened referencepoint, and the frequency response of each antenna elementis measured for a sufcient number of angles. Interpolationto an arbitrary angle can be achieved, e.g., through a Fourierseries representation, such as Effective Aperture DistributionFunction (EADF) [21], [22]. The EADF also provides efcientmeans to obtain the derivatives, required by the estimationalgorithm described in Section IV.For the experiments in this paper, a virtual antenna array is

employed. A virtual array is formed by moving a single antennasuch that its different positions form an array. This method notonly reduces the hardware requirements, but also has the addedbenet of being free frommutual coupling effects; on the down-side, the channel to be measured by the array has to stay staticfor the duration that is required to move the antenna to all itspositions. The model (1) for the virtual array can be constructedby rst obtaining the angular-frequency response for the singleantenna , dened at the origin of the coordinatesystem. The response of the th virtual antenna element, havinga position vector , and a rotation , isgiven by

(2)

where isthe unit vector in the direction , . Note that the frequencydependency in (2) results both from the directional frequencyresponse of a single antenna, as well as the phase evolution atdifferent frequencies according to the antenna’s position in thearray.

B. Double Directional Propagation Path ModelA realization of the multidimensional UWB MIMO channel

tensor is dened as the frequency domaintransfer function of the channel between each MIMO antennapair measured at the antenna feeds, see Fig. 1. The propagationbetween the two antenna arrays is described as a superpositionof discrete MPCs . The model for a singlepath is illustrated in Fig. 1(b) and is given by

(3)

where denotes Khatri-Rao (column-wise Kronecker) product,is a matrix slice of (1)

for a single direction (that of path ), and isthe frequency response (phase shifts) resulting from the delay. The variable denotes the complex path weight of the

polarization component. Note thatfor free space propagation, as well as reections from materialssuch as large metallic surfaces, the phase shift and attenuationfrom the propagation channel (excluding the antennas) can be

TABLE IMEASUREMENT PARAMETERS

considered frequency independent. However, for more complexpropagation mechanisms, a frequency dependent path weightmodel may be required [17]; this is not taken into accountin the remainder of the paper. Possible effects of neglectingfrequency-dependent propagation would be the occurrenceof “ghost components”. The wideband path model (3) differsfrom the well know narrowband model, see e.g., [23], in thatthe antenna array responses are frequency dependent. Hence,the response of a single path is no longer an outer product (orKronecker product) of the steering vectors of the individualsampling apertures.The superposition of the MPCs (3) can be expressed as

(4)

where and

contain the re-sponses for paths, and

, where denotes the number of polarization co-efcients (here ).

III. EXPERIMENTAL SETUPThe experiment aims at a reproducible measurement of a

UWB channel in an environment with a breathing human. Themeasurement was performed using a Vector Network Analyzer(VNA) and a virtual antenna array, i.e., a single antenna wasmoved using a high precision positioner. The VNA was cal-ibrated to the antenna feed points, and a stepped frequencysweep was conducted for 801 points on the 2–8 GHz frequencyrange, see Table I. These measurements are time consuming,and can not be used for real time measurement of a humansubject. They serve only as a proof-of-principle; real-timemeasurements could be performed with real arrays, excited byshort large-bandwidth signals, such as chirps or impulses.Two types of measurements were performed. In the rst ones,

an object that reects similar amount of RF radiation as a humanwas positioned in a controlled manner, imitating the movementof the chest while breathing. Another measurement was per-formedwith a human subject, whowas holding his breath duringinhale/exhale periods for the duration of each VNA frequencysweep at each antenna position. Before each measurement, areference measurement was taken without the object of interestinside the chamber to facilitate background removal in the post-processing of the data, discussed in Section IV.


Fig. 2. (a) Antennas used in the measurements, along with the magnitudes (indB) of their (V-polarized) angular frequency responses for (b) UWB horn an-tenna, and (c) UWB planar monopole antenna.

A. UWB Antennas and the Virtual ArrayThe antennas used in the measurements are custom built

UWB antennas [24], [25], shown in Fig. 2(a). The frequencyresponse of the antennas as a function of azimuth angle (ele-vation xed to horizontal plane) are obtained by a calibrationmeasurement, and the magnitudes in the range 0.05–16 GHzare shown in Fig. 2(b) and (c). The color scale can be inter-preted directly as magnitude (attenuation in dB) of the complextransfer function of the antenna for a far eld plane wave. Theplanar monopole antenna1 is preferred over the UWB horn [25]due to its omnidirectional beampattern for situations wherethe location of the object is not known a priori. However,the frequency range where the omnidirectionality applies islimited to approximately 2.2–7.3 GHz. In the measurements,different combinations of these antennas were used based ontheir suitability and availability.Fig. 3 illustrates the ambiguity function of a virtual 10-ele-

ment uniform linear antenna array (ULA-10) with1The planar monopole antenna follows the design of solution A, listed in [24,

Table I].

antenna spacing, using the planar monopole antenna at 2.2–7.3GHz. The ambiguity function is dened as

(5)

where is dened as in (1), and reduces to anarrowband steering vector for a single fre-quency. Fig. 3 compares the ambiguity of the wideband modelto the narrowband ones at lowest and highest frequency. It canbe observed that the wideband array steering vectors do notsuffer from angular ambiguity, or grating lobes, which occur fornarrowband steering vectors should the antenna spacing exceed

, see e.g., the plot at 7.3 GHz where . This stemsfrom the fact that the grating lobes for different frequenciesoccur at different angles. Hence their inuence is effectively re-duced using the wideband modeling. Furthermore, the angularresolution, i.e., the width of the main lobe is much narrower forthe wideband case than the lowest frequency alone. It should bementioned that one can achieve acceptable wideband ambiguityproperties even with signicantly smaller number of antennas.However, such analysis is outside the scope of this paper. Fordiscussion on ultrawideband arrays, see e.g., [26], [27].

B. Measurement With Articial “Breathing” ObjectThe measurement setup is summarized in Table I, and illus-

trated in Fig. 4. Two linear positioners, one for the uniformlinear antenna array (ULA) and one for the breathing object,were placed inside the anechoic chamber at UltRa Lab [28]. Thepositions of the Rx antenna and the object, as well as the fre-quency sweep of the VNA, were controlled by a Labview scripton a PC.Fig. 4(a) shows the approximate layout of the anechoic

chamber. Two static scatterers (metallic poles) were placedin the chamber to create (controlled) multipath propagation.The Rx array positioner was sequentially placed in eachcorner of the chamber, and each measurement was repeatedin non-line-of-sight (NLOS) conditions by blocking theline-of-sight (LOS) between the Tx and the object using ametallic bookshelf. LOS measurements were conducted usingUWB horn antennas, whereas NLOS measurements were per-formed with UWB planar antennas. In this paper results fromRx1 position only, corresponding to Fig. 4, are reported. Thepath lengths and angles based on the measured center points ofthe interacting objects are listed in Table II.Before the actual measurement, a test measurement was per-

formed in order to nd a suitable object to be used in the mea-surement to replace a human. Fig. 5 illustrates the test resultsby comparing the signal level reected from different objects.Based on this test, a setup with two basketballs covered by alu-minum foil was chosen as the “breathing” object.

C. Measurement With a Human SubjectThe measurement with a human subject was limited to one

Rx array location (same 10-element ULA), and two “object”positions, namely “inhale” and “exhale”. The test person wassitting inside the chamber in a comfortable chair, see Fig. 6.At each virtual antenna array position, two measurements weretaken, one for inhale and one for exhale. The person indicated


Fig. 3. Ambiguity function of a ULA-10 UWB (2.2–7.3 GHz) antenna array model compared to narrowband model at 2.2 GHZ and 7.3 GHz.

Fig. 4. (a) Measurement setup inside the anechoic chamber. (b) The breathingobject and two scattering poles. (c) View from the opposite door.

his hold of breath, either with empty lungs, or lungs full of air,using a thumb operated light switch. Otherwise, he was im-mobile during the approximately 10 minute measurement. Themeasurement was repeated in NLOS conditions, while blockingthe direct path between Tx and the person using a metallic book-shelf. In addition, each measurement was repeated so that theperson had an aluminium foil wrapped around the chest. Thisfacilitates the identication of the specic MPC, which corre-sponds to the reection from the chest.

TABLE IIPOTENTIAL SIGNAL ROUTES FOR RX1 POSITION IN THE ANECHOIC CHAMBER,

SEE FIG. 4(a). S1 AND S2 REFER TO THE SCATTERERS, ANDB (BALL) DENOTES THE OBJECT

Fig. 5. Comparison of measured magnitude of the impulse response at1.6–3 GHz from different types of objects: a human, one or two aluminiumfoil covered basketballs, and a small dummy. Two balls have the closestresemblance to that of human in terms of reected signal level.

Fig. 6. Chair on which the person was sitting inside the chamber. Holding thebreath was indicated by a light switch, attached on the armrest.


IV. PARAMETER ESTIMATION

A. Reduced Measurement ModelFor brevity, we describe the estimation methods w.r.t. a re-

duced measurement model, namely the one supporting the mea-surement setup described in Section III. The difference to thefull model (4) is in that a (virtual) -polarized2 antenna arraywas employed at Rx only, whereas a single, -polarized antennawas used as a transmitter. In addition, the employed virtual arraywas a uniform linear array, and hence the angular modeling islimited to the azimuthal plane. It is assumed that these assump-tions do not signicantly deteriorate the system performance inthe studied anechoic chamber environment, however, this as-sumption does not hold in general, see e.g., [22] for a discus-sion. With these assumptions, the model for a single MPC re-duces from (3) to

(6)

and the superposition of paths can be written as

(7)

where . The pa-rameter vector for paths and parameters can be denedas

(8)

where the complex path weight is reparameterized into tworeal valued parameters and as . A single snapshotof the measured channel realization is modeled as

(9)

where is complex, circular symmetric whiteGaussian measurement noise.

B. Background RemovalAs we are only interested in estimating the inuence of

moving a specic object in the environment, we perform thefollowing background removal from the measured channelfrequency responses. Before the actual measurement, a refer-ence channel is measured for all antennapositions, with the object or person of interest not being insidethe chamber. The MPC parameter estimation is then conductedfor a data set obtained by

(10)

where the reference channel is subtracted from the mea-sured channel frequency response . Ideally, all remaining, sig-nicant components in the channel should result from interac-tion with the scattering object; note that this interaction can2The term V-polarized is used to highlight that the polarization alignment of

the antennas was close to vertical.

either create new MPCs, or block or attenuate existing ones.Hence, it is assumed that , where denotes theMPCs resulting from the interaction with the object. From (10),the delays and azimuth angles along with correspondingpath weights are estimated for a number of paths.

C. Path DetectionThe initialization of the parameter estimation is performed

using a successive cancellation type of grid search, where thedetection of paths is based on single path maximum likelihood(ML) criterion. The approach is similar to [29], generalized forthe wideband antenna array model (2). Typically, this initializa-tion is performed for a larger number of paths at the rst snap-shot, and for a few new paths at each snapshot. The objective ofthe ML is to maximize the likelihood function

(11)

Consequently, taking the logarithm of (11) and maximizing itw.r.t yields

(12)

As the path weights are linear in (7), their best linear unbiasedestimate can be expressed as

(13)

where in (7). Inserting (13) in (12) yields aftersome manipulation

(14)Evaluating (14) for a single path, and assuming the non-polari-metric wideband path model (6), the ML criterion reduces to

(15)

where . A new path es-timate is obtained as the set of parameters maximizing (15),and then solving for (13). The inuence of this path can be sub-tracted from the data as , and the procedure maybe repeated to detect more paths. It is also possible to optimizethe already obtained path estimates jointly between detections,using the algorithm outlined in Section V.Equation (15) can also be interpreted as a matched lter, or a

generalized beamformer, and the objective is to nd the param-eters that maximize the correlation with the measurement.Note that by setting , (15) can also be interpreted asthe multidimensional power prole of the propagation channel.This has been used for the illustrations in Section V. An exampleof a computationally efcient implementation of a grid searchover the parameters and for evaluating (15) is outlined inthe Appendix.


D. Parameter OptimizationThe initialization of the path estimates is based on a subop-

timal strategy of successive detection and cancellation using ofthe ML criterion for a single-path only (15). Therefore, it is nec-essary to perform joint optimization of the estimates. It can beshown that nding the joint ML estimate of the parameters in(8) equals

(16)

No closed form solution exist for this nonlinear least squaresoptimization problem, so we resort to an iterative optimiza-tion technique, namely the Levenberg-Marquardt method [30],which is also used for a narrowband signal model in the RIMAXalgorithm [16]. As the algorithm is gradient-based, it requiresthe derivatives of the data model (7) w.r.t. the estimated param-eters (8). Let us dene the Jacobian matrix as , the Scorefunction , and the Fisher Information Matrix as

(17)

(18)

(19)

where denotes the log-likelihood function. The esti-mates are then optimized by iterating

(20)where denotes element-wise matrix product. The step sizetuning parameter can be decreased if the iteration improvedthe t (16), otherwise should be increased, see [16] fordiscussion. Convergence can be evaluated, e.g., by testing if

is smaller than 10% of the Cramér-Rao bound,obtained from the diagonal values of in (19).After convergence, it is possible to either detect more paths

from the residual , or use the current estimates as theinitial values for the next snapshot of data.

V. RESULTS

A. Results With the Object—Los Case

This section describes results from a measurement, wherethe breathing object (two aluminum foil covered basketballs)was moved to eight positions in the range , see Fig. 4.Fig. 7 shows the Power-Angular-Delay Prole (PADP) of themeasurement, evaluated using (15) with and averagedover the eight measured ball positions. Some residual signalcan still be observed after the reference channel cancelation

Fig. 7. (a) Power-Angular-Delay Prole (PADP) of the measurement averagedover the eight snapshots (ball positions). (b) PADP of , see (10), i.e., afterbackground removal. (c) PADP zoomed to the area of interest. White x-marksindicate estimated path components (36 in total). (d) PADP at the direct reec-tion for the eight snapshots.

(10), especially at the LOS between the antennas around pathlengths of less than 2 m, as well as for Scatterer #1 after 4m path length. Fig. 7(c) shows the PADP zoomed at the pathsof interest. Also some of the probable signal routes are iden-tied. The white crosses drawn over the PADP denote the lo-cations of estimated MPCs. When comparing the path lengthsfrom Table II, it should be noted that the basketball has a ra-dius of about 12 cm, and the scattering poles about 3 cm, whichshorten the actual path length compared to measured objectcenter points. In addition, a separate calibration was performedto determine the effect of the signal delay of the pair of UWBhorn antennas to the path length estimate. This calibration re-sulted in an increase by 11 cm compared to the physical distancebetween the antennas.We limit the discussion to evaluating the strongest MPC

resulting from the direct reection from the object. Fig. 7(d)shows the corresponding PADPs for the eight individualsnapshots. The small white crosses denote the position ofthe ML estimate of the strongest MPC. It can be observedthat the sinusoidal movement of the ball is well captured bythe path estimate. Comparing the estimate of the path length

in Fig. 7(d) to the signal routes in Table II, itcan be seen that it matches well with the direct path (route C)with , after compensating

(twice the radius) for the reection on the surface ofthe basketball, and adding due to electric length of theantennas.


Fig. 8. (a) Breathing object displacement, the estimated path length difference of the strongest path , and the mapping of the path weight phase difference(using , with ) into equivalent distance . (b) Estimation error standard deviation for both the delay and the phasemapped on the path length. The estimates are obtained from the inverse of (19), see [16] for discussion.

Fig. 8 illustrates the evolution of the estimated path length dif-ference (or differential delay, ) as well as the pathweight phase difference of the strongest MPCalong with the known relative object displacement . It canbe observed that the relative delays and phases capture well thesinusoidal trend in the true displacement of the object. Note thatalthough the axes are in the same scale (in mm), the inuence ofthe object displacement on the path length depends on the pro-jection of the displacement direction w.r.t. the angle to both thetransmitter and the receiver, i.e., , wheredenotes the speed of light. Note also that the obtained path

length resolution is much higher than , assumede.g., in [10]. In fact, the estimation error standard deviations inFig. 8(b), obtained as the square root of the diagonal values ofthe inverse of the Fisher Information Matrix (19), indicate thatthe estimation error can be expected to be in the order of 1 mm.

B. Results With the Object—NLOS Case

In the NLOS measurement, a metallic bookshelf was placedbetween the Tx antenna and the breathing object. Also, the om-nidirectional UWB planar antennas, see Fig. 2, were employedinstead of the UWB horns. The pair of UWB planar antennaswas determined to have an electric length equivalent to 16 cmincrease in the MPC path length.Fig. 9 shows the zoomed PADP of the NLOS measurement,

comparable to Fig. 7(c) and (d). The strongest component canbe identied to be the one corresponding to route A in Table II,with , while the measured path length for routeA after corrections (diameters of the pole, 0.06 m, and the ball,0.24 m, electric length of the antenna pair, 0.16 m) should havebeen . The5 cm difference may result, e.g., from tilting of the Scatterer #1pole and other uncertainties. However, it can be observed thatthe movement of the object is very well captured by the pathdelay estimate, shown as the white cross at the maximum of thePADP in Fig. 9(b).It should be noted, although not explicitly shown here, that

both for LOS and NLOS cases it is possible to identify severalother MPCS whose parameters capture the sinusoidal trend ofthe object movement. On the other hand, there are also manyMPCs that do not reveal such information, either due to poorangle of reection w.r.t. the direction of movement, or the

Fig. 9. PADPs for the NLOS case. White x-marks indicate estimated path com-ponents. (a) PADP of the overall area of interest averaged over the eight snap-shots. (b) PADP at the strongest component (route A in Table II).

fact that those paths are residual errors from the backgroundremoval. Nevertheless, whenever such a trend is observed, itcould be used in identifying the MPCs interacting with thetarget, and the path parameters could be further utilized fortarget localization.

C. Results With a Human TargetFig. 10 shows the PADP of the measurement with the human

target before (Fig. 10(a)) and after (Fig. 10(b)) backgroundremoval. The measurement setup was improved (comparedto measurements in Sections V-A and V-B) by stabilizing thecable while the positioner was moving. This results in smallerresidual error after background removal in Fig. 10(b) comparedto Fig. 7(b). Fig. 10(c) and (d) show a comparison of the PADPsand MPC estimates in two separate measurements, where theonly difference is that in Fig. 10(d), an aluminium foil waswrapped around the chest of the test subject. This resulted ina stronger reection, which helps to identify the sources ofthe peaks in the PADPs, as indicated in the gures. Fig. 10(e)illustrates the estimated MPCs in the range of chest and head.It can be observed that, in addition to a path length change ofabout 3 cm (corresponding to about 1.5 cm chest displacement),even a slight angular shift during inhale and exhale periods iscaptured in the MPC estimate (P3), whereas the estimate fromthe head reection MPC (P1) remains more or less constant.


Fig. 10. PADPs of the measured channel for the human target. (a) and (b) areaveraged over the two (inhale and exhale) snapshots and have the same colorscale. (a) is before, and (b) is after background removal. (c) shows the PADPzoomed into the area of interest. (d) is the same as (c), but from a repeatedmeasurement with aluminium foil around the chest. (e) illustrates the estimatedpropagation paths in the range of chest and head for the two snapshots.

Fig. 11 shows the PADP and MPC estimates from the humanmeasurement in NLOS,while ametallic bookshelf was blockingthe LOS between Tx and the test subject. It can be observed thatthe estimated MPC (P2, denoted by green x-mark) of the re-ection from the chest converged to another, weaker, maximumat the second snapshot, and a new path (P21) was detected forthe chest location. The path length difference of the old

to the new estimateis 4 cm, corresponding to a chest displacement of about 2 cm,whereas the head component remains at a constant path length

. It should be noted that in a real system,the sampling rate would be much higher than two samples perbreath cycle; hence, it would be possible to employ a state-space

Fig. 11. PADP of the human target measurement in NLOS conditions.(a) PADP zoomed into the area of interest. (b) Estimated propagation paths inthe range of chest and head for the two snapshots. It can be observed that thechest estimate of the inhale snapshot converged to another maximum, and anew path was detected at the chest position in the exhale snapshot.

model along with sequential estimation technique to track theMPCs over time [29].

VI. CONCLUSIONS

UWB signalling combined with MIMO processing enables aradar having very high delay resolution as well as angular in-formation. This paper presented a study on UWB propagationfor estimating small scale movement such as human respiratoryactivity. A model based on a superposition of MPCs, along witha wideband antenna array model was employed. We showedthat the wideband antenna array model does not suffer fromambiguities, which are present for narrowband signal models,even if the antenna spacing is not strictly less than half a wave-length. Measurements were performed under ideal conditions inan anechoic chamber with a VNA and a virtual antenna array,using both an articial “breathing object” as well as a humansubject. After removal of the static background, the MPCs re-sulting from the interaction with the test objects were estimatedand analyzed. The displacement of the articial object, as wellas the human chest while breathing, were captured non-intru-sively from about 5 m distance. Based on the results, it may bepossible to develop a systemwhere the breathing rate of a personwithin a room could be determined. The information of anglesand delays corresponding to the propagation paths showing suchmovement, possibly also from NLOS paths, and potentially ob-served with multiple receiver units, could be used to determineand track the position of the person(s) in a room. However, ad-ditional effort is required to study the performance of the en-visioned system in realistic SNR conditions obtainable with apractical UWB setup. Further research should also be put on


determining a good trade-off between the signal bandwidth andthe number of antennas.

APPENDIXWIDEBAND DATA TRANSFORMATION

Wideband Data Transformation (WBDT) is a computation-ally efcient solution for evaluating the single path, single po-larization ML criterion (15), e.g., for path detection or powerprole estimation purposes. The idea is to employ the wide-band array responses (steering vectors) of the antenna array(s)to transform the data from the samples collected at the antennafeeds into angular domain, and in the end employing the fre-quency domain steering vectors to transform into delay domain.This can be viewed as transformation from the MIMO channeltensor observed at the antenna ports, see Fig. 1(a), into a sam-pling grid dened by the geometrical parameters, see Fig. 1(b).For simplicity, we limit the discussion here to the reduced datamodel (7), i.e., Rx array only.The approach proceeds as follows, let us have a measurement

(or residual) vector (10) in matrix form as

(21)

as well as the wideband response functions

(22)

(23)

for frequency domain with delay detection points, and Rxarray with angular detection points, respectively. Further-more, let as dene the following transformation matrices

and as

(24)

(25)

where is the matrix slice of thetensor (23) and is the column ofthe matrix (22).The data tensor is then transformed (ltered) from the mea-

surement data to the parameter domain as follows.1) First, is transformed from Rx array domainto Rx angular domain to obtain as

(26)

where denotes an vector of all ones (usedhere to sum over antenna elements).

2) Then, is transformed from frequency domain todelay domain as

(27)

3) The matrix of detection values, or the power prole of thechannel, whose elements are equivalent to (15), is obtainedby

(28)

where denotes the element-wise product.

ACKNOWLEDGMENT

The authors would like to acknowledge the efforts of Dr. X.Yang, S. Sangodoyin, and J. Shen in helping to conduct themeasurements, as well as thank Dr. S.H. Chang for helping toset up the experiments, and Prof. H. Hashemi for many fruitfuldiscussions. Dr. T. Lewis is also acknowledged for designingand manufacturing the UWB horn antennas, and L. Baumgartelfor manufacturing the UWB planar antennas. The rst authorwould like to thank the Academy of Finland, the Finnish Tech-nology Promotion Foundation, and the Walther Ahlström Foun-dation for their nancial support.

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Jussi Salmi (S’05–M’09) was born in Finland in1981. He received the M.Sc. and D.Sc. degrees, bothwith honors, from Helsinki University of Technology(HUT), Finland, in 2005 and 2009, respectively.In 2009–2010 he worked as a Postdoctoral Re-

search Associate in the Department of ElectricalEngineering, University of Southern California, LosAngeles, CA. Currently, he works as a Postdoctoralresearcher in the Department of Signal Processingand Acoustics, Aalto University School of ElectricalEngineering (former HUT), Finland. His current

research interests include RF-based vital sign detection, UWB MIMO radar,indoor positioning, measurement based MIMO channel modeling, and param-eter estimation. He is the author of over 30 research papers in internationaljournals and conferences.Dr. Salmi received the Best Student Paper Award in EUSIPCO’06, and co-au-

thored a paper receiving the Best Paper Award in Propagation in EuCAP’06.

Andreas F. Molisch (S’89–M’95–SM’00–F’05) re-ceived the Dipl. Ing., Dr. techn., and habilitation de-grees from the Technical University Vienna, Austria,in 1990, 1994, and 1999, respectively.From 1991 to 2000, he was with the TU Vienna,

becoming an Associate Professor there in 1999.From 2000 to 2002, he was with the WirelessSystems Research Department at AT&T (Bell)Laboratories Research, Middletown, NJ. From 2002to 2008, he was with Mitsubishi Electric ResearchLabs, Cambridge, MA, most recently as Distin-

guished Member of Technical Staff and Chief Wireless Standards Architect.Concurrently, he was also Professor and Chairholder for radio systems at LundUniversity, Sweden. Since 2009, he has been Professor of electrical engineeringat the University of Southern California, Los Angeles, CA, where he headsthe Wireless Devices and Systems (WiDeS) group. He has done researchin the areas of SAW lters, radiative transfer in atomic vapors, atomic linelters, smart antennas, and wideband systems. His current research interestsare measurement and modeling of mobile radio channels, UWB, cooperativecommunications, and MIMO systems. He has authored, co-authored, or editedfour books (among them the textbook Wireless Communications, Wiley-IEEEPress), 11 book chapters, some 130 journal papers, and numerous conferencecontributions, as well as more than 70 patents and 60 standards contributions.Dr. Molisch is Area Editor for Antennas and Propagation of the IEEE

TRANSACTIONS ON WIRELESS COMMUNICATIONS and has been co-editor ofspecial issues of several journals. He has been General Chair, TPC Chair,or Track/Symposium Chair of numerous international conferences. He waschairman of the COST 273 working group on MIMO channels, the IEEE802.15.4a channel model standardization group, Commission C (signals andsystems) of URSI (International Union of Radio Scientists, 2005–2008), andthe Radio Communications Committee of the IEEE Communications Society(2009–2010). He has received numerous awards, most recently the JamesEvans Avant-Garde Award of the IEEE VT Society and the Donald Fink Awardof the IEEE. Dr. Molisch is a Fellow of the IEEE, Fellow of the IET, and anIEEE Distinguished Lecturer.

Documents

J. Salmi and A. F. Molisch, “Propagation parameter estimation