Optimal System Design Considerations For The Ultra-Wideband . - MIT
Optimal System Design Considerations for theUltra-Wideband Multipath ChannelWasim Q. Malik, David J. Edwards, and Christopher J. StevensDepartment of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, U.K.Email: {wasim.malik, david.edwards, christopher.stevens}@eng.ox.ac.ukTel: 44 1865 283040Abstract—Multipath propagation in the indoor ultra-widebandchannel is investigated using experimental techniques. Thedependence of multipath statistics on bandwidth and centrefrequency is established, and it is shown that the multipathbehavior in different sub-bands is non-uniform. The multipathdegrees of freedom and relative power gains are calculated. Thesmall-scale variation in the number of multipaths over an area ischaracterized, and stationary wave patterns with wavelengthrelated to signal bandwidth are reported. In the light of thesefindings, optimal design parameters for rake and antennadiversity systems are presented.Keywords- Indoor channel; multipath; rake; small-scale fading,ultra-wideband (UWB).I.INTRODUCTIONUltra-wideband (UWB) communications systems aredefined by their large absolute or fractional bandwidths, aconsequence of which is high multipath resolution capability[1, 2]. Thus a majority of the incident multipaths are resolvedin a typical indoor UWB channel, depending on thepropagation environment, system bandwidth and receiversensitivity [3]. A full-band UWB system occupying a 7.5 GHzwide spectrum can resolve differential multipath delays of upto about 0.1 ns, or differential pathlengths of 4 cm. As aconsequence of such high resolution, the fading and dispersionproperties of the channel differ greatly from those ofnarrowband channels [4].Practical system components such as antennas and filters donot provide a perfectly flat response over a very wide range offrequencies [5, 6]. Various wave propagation modes, such asscattering, diffraction and material penetration, also depend onfrequency. This renders the multipath characteristics of thechannel sensitive to bandwidth and frequency. Such spectrallynon-uniform behavior can severely degrade the performance ofboth single- and multi-band UWB systems unless characterizedand modeled appropriately.The multipath effect leads to spatial small-scale fading inthe time-stationary indoor channel [7]. Due to this fading, asmall movement of a UWB receiver can cause the receivedpower to vary by 5-6 dB [8]. While this is much lower than thedeep fades observed in narrowband channels, it is neverthelesssignificant for the severely power-constrained UWB systems.This power fluctuation is directly related to the multipath0-7803-9152-7/05/ 20.00 2005 IEEE2622arrivals at a given location and their variation withdisplacement. The analysis of multipath properties over a shortrange therefore provides an insight into the small-scale fadingexperienced by a receiver.Antenna diversity can be used effectively to reduce fadingand extend the coverage range of a UWB communicationssystem [9-11]. The optimal MIMO antenna separation and theconsequent improvement in link quality depends, among otherfactors, on the system bandwidth, operating frequency, andmultipath. This raises questions about the impact of widebandwidth on the design and performance of antenna arraysystems. Similarly, the SNR gain of a rake receiver depends onthe number of incident and resolved multipaths, their amplitudedistributions and mutual independence [12]. These are in turndetermined by the multipath environment and bandwidth,which therefore have a strong impact on the performance ofthese specialized receivers.This paper addresses the problem of optimal UWBcommunications system design for dense multipath channels.The dependence of multipath resolution on bandwidth andcentre frequency is evaluated. The achievable multipathdiversity gain, and the complexity of a receiver required toachieve it, is estimated using information theoretic criteria. Thevariation of the number of received multipaths over a planararea is investigated in order to determine the antenna spacingfor a multiple-antenna receiver.II.CHANNEL MEASUREMENT AND PROCESSINGThe analysis in this paper is based on experimental resultsobtained from complex frequency-domain channel sounding inthe UWB band (3.1–10.6 GHz). A computer-controlled vectornetwork analyzer (VNA) system was used for this purpose in atypical office environment, as shown in Fig. 1. The distancebetween the transmitting antenna and the centre of the grid was4.5 m, and the antennas were at a height of 1.5 m. Both line-ofsight (LOS) and non-line-of-sight (NLOS) scenarios weremeasured. A large grounded aluminum sheet was placedbetween the transmitter and receiver to create the blockage forNLOS. A planar grid arrangement with an automatedpositioner for the receiving antenna scanned a 1 m2 area with a0.01 m resolution. Omni-directional, vertically polarizeddiscone antennas were used at each end of the link. A lownoise amplifier with 30 dB gain was connected to the receiving
LOSTxAntennaWoodenBenchVNANorm. power, dB0ComputerBlockingScreen (NLOS) 10 20 30x10204030Multipath indexNLOS50607010203040Multipath index506070yNorm. power, dB0RxAntennaGridMetallicCabinetsDoorFigure 2. Average multipath profiles for LOS and NLOS channels normalizedto the peak mean multipath powerantenna. The cables, connectors and amplifier were calibratedto remove frequency-dependent phase distortion andattenuation. A total of 20,000 channel responses were thusmeasured.The complex transfer function obtained at each grid point(x, y) was converted to the channel impulse response throughthe inverse Fourier transform to obtainK ax, y ,k ejϕ x , y ,kk 1δτ ,τ x , y ,k ,(1)where a and φ represent the magnitude and phase response atthe kth time-bin, and τ represents time delay with reference tothe first multipath arrival. This was thresholded to 25 dBbelow the peak power level and squared to obtain the powerdelay profile (PDP). For each measured PDP, a local peakdetection algorithm was used to resolve the multipaths andobtain the multipath profileLmx , y , l α x , y ,l el 1jϕ x , y ,lδτ ,τx , y ,l(2)where l is the time-bin where a multipath is detected, L is thetotal number of multipaths in the PDP, and 2 K 2 ak (3) k 1 is the multipath magnitude with power-normalization toremove pathloss. The average PDP, obtained from a largenumber of measured or simulated channel impulse responses,is often used to represent the multipath behavior of a channel.An alternative representation used here is the average multipathprofile, which is the ensemble mean of the multipath powers inthe order of times-of-arrival, i.e.,α a 20 30Figure 1. Indoor UWB channel measurement system with a vector networkanalyzer and a positioning gridh x, y ,τ 10n ,n1 x yml (4) mx, y ,l ,nx n y x , y 1where l is the multipath index and nx ny 100 is the numberof measurement points in each direction for our positioninggrid. Fig. 2 shows ml for the LOS and NLOS indoor UWB2623channels, normalized with respect to the global peak signallevel max {ml } , for L 70. The first path in LOS is muchlstronger than that in NLOS because of the presence of theobstruction in the latter. The first cluster in the LOS appears tobe missing in the NLOS profile, but the rest of the clusters andrays appear to be largely unaffected from the NLOS blockageand appear in nearly the same order as expected. Multipathclustering can be observed in both scenarios.Also, from our measurement, the direct path is not alwaysthe strongest path in the LOS profile, and indeed the 13thmultipath in Fig. 2(top) has the highest power, which becomesthe 8th path in NLOS, as in Fig. 2(bottom). This observationindicates that the multipath arrivals are not always temporallyorthogonal and some degree of multipath overlapping doesindeed take place in the indoor channel even with the fullUWB bandwidth.III. SPECTRAL VARIATIONIt is well known that the time resolution of a system isinversely related to bandwidth B, which suggests that anincrease in B should lead to detection of a higher number ofmultipaths. This behavior is similar to the greater number ofresonant modes observed in a cavity when a widebandexcitation is applied. Thus the bandwidth is expected tostrongly impact the propagation properties of the channel. Theassumption here is that the system is operating in a densemultipath channel with high multipath incidence, so thatincreasing the temporal resolution continues to result in aproportionate increase in the number of resolved multipaths.This assumption may not necessarily be true for all channelsand UWB bandwidths, and will be assessed in this nsignificantly impact UWB signal propagation. Variouspropagation modes, such as diffraction and materialpenetration, are frequency-dependent. It can therefore beexpected that the multipath characteristics in different subbands within the full channel would be dissimilar.
0.75CDF7550250Number of multipathsLOS10.501234Bandwidth, GHzNLOS56071001750.75502503.1 4.6 GHz4.6 6.1 GHz6.1 7.6 GHz7.6 9.1 GHz9.1 10.6 GHz3.1 10.6 GHz0.25CDFNumber of multipathsLOS100200408060Number of multipathsNLOS1001203.1 4.6 GHz4.6 6.1 GHz6.1 7.6 GHz7.6 9.1 GHz9.1 10.6 GHz3.1 10.6 GHz0.50.2501234Bandwidth, GHz5607Figure 3. Influence of bandwidth on the number of resolved multipaths. Thelines and errorbars indicate the mean and standard deviation020406080Number of multipaths100120Figure 4. Empirical CDFs of the number of multipaths in the full-band UWBchannel and in its five equal sub-bandsA. Variation with BandwidthFrom our experimental analysis, the mean number ofmultipaths L varies approximately linearly with B, as shown inFig. 3, with slopes of 10.85 and 10.98 paths/GHz for LOS andNLOS channels. The errorbars in the figure indicate that thestandard deviation increases with the number of resolvedmultipaths and bandwidth. This information can be used inchoosing the required rake receiver diversity order for singleband or multi-band UWB systems with a given bandwidth. Fora full-band UWB system, a mean of about 85 multipaths areobserved from our measurements, with a 25 dB threshold.B. Sub-Band ComparsionSub-band analysis is performed by dividing the measured7.5 GHz wide frequency band into b 5 equal sub-bands, each1.5 GHz wide. The sub-band transfer functions, zero-padded tokeep the number of samples constant, are then used to obtainthe multipath profiles for the signals contained in those spectralregions. The multipath profiles are thresholded using a 25 dBthreshold below the strongest signal level in the full-bandimpulse response in order to perform a fair comparison. Thenumber of resolved multipaths, L, is used as the test statistic.The cumulative distribution functions (CDFs) of Li, i 1, ,b, for each sub-band are shown in Fig. 4. The full-band LCDF is also shown for reference. The full-band L assumes avalue that is generally about five times that of Li, due to thefive-fold bandwidth. Li shows a progressive decrease withincrease in the centre frequency. This can be attributed tofrequency-selective pathloss induced by omni-directionalantennas, which causes the signal in the higher frequencies toundergo greater attenuation and fall below the threshold. Thechannel frequency selectivity due to the propagationenvironment also contributes towards the non-uniformity in Li.Thus the lowest sub-band perceives 20 additional multipaths ascompared to the highest sub-band. This observation establishesthat the sub-band multipath behavior is non-uniform, and thedependence of multipath propagation on both bandwidth and2624centre frequency must be taken into account during UWBchannel modeling.IV. DEGREES OF FREEDOMConsidering that the multipath arrivals can be representedby discrete random variables with finite probabilities, aneffective multipath diversity measure can be obtained in theform of entropy. The entropy H corresponding to the multipathprofile at receiver location (x, y) can be calculated as [13]LH x, y ml 12x , y ,llog Lx , y m 2x , y ,l ,(5)and can be used to derive the effective number of multipaths,or the degrees of freedom, i.e.,HLˆ x, y Lx, xy, y .(6)The CDFs of Lˆx , y for the measured LOS and NLOS channelsare shown in Fig. 5, with mean values of about 27 from ourmeasurement data. This is a high diversity order, and a suitablemultipath combining scheme can use it to reduce the outageprobability significantly. However, the effective multipathdiversity, in terms of the degrees of freedom, is offered by onlya fraction of the resolved multipaths, as shown in Fig. 5. Thepercentage of effective multipaths is calculated asL x, y Lˆ x , y(7) 100.Lx , yOn average, only about 30% of the resolved multipaths meetthis criterion. Depending on the desired performance level ofmultipath diversity combining, this information can be used toobtain the required complexity for a rake order.Also, as the multipath degrees of freedom are, on average,much lower than the number of resolved multipaths, it can beinferred that the multipaths have a finite correlation, and theusual assumption of an uncorrelated scattering channel is onlyapplicable to indoor UWB channels as an approximation.
0101LOSNLOSCDF0.750.250Percentage of power0.5LOSNLOS101203040Effective multipath degrees of freedom50601CDF0.75 110 2100.50.250LOSNLOS010403020Percentage of effective multipaths, %50 31060Figure 5. CDFs of the multipath degrees of freedom (top), and the ratio of thedegrees of freedom to the number of received multipaths in terms of thepercetage derived from each impulse response (bottom)(8)Hwhere (.) denotes the Hermitian transpose. The empiricalcovariance matrix for the measured frequency-selectivechannel is thereforeK x, y 1nx n yL (mx , y ,l mx , y , ll 1) ( m x , y ,l m x , y ,l )H(9)Next, the eigenvalues, λi, of Kx,y are computed and normalizedsuch that λi 1.(10)iThe largest non-trivial eigenvalues can be obtained by using apower sum threshold s, such thatLs λ s,i0 s 1,101520Eigenvalue index2530Figure 6. Mean normalised eigenvalues for the first thirty modes and thepercentage of the total power that they containedV. POWER GAINSThe multipath power gains in a channel determine therelative distribution of power across the multipaths. Thisprovides a measure of the performance of a multipathcombining receiver and predicts the upper bounds on its powercapture capability. The covariance matrix of the channel withmultipath profile mx,y,l is given byK x, y E mx, y ,l mxH, y ,l 5(11)i 1provides an estimate of the number of significant eigenvalues,with the λi in descending order. The threshold s is usually takenas 90% or 98%. The 90% LS for LOS and NLOS are 9 and 13respectively, while the 98% values are 56 and 62 respectively.The mean eigenvalues for some of the most dominant modesare shown in Fig. 6, illustrating the percentage of powercontained in each. Both LOS and NLOS eigenvalues follow anexponential decay with similar decay constants.2625VI. SMALL-SCALE SPATIAL VARIATIONThe evidence of small-scale fading in the UWB channel isprovided by spatial variability analysis. This technique alsooffers an insight into the signal variation resulting from a smallrelocation of the receiver within the coverage area. Suchcharacterization is immensely useful in the assessment ofsystem robustness. We perform this analysis by inspecting thenumber of multipaths L at all locations on the measurementgrid. The results are displayed in the form of planar intensityplots, such that the transmitter is located to the south of thesynthetic aperture array in its far field, as illustrated by Fig. 1.Fig. 7 shows alternating regions of high and low L in aplanar region, forming a standing wave pattern. The horizontalhigh-L lines are aligned with the wavefronts of the direct path,as can be inferred from a comparison with Fig. 1. The lines arepresent in both LOS and NLOS. In the latter, a strong diagonalpattern is also superimposed, which arises from a cornerreflection. This suggests that the pattern is dependent on theroom geometry, the location of the transmitter, and thepresence of the direct path. This pattern is formed due to theLloyd’s mirror phenomenon [14]. The higher contrast in NLOSindicates the greater variation of the number of multipaths atvarious locations. The sharp variation in L implies that the totalreceived power is not constant over an area, and fading ispresent. The standing wave pattern has a 4 cm wavelength,which corresponds well to the signal bandwidth B 7.5 GHz.This pattern can be used to determine the optimal antennaseparation for a two-branch diversity system. In such a system,it would be desirable to place the antennas at such a distancethat at least one of them is in a low fade position at any giventime but with sufficient separation to obtain uncorrelated smallscale fading across the branches. From the interference patternsfor a full-band UWB system, this optimal spacing is equivalentto half a wavelength of the fading standing wave, i.e. about 2cm. Thus this simple analysis shows the feasibility ofcompactly placed diversity antennas in UWB systems. If amulti-band UWB signal with a relatively smaller bandwidth is
(a)(b)Figure 7. Spatial variation of number of received multipaths in a 0.5 m x 0.5 m area for (a) LOS and (b) NLOS scenarios. The transmitter is located to the south ofthe synthetic aperture in the far field. A standing wave pattern with wavelength corresponding to the signal bandwidth is obtainedused, however, this distance will be proportionately larger.Also, the power captured by a rake receiver increases with thenumber of resolved multipaths incident at the receiver,assuming a high diversity order. Thus the performance of arake would also vary with a small movement of the receivingantenna, according to Fig. 7. From the relationship between thebandwidth and the wavelength of these standing waves, it canbe inferred that relatively narrowband systems would havelarger regions with such variations, as suggested in [15].Conversely, with an even wider signal, these interferencefringes would be closer together, so that in the infinitebandwidth limit there would be a spatially uniform distributionof L and no small-scale fading, as is observed with opticalsignals for instance.VII. CONCLUSIONMultipath propagation in indoor ultra-wideband channelshas been characterized experimentally and the implications forefficient system design have been considered. The number ofresolved multipaths, L, is shown to increase linearly withbandwidth with a slope of 11 paths/GHz. In different sub-bandswithin the UWB frequency range, L falls monotonically withincrease in the centre frequency. From our measurement, thereceived multipaths have approximately 27 degrees of freedom– about 30% of the number of resolved multipaths – whichprovides an estimate for the required rake fingers to achievenear-optimal SNR gain in a given multipath channel. Theoptimal antenna separation for diversity systems is found to be2 cm for a full-band UWB system, increasing at lowerbandwidths. Thus UWB systems can use compact diversityarrays to combat small-scale fading. This work provides aframework for the design of channel-optimized UWB systems.REFERENCES[1] M. Z. Win and R. A. Scholtz, "Charaterization of ultra-widebandwireless indoor channels: a communication-theoretic view," IEEE J.Select. Areas Commun., vol. 20, Dec. 2002.2626[2] S. S. Ghassemzadeh, R. Jana, C. W. Rice, W. Turin, and V. Tarokh,"Measurement and modeling of an ultra-wide bandwidth indoorchannel," IEEE Trans. Commun., vol. 52, Oct. 2004.[3] W. Q. Malik, C. J. Stevens, and D. J. Edwards, "Synthetic apertureanalysis of multipath propagation in the ultra-wideband communicationschannel," in Proc. IEEE SPAWC. New York, USA, June 2005.[4] A. F. Molisch, "Ultrawideband propagation channels - theory,measurement, and modeling," IEEE Trans. Veh. Technol., 2005 (inpress).[5] W. Q. Malik, D. J. Edwards, and C. J. Stevens, "Angular-spectralantenna effects in ultra-wideband communications links," IEE Proc.Commun., (in press).[6] W. Q. Malik, D. J. Edwards, and C. J. Stevens, "The impact of physicallayer frontend characteristics on ultra-wideband radio," in Proc. 12th Int.Conf. Telecom. Cape Town, South Africa, May 2005.[7] T. S. Rappaport, Wireless Communications: Principles and Practice,2nd ed: Prentice Hall, Dec. 2001.[8] R. J.-M. Cramer, R. A. Scholtz, and M. Z. Win, "Evaluation of an ultrawide-band propagation channel," IEEE Trans. Antennas Propagat., vol.50, May 2002.[9] W. Q. Malik, M. C. Mtumbuka, D. J. Edwards, and C. J. Stevens,"Performance analysis of ultra-wideband spatial MIMO communicationssystems," in Proc. IST Mobile Comm. Summit. Dresden, Germany, June2005.[10] M. C. Mtumbuka, W. Q. Malik, C. J. Stevens, and D. J. Edwards,"Performance of spatial diversity in ultra-wideband systems," IEE Proc.Commun., (in press).[11] W. Q. Malik, M. C. Mtumbuka, C. J. Stevens, and D. J. Edwards,"Increasing MIMO capacity in ultra-wideband communications throughorthogonal polarizations," in Proc. IEEE SPAWC. New York, USA, June2005.[12] W. Q. Malik, D. J. Edwards, and C. J. Stevens, "Experimental evaluationof Rake receiver performance in a line-of-sight ultra-wideband channel,"in Proc. Joint IEEE UWBST & IWUWBS. Kyoto, Japan, May 2004.[13] F. Patenaude, J. Lodge, and J.-Y. Chouinard, "Eigen analysis of wideband fading channel impulse response," IEEE Trans. Veh. Technol., vol.48, Mar. 1999.[14] E. Hecht and A. Zajac, Optics, 4th ed. London, UK: Addison-Wesley,2001.[15] M. S. Varela, M. G. Sanchez, L. Lukama, and D. J. Edwards, "Spatialdiversity analysis for digital TV systems," IEEE Trans. Broadcast., vol.47, Sept 2001.
band or multi-band UWB systems with a given bandwidth. For a full-band UWB system, a mean of about 85 multipaths are observed from our measurements, with a 25 dB threshold. B. Sub-Band Comparsion Sub-band analysis is performed by dividing the measured 7.5 GHz wide frequency band into b 5 equal sub-bands, each 1.5 GHz wide.
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