How Different are UWB Channels from Conventional Wideband Channels? Ulrich Schuster and Helmut B¨ olcskei ETH Zurich 4 November 2005 UWB for Sensor Networks Workshop, 4 November 2005 1
Modeling Conventional Wireless Wideband Channels • Physical channel is linear • Communication systems use (effectively) band-limited signals ⇒ Effective input-output relation is discrete in time L − 1 � h [ l ] s [ m − l ] + w [ m ] y [ m ] = l =0 • Channels that have several taps h [ l ] are called wideband channels • Taps are modeled as random variables So where exactly is the difference to U WB channels? UWB for Sensor Networks Workshop, 4 November 2005 2
Conventional Wideband Channel Model • L � 20 taps, several MHz bandwidth • Power–delay profile (PDP) E [ | h [ l ] | 2 ] decays exponentially • h [ l ] ∼ CN (0 , σ 2 l ) → Rayleigh fading • h [0] ∼ CN ( µ, σ 2 0 ) → Ricean fading • Taps are statistically independent because the channel is assumed to be discrete-time uncorrelated scattering (US) • Diversity order increases linearly with bandwidth W Some modeling assumptions may be questionable for large bandwidths. UWB for Sensor Networks Workshop, 4 November 2005 3
Two UWB Measurement Campaigns • Common environment: indoor public open space • Measurement band: 2 GHz–5 GHz • Measurement campaign I (MC I)—channel varies over space – static environment – moving antenna at the transmitter (virtual array) – N=90 frequency-domain (VNA) measurements • Measurement campaign II (MC II)—channel varies over time – dynamic environment (people moving) – static antennas – up to N=2722 time-domain (DSO) measurements UWB for Sensor Networks Workshop, 4 November 2005 4
Measurement Environment moving terminals static terminals 0 1 0 2 0 3 0 m transmitter TX array receiver receiver RX NLOS 13 m TX NLOS RX OLOS 21 m TX LOS/OLOS 20 m RX LOS UWB for Sensor Networks Workshop, 4 November 2005 5
MC I: Power–Delay Profile, LOS, d = 27.2 m 0 –5 –10 –15 normalized power (dB) –20 –25 –30 –35 –40 –45 –50 0 50 100 150 200 250 300 350 400 excess delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 6
MC II: Power–Delay Profile, LOS, d = 20 m 0 –5 –10 –15 –20 normalized power (dB) –25 –30 –35 –40 –45 –50 –55 0 100 200 300 400 500 600 excess delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 7
MC I vs. MC II • Similarities – exponential decay of the PDP with comparable decay constant – clustering in the LOS setting – soft onset of the PDP in the OLOS and NLOS settings • PDPs look very different, more random in MC II What are the reasons for the differing PDPs? ⇒ Spatial vs. temporal variations of the channel: strong mean component present in MC II Also observed for narrowband NLOS channels with static terminals [Bultitude, 1987]. UWB for Sensor Networks Workshop, 4 November 2005 8
Statistical Modeling is about Approximating Reality Channel taps h [ l ] are distributed according to the operating model F : • F is unknown • F might be arbitrarily complex Goal : approximate F as well as possible with a CDF G j Θ j from a family of J parametric candidate CDFs with parameter vector Θ j . • A good model should: – lead to consistent predictions – be based on physics and measured data – be mathematically tractable Use Akaike’s Information Criterion (AIC) to estimate a measure of approximation (discrepancy) based on the Kullback-Leibler distance. UWB for Sensor Networks Workshop, 4 November 2005 9
Modeling the Small-Scale Tap Fading Statistics • Goal: assess the distributions proposed in the literature • Consider amplitude only—phase information is difficult to obtain • Candidate distributions for the tap amplitudes – Rayleigh, Rice [Kunisch & Pamp, 2002, Ghassemzadeh et al., 2002] – Nakagami [Cassioli, Win, Molisch, 2002] – Lognormal [Foerster, 2002; Keignart & Daniele, 2003] – Weibull [Pagani, 2004] • Rice, Nakagami and Weibull contain Rayleigh as special case UWB for Sensor Networks Workshop, 4 November 2005 10
MC I: Akaike Weights & PDP, OLOS, d = 21 m 1 Rayleigh ø 0.34 0 1 Rice ø 0.18 0 Akaike weights 1 Nakagami ø 0.22 0 1 Lognormal ø 0.04 0 1 Weibull ø 0.22 0 0 power (dB) -10 PDP -20 -30 0 100 200 300 400 500 600 700 800 channel tap number UWB for Sensor Networks Workshop, 4 November 2005 11
MC II: Akaike Weights & PDP, OLOS, d = 20 m 1 Rayleigh 0 1 Rice 0 Akaike weights 1 Nakagami 0 1 Lognormal 0 1 Weibull 0 0 power (dB) -10 PDP -20 -30 -40 -50 0 200 400 600 800 1000 1200 1400 1600 channel tap number UWB for Sensor Networks Workshop, 4 November 2005 12
Summary—Marginal Tap Distribution • Amplitude distribution – Rayleigh for channels with moving terminal – Rice for static terminals and moving scatterers – difference to other distributions often small in MC I – different effective channels in MC I and MC II • Rayleigh amplitude plus uniform phase assumption leads to circularly symmetric complex Gaussian tap distribution – robust model – amenable for analytical work – supported by our measurements • IEEE 802.15.3a lognormal fading not a good model UWB for Sensor Networks Workshop, 4 November 2005 13
Uncorrelated Scattering and Stochastic Degrees of Freedom • Assume a jointly circularly symmetric complex Gaussian tap distribution around the mean – mean: m = E [ h ] � ( h − m )( h − m ) H � – covariance matrix: K = E joint Gaussianity is difficult to verify via AIC • Stochastic degrees of freedom: number of independent diversity branches • Discrete-time uncorrelated scattering (US) leads to a linear increase of the number of stochastic degrees of freedom with bandwidth UWB for Sensor Networks Workshop, 4 November 2005 14
Stochastic Degrees of Freedom • Need to estimate the covariance matrix � N m = 1 – mean: � n =1 h n N � N – covariance: � K = 1 m ) H n =1 ( h n − � m )( h n − � N • Truncate h n to L=701 taps ⇒ � K is of size 701 × 701 • Consider MC II OLOS setting with N=2722 samples (Ricean channel) • Declare normalized eigenvalues � λ k of � K to be significant, if k ≤ L s , where � L s k =1 � λ k ≤ s • Scaling is approximately linear • Results differ from [Saadane et al., 2004], but our measurement methodology is different UWB for Sensor Networks Workshop, 4 November 2005 15
MC II, OLOS: Number of Significant Eigenvalues 400 s=0.9 s=0.9, US 350 s=0.8 s=0.7 number of significant eigenvalues 300 250 200 150 100 50 0 0.5 1 1.5 2 2.5 3 bandwidth W (GHz) UWB for Sensor Networks Workshop, 4 November 2005 16
Discussion • Main findings: – the measured UWB indoor channels can be modeled as having correlated complex Gaussian taps – the number of stochastic degrees of freedom scales approximately linearly with bandwidth – the same physical environment can lead to different effective channels if the source of randomness differs • Nakagami, lognormal, and Weibull distributions are also reported in the UWB literature—may result from different statistical methods like goodness-of-fit tests or least-squares fitting • Sublinear degree-of-freedom scaling (Saadane et al. 2004)—different measurement setting, similar to MC I UWB for Sensor Networks Workshop, 4 November 2005 17
BACKUP Backup UWB for Sensor Networks Workshop, 4 November 2005 18
BACKUP MC I: Setup measurement control HP 8722D VNA Skycross STM-3TO10M UWB antenna 2 m Minicircuits ZVE 8G 2 m Diadrive positioner H&S Sucoflex 104 cables Skycross STM-3TO10M UWB antenna 25 m 2 m custom RF amp UWB for Sensor Networks Workshop, 4 November 2005 19
BACKUP MC II: Setup Anaren 41130 Centellax TG1P1A HP 83640B H&S Sucoform power divider PN generator signal generator SM86 cable 0.5 m Minicircuits ZVE 8G 2 m power amplifier Skycross STM-3TO10M measurement control UWB antenna H&S Sucoflex 104 cables Agilent DSO81204A custom RF amp Skycross STM-3TO10M UWB antenna H&S Sucoform SM86 cable UWB for Sensor Networks Workshop, 4 November 2005 20
BACKUP The Lobby, LOS Measurement Setting UWB for Sensor Networks Workshop, 4 November 2005 21
BACKUP MC I: Impulse Response Magnitude, LOS, d = 27.2 m 0 –10 –20 normalized power (dB) –30 –40 –50 –60 –70 0 50 100 150 200 250 300 350 400 450 500 delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 22
BACKUP MC I: Power–Delay Profile, OLOS, d = 27.2 m 0 –5 –10 normalized power (dB) –15 –20 –25 –30 –35 –40 0 50 100 150 200 250 300 350 400 excess delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 23
BACKUP MC I: Power–Delay Profile, NLOS, d = 20 m 0 –10 –20 normalized power (dB) –30 –40 –50 –60 –70 0 50 100 150 200 250 300 350 400 excess delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 24
BACKUP MC II: Impulse Response Magnitude, LOS, d = 20 m 0 –10 –20 normalized power (dB) –30 –40 –50 –60 –70 0 100 200 300 400 500 600 excess delay (ns) UWB for Sensor Networks Workshop, 4 November 2005 25
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