How Different are UWB Channels from Conventional Wideband Channels? - - PowerPoint PPT Presentation

How Different are UWB Channels from Conventional Wideband Channels?

Ulrich Schuster and Helmut B¨

• lcskei

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 y[m] =

L−1

• l=0

h[l]s[m − l] + w[m]

• Channels that have several taps h[l] are called wideband channels
• Taps are modeled as random variables

So where exactly is the difference to UWB 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, σ2

l ) → Rayleigh fading

• h[0] ∼ CN(µ, σ2

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

1 2 3 0 m

20 m moving terminals TX array receiver static terminals transmitter receiver RX LOS RX OLOS RX NLOS TX NLOS TX LOS/OLOS 21 m 13 m UWB for Sensor Networks Workshop, 4 November 2005 5

MC I: Power–Delay Profile, LOS, d = 27.2 m

50 100 150 200 250 300 350 400 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 6

MC II: Power–Delay Profile, LOS, d = 20 m

100 200 300 400 500 600 –55 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 excess delay (ns) normalized power (dB)

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 Gj

Θj from a family of

J parametric candidate CDFs with parameter vector Θj.

• 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

200 400 600 800

channel tap number

Rayleigh Rice Nakagami Lognormal Weibull PDP

100 300 500 700 1 1 1 1 1

• 10
• 20
• 30

Akaike weights power (dB)

ø 0.18 ø 0.34 ø 0.22 ø 0.04 ø 0.22

UWB for Sensor Networks Workshop, 4 November 2005 11

MC II: Akaike Weights & PDP, OLOS, d = 20 m

Akaike weights

200 400 600 800 1000 1200 1400 1600

channel tap number power (dB)

• 10
• 20
• 30
• 40
• 50

1 1 1 1 1

Rayleigh Rice Nakagami Lognormal Weibull PDP

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] – covariance matrix: K = E

• (h − m)(h − m)H

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

– mean: m = 1

N

N

n=1 hn

– covariance: K = 1

N

N

n=1(hn −

m)(hn − m)H

• Truncate hn to L=701 taps ⇒

K is of size 701 × 701

• Consider MC II OLOS setting with N=2722 samples (Ricean channel)
• Declare normalized eigenvalues

λk of K to be significant, if k ≤ Ls, where Ls

k=1

λk ≤ 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

0.5 1 1.5 2 2.5 3 50 100 150 200 250 300 350 400 bandwidth W (GHz) number of significant eigenvalues s=0.9 s=0.9, US s=0.8 s=0.7

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

MC I: Setup

BACKUP Minicircuits ZVE 8G Diadrive positioner Skycross STM-3TO10M UWB antenna Skycross STM-3TO10M UWB antenna custom RF amp HP 8722D VNA 2 m 2 m 2 m 25 m H&S Sucoflex 104 cables measurement control

UWB for Sensor Networks Workshop, 4 November 2005 19

MC II: Setup

BACKUP

Minicircuits ZVE 8G power amplifier HP 83640B signal generator Skycross STM-3TO10M UWB antenna 2 m 0.5 m H&S Sucoflex 104 cables custom RF amp Agilent DSO81204A Centellax TG1P1A PN generator Anaren 41130 power divider Skycross STM-3TO10M UWB antenna H&S Sucoform SM86 cable H&S Sucoform SM86 cable measurement control UWB for Sensor Networks Workshop, 4 November 2005 20

The Lobby, LOS Measurement Setting

BACKUP

UWB for Sensor Networks Workshop, 4 November 2005 21

MC I: Impulse Response Magnitude, LOS, d = 27.2 m

BACKUP

50 100 150 200 250 300 350 400 450 500 –70 –60 –50 –40 –30 –20 –10 delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 22

MC I: Power–Delay Profile, OLOS, d = 27.2 m

BACKUP

50 100 150 200 250 300 350 400 –40 –35 –30 –25 –20 –15 –10 –5 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 23

MC I: Power–Delay Profile, NLOS, d = 20 m

BACKUP

50 100 150 200 250 300 350 400 –70 –60 –50 –40 –30 –20 –10 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 24

MC II: Impulse Response Magnitude, LOS, d = 20 m

BACKUP

100 200 300 400 500 600 –70 –60 –50 –40 –30 –20 –10 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 25

MC II: Power–Delay Profile, OLOS, d = 20 m

BACKUP

100 200 300 400 500 600 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 26

MC II: Power–Delay Profile, NLOS, d = 13 m

BACKUP

100 200 300 400 500 600 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 excess delay (ns) normalized power (dB)

UWB for Sensor Networks Workshop, 4 November 2005 27

Goodness-of-Fit Tests are not Suitable for Channel Modeling

BACKUP

• Main critique: GOF test do not measure approximation quality

– probability that GΘ = F is zero – significance level and passing percentage are not well defined measures of approximation quality

• Secondary problem: hypothesis testing is often applied carelessly

– significance level arbitrary – some tests rely on binning—how to choose the bins? – only tests a null hypothesis against an alternate hypothesis – parameter estimates based on the same data as the test statistic

UWB for Sensor Networks Workshop, 4 November 2005 28

MC II, OLOS: Correlation Between Taps

BACKUP

100 200 300 400 500 600 700 800 0.2 0.3 0.4 0.5 0.6 0.7 channel tap number i correlation maximum correlation coefficient mean correlation coefficient 0.1

UWB for Sensor Networks Workshop, 4 November 2005 29