Measurement and Modeling of Wireless Channels

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Wireless Channel Modeling and ItsWireless Channel Modeling and ItsImpact on Radio System DesignImpact on Radio System Design

Reporter: Prof. Reporter: Prof. ChiaChia--Chi HuangChi HuangDepartment of Communication Engineering, Department of Communication Engineering,

National National ChiaoChiao--TungTung UniversityUniversity

2

Outline

Characteristics of Wireless ChannelsMeasurement and Modeling of Wireless ChannelsChannel Effects on Wireless System Design

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Characteristics of Wireless Channels

Propagation LossAnd

Shadowing Effect

4


Path Loss: a distance effect, ≈ d -4 , i.e., 12 dB/octave

Shadowing Fading: lognormal distributionσ ≈ 8 dB

Multipath Fading

≈

5

Characteristics of Wireless ChannelsCellular Structure

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Mathematical Model for a Multipath Channel(G.L. Turin 1956)

L number of pathsδ(t) impulse functionA ℓ amplitude of ℓ-th pathτℓ time delay of ℓ-th pathφℓ carrier path shift of ℓ-th path

( )1

( ) L

j ll l

l

h t A t e φδ τ=

= −∑

7

Characteristics of Wireless ChannelsNarrowband Transmission

S(t) equivalent baseband of the transmitted signalR(t) equivalent baseband of the received signal

( )

( )

( )

1

1

( )

Lj l

l ll

Lj l

ll

j

R t A S t e

A e S t

e S t

ϕ

ϕ

φ

τ=

=

= −

Α

∑

∑

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Characteristics of Wireless ChannelsNarrowband Transmission

The frequency response of the channel is just a complex gain A e jΦflat fading when the receiver is moving aroundA is called amplitude fading, Φ is called random phasecoherence distance (time) is the distance (time) over which A is correlated

( )

( )

1

( ) j

1 1

( )

= = Ae

if 1 , when , where W is the bandwith of the transmitted signal S(t)2

L j ll l

l

L Lj jl l l

l ll l

L

h t A t e

A e A e

W

ϕ

ωτ ϕ ϕ φ

δ τ

ω

ωωτπ

=

− −

= =

= −

Η

≤

∑

∑ ∑

9


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Characteristics of Wireless ChannelsWideband Transmission

The frequency response of the channel shows frequency selectivity

the transmitted signal is distorted by the channel

frequency selective fading when the receiver is moving around

coherence bandwidth is the bandwidth over which |H(ω)| is correlated

( )

( )

( )

1

( )

1

1

( )

=

if cannot be neglected, when 2

( )

L j ll l

l

Lj l l

ll

L

Lj l

l ll

h t A t e

A e

W

R t A S t e

ϕ

ωτ ϕ

ϕ

δ τ

ω

ωωτπ

τ

=

− −

=

=

= −

Η

≤

= −

∑

∑

∑

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Characteristics of Wireless ChannelsWideband transmission: a two-path example

h(t)=δ(t)+δ(t-Δ)

H(ω)=1+e-jωΔ

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Characteristics of Wireless ChannelsFour types of Wireless Channels

τc = coherence time, Bc = coherence bandwidth.

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Characteristics of Wireless ChannelsWideband transmission: spatial and time resolution

Wideband Time resolution

Directional Antenna or Antennal Array Spatial (Angle) resolution

Tx Rx

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Measurement and Modeling of Wireless Channels

Narrowband Channel Measurement transmitted signal: a single tonereceiver: RF signal first down coverted to IF, and

bandpass filtered (BPF with bandwidth > fD, where fD is the Doppler frequency, i.e., fD = vehicle speed / wavelength)

(a) use an IQ demodulator to down convert to equivalent baseband to get the complex fading pattern A e jΦ

(b) use the AGC signal at IF to derive the amplitude fading signal A.

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Narrowband Channel Modeling: Scattering Model

Amplitude fading “A” has Rayleigh distributionRandom phase “Φ” has uniform distributionLet E(t)=A(t)ejΦ(t), complex Gaussian random processR E (τ) = E{A2} J0(2ΠfDτ), ρA (τ) = J0

2(2ΠfDτ)

s(f) = E{A2} [p(α)G(α)+ p(-α)G(-α)]/(fD-f)2 : U-shaped Spectrum

p(α) : fraction of power at angle αG(α) : antenna gain at angle α, f = fD cos(α)

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Narrowband Channel Modeling: Jake’s Model

P is the average power, N is the total number of paths

0

0

2 2 2 2( )

1

1

0

( ) 2 [ ] [ ] }

2 2 [cos 2 cos cos 2 sin ] cos 2 cos cos 2 sin }

where cos , is uniformly distributed in [0, / 2],

{

{

n n n D D

Nj f t j f t j j f t j f tj t j

nN

n n n n D Dn

n D n n

PA t e e e e e e eN

P f t j f t f t j f tN

f f N

π π β π πφ α

π β π β π α π α

φ φ π

− −

=

=

= + + +

= + + +

= =

∑

∑1 ( 1),2 2

is uniformly distributed in [0, ], and / 4n

N

β π α π

−

=

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Wideband Channel Measurement transmitted signal: a direct (PN, pseudo noise) sequence

spread spectrum signal receiver: RF signal first down coverted to IF, and

bandpass filtered (BPF with bandwidth > W, where W is the bandwidth of the transmitted signal i.e., W = 1-2 times of PN sequence chip rate), (a) use a sliding correlator and an IQ demodulator

to down convert to equivalent baseband toget a time-scaled version of the complex impulse response of the channel.

(b) use an IQ demodulator to down convert to equivalent baseband and then use two matched filters to get the complex impulse response of the channel.

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PN sequence

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A Simplified Sliding Correlator

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Wideband Channel Modeling: Wide Sense Stationary Uncorrelated Scattering (WSSUS) and Power Delay Profile

Power

Delay

Maximum path delay: ГM

Mean delay: Гm

RMS delay:Гrms

Power

Delay

Maximum path delay: ГM

Mean delay: Гm

RMS delay:Гrms

1 1

2 2

1 1

( )/( ) Mean Delay

( )/( ) RMS Delay Spread

N N

m i i ii i

N N

rms i i i mi i

P P

P P

τ τ

τ τ τ

= =

= =

=

= −

∑ ∑

∑ ∑

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Wideband Channel Modeling

( )( )

( )

( ) ( )

1

*

h

h h

( ( ) ( ))

1

*H

H H

( , ) ( ) ( )

R ( , ) [ ( , ) ( , )]

Let 0, R ( , 0) R ( ) power delay profile

, = ( )

R ( , ) E[H , H , ]

Let 0, R ( ,0) R ( )

L j tll l

l

Lj t tl l

ll

h t A t t e

t E h t h t t

t

t A t e

t t t t

t

ϕ

ωτ ϕ

τ δ τ τ

τ τ τ τ

τ τ

ω

ω ω ω ω

ω ω

=

− −

=

= −

∆ ∆ = + ∆ + ∆

∆ = ∆ ≡ ∆ →

Η

∆ ∆ = +∆ +∆

∆ = ∆ ≡ ∆

∑

∑

h H

spaced frequency correlation function

R ( ) R ( )

delay spread coherence bandwidth

Fourier Transformτ ω

→

∆ ←⎯⎯⎯⎯⎯⎯→ ∆

↑ ↔ ↓

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Wideband Channel Modeling

( )( )

( )

( ) ( )

1

( ( ) ( ))

1

*H

H H H

H

( , ) ( ) ( )

, = ( )

R ( , ) E[H , H , ]

Let 0, R (0, R ( ) ) R ( ) spaced time correlation function

R ( ) Dop

L j tll l

l

L j t tl ll

l

Fourier Transform

h t A t t e

t A t e

t t t t

t t t

t

ϕ

ωτ ϕ

τ δ τ τ

ω

ω ω ω ω

ω

=

− −

=

= −

Η

∆ ∆ = +∆ +∆

∆ = ∆ ∆ ≡ ∆ →

∆ ←⎯⎯⎯⎯⎯⎯→

∑

∑

pler spectrum

coherence time Doppler spread ↑ ↔ ↓

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Wideband Channel Modeling: Tapped Delay Line Model

R1, R2, …, RN are independent, zero mean, complex Gaussian noises with U-shaped power spectrum

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Channel Effects on Wireless System DesignThe AMPS system (1984) is the first generation cellular system which uses narrowband frequency modulation (total BW ≈ 30 KHz)

The equivalent baseband of the transmitted signal is

The equivalent baseband of the received signal (including AWGN)

The received signal is bandpass filtered and limited to remove the amplitude fading effect

2 ( ) 2

( ) cos(2 2 ( ) )

Re{[ ] }d t c

c c d t

j f m d j f tc

X t A f t f m d

A e eπ α α π

π π α α= +

∫=

∫

2 ( )( ) d t

j f m d

cX t A eπ α α∫=

[2 ( ) ( )]( ) ( ) ( )d t

j f m d t

BL BL c sY t A e n t jn tπ α α φ+∫= + +

[ 2 ( ) ( ) ]( ) ( ) ( )d t

j f m d t

cY t A A t e n tπ α α φ+∫= +

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Channel Effects on Wireless System DesignBefore frequency modulation, syllabic companding, pre-emphasis, clipping, and bandpass filtering are used toenhance the voice signal quality

syllabic compandorAfter frequency discrimination, bandpass filtering is first used to eliminate the random phase effect of the narrowband fadingchannel. Then de-emphasis and syllabic expanding are used to recover the original voice signalFM is adopted in the first generation cellular system because it is simple and it is effective in combating the narrowband fadingeffect.

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Channel Effects on Wireless System DesignIn early 1980’s, single sideband amplitude modulation with atone pilot (total BW≈5 KHz) was considered as a potential modulation scheme for voice based narrowband cellular systems to solve the impending capacity problem.

The tone pilot is used to estimate the narrowband fading channeland for the coherent demodulation of the voice signal.

This pilot based signal recovering method in a narrowband fading channel was given the name “Feed-forward Signal Regeneration”.

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Channel Effects on Wireless System DesignAround 1988-89, π/4-shifted QPSK modulation was usedas the digital modulation scheme for the United States digital cellular (USDC) system.

The USDC system has a packet size of 6.67 ms and transmits 48.6 Kbit/sec within a bandwidth of 30 KHz. It is a narrowband system encountering flat fading for the most of the time. However, in a mobile radio environment with a very large delay spread, it might still need adaptive equalization.

Either decision feedback equalizer or maximum likelihood sequence estimation (MLSE) algorithm can be used for data detection. The stability of the adaptive algorithm might be a potential problem in a rapidly fading channel.

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Channel Effects on Wireless System Design

An MLSE Equalizer

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Channel Effects on Wireless System DesignPerformance of binary signaling schemes over a Rayleigh fading channel, random phase effects cause error floors – not shown

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Channel Effects on Wireless System DesignSpace diversity: maximum ratio combining technique improves receiver performance over a Rayleigh fading channel – channelestimation is needed

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Channel Effects on Wireless System DesignSpace diversity: maximum ratio combining technique

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Around 1991-92, GMSK modulation was used as the digital modulation scheme for the Pan-European GSM cellular system.

The GSM system has a packet size of 577μsec and transmits 270 Kbit/sec within a bandwidth of 200 KHz. Strictly speaking, GSM is more like a wideband system than a narrowband system.

The multipath channel is approximately quasi-static within a packet period at most vehicle speeds. A channel sounding midamble is sent within a packet for channel estimation purpose. Equalization is needed for data detection. Adaptive equalization helps to improve the receiver performance when the vehicle speed is very high.

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GSM Frame Structure

Either decision feedback equalizer or maximum likelihood sequence estimation (Viterbi) algorithm can be used for data detection.

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Channel Effects on Wireless System DesignBoth USDC and GSM systems use coding and interleaving to protect the important bits of encoded speech signal.

Slow frequency hopping can be used in GSM to further improve the system performance when the vehicle speed is very low.

. FR

EQU

ENC

Y

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Channel Effects on Wireless System DesignAround 1995, direct sequence spread spectrum with BPSK was used as the modulation scheme for the United States IS-95 cellular system.

An unmodulated PN sequence with a period of 32,768 chips and clocked at a rate of 1.2288 M chip/sec is sent as a pilot signal for code synchronization and channel estimation purposes.

A RAKE receiver is used to collect the received multipath signalenergy by maximal ratio combing for data detection.

IS-95 system achieves single-cell frequency reuse through using a very complicated power control schemes.

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Channel Effects on Wireless System DesignA RAKE Receiver

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Channel Effects on Wireless System DesignIn order to achieve high data rates, orthogonal frequency division multiplexing (OFDM) was proposed as modulation schemes for the European digital audio broadcasting (DAB), digital video broadcasting (DVB), and the IEEE 802.11a wireless LAN standards in the 1990’s.

With OFDM modulation, a wideband frequency selective fading channel is transformed into a very large number of narrowband flat fading sub-channels.

The most important parameter of an OFDM system is theOFDM symbol length. It should be selected short enoughsuch that the channel is quasi-static during an OFDM symboland long enough such that each sub-channel is narrowband.

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Channel Effects on Wireless System DesignA cyclically-extended prefix is added in front of an OFDM symbol as a guard interval

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Channel Effects on Wireless System DesignOFDM system transforms the frequency selective fading channels into multiple flat subchannels. However, it suffers from deep fades over some subchannels.To solve this problem, conventional OFDM systems use coding and interleaving.

Pilot symbols or pilot signals are usually transmitted in OFDM systems for channel estimation purpose. A simple one-tap equalizer is used at the receiver side after the FFT computation.

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Transmitter diversity with space time coding could further enhance the performance of a wireless system. With this method, diversity gain can be achieved by transmitting from multiple spatially separated antennas at the base station without too much increasing the complexity of a receiver.

⊕1n0n

2h1h

0

*

1

ss−

1

*

0

ss

1h

2h

0s% 1s%

0s 1s

( )( )

0 1 0 2 1 0* *

1 1 1 2 0 1

r r t h s h s n

r r t T h s h s n

= = + +

= + = − + +

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Simulation Results

Receiver architecture with two receiver antennas

⊕

0

*

1

ss−

1

*

0

ss

⊕

3h2h

1h 4h

1

0

nn

3

2

nn

1h

2h

3h

4h

⊕⊕

0~s 1

~s

0s 1s

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Conclusion

In this talk, we described the characteristics of a wireless channel, covered the measurement and modeling of a wirelesschannel, and discussed the channel impacts on wireless system design.

We also briefly described the history of cellular system developments and discussed various methods to improve system performance in a multipath fading evironment.

Future research directions will emphasize on the development of the next generation digital broadcasting system, wireless LAN system, ultra-wideband short range radio system, and the 4G cellular system.

Documents

Measurement and Modeling of Wireless Channels