Cours3 radio link - INSA Lyon
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Physical layer modelling for future wireless networks 3- Modulation, BER and radio link quality
Transcript of Cours3 radio link - INSA Lyon
Physical layer modelling for future wireless networks
3- Modulation, BER and radio link quality
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Modulation, BER and radio linkModulation, BER and radio link
1- Introduction
2- Basis of modulation� Carrier frequency
� Modulation principle
� Binary modulation
� Digital modulation
� Frequency modulation
3- BER modelling� AWGN
� BPSK /QPSK
� BER for other modulations
4- BER on fading� Time-varying channel
� Rayleigh fading
� Rice fading
� Outage probability
5- PER modelling� pseudo-stationary
� PER computation
� Error coding
� Memory channels
6- Conclusion
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II --introductionintroduction
� The quality of a radio link relies on the transmission success probability � reliability– Transmission errors depend on SNR, interference,…
– Packet error rate (PER) depends on bit error rate (BER) and packet size, coding, …
– The instantaneous BER depends on the instantaneous SNR
– Time-varying properties of transmission errors (due to fading, shadowing, …) impact the resulting mean error rate
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IntroductionExample
– Setup• AWGN channel• mod BPSK• White noise • Nb bits (200) �PER ~ Nb.BER
AB
SNR
0 100 200 300 400 500-80
-70
-60
-50
-40
-30
-20P(d) dBm
PER
0 100 200 300 400 50000.10.20.30.40.50.60.70.80.9
1
d
PE
R
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IntroductionExample (cont.)
– Coverage area ?
– range?– threshold ???
We have : Surf2 > Surf1
0 100 200 300 400 50000.10.20.30.40.50.60.70.80.9
1
d
PE
R
Critical zone
AB
SNR
PER
321
321
d
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IntroductionExample (cont.)
• Fading– Rayleigh channel
Γ
Fading duration
-5 0 5 10 1510-5
10-4
10-3
10-2
10-1
100BER in AWGN and Rayleigh channels
Eb/No
BE
R
AWGN Rayleigh
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IntroductionExample (cont.)
• AWGN vs Rayleigh– In Rayleigh conditions, no reliable transmissions
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d
PE
R
AWGN
Rayleigh+13dB
Rayleigh
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22-- ModulationModulation
Basis of modulation1) Carrier frequency
2) Modulation principle
3) Binary modulation
4) Digital modulation
5) Frequency modulation
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modulation1) Carrier frequency
( )000 2cos)( ϕπ +⋅= tfAtp
frequencyf0-f0
Q
I
A0
ϕ0
time
tfjj eeAtp 00 20)( πϕ ⋅⋅=
Amplitude-phase representation
Complex notations
0A
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modulation2) Modulation principle
– Modulation = the carrier signal characteristics are slowly modified (such as W <<f0)
The RF signal : tfjRF etAts 02)()( π⋅=
time
W
f0-f0
frequency
W ~ 1,4.Rs.
-4 -3 -2 -1 0 1 2 3 40
0.5
1
Time (t/Ts)
0.20.40.60.8
1
Ts Rs =1/Ts.
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modulation3) Binary modulation
Carrier frequency
Amp. mod.
Freq. mod.
Phase mod.
1 0 1 0 1 1
( ) ( )tfjntnfjRF eAenkts 02
0)()(2)()( πϕπ ⋅⋅⋅= +∆
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modulation4) Digital Modulation
BPSK / QPSK
Q
I
osc.
sRF(t)m(t)
BPSK (Binary Phase Shift Keying)
Q
I
QPSK (Quadrature Phase Shift Keying)
osc.
m(t) sRF(t)
e(-j2πf0t)
( ) ( )tf2jRFRF
0e)t(m)t(s)t(s π−⋅ℜ=ℜ=
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modulation4) Digital Modulation (cont.)
Generalization : A bit word is coded in the amp./phase plan = constellation
M-PSK (M-ary Phase Shift Keying) M-QAM (Quadrature amplitude modulation)
+1-1
j
-j
j
+1-1
-j
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modulation4) Digital Modulation (cont.)
• Some properties– Baseband coding– Mean power ?
• Symbol probability
– Number of bits per symbol• Bit rate vs symbol rate
– Constant amplitude modulation ?
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modulation
• FSK coding– Transmitted signal
– Baseband coding ??m(t) =??
(((( ))))(((( ))))(((( ))))tff2jexpARe)t(e c ∆∆∆∆±±±±ππππ⋅⋅⋅⋅====
+1-1
j
-j
+∆ω∆ω∆ω∆ω
-∆ω∆ω∆ω∆ω
I-3 exemples de modulation
5) Frequency modulation
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modulation
• MSK / GMSK coding– Baseband Waveform?
– The coder works directly with the phase
+1-1
j
-j
( ) ( ) ( ) ( )tfT
ttmtf
T
ttmtS c
bQc
bIMSK ππππ
2sin2
sin2cos2
cos)(
+
=
I-3 exemples de modulation
Peculiar case :
5) Frequency modulation (cont.)
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modulation
tTime Domain Frequency Domain
Modulation Domain
6) Signal analysis : VSA
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33-- BER modelingBER modeling
1) AWGN
2) BPSK / QPSK error
3) BER for binary modulations
4) BER for higher order modulations
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Fading1- AWGN
Received power• Signal model :
• Noise level– AWGN noise
Symbol power : Sk=Ak2 /2
Received energy per bit: Eb=Ak
2.Tb /2
0 Ttime
Ak
0 Ttime
Noise power : N=κ.T°.W=N0.W
Noise energy per symbol :EN=N0.W.Ts
κ=1.38.10-23 J/K Tk = 290 K (en réf. , T° en Kelvin)
note : ideal modulation : if Ts=1/W � EN=N0.
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Fading
– Theoretical BER of a BPSK in AWGN
( )2
20
2
xx
e2
1)x(p σ
−−
σπ=
)1a(P)1a/1a(P)1a(P)1a/1â(P))k(err(P kkkkkk −=⋅−===⋅=−== +
u0
( ) ∫∞
− ⋅=
⋅=<
x
u duexerfc
xerfcxp
22
22
1)0( 0
π
σ
=
02
1
N
EerfcP b
e
2- BPSK/QPSK error
0 2 4 6 8 1010-6
10-5
10-4
10-3
10-2
10-1
Eb/N0 (dB)
BE
R
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Fading
• An usual function for BER
– Q-function :
– BPSK / QPSK :
– DPSK :
– FSK :
– GMSK :
3- BER for binary modulations
( )
=22
1 zerfczQ
=
0
2
N
EQP b
e
0 2 4 6 8 1010-6
10-5
10-4
10-3
10-2
10-1
Eb/N0 (dB)
BE
R
BPSKQPSKDPSKFSK GMSK
=
0N
EQP b
e
−=
0
exp2
1
N
EP b
e
⋅=0
2
N
EQP b
e
α
68,0=α for GMSK with BT=0.25 (GSM)
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Fading
• Increasing the modulation order, decreases the distance between points, at constant power :– Example : M-PSK
distance between symbols:
Symbol error rate
4- BER for higher order modulations
+1-1
j
-j
=M
Ed sM
πsin2
( )
=
≤MN
EQ
MN
MEQP sb
s
ππsin
42sin
log22
00
2
Note : find the best coding scheme with M=8What is the corresponding BER?
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Fading
• The symbol error rate (SER) can be often approximated by:
• Find the performance of M-FSK, M-QAM, M-PSK
• Further readings– Spreading spectrum (DSSS)– OFDM
5- Conclusion
⋅=
0N
EkQP s
s α
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44-- BER on fading channelsBER on fading channels
1) Time-varying channel
2) Rayleigh Fading
3) Rice fading
4) Outage probability
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Fading1- time-varying channels
Γ
Fading duration
γγγ dppp eerr )()(0
⋅= ∫∞
[ ] )t(m)t(h)t(h)t(h)t('m N21 ⊗+++= L
m(t)
m’(t)
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Fading
• No main path : NLOS : – The resulting baseband signal is random (complex gaussian)
Diffuse response :
+1-1
BPSK
2- Rayleigh fading
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Fading
A α(t) η(t)
sRF(t) yRF(t)
( ) ( ) ( ) ( )ttstAty RFRF ηα +⋅=
( ) ( ) ( )tjett ϕαα ⋅=
Normalized, i.e. unitary mean gain :
( ) ( ) ( ) 12 2222 ==+== σαα yExEEG
xRF(t)
pathloss fading noise
2- Rayleigh fading (cont.)
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Fading
Instantaneous SNR : ( ) ( )( )( )( ) ( )
0
2
2
2
N
Et
tE
txEt bRF α
ηγ ==
( )( ) ( )( )00
2
N
E
N
EtEtE bb ===Γ αγMean SNR :
2- Rayleigh fading (cont.)
<
≥=−
00
0exp)(2
2
22
αα
σα
α σα
p
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ξ=α/σ
distribution de Rayleigh normalisée p(x)
Γ−
Γ=⋅=
γ
γααγ exp
1)()(
d
dpp
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Fading
– Consequences are fundamental
Γ−Γ−=
⋅= ∫∞
11
2
1
)()(0
γγγ dppp eerr
-5 0 5 10 1510-5
10-4
10-3
10-2
10-1
100
BER in AWGN and Rayleigh channels
Eb/No
BE
R
AWGN Rayleigh
2- Rayleigh fading (cont.)
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Fading
• AWGN channel � Rayleigh channel
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d
PE
R
AWGN
Rayleigh+13dB
Rayleigh
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Fading
• One main path + diffuse componentsRice distribution
3- Rice fading
+1-1
BPSK
<
≥≥
⋅⋅=+−
00
00;exp)( 202
2
2
22
α
ασ
ασα
α σα
AA
Ip
A
k=A2/2σ2
1 key parameter :
Ratio between LOS and diffusecomponents
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
1.2
1.4
Instantaneous amplitude x
f(x)
Rice distribution at constant power (A2/2+σ2=1)
k=5k=2 k=1 k=0
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Fading
– Def : probability that the instantaneous SNR falls below a certain threshold
4- outage probability
( ) ( ) γγγγγ
dpPPth
thout ⋅=≤≤= ∫0
0:
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55-- Packet (Frame) Error Rate Packet (Frame) Error Rate
1- pseudo-stationary hypothesis
In wireless networks, packets are frame-based :
The frame-based channel model:
Pseudo-stationary model :
the channel is assumed stationary during a frame
Γ
Fading durationFrame
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PER2- PER computation
In AWGN, the BER is stationary :
In fading channel, the PER is averaged over time
In a general way, the PER is NOT given by:
For high SNR : ???
( ) ( )[ ]Nbp PerrcPP γ−−=≥= 110)(:
( ) ( )[ ]Nbp PP γγ −−≠ 11
( ) ( ) ( )[ ]( ) γγγγγγ
dPpP Nbp ⋅−−⋅= ∫
∞
=0
11/
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PER
• Exple :BCH codes
– bloc length– redundancy – minimal distance
3- Error coding
12 −= mntmknr *≤−=1*2 +≥ td
k bits (n-k) bits
Partie information Partie contrôleInformation part control part
(m >3)
( )
( ) ( )( )∑=
−
−⋅⋅
=t
k
kN
bkb
succ
bppk
N
P
0
1 γγ
γ
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PER4- Memory channels
– Errors often appear in burst� discrete Markov chain Gilbert-Elliott (GE) model
G B
α
β α−1
β−1
)(GPe )(BPe
0 0
1 1
)(GPe
)(GPe
)(1 GPe−
)(1 GPe−
0 0
1 1
)(BPe
)(BPe
)(1 BPe−
)(1 BPe−
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66-- conclusion conclusion
1- modulation principles have been derived
the throughput and the BER are closely related
2- BER has been derived
it is related to the SNR distribution
3- PER has been derived
realistic fading channels have been taken into account
coding is discussed
time-varying properties have been discussed
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More readingsMore readings
� Books – T.H. Rappaport, Wireless communications, principle and practice
– S. Saunders, antennas and propagation for wireless communication systems
� PapersZ. Wang et al; “a simple and general parametrization quantifying performance in fading channels”, IEEE trans on
Communications, 2003
H. Bai et al; “error modeling schemes for fading channels in wireless communications: a survey”, IEEE communications surveys, vol5(2), 2003, http://www.comsoc.org
P. Pham et al; “New cross-layer design approach to ad hoc networks under Rayleigh fading”, IEEE J. on selected areas in communications, Janv2005
G. Zhou et al; “Models and solutions for radio irregularity in wireless sensor networks”. In ACM Trans. on sensor networks 2006
M. Takai et al; “Efficient wireless network simulations with detailed propagation models,” Wireless. Networks,01
P. J M. Belding-Royer et al; “Real-world environment models for mobile network evaluation,” IEEE Journal on selected areas in communications, 2005.
B. Miorandi & E. Altman; “Coverage and connectivity of ad-hoc networks in presence of channel randomness” In IEEE INFOCOM, Miami, USA, 2005
C. Bettstetter and C. Hartman; “Connectivity of wireless multihop networks in a shadow fading environment”. In Wireless Networks, 2005
R. Hekmat and P. Van Mieghem. “Study of connectivity in wireless ad-hoc networks with an improved radio model”. In Proc. of Intl’ workshop WiOpt, 2004.
N. Sadagopan et al. “ PATHS: Analysis of path duration statistics and their impact on reactive MANET routing protocols”, in: Proc. ACM MobiHoc, 2003.
