Transcript P s

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Wireless Digital Modulation
Outlines
Digital Modulation Review
Digital Modulation Performance in AWGN
Modulation Performance in Fading
Outage Probability
Average Ps (Pb)
Combined average and outage Ps
Ps due to Doppler and ISI
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Outlines
Digital Modulation Review
Digital Modulation Performance in AWGN
Modulation Performance in Fading
Outage Probability
Average Ps (Pb)
Combined average and outage Ps
Ps due to Doppler and ISI
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Wireless Digital Modulation
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Convert data information into a carrier wave by
changing 3 properties of the sine/cosine EM wave:
 Amplitude
 Frequency
 Phase
Carrier signal A cos  2 fct   
Modulated & Transmitted Signal


s (t )   A  A(t )  cos  2  f c  f (t )  t     (t )  


AM
FM
PM


Types of Digital Modulation
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Digitally modulated M-ary signal (M=2k)
s(t )  An cos  2 f nt  n 
n  1, 2, M
Amplitude Shift Keying (ASK) ——An
 Common in infra-red remote & optical comms
Frequency Shift Keying (FSK) —— fn
 Common in wireless remote control & pagers
Phase Shift Keying (PSK) —— фn
 QPSK in 802.11b, 3G CDMA; 8-PSK in EDGE
Quadrature Amplitude Modulation (QAM) ——An &фn
 With OFDM in WiMAX, WiFi 802.11g, et.al.
Other Common Wireless Modulations
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 Continuous Phase FSK (CPFSK)
 A variant of FSK that uses less bandwidth than FSK
 Frequency changes continuously (rather than abruptly) with
time
 Used in military radios
 Gaussian Minimum Shift Keying (GMSK)
 A variant of FSK similar to CPFSK and uses even less bandwidth
 Used in GSM cellular systems & Bluetooth (GFSK)
 Offset-QPSK & pi/4-QPSK
 Variations of QPSM/4-QAM such that the in-phase and
quadrature phase data are offset by ½ a symbol period.
 O-QPSK used in Satcom & CDMA 2000
 Pi/4-QPSK found in NADC, PDC & Tetra
Passband Modulation Tradeoffs
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 Want high rates, high spectral efficiency, high power
efficiency, robust to channel, cheap.
Our focus
 Amplitude/Phase Modulation (MPSK,MQAM)
 Information encoded in amplitude/phase
 More spectrally efficient than frequency modulation
 Issues: differential encoding, pulse shaping, bit mapping.
 Frequency Modulation (FSK)
 Information encoded in frequency
 Continuous phase (CPFSK) special case of FM
 Bandwidth determined by Carson’s rule (pulse shaping)
 More robust to channel and amplifier nonlinearities
Linear Modulation
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 Linear modulations are bandwidth efficient.
 In linear modulation, the amplitude of the transmitted
signal varies linearly with the modulating digital signal.
 RF signal has non-constant envelope (like AM)
 Need linear RF amplifier (which has poor power
efficiency).
 Some well-known linear modulations
 M-ary Phase Shift Keying (MPSK) such as BPSK, QPSK
 OQPSK –Offset QPSK
 π/4-DQPSK
 M-ary Quadrature Amplitude Modulation (QAM)
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Amplitude/Phase Modulation
Signal over ith symbol period:
s(t )  si1 g (t ) cos(2f ct  0 )  si 2 g (t ) sin( 2f ct  0 )
Pulse shape g(t) typically Nyquist
Signal constellation defined by (si1,si2) pairs
Can be differentially encoded
M values for (si1,si2)log2 M bits per symbol
Ps depends on
Minimum distance dmin (depends on gs)
# of nearest neighbors aM
Ps  a M Q
Approximate expression:

Mg s

Nyquist Pulse Shaping for Linear Modulations
 Pulse shaping at the
transmitter is required to
limit the transmission
bandwidth.
 Nyquist pulse with roll-off
factor α is used to
eliminate ISI while
keeping the transmission
bandwidth low.
 At the correct sampling
instant, the ISI is zero.
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Example: QAM Modulator
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Non Linear Modulator
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 Non-linear modulations are power efficient.
 In non-linear modulation, the amplitude of the transmitted
signal is constant, regardless of the variation in the
modulating digital signal – Constant enveloppe
 The phase of the transmitted signal is usually continuous.
 Use power efficient Class C amplifier.
 May occupy a larger bandwidth (than linear modulations)
 MFSK – M-ary Frequency Shift Keying
 MSK – Minimum Shift Keying (actually CPFSK with modulation
index of 0.5)
 GMSK – Gaussian MSK
Example: Minimum Shift Keying (MSK)
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Factors Affecting Modulation Performance
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 Performance of modulation is dependent on the
minimum distance between any two constellation
points.
 For comparisons, the average energy of the modulated
symbols must be the same (so need to normalize).
 Higher-order (means larger M) constellations means
more points per unit area (more dense) and hence the
chance of error is higher (due to noise). BER ↑
 Therefore for same performance & bandwidth
 higher data rate → shorter distance
 lower data rate → longer distance
Modulation :Bandwidth vs Power Efficiency
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 Power efficiency → the ability of a modulation to
provide a good signal quality (probability of error) with
a limited transmit power level.
 Comm systems where transmission power is a premium
 Examples : Satellite comms, Bluetooth, GSM cellular
 Bandwidth efficiency → the ability of a modulation to
provide a high transmission data rate within a limited
(given) bandwidth.
 Comm systems where transmission bandwidth is a
premium
 Examples : 802.11g (Wifi), 802.16 (Wimax), 802.22 (WRAN)
BW vs Power Efficiency Plane
BW Efficiency:
 R/W
Power Efficiency:
 Eb/N0
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无线信道中数字调制的性能
 衡量性能的指标：
 错误率
• 误码率
• 误比特率
 中断率：瞬时信噪比低于给定门限的概率
 影响性能的因素：
 平坦衰落
• 增加平均误码率
• 增加中断率
 频率选择性衰落
• 引起码间串扰，带来误码平台
 多普勒频移
• 频谱扩展，带来邻道干扰
• 相隔一个码元周期的相位去相关，带来差分PSK误码平台
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Outlines
Digital Modulation Review
Digital Modulation Performance in AWGN
Modulation Performance in Fading
Outage Probability
Average Ps (Pb)
Combined average and outage Ps
Ps due to Doppler and ISI
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SNR, Eb and Es
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SNR per bit/symbol
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SER/BER for Modulations in AWGN
Coherent Detection

Ps  a M Q  M g s
Non-Coherent Detection

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Alternate Q Function Representation
Traditional Q function representation
Q ( z )  p( x  z )  

z
1  x2 / 2
e
dx, x ~ N (0,1)
2
Infinite integrand
Argument in integral limits
New representation (Craig’93)
Q( z) 
1
 /2

0
e
 z 2 /(sin2  )
d
Leads to closed form solution for Ps in PSK
Very useful in fading and diversity analysis
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Outlines
Digital Modulation Review
Digital Modulation Performance in AWGN
Modulation Performance in Fading
Outage Probability
Average Ps (Pb)
Combined average and outage Ps
Ps due to Doppler and ISI
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Linear Modulation in Fading
In fading gs and therefore Ps random
Performance metrics:
Outage probability: p(Ps>Ptarget)=p(g<gtarget)
Average Ps , Ps:

Ps   Ps (g ) p(g )dg
0
Combined outage and average Ps
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Outage Probability
Ps
Outage
Ts
Ps(target)
t or d
 Probability that Ps is above target
 Equivalently, probability gs below target
 Used when Tc>>Ts
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Average Ps
Ts
Ps   Ps (g s ) p(g s )dg s
Ps
Ps
t or d
 Expected value of random variable Ps
 Used when Tc≈Ts
 Error probability much higher than in AWGN alone
Combined outage and average Ps
Ps(gs)
Ps(gs)
Outage
Pstarget
Ps(gs)
Used in combined shadowing and flat-fading
Ps varies slowly, locally determined by flat fading
Declare outage when Ps above target value
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Outlines
Digital Modulation Review
Digital Modulation Performance in AWGN
Modulation Performance in Fading
Outage Probability
Average Ps (Pb)
Combined average and outage Ps
Ps due to Doppler and ISI
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Doppler Effects
High doppler causes channel phase to
decorrelate between symbols
Leads to an irreducible error floor for
differential modulation
Increasing power does not reduce error
Error floor depends on BdTs
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ISI Effects
Delay spread exceeding a symbol time
causes ISI (self interference).
1
2
0
Ts
3
4
5
Tm
ISI leads to irreducible error floor
 Increasing signal power increases ISI power
ISI requires that Ts>>Tm (Rs<<Bc)
Main Points
Linear modulation more spectrally efficient but less
robust than nonlinear modulation
Ps approximation in AWGN:

Ps  a M Q  M g s

 Alternate Q function approach simplifies Ps calculation,
especially its average value in fading (Laplace Xfm).
Main Points
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In fading Ps is a random variable, characterized by
average value, outage, or combined outage/average
 Outage probability based on target SNR in AWGN.
 Fading greatly increases average Ps .
Doppler spread only impacts differential modulation
causing an irreducible error floor at low data rates
Delay spread causes irreducible error floor or imposes
rate limits
Need to combat flat and frequency-selective fading
 Focus of the remainder of the course