lecture 5. announcements mid term test on wednesday april 24. project proposals
TRANSCRIPT
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Wireless ModulationSchemes
Lecture 5
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Announcements Mid term test on Wednesday April 24.Project proposals
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Wireless Modulation TradeoffsWant high rate, low power, robust to channel
variations, low cost.
Amplitude/Phase Modulation (MPSK,MQAM)Linear: Information encoded in amplitude/phaseHigh spectrum efficiencyMajor issue: sensitive to channel variations
Frequency Modulation (FSK)Nonlinear: Information encoded in frequencyMore robust to channel variationsMajor issue: Low spectrum efficiency
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Amplitude/Phase ModulationSignal over ith symbol period:
Signal constellation defined by (si1,si2) pairs
M possible sets for (si1,si2): log2 M bits per symbol
Probability of symbol error (Ps ) depends on:
Minimum distance dmin (depends on gs)
Number of nearest neighbors aM
Approximate expression:
)2sin()()2cos()()( 0201 tftgstftgsts cici
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Alternate Q Function RepresentationTraditional Q function representation
Infinite integrandArgument in integral limits
New representation (Craig’93)
Leads to closed form solution for Ps in PSKVery useful in fading and diversity analysis
)1,0(~,2
1)()( 2/2 NxdxezxpzQ x
z
dezQ z )/(sin2/
0
221)(
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Receiver Structure in AWGN Channel
Si1(t)
SiN(t)
MAX
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Performance Comparison
Goldsmith, Table 6.1 Notice that for higher order constellation become
higher the modulation scheme become less efficient
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Linear Modulation in FadingIn fading gs and therefore Ps randomPerformance metrics:
Outage probability: Prob(Ps>Ptarget)=Prob(g<gtarget)
Average Ps , Ps:
dpPP ss )()(0
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Outage Probability
Probability that Ps is above target
Equivalently, probability gs below target
Used when Tc>>Ts
Ps
Ps(target)
Outage
Ts
t or d
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Average Ps
Expected value of random variable Ps
Used when Tc~Ts
Error probability much higher than in AWGN aloneAlternate Q function approach:
Simplifies calculations
sssss dpPP )()(Ps
Ps
Ts
t or d
dezQ z )/(sin2/
0
221)(
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Average BER for Common Schemeswith Rayleigh fading
In general:
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Loss of Fading (BPSK)
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Fading Performance of MQAM
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Main PointsLinear modulation more spectrally efficient but
less robust than nonlinear modulation
Ps approximation in AWGN:
In fading Ps is a random variable, characterized by average value
Fading greatly increases average Ps .