Wireless ModulationSchemes

Lecture 5

Announcements Mid term test on Wednesday April 24.Project proposals

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

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

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)(

Receiver Structure in AWGN Channel

Si1(t)

SiN(t)

MAX

Performance Comparison

Goldsmith, Table 6.1 Notice that for higher order constellation become

higher the modulation scheme become less efficient

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

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

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)(

Average BER for Common Schemeswith Rayleigh fading

In general:

Loss of Fading (BPSK)

Fading Performance of MQAM

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 .