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**Wireless Modulation Schemes**

Lecture 5

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Announcements Mid term test on Wednesday April 24. Project proposals

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**Wireless Modulation Tradeoffs**

Want high rate, low power, robust to channel variations, low cost. Amplitude/Phase Modulation (MPSK,MQAM) Linear: Information encoded in amplitude/phase High spectrum efficiency Major issue: sensitive to channel variations Frequency Modulation (FSK) Nonlinear: Information encoded in frequency More robust to channel variations Major issue: Low spectrum efficiency

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**Amplitude/Phase Modulation**

Signal 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:

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**Alternate Q Function Representation**

Traditional Q function representation Infinite integrand Argument in integral limits New representation (Craig’93) Leads to closed form solution for Ps in PSK Very useful in fading and diversity analysis

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**Receiver Structure in AWGN Channel**

Si1(t) MAX SiN(t)

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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 Fading**

In fading gs and therefore Ps random Performance metrics: Outage probability: Prob(Ps>Ptarget)=Prob(g<gtarget) Average Ps , Ps:

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**Outage Probability Ps t or d Outage**

Ps(target) Outage Ts t or d Probability that Ps is above target Equivalently, probability gs below target Used when Tc>>Ts

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**Average Ps Ps Ps t or d Ts Expected value of random variable Ps**

Used when Tc~Ts Error probability much higher than in AWGN alone Alternate Q function approach: Simplifies calculations

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**Average BER for Common Schemes with 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 Points Ps approximation in AWGN:**

Linear 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 .

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