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Lecture 5. Announcements Mid term test on Wednesday April 24. Project proposals.

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Presentation on theme: "Lecture 5. Announcements Mid term test on Wednesday April 24. Project proposals."— Presentation transcript:

1 Lecture 5

2 Announcements Mid term test on Wednesday April 24. Project proposals

3 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

4 Amplitude/Phase Modulation Signal over i th symbol period: Signal constellation defined by (s i1,s i2 ) pairs M possible sets for (s i1,s i2 ): log 2 M bits per symbol Probability of symbol error (P s ) depends on: Minimum distance d min (depends on  s ) Number of nearest neighbors  M Approximate expression:

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

6 Receiver Structure in AWGN Channel Si1(t) S iN (t) MAX

7 Performance Comparison Goldsmith, Table 6.1 Notice that for higher order constellation become higher the modulation scheme become less efficient

8 Linear Modulation in Fading In fading  s and therefore P s random Performance metrics: Outage probability: Prob(P s >P target )=Prob(  <  target ) Average P s, P s :

9 Outage Probability Probability that P s is above target Equivalently, probability  s below target Used when T c >>T s PsPs P s(target) Outage TsTs t or d

10 Average P s Expected value of random variable P s Used when T c ~T s Error probability much higher than in AWGN alone Alternate Q function approach: Simplifies calculations PsPs PsPs TsTs t or d

11 Average BER for Common Schemes with Rayleigh fading In general:

12 Loss of Fading (BPSK)

13 Fading Performance of MQAM

14 Main Points Linear modulation more spectrally efficient but less robust than nonlinear modulation P s approximation in AWGN: In fading P s is a random variable, characterized by average value Fading greatly increases average P s.

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