1. Wireless Modulation Schemes
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 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:

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 Ps in PSK
Very useful in fading and diversity analysis

6. Receiver Structure in AWGN Channel
Si1(t)
MAX
SiN(t)

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

9. 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

10. 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

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

12. Loss of Fading (BPSK)

13. Fading Performance of MQAM

14. 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 .