EE359 – Lecture 12 Outline

1. EE359 – Lecture 12 Outline • Announcements • Midterm announcements • HW 5 due Friday, 11/4, at noon (no late HWs) • No HW next week (work on projects) • MGF Approach for Performance of MRC • EGC • Transmit Diversity • Adaptive Modulation • Adaptive MQAM

2. Review of Last Lecture • Introduction to Diversity • Combining Techniques • Performance of SC Diversity in Fading • Combiner SNR is maximum of branch SNRs. • CDF easy to obtain, pdf found by differentiating. • Diminishing returns with number of antennas. • Can get up to about 10-20 dB of gain. • Performance of MRC Diversity in Fading • Hard to get pdf of output SNR, except Rayleigh fading • In Rayleigh fading, obtain Pout and average Ps.

3. Midterm Announcements • Exam is November 7, 11am-1pm in this room. • Open book/notes (bring book/calculators) • Covers Chapters 1-7, HW 1-5. • HW solutions available online • Graded HW 3 back today, HW 4 maybe back tomorrow • Review Session Thursday 5-6 or 6-7, room TBD • Ritesh Extra OHs: Sat-Sun 11-1, Bytes café • My Extra OHs: Th 3-4pm, F 11-12am, M 9:30-10:30am. • Midterms and Solutions from ’02, ’03, ’04 on web • 10 bonus points for taking practice exam (due by exam) • These exams cover Chps. 1-7, similar format as our exam • Remote SCPD students must have arrangements

4. MRC and its Performance • With MRC, gS=gi for branch SNRsgi • Optimal technique to maximize output SNR • Yields 20-40 dB performance gains • Distribution of gS hard to obtain • Standard average BER calculation • Hard to obtain in closed form • Integral often diverges • MGF Approach

5. EGC and Transmit Diversity • EGQ simpler than MRC • Harder to analyze • Performance about 1 dB worse than MRC • Transmit diversity • With channel knowledge, similar to receiver diversity, same array/diversity gain • Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols

6. Adaptive Modulation • Change modulation relative to fading • Parameters to adapt: • Constellation size • Transmit power • Instantaneous BER • Symbol time • Coding rate/scheme • Optimization criterion: • Maximize throughput • Minimize average power • Minimize average BER Only 1-2 degrees of freedom needed for good performance

7. One of the M(g) Points log2 M(g) Bits To Channel M(g)-QAM Modulator Power: P(g) Point Selector Uncoded Data Bits Delay g(t) g(t) 16-QAM 4-QAM BSPK Variable-Rate Variable-Power MQAM Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]

8. gk g Optimal Adaptive Scheme • Power Adaptation • Spectral Efficiency g Equals Shannon capacity with effective power loss K=-1.5/ln(5BER).

9. K2 K1 K=-1.5/ln(5BER) Spectral Efficiency Can reduce gap by superimposing a trellis code

10. Main Points • Analysis of MRC simplified using MGF approach • EGC easier to implement than MRC: hard to analyze. • Performance about 1 dB worse than MRC • Transmit diversity can obtain diversity gain even without channel information at transmitter. • Adaptive modulation varies modulation parameters relative to fading. • Variable-rate variable-power MQAM comes within 5-6 dB of capacity (power penalty K) • Same adaptation that achieves capacity

11. Enjoy the Treats