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 P out and average P s.

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,   =  i for branch SNRs  i Optimal technique to maximize output SNR Yields 20-40 dB performance gains Distribution of   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. Variable-Rate Variable-Power MQAM Uncoded Data Bits Delay Point Selector M(  )-QAM Modulator Power: P(  ) To Channel  (t) log 2 M(  ) Bits One of the M(  ) Points BSPK 4-QAM 16-QAM Goal: Optimize P(  ) and M(  ) to maximize R=Elog[M(  )]

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

9. 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