1. EE359 – Lecture 13 Outline Annoucements Midterm announcements No HW this week (study for MT; HW due next week) Introduction to adaptive modulation Variable-rate variable-power MQAM Optimal power and rate adaptation Finite constellation sets

2. Midterm Announcements Midterm: Wed (11/4), 6-8 pm in Hewlett 101 Food will be served after the exam! Review sessions My midterm review was at the end of last Thursdays lecture TA review was Sunday Midterm logistics: Open book/notes Bring textbook/calculators (have extras; adv. notice reqd) Covers Chapters 1-7 (see my MT review for exact sections) Extra OHs: Andrea: Today (3-4.30 pm) and Wed. (2.30-4 pm), TAs: today 5:30-7:30 (Packard 109+email) and Wed 12-1 (Packard 109). Midterms from past 3 MTs posted: 10 bonus points for “taking” a practice exam Solutions for all exams given when you turn in practice exam

3. Review of Last Lecture Maximal Ratio Combining MGF Approach for Performance of MRC Transmit diversity With channel knowledge, similar to receiver diversity, same array/diversity gain Without channel knowledge, can obtain diversity gain through Alamouti scheme over 2 consecutive symbols

4. 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

5. 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(  )]

6. Optimization Formulation Adaptive MQAM: Rate for fixed BER Rate and Power Optimization Same maximization as for capacity, except for K=-1.5/ln(5BER).

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

8. Spectral Efficiency Can reduce gap by superimposing a trellis code

9. Constellation Restriction Restrict M D (  ) to {M 0 =0,…,M N }. Let M(  )=  /   *, where   * is optimized for max rate Set M D (  ) to max j M j : M j  M(  ) (conservative) Region boundaries are  j =M j   *, j=0,…,N Power control maintains target BER M(  )=  /   *  00  1 =M 1  K * 22 33 0 M1M1 M2M2 Outage M1M1 M3M3 M2M2 M3M3 MD()MD() M(  )=  /  

10. Power Adaptation and Average Rate Power adaptation: Fixed BER within each region l E s /N 0 =(M j -1)/K l Channel inversion within a region Requires power increase when increasing M(  ) Average Rate

11. Efficiency in Rayleigh Fading Spectral Efficiency (bps/Hz) Average SNR (dB)

12. Practical Constraints Constellation updates: fade region duration Estimation error and delay (explored in HW) Estimation error at RX can cause error in absence of noise (e.g. for MQAM) Estimation error at TX can be caused by imperfect estimator and/or delay in the feedback path Causes mismatch of adaptive power and rate to actual channel Can lead to large errors

13. Main Points Adaptive modulation leverages fast fading to improve performance (throughput, BER, etc.) Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K. Comes within 5-6 dB of capacity Discretizing the constellation size results in negligible performance loss. Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers. Estimation error/delay causes error floor