EE359 – Lecture 16 Outline

1. EE359 – Lecture 16 Outline • Announcements: • HW due Friday • Midterms graded: grade distribution • Rest of term announcements • MIMO Beamforming • MIMO Diversity/Multiplexing Tradeoffs • MIMO Receiver Design • Maximum-Likelihood, Decision Feedback, Sphere Decoder • Other MIMO Design Issues • Adaptive techniques • Limited feedback

2. Midterm Distribution 95-100: A+ 90-95: A/A+ 85-90: A 80-85: A/A- 75-80:A-/B+ 70-75: B+/B 65-70: B

3. End of Quarter Schedule • Remaining lectures: • Today: MIMO • 11/18 week (3 lectures): Should complete all EE359 material • Finish MIMO, multicarrier modulation/OFDM, SS/CDMA • 11/25 week: Thanksgiving • 12/2 week (1 lecture): Course Summary, Advanced topics • No regular lectures Dec 3 or Dec. 5 • Makeup 11/22 (Fri) 12:50-2:05 (pizza@12:30): SS/CSMA • Makeup 12/6 (Fri): 12:30-1:45 (pizza@12): SS/359 wrapup • Wrapupincludes summary & advanced topics • May extend this lecture by 15 mins

4. Review of Last Lecture • MIMO Channel Decomposition • MIMO Channel Capacity • For static channel with perfect CSI at TX and RX, power water-filling over space is optimal • In fading waterfill over space (based on short-term power constraint) or space-time (long-term constraint) • Without transmitter channel knowledge, capacity metric is based on an outage probability, Pout=p(C(H)<R) ~ ~ ~ y=S x+n y=Hx+n H=USVH ~ ~ ~ yi=six+ni

5. Beamforming • Scalar codes with transmit precoding y=uHHvx+uHn • Transforms system into a SISO system with diversity. • Array and diversity gain • Greatly simplifies encoding and decoding. • Channel indicates the best direction to beamform • Need “sufficient” knowledge for optimality of beamforming

6. Error Prone Low Pe Diversity vs. Multiplexing • Use antennas for multiplexing or diversity • Diversity/Multiplexing tradeoffs (Zheng/Tse)

7. ST Code High Rate High-Rate Quantizer Decoder Error Prone ST Code High Diversity Low-Rate Quantizer Decoder Low Pe How should antennas be used? • Use antennas for multiplexing: • Use antennas for diversity Depends on end-to-end metric: Solve by optimizing app. metric

8. MIMO Receiver Design • Optimal Receiver: • Maximum likelihood: finds input symbol most likely to have resulted in received vector • Exponentially complex # of streams and constellation size • Decision-Feedback receiver • Uses triangular decomposition of channel matrix • Allows sequential detection of symbol at each received antenna, subtracting out previously detected symbols • Sphere Decoder: • Only considers possibilities within a sphere of received symbol.

9. Other MIMO Design IssuesNot covered in lecture/HW/exams • Space-time coding: • Map symbols to both space and time via space-time block and convolutional codes. • For OFDM systems, codes are also mapped over frequency tones. • Adaptive techniques: • Fast and accurate channel estimation • Adapt the use of transmit/receive antennas • Adapting modulation and coding. • Limited feedback: • Partial CSI introduces interference in parallel decomp: can use interference cancellation at RX • TX codebook design for quantized channel

10. Main Points • MIMO introduces diversity/multiplexing tradeoff • Optimal use of antennas depends on application • MIMO RX design trades complexity for performance • ML detector optimal; exponentially complex • DF receivers prone to error propagation • Sphere decoders allow performance tradeoff via radius • Space-time processing (i.e. coding) used in most systems • Adaptation requires fast/accurate channel estimation • Limited feedback introduces interference between streams: requires codebook design