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EE359 – Lecture 16 Outline Announcements: HW due Thurs., last HW will be posted Thurs., due 12/4 (no late HWs) Friday makeup lecture 9:30-10:45 in Gates B03 End-of-Quarter schedule and possible bonus lecture MIMO Diversity/Multiplexing Tradeoffs MIMO Receiver Design Maximum-Likelihood, Decision Feedback, Sphere Decoder Other MIMO Design Issues Space-time coding, adaptive techniques, limited feedback ISI Countermeasures Multicarrier Modulation

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End of Quarter Schedule Lectures this week Today: MIMO+OFDM Intro Wednesday: OFDM Friday: OFDM + CDMA Intro Lectures week of 11/24: None! Lectures week of 12/1: 12/1 (Mon): Finish CDMA – end of EE359 course material! Options with/without bonus “advanced topics” lecture l No bonus: 12/3 -Course summary (last scheduled lecture) l With bonus: Course summary+bonus together (1.5-2 hrs) 12/3 (start 9am) or 12/1 or 12/2 @4/5/6 with pizza/cake/beer Can also do course summary and bonus separately

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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, P out =p(C(H)<R) H=U V H y=Hx+n y= x+n ~~ y i = x+n i ~ ~~ ~

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Review Continued Beamforming Scalar codes with transmit precoding 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 y=u H Hvx+u H n

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Diversity vs. Multiplexing Use antennas for multiplexing or diversity Diversity/Multiplexing tradeoffs (Zheng/Tse) Error Prone Low P e

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

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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 Linear Receivers Zero-Forcing: forces off-diagonal elements to zero, enhances noise Minimum Mean Square Error: Balances zero forcing against noise enhancement Sphere Decoder: Only considers possibilities within a sphere of received symbol. l If minimum distance symbol is within sphere, optimal, otherwise null is returned

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Other MIMO Design Issues Not 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

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ISI Countermeasures Equalization Signal processing at receiver to eliminate ISI Can completely eliminate ISI: H eq (f)=1/H(f), but this leads to noise enhancement for f:H(f) small Must balance ISI removal with noise enhancement Complex at high data rates, performs poorly in fast-fading Not that common in state-of-the-art wireless systems Multicarrier Modulation Break data stream into lower-rate substreams modulated onto narrowband flat-fading subchannels Spread spectrum Superimpose a fast (wideband) spreading sequence on top of data sequence, allows resolution for combining or attenuation of multipath components.

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Multicarrier Modulation Breaks data into N substreams Substream modulated onto separate carriers Substream bandwidth is B/N for B total bandwidth B/N<B c implies flat fading on each subcarrier (no ISI) x cos(2 f 0 t) x cos(2 f N t) R bps R/N bps QAM Modulator QAM Modulator Serial To Parallel Converter

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Overlapping Substreams Can have completely separate subchannels Required passband bandwidth is B. OFDM overlaps substreams Substreams (symbol time T N ) separated in RX Minimum substream separation is 1/ T N for rectancular pulses Total required bandwidth is B/2 f0f0 f N-1 B/N

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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 Other MIMO design issues include space-time coding, adaptation, codebooks for limited feedback ISI mitigated through equalization, multicarrier modulation (MCM) or spread spectrum Today, equalizers often too complex or can’t track channel. MCM splits channel into NB flat fading subchannels Can overlap subcarriers to preserve bandwidth

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