1. EE359 – Lecture 16 Outline Announcements Proposals due this Friday, 5pm (create website, email url) HW 7 posted today, due 12/1 TA evaluations: 10 bonus points Sensor networks laboratory course next quarter MIMO TX Precoding/RX Shaping MIMO Channel Capacity MIMO Beamforming (Diversity) MIMO Diversity/Multiplexing Tradeoffs Introduction to ISI Countermeasures

2. Review of Last Lecture Practical Issues in Adaptive Modulation Update rate based on AFRD in Markov fading model: At f D =80 Hz and 100 Kbps, adapt every 10-100 Ts. Estimation error/delay in adaptive MQAM lead to irreducible errors floors: must estimate and feedback in t<<T c MIMO Systems Channel decomposes into R H independent channels R H -fold capacity increase over SISO system and reduced complexity Can also use antennas for diversity (beamforming) l Leads to capacity versus diversity tradeoff in MIMO y=Hx+n

3. MIMO Decomposition Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=U H y) Leads to R H  min(M t,M r ) independent channels with gain  i (i th singular value of H) and AWGN Independent channels lead to simple capacity analysis and modulation/demodulation design H=U  V H y=Hx+n y=  x+n ~~ y i =   x+n i ~ ~~ ~ ~ ~

4. Capacity of MIMO Systems Depends on what is known at TX and RX and if channel is static or fading 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 is the probability that the channel capacity given the channel realization is below the transmission rate.

5. 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

6. Optimality of Beamforming Mean Information Covariance Information

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

8. ISI Countermeasures Equalization Signal processing at receiver to eliminate ISI Multicarrier Modulation Break data stream into narrowband substreams, so each subchannel experiences narrowband fading Spread spectrum Superimpose a wideband spreading sequence on top of modulated data, allows individual multipath components to be resolved and removed/combined.

9. Main Points Multiple antennas at both TX and RX greatly enhance capacity and reduce complexity. With transmitter and receiver CSI, capacity of MIMO channel uses water-filling of power in space/time Leads to min(M t,M r ) capacity increase Same capacity increase without transmitter CSI Without transmitter CSI, need outage as a capacity metric Multiple antennas can also be used for diversity via beamforming – this can be optimal Fundamental diversity/multiplexing tradeoff in MIMO