EE359 – Lecture 14 Outline Announcements: MT announcements HW posted today, due next Friday Finite constellation sets in adaptive MQAM Practical Issues in Adaptive Modulation Introduction to MIMO Communications MIMO Channel Decomposition MIMO Channel Capacity

Midterm Announcements Midterm: Today (11/10), 6-8 pm in 200-303 Food will be served after the exam! SCPD students can take 2 hour exam in any 24 hour period starting at exam time Midterm logistics: Open book/notes Bring textbook/calculators (have extras; adv. notice reqd) Covers Chapters 1-7 (sections covered in lecture and/or HW) Last OH today: Thu 3-5 pm (Mainak, outside Packard 340) No HW this week 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

Review of Last Lecture Introduction to adaptive modulation Vary different parameters of modulation relative to fading Variable-rate variable-power MQAM Maximize average throughput by changing rate and power Optimal power adaptation is water-filling Optimal rate adaptation: gk g Equals capacity with effective power loss K=-1.5/ln(5BER).

Constellation Restriction Restrict MD(g) to {M0=0,…,MN}. Let M(g)=g/gK*, where gK* is optimized for max rate Set MD(g) to maxj Mj: Mj  M(g) (conservative) Region boundaries are gj=MjgK*, j=0,…,N Power control maintains target BER M(g)=g/gK* M3 M(g)=g/gK MD(g) M3 M2 M2 M1 M1 Outage g0 g1=M1gK* g2 g3 g

Power Adaptation and Average Rate Fixed BER within each region Es/N0=(Mj-1)/K Channel inversion within a region Requires power increase when increasing M(g) Average Rate Practical Considerations: Update rate/estimation error and delay

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

Practical Constraints Constellation updates: How long g stays continuously within a region (gj,gj+1) Estimation error (covered in HW) Estimation error at TX can be caused by estimator and/or delay in the feedback path Causes mismatch of power and rate to actual channel Can lead to large errors when g>g; irreducible error floor M(g)=g/gK* g g0 g1 g2 g3 M1 M2 Outage M3 MD(g) For Dopplers around 80Hz, M(g) constant for 10Ts-100Ts (9.3.5 of text, optional material) ^

Multiple Input Multiple Output (MIMO)Systems MIMO systems have multiple transmit and receiver antennas (Mt at TX, Mr at RX) Input described by vector x of dimension Mt Output described by vector y of dimension Mr Channel described by MrxMt matrix Design and capacity analysis depends on what is known about channel H at TX and RX If H unknown at TX, requires vector modulation/demod x=[x1,…,xMt] y=[y1,…,yMr] TX power constraint: E[xxH]=r=P/s2 y=Hx+n

MIMO Decomposition Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=UHy) Leads to RHmin(Mt,Mr) independent channels with gain si (ith singular value of H) and AWGN Independent channels lead to simple capacity analysis and modulation/demodulation design ~ ~ y=S x+n ~ y=Hx+n H=USVH yi=six+ni ~

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 Pout is the probability that the channel capacity given the channel realization is below the transmission rate.

Main Points 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 MIMO systems exploit multiple antennas at both TX and RX for capacity and/or diversity gain With TX and RX channel knowledge, channel decomposes into independent channels Linear capacity increase with number of TX/RX antennas Without TX CSI, capacity vs. outage is the capacity metric