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## Short Course: Wireless Communications : Lecture 3

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**Short Course:**Wireless Communications: Lecture 3 Professor Andrea Goldsmith UCSD March 22-23 La Jolla, CA**Capacity of Flat Fading Channels**• Four cases • Nothing known • Fading statistics known • Fade value known at receiver • Fade value known at receiver and transmitter • Optimal Adaptation • Vary rate and power relative to channel • Optimal power adaptation is water-filling • Exceeds AWGN channel capacity at low SNRs • Suboptimal techniques come close to capacity**P**Bc Frequency Selective Fading Channels • For TI channels, capacity achieved by water-filling in frequency • Capacity of time-varying channel unknown • Approximate by dividing into subbands • Each subband has width Bc (like MCM). • Independent fading in each subband • Capacity is the sum of subband capacities 1/|H(f)|2 f**Linear Modulation in Fading**• BER in AWGN: • In fading gsand therefore Psrandom • Performance metrics: • Outage probability: p(Ps>Ptarget)=p(g<gtarget) • Average Ps , Ps: • Combined outage and average Ps**One of the**M(g) Points log2 M(g) Bits To Channel M(g)-QAM Modulator Power: S(g) Point Selector Uncoded Data Bits Delay g(t) g(t) 16-QAM 4-QAM BSPK Variable-Rate Variable-Power MQAM Goal: Optimize S(g) and M(g) to maximize EM(g)**gk**g Optimal Adaptive Scheme • Power Water-Filling • Spectral Efficiency • Practical Constraints • Constellation and power restriction • Constellation updates. • Estimation error and delay. Equals Shannon capacity with an effective power loss of K. g**Diversity**• Send bits over independent fading paths • Combine paths to mitigate fading effects. • Independent fading paths • Space, time, frequency, polarization diversity. • Combining techniques • Selection combining (SC) • Equal gain combining (EGC) • Maximal ratio combining (MRC) • Can almost completely eliminate fading effects**Multiple Input Multiple Output (MIMO)Systems**• MIMO systems have multiple (r) transmit and receiver antennas • With perfect channel estimates at TX and RX, decomposes into r independent channels • RH-fold capacity increase over SISO system • Demodulation complexity reduction • Can also use antennas for diversity (beamforming) • Leads to capacity versus diversity tradeoff in MIMO**S**cos(2pf0t) cos(2pfNt) x x MCM and OFDM R/N bps • MCM splits channel into flat fading subchannels • Fading across subcarriers degrades performance. • Compensate through coding or adaptation • OFDM efficiently implemented using FFTs • OFDM challenges are PAPR, timing and frequency offset, and fading across subcarriers QAM Modulator R bps Serial To Parallel Converter R/N bps QAM Modulator**Tc**Spread Spectrum • In DSSS, bit sequence modulated by chip sequence • Spreads bandwidth by large factor (K) • Despread by multiplying by sc(t) again (sc(t)=1) • Mitigates ISI and narrowband interference • ISI mitigation a function of code autocorrelation • Must synchronize to incoming signal • RAKE receiver used to combine multiple paths S(f) s(t) sc(t) Sc(f) S(f)*Sc(f) 1/Tb 1/Tc Tb=KTc 2**Course Outline**• Overview of Wireless Communications • Path Loss, Shadowing, and WB/NB Fading • Capacity of Wireless Channels • Digital Modulation and its Performance • Adaptive Modulation • Diversity • MIMO Systems • Multicarrier Modulation • Spread Spectrum • Multiuser Communications • Wireless Networks • Future Wireless Systems Lecture 3**Course Outline**• Overview of Wireless Communications • Path Loss, Shadowing, and WB/NB Fading • Capacity of Wireless Channels • Digital Modulation and its Performance • Adaptive Modulation • Diversity • MIMO Systems • Multicarrier Modulation • Spread Spectrum • Multiuser Communications • Wireless Networks • Future Wireless Systems**Uplink (Multiple Access**Channel or MAC): Many Transmitters to One Receiver. Downlink (Broadcast Channel or BC): One Transmitter to Many Receivers. x x x x h1(t) h21(t) h22(t) h3(t) Multiuser Channels:Uplink and Downlink R3 R2 R1 Uplink and Downlink typically duplexed in time or frequency**Code Space**Code Space Code Space Time Time Time Frequency Frequency Frequency Bandwidth Sharing • Frequency Division • Time Division • Code Division • Multiuser Detection • Space (MIMO Systems) • Hybrid Schemes 7C29822.033-Cimini-9/97**Multiple Access SS**• Interference between users mitigated by code cross correlation • In downlink, signal and interference have same received power • In uplink, “close” users drown out “far” users (near-far problem) a2 a1**Multiuser Detection**• In all CDMA systems and in TD/FD/CD cellular systems, users interfere with each other. • In most of these systems the interference is treated as noise. • Systems become interference-limited • Often uses complex mechanisms to minimize impact of interference (power control, smart antennas, etc.) • Multiuser detection exploits the fact that the structure of the interference is known • Interference can be detected and subtracted out • Better have a darn good estimate of the interference**Ideal Multiuser Detection**- Signal 1 = A/D Signal 1 Demod A/D A/D A/D A/D Iterative Multiuser Detection Signal 2 Signal 2 Demod - = Why Not Ubiquitous Today? Power and A/D Precision**Random Access**RANDOM ACCESS TECHNIQUES • Dedicated channels wasteful for data • use statistical multiplexing • Techniques • Aloha • Carrier sensing • Collision detection or avoidance • Reservation protocols • PRMA • Retransmissions used for corrupted data • Poor throughput and delay characteristics under heavy loading • Hybrid methods 7C29822.038-Cimini-9/97**Multiuser Channel CapacityFundamental Limit on Data Rates**Capacity: The set of simultaneously achievable rates {R1,…,Rn} • Main drivers of channel capacity • Bandwidth and received SINR • Channel model (fading, ISI) • Channel knowledge and how it is used • Number of antennas at TX and RX • Duality connects capacity regions of uplink and downlink R3 R2 R3 R2 R1 R1**Multiuser Fading Channel Capacity**• Ergodic (Shannon) capacity: maximum long-term rates averaged over the fading process. • Shannon capacity applied directly to fading channels. • Delay depends on channel variations. • Transmission rate varies with channel quality. • Zero-outage (delay-limited*) capacity: maximum rate that can be maintained in all fading states. • Delay independent of channel variations. • Constant transmission rate – much power needed for deep fading. • Outage capacity: maximum rate that can be maintained in all nonoutage fading states. • Constant transmission rate during nonoutage • Outage avoids power penalty in deep fades**H1(w)**H2(w) Broadcast Channels with ISI w1k • ISI introduces memory into the channel • The optimal coding strategy decomposes the channel into parallel broadcast channels • Superposition coding is applied to each subchannel. • Power must be optimized across subchannels and between users in each subchannel. xk w2k**Broadcast MIMO Channel**Non-degraded broadcast channel MIMO MAC capacity easy to find MIMO BC channel capacity obtained using dirty paper coding and duality with MIMO MAC**Course Outline**• Overview of Wireless Communications • Path Loss, Shadowing, and WB/NB Fading • Capacity of Wireless Channels • Digital Modulation and its Performance • Adaptive Modulation • Diversity • MIMO Systems • Multicarrier Modulation • Spread Spectrum • Multiuser Communications • Wireless Networks • Future Wireless Systems**BS**Spectral Reuse In licensed bands and unlicensed bands Wifi, BT, UWB,… Cellular, Wimax • Reuse introduces interference Due to its scarcity, spectrum is reused**BASE**STATION Cellular System Design • Frequencies, timeslots, or codes reused at spatially-separate locations • Efficient system design is interference-limited • Base stations perform centralized control functions • Call setup, handoff, routing, adaptive schemes, etc.**Design Issues**• Reuse distance • Cell size • Channel assignment strategy • Interference management • Multiuser detection • MIMO • Dynamic resource allocation 8C32810.44-Cimini-7/98**Interference: Friend or Foe?**Increases BER, reduces capacity Multiuser detection can completely remove interference • If treated as noise: Foe • If decodable: Neither friend nor foe**MIMO in Cellular**• How should MIMO be fully exploited? • At a base station or Wifi access point • MIMO Broadcasting and Multiple Access • Network MIMO: Form virtual antenna arrays • Downlink is a MIMO BC, uplink is a MIMO MAC • Can treat “interference” as a known signal or noise • Can cluster cells and cooperate between clusters**MIMO in Cellular:Other Performance Benefits**• Antenna gain extended battery life, extended range, and higher throughput • Diversity gain improved reliability, more robust operation of services • Multiplexing gain higher data rates • Interference suppression (TXBF) improved quality, reliability, robustness • Reduced interference to other systems**Rethinking “Cells” in Cellular**How should cellular systems be designed? • Traditional cellular design “interference-limited” • MIMO/multiuser detection can remove interference • Cooperating BSs form a MIMO array: what is a cell? • Relays change cell shape and boundaries • Distributed antennas move BS towards cell boundary • Femtocells create a cell within a cell • Mobile cooperation via relays, virtual MIMO, network coding. Coop MIMO Femto Relay Will gains in practice be big or incremental; in capacity or coverage? DAS**Cellular System Capacity**• Shannon Capacity • Shannon capacity does no incorporate reuse distance. • Some results for TDMA systems with joint base station processing • User Capacity • Calculates how many users can be supported for a given performance specification. • Results highly dependent on traffic, voice activity, and propagation models. • Can be improved through interference reduction techniques. (Gilhousen et. al.) • Area Spectral Efficiency • Capacity per unit area In practice, all techniques have roughly the same capacity**Area Spectral Efficiency**• S/I increases with reuse distance. • For BER fixed, tradeoff between reuse distance and link spectral efficiency (bps/Hz). • Area Spectral Efficiency: Ae=SRi/(.25D2p) bps/Hz/Km2. BASE STATION A=.25D2p =**ASE vs. Cell Radius**fc=2 GHz 101 100 D=4R Average Area Spectral Efficiency [Bps/Hz/Km2] D=6R D=8R 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cell Radius R [Km]**Improving Capacity**• Interference averaging • WCDMA • Interference cancellation • Multiuser detection • Interference reduction • Sectorization and smart antennas • Dynamic resource allocation • Power control • MIMO techniques • Space-time processing**BASE**STATION Dynamic Resource AllocationAllocate resources as user and network conditions change • Resources: • Channels • Bandwidth • Power • Rate • Base stations • Access • Optimization criteria • Minimize blocking (voice only systems) • Maximize number of users (multiple classes) • Maximize “revenue” • Subject to some minimum performance for each user**Interference Alignment**• Addresses the number of interference-free signaling dimensions in an interference channel • Based on our orthogonal analysis earlier, it would appear that resources need to be divided evenly, so only 2BT/N dimensions available • Jafar and Cadambe showed that by aligning interference, 2BT/2 dimensions are available • Everyone gets half the cake!**Ad-Hoc Networks**• Peer-to-peer communications • No backbone infrastructure or centralized control • Routing can be multihop. • Topology is dynamic. • Fully connected with different link SINRs • Open questions • Fundamental capacity • Optimal routing • Resource allocation (power, rate, spectrum, etc.) to meet QoS**Capacity**• Much progress in finding the Shannon capacity limits of wireless single and multiuser channels • Little known about these limits for mobile wireless networks, even with simple models • Recent results on scaling laws for networks • No separation theorems have emerged • Robustness, security, delay, and outage are not typically incorporated into capacity definitions**Network Capacity Results**• Multiple access channel (MAC) • Broadcast channel • Relay channel upper/lower bounds • Interference channel • Scaling laws • Achievable rates for small networks**Capacity for Large Networks(Gupta/Kumar’00)**• Make some simplifications and ask for less • Each node has only a single destination • All nodes create traffic for their desired destination at a uniform rate l • Capacity (throughput) is maximum l that can be supported by the network (1 dimensional) • Throughput of random networks • Network topology/packet destinations random. • Throughput l is random: characterized by its distribution as a function of network size n. • Find scaling laws for C(n)=l as n .**Extensions**• Fixed network topologies (Gupta/Kumar’01) • Similar throughput bounds as random networks • Mobility in the network (Grossglauser/Tse’01) • Mobiles pass message to neighboring nodes, eventually neighbor gets close to destination and forwards message • Per-node throughput constant, aggregate throughput of order n, delay of order n. • Throughput/delay tradeoffs • Piecewise linear model for throughput-delay tradeoff (ElGamal et. al’04, Toumpis/Goldsmith’04) • Finite delay requires throughput penalty. • Achievable rates with multiuser coding/decoding (GK’03) • Per-node throughput (bit-meters/sec) constant, aggregate infinite. • Rajiv will provide more details S D**Application metric: f(C,D,E):**(C*,D*,E*)=arg max f(C,D,E) (C*,D*,E*) Is a capacity region all we need to design networks? Yes, if the application and network design can be decoupled Capacity Delay Energy**2**3 5 4 1 Ad Hoc Network Achievable Rate Regions • All achievable rate vectors between nodes • Lower bounds Shannon capacity • An n(n-1) dimensional convex polyhedron • Each dimension defines (net) rate from one node to each of the others • Time-division strategy • Link rates adapt to link SINR • Optimal MAC via centralized scheduling • Optimal routing • Yields performance bounds • Evaluate existing protocols • Develop new protocols**Achievable rate**vectors achieved by time division Capacity region is convex hull of all rate matrices Achievable Rates • A matrix R belongs to the capacity region if there are rate matrices R1, R2, R3 ,…, Rn such that • Linear programming problem: • Need clever techniques to reduce complexity • Power control, fading, etc., easily incorporated • Region boundary achieved with optimal routing**Example: Six Node Network**Capacity region is 30-dimensional**Capacity Region Slice(6 Node Network)**(a): Single hop, no simultaneous transmissions. (b): Multihop, no simultaneous transmissions. (c): Multihop, simultaneous transmissions. (d): Adding power control (e): Successive interference cancellation, no power control. Multiple hops SIC Spatial reuse Extensions: - Capacity vs. network size - Capacity vs. topology - Fading and mobility - Multihop cellular**Ad-Hoc NetworkDesign Issues**• Ad-hoc networks provide a flexible network infrastructure for many emerging applications. • The capacity of such networks is generally unknown. • Transmission, access, and routing strategies for ad-hoc networks are generally ad-hoc. • Crosslayer design critical and very challenging. • Energy constraints impose interesting design tradeoffs for communication and networking.**Hidden**Terminal Exposed Terminal 1 2 3 4 5 Medium Access Control • Nodes need a decentralized channel access method • Minimize packet collisions and insure channel not wasted • Collisions entail significant delay • Aloha w/ CSMA/CD have hidden/exposed terminals • 802.11 uses four-way handshake • Creates inefficiencies, especially in multihop setting**Frequency Reuse**• More bandwidth-efficient • Distributed methods needed. • Dynamic channel allocation hard for packet data. • Mostly an unsolved problem • CDMA or hand-tuning of access points.