Andrea Goldsmith Stanford University 2010 School of Information Theory
University of Southern California
Aug. 5, 2010
Future Wireless Networks Ubiquitous Communica/on Among People and Devices Next-­‐genera4on Cellular Wireless Internet Access Wireless Mul4media Sensor Networks Smart Homes/Spaces Automated Highways In-­‐Body Networks All this and more … Challenges   Fundamental capacity limits of wireless networks are unknown and, worse yet, poorly defined.   Wireless network protocols are generally ad-­‐hoc   Applica4ons are heterogeneous with hard constraints that must be met by the network   Energy and delay constraints change fundamental design principles Fundamental Network Capacity The Shangri-­‐La of Informa/on Theory   Much progress in finding the capacity limits of wireless single and mul4user channels   Limited understanding about the capacity limits of wireless networks, even for simple models   System assump4ons such as constrained energy and delay may require new capacity defini4ons   Is this elusive goal the right thing to pursue? Shangri-La is synonymous with any earthly paradise;
a permanently happy land, isolated from the outside world
Wireless Channel and Network Capacity Fundamental Limit on Data Rates The set of simultaneously achievable rates with Pe→0
R1
R2
R3
(R12, R13,,…,R1n)
  Main drivers of channel capacity   Bandwidth and power   Sta4s4cs and dynamics of the channel   What is known about the channel at TX and/or RX   If feedback is available   Number of antennas   Single or mul4-­‐hop In the beginning...   Shannon’s Mathema/cal Theory of Communica/on derived fundamental data rate limits of digital communica4on channels.   Shannon capacity is independent of the transmission and recep4on strategy; Depends only on channel characteris4cs   Shannon capacity for sta4onary and ergodic channels is the channel’s maximum mutual informa4on   Significance of capacity comes from Shannon's coding theorem and converse   Show capacity is the channel’s maximum “error-­‐free” data Shannon Capacity   Discrete memoryless channel w/ input X∈X, output Y∈ Y has mutual informa/on (MI)   Related to the no4on of entropy:   Shannon proved DMC has capacity equal to it’s maximum MI   Maximum is taken over all possible input distribu4ons Coding Theorem   Coding theorem: A code exists with rate R=C-­‐∈ with probability of error approaching zero with blocklength   Shannon provided a random code with this property   Decoding is based on the no4on of typical sets:   Sets where the probability of the realiza4on of xn, yn, (xn,yn) approximates that of their entropies   Decode sequence xn that is jointly typical with received sequence yn   For codes with large blocklengths, probability of error approaches 0   Shannon’s “Communica4on in the presence of noise” P+N
uses geometry for AWGN coding theorem proof   Input occupies sphere of radius P   Output occupies sphere of radious P+N   Capacity corresponds to number of input messages that lie in nonoverlapping output spheres Converse   Oben based on Fano’s inequality for message W
nR=H(W)=H(W|Yn)+I(W;Yn)
≤ H(W|Yn)+I(Xn(W);Yn) since W=f(Xn)
≤  1+Pe(n)nR+ I(Xn(W);Yn)≤ H(W|Yn)+nC
  This implies Pe(n)≥1-1/(nR)-C/R as n→∞
Error bounded away from zero for R>C
  Fano’s inequality based on cutset bound   Loose for many channels /networks Capacity of AWGN Channels n[i]
x[i]
+
y[i]
  Discrete-­‐4me channel; x[i] is input at 4me i, y[i] is output, n[i] is iid sample of white Gaussian noise process w/ PSD N0   Channel bandwidth is B, received power is P   Received signal-­‐to-­‐noise power ra4o (SNR) is SNR=γ=P/(N0B)   Maximum mutual informa4on achieved with Gaussian inputs C=Blog2(1+SNR) bps
Wireless Channels   Received signal power diminishes with distance   Self-­‐interference due to mul4path (flat or frequency selec4ve fading)   Channel changes as users move around   Signal blocked (shadowed) by objects (cars, people, etc.)   Broadcast medium – everyone interferes d Flat-­‐Fading Channel Model   System Model   Channel es4mates can be fed back to transmiger   Transmiger then adapts power and rate Capacity of Flat-­‐Fading Channels   Capacity defines theore4cal rate limit   Maximum error free rate a channel can support   Depends on what is known about channel   Sta4s4cs completely unknown: don’t know how to solve   Fading Sta4s4cs Known   Hard to find capacity   Know for iid Rayleigh fading and finite-­‐state Markov channels   Fading Known at Receiver Only Fading Known at Transmiger and Receiver   For fixed transmit power, same as with only receiver knowledge of fading   Transmit power P(γ) can also be adapted (ave. constraint)   Leads to op4miza4on problem   Capacity proof based on mul4plexing op4mal encoders and decoders for each channel realiza4on Op4mal Adap4ve Scheme   Power Adapta4on Waterfilling
1
γ
  Capacity γ0
γ
Channel Inversion   Fading inverted to maintain constant SNR   Simplifies design (fixed rate)   Greatly reduces capacity   Capacity is zero in Rayleigh fading   Truncated inversion   Invert channel above cutoff fade depth   Constant SNR (fixed rate) above cutoff   Cutoff greatly increases capacity   Close to op4mal Capacity in Flat-­‐Fading Rayleigh Log-­‐Normal Variable-­‐Rate Variable-­‐Power MQAM One of the
M(γ) Points
log2 M(γ) Bits
Uncoded
Data Bits
M(γ)-QAM
Modulator
Power: P(γ)
Point
Selector
Delay
To Channel
γ(t)
γ(t)
BSPK
4-QAM
16-QAM
Goal: Optimize P(γ) and M(γ) to maximize R=Elog[M(γ)]
Op4miza4on Formula4on   Adap4ve MQAM: Rate for fixed BER   Rate and Power Op4miza4on Same maximization as for capacity, except for K=-1.5/ln(5BER).
Op4mal Adap4ve Scheme   Power Adapta4on γk
γ
  Spectral Efficiency γ
Equals capacity with effective power loss K=-1.5/ln(5BER).
Spectral Efficiency K2
K1
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code
Frequency Selec4ve Fading Channels   For 4me-­‐invariant channels, capacity achieved by water-­‐filling in frequency: sum capacity in each subchannel 1/|H(f)|2
P
f
  Proof decomposes the frequency-­‐selec4ve channel into a set of AWGN channels via Karhunen-­‐Loeve or DFT transforma4on   Capacity of 4me-­‐varying channel unknown (decomposi4ons don’t converge); Approximate by dividing into subbands   Each subband has width Bc (channel coherence bandwidth)   Independent fading in each subband   Capacity is the sum of subband capaci4es MIMO Decomposi4on   Decompose channel through transmit precoding ~
(x=Vx) and receiver shaping (y=U~Hy) y=Hx+n
H=UΣVH
~
~ ~
y=Σ x+n
~
yi=σι~
x+n~i
  Leads to RH≤min(Mt,Mr) independent channels with gain σi (ith singular value of H) and AWGN   Independent channels lead to simple capacity analysis and modula4on/demodula4on design Capacity of MIMO Systems   Depends on what is known at TX and RX and if channel is sta4c or fading   For sta4c channel with perfect CSI at TX and RX, power water-­‐filling over space is op4mal:   In fading waterfill over space (based on short-­‐term power constraint) or space-­‐4me (long-­‐term constraint)   Without transmiger channel knowledge, capacity metric is based on an outage probability   Pout is the probability that the channel capacity given the channel realiza4on is below the transmission rate. 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 direcGon to beamform • Need “sufficient” knowledge for opGmality of beamforming Op4mality of Beamforming Mean Information
Covariance Information
Diversity vs. Mul4plexing   Use antennas for mul4plexing or diversity Error Prone
Low Pe
  Diversity/Mul4plexing tradeoffs (Zheng/Tse) How should antennas be used?   Use antennas for mul4plexing: High-Rate
Quantizer
ST Code
High Rate
Decoder
Error Prone
  Use antennas for diversity Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
Low Pe
Depends on end-to-end metric: Solve by optimizing app. metric
Mul4user Channel Capacity Fundamental Limit on Data Rates Capacity: The set of simultaneously achievable rates {R1,…,Rn}
R3
R1
R2
R3
R2
R1
  Capacity depends on channel model   AWGN   Fading   ISI   MIMO Broadcast Channel Capacity Region in AWGN   Model   One transmiger, two receivers with spectral noise density n1, n2: n1<n2.   Transmiger has average power Pand total bandwidth B.   Single User Capacity:   Maximum achievable rate with asympto4cally small Pe   Set of achievable rates includes (C1,0) and (0,C2), obtained by alloca4ng all resources to one user. Rate Region: Time Division  Time Division (Constant Power)   Frac4on of 4me τ allocated to each user is varied  Time Division (Variable Power)   Frac4on of 4me τ and power σi allocated to each user is varied Rate Region: Frequency Division  Frequency Division   Bandwidth Bi and power Si allocated to each user is varied. Equivalent to TD for Bi=τiB and Pι=τiσi.
Superposi4on Coding Best user decodes fine points
Worse user decodes coarse points
Code Division   Superposi4on Coding   Coding strategy allows beger user to cancel out interference from worse user.   DS spread spectrum with spreading gain G and cross correla4on ρ12= ρ21 =G:   By concavity of the log func4on, G=1 maximizes the rate region.   DS without interference cancella4on Comparison of Achievable Rates Broadcast and MAC Fading Channels Broadcast: One Transmiger to Many Receivers. Mul4ple Access: Many Transmigers to One Receiver. x
x
g2(t)
x
g3(t)
g1(t)
R2
R1
Goal: Maximize the rate region {R1,…,Rn}, subject to some minimum rate constraints, by dynamic alloca4on of power, rate, and coding/decoding. Assume transmit power constraint and perfect TX and RX CSI R3
Fading Capacity Defini4ons   Ergodic (Shannon) capacity: maximum long-­‐term rates averaged over the fading process. 


Shannon capacity applied directly to fading channels. Delay depends on channel varia4ons. 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 varia4ons. 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 *Hanly/Tse, IT, 11/98
Two-­‐User Fading Broadcast Channel √h1[i]
X[i]
ν1[i]
x
+
Y1[i]
x
+
Y2[i]
√h2[i]
ν2[i]
At each time i:
n={n1[i],n2[i]}
n1[i]=ν1[i]/√h1[i]
X[i]
+
Y1[i]
+
Y2[i]
n2[i]=ν2[i]/√h2[i]
Ergodic Capacity Region*   Capacity region: ,where   The power constraint implies   Superposi4on coding and successive decoding achieve capacity   Best user in each state decoded last   Power and rate adapted using mul4user water-­‐filling: power allocated based on noise levels and user priori4es *Li/Goldsmith, IT, 3/01
Outage Capacity Region   Two different assump4ons about outage:   All users turned off simultaneously (common outage Pr)   Users turned off independently (outage probability vector Pr)   Outage capacity region implicitly defined from the minimum outage probability associated with a given rate   Common outage: given (R,n), use threshold policy   If Pmin(R,n)>s* declare an outage, otherwise assign this power to state n.   Power constraint dictates s* :   Outage probability: Independent Outage   With independent outage cannot use the threshold approach:   Any subset of users can be ac4ve in each fading state.   Power alloca4on must determine how much power to allocate to each state and which users are on in that state.   Op4mal power alloca4on maximizes the reward for transmiung to a given subset of users for each fading state   Reward based on user priori4es and outage probabili4es.   An itera4ve technique is used to maximize this reward.   Solu4on is a generalized threshold-­‐decision rule. Minimum-­‐Rate Capacity Region   Combines ergodic and zero-­‐outage capacity:   Minimum rate vector maintained in all fading states.   Average rate in excess of the minimum is maximized.   Delay-­‐constrained data transmiged at the minimum rate at all 4mes.   Channel varia4on exploited by transmiung other data at the maximum excess average rate. Minimum Rate Constraints

Define minimum rates R* = (R*1,…,R*M):
  These rates must be maintained in all fading states.

For a given channel state n:

R* must be in zero-outage capacity region
  Allocate excess power to maximize excess ergodic rate
  The smaller R*, the bigger the min-rate capacity region
Comparison of Capacity Regions   For R* far from Czero boundary, Cmin-­‐rate ≈Cergodic   For R* close to Czero boundary, Cmin-­‐rate ≈Czero∩R* Mul4ple Access Channel   Mul4ple transmigers   Transmiger i sends signal Xi with power Pi   Common receiver with AWGN of power N0B   Received signal: X1
X2
X3
MAC Capacity Region   Closed convex hull of all (R1,…,RM) s.t.   For all subsets of users, rate sum equals that of 1 superuser with sum of powers from all users   Power Alloca4on and Decoding Order   Each user has its own power (no power alloc.)   Decoding order depends on desired rate point Two-­‐User Region Superposition coding
w/ interference canc.
C2
Time division
SC w/ IC and time
sharing or rate splitting
Ĉ2
Frequency division
SC w/out IC
Ĉ1
C1
Comparison of MAC and BC P
  Differences:   Shared vs. individual power constraints P1
  Near-­‐far effect in MAC   Similari4es: P2
  Op4mal BC “superposi4on” coding is also op4mal for MAC (sum of Gaussian codewords)   Both decoders exploit successive decoding and interference cancella4on MAC-­‐BC Capacity Regions   MAC capacity region known for many cases   Convex op4miza4on problem   BC capacity region typically only known for (parallel) degraded channels   Formulas oben not convex   Can we find a connec4on between the BC and MAC capacity regions? Duality
Dual Broadcast and MAC Channels Gaussian BC and MAC with same channel gains
and same noise power at each receiver
x
+
x
+
x
+
Broadcast Channel (BC)
x
Multiple-Access Channel (MAC)
The BC from the MAC P1=0.5, P2=1.5
Blue = BC
Red = MAC
P1=1, P2=1
P1=1.5, P2=0.5
MAC with sum-power constraint
Sum-Power MAC

MAC with sum power constraint
  Power pooled between MAC transmitters
  No transmitter coordination
Same capacity region!
MAC
BC
BC to MAC: Channel Scaling




Scale channel gain by √α, power by 1/α
MAC capacity region unaffected by scaling
Scaled MAC capacity region is a subset of the scaled BC
capacity region for any α
MAC region inside scaled BC region for any scaling
MAC
+
+
+
BC
The BC from the MAC
Blue = Scaled BC
Red = MAC
Duality: Constant AWGN Channels

BC in terms of MAC

MAC in terms of BC
Can also find a duality between
the optimal transmission strategies.
Duality Applies to Different Fading Channel Capaci4es   Ergodic (Shannon) capacity: maximum rate averaged over all fading states.   Zero-­‐outage capacity: maximum rate that can be maintained in all fading states.   Outage capacity: maximum rate that can be maintained in all nonoutage fading states.   Minimum rate capacity: Minimum rate maintained in all states, maximize average rate in excess of minimum Explicit transformaGons between transmission strategies Duality: Minimum Rate Capacity
MAC in terms of BC
Blue = Scaled BC
Red = MAC
  BC
region known
  MAC region can only be obtained by duality
What other capacity regions can be obtained by duality?
Broadcast MIMO Channels
Broadcast MIMO Channel t≥1 TX antennas
r1≥1, r2≥1 RX antennas
Perfect CSI at TX and RX
Non-degraded broadcast channel
Dirty Paper Coding (Costa’83)   Basic premise   If the interference is known, channel capacity same as if there is no interference   Accomplished by cleverly distribu4ng the wri4ng (codewords) and coloring their ink   Decoder must know how to read these codewords Dirty
Paper
Coding
Clean Channel
Dirty
Paper
Coding
Dirty Channel
Modulo Encoding/Decoding   Received signal Y=X+S, -­‐1≤X≤1   S known to transmiger, not receiver   Modulo opera4on removes the interference effects   Set X so that ⎣Y⎦[-­‐1,1]=desired message (e.g. 0.5)   Receiver demodulates modulo [-­‐1,1] -1
0
+1
…
…
-7
-5
-3
-1
0
+1
+3
S
+5
X
-1
0
+1
+7
Capacity Results   Non-­‐degraded broadcast channel   Receivers not necessarily “beger” or “worse” due to mul4ple transmit/receive antennas   Capacity region for general case unknown   Pioneering work by Caire/Shamai (Allerton’00):   Two TX antennas/two RXs (1 antenna each)   Dirty paper coding/lauce precoding (achievable rate)   Computa4onally very complex   MIMO version of the Sato upper bound   Upper bound is achievable: capacity known! Dirty-­‐Paper Coding for MIMO BC   Coding scheme:   Choose a codeword for user 1   Treat this codeword as interference to user 2   Pick signal for User 2 using “pre-­‐coding”   Receiver 2 experiences no interference:   Signal for Receiver 2 interferes with Receiver 1:   Encoding order can be switched   DPC op4miza4on highly complex:   Op4mize MIMO MAC and use duality to get op4mal DPC Full Capacity Region   DPC gives us an achievable region   Sato bound only touches at sum-­‐rate point   Bergman’s entropy power inequality is not a 4ght upper bound for nondegraded broadcast channel   A 4ghter bound was needed to prove DPC op4mal   It had been shown that if Gaussian codes op4mal, DPC was op4mal, but proving Gaussian op4mality was open.   Breakthrough by Weingarten, Steinberg and Shamai   Introduce no4on of enhanced channel, applied Bergman’s converse to it to prove DPC op4mal for MIMO BC. MIMO BC Capacity Region Single User Capacity Bounds
Dirty Paper (Capacity) Region
BC Sum Rate Point
Sato Upper Bound
Summary so far   Shannon capacity gives fundamental data rate limits for wireless channels   Fading mul4user channels op4mize at each channel instance for maximum average rate   Outage capacity provides higher rates with some outage probability.   Broadcast channels with ISI can use OFDM with near-­‐
op4mality   Duality connects BC and MAC channels; is used to obtain capacity of broadcast MIMO channels. Cellular Systems BASE
STATION
  Frequencies, 4meslots, or codes reused at spa4ally-­‐
separate loca4ons   Efficient system design is interference-­‐limited   Base sta4ons perform centralized control func4ons   Call setup, handoff, rou4ng, adap4ve schemes, etc. What does Shannon say?   “Shannon-­‐theore4c approach to a Gaussian cellular mul4ple-­‐access channel, A. Wyner, IT Trans, 1994   Cellular uplink   Received signal at BS is sum of the signals transmiged from mobiles within the cell   Plus α 4mes sum of signals transmiged from mobiles in adjacent cells (plus noise) α
α
Linear Cellular Array   Capacity as a func4on of α
  K transmigers per cell , Power P per transmiger   Op4mal joint processing at BS   Receiver noise is σ2   Subop4mal techniques   Treat interference as noise (MMSE)   TDMA Capacity Comparison Many Extensions   Fading   Wyner & Shamai, 1997, Somekh & Shamai’00   ISI Channels   Shental, Shental, Shamai, Kanter, Weiss’08   Limited Backhaul   Marsch, Fegweis’07; Sanderovich, Somekh, Poor, Shamai’09   Downlink   Jing, Tse, Hou, Soriaga, Smee, and Padovani’07, Liang, Goldsmith’06 Virtual MIMO in Cellular Currently being inves/gated for next-­‐gen systems   Network MIMO: Coopera4ng BSs form a MIMO array   Downlink is a MIMO BC, uplink is a MIMO MAC   Can treat “interference” as known signal (DPC) or noise   Can cluster cells and cooperate between clusters   Can also install low-­‐complexity relays   Mobiles can cooperate via relaying, virtual MIMO, conferencing, analog network coding, …   Capacity unknown Adap4ve Reuse w/ BS Coopera4on Performance Comparison 73
Multicasting with a Relay
  Develop structured codes that exploit network topology
  Relay decodes and multicasts modulo sum of messages
  Linear codes achieve the capacity region for finite-field
modulo additive channels
  Nested-lattice codes approach upper bound for Gaussian
channels and surpass standard random coding schemes
Ad-­‐Hoc Networks   Peer-­‐to-­‐peer communica4ons   No backbone infrastructure or centralized control   Rou4ng can be mul4hop.   Topology is dynamic.   Fully connected with different link SINRs   Open ques4ons   Fundamental capacity region   Resource alloca4on (power, rate, spectrum, etc.)   Rou4ng Network Capacity:What is it?   n(n-­‐1)-­‐dimensional region R34
Upper Bound
  Rates between all node pairs   Upper/lower bounds 

Lower bounds achievable Upper bounds hard   Other axes Lower Bound
Capacity
Upper Bound
R12
Delay
  Energy?   Delay? Lower Bound
Energy
Achievable Region Slice (6 Node Network) Multiple
hops
Spatial
reuse
SIC
(a): Single hop, no simultaneous
transmissions.
(b): Multihop, no simultaneous
transmissions.
(c): Multihop, simultaneous
transmissions.
(d): Adding power control
(e): Successive IC, no power
control.
Ad-­‐Hoc Network Capacity Today   Much progress in finding the Shannon capacity limits of wireless single and mul4user channels   Ligle known about these limits for mobile wireless networks, even with simple models   Recent results on scaling laws for networks   No separa4on theorems have emerged   Delay, outage, and energy are not typically incorporated into capacity defini4ons Network Capacity Results   Mul4ple access channel (MAC)   Broadcast channel   Relay channel upper/lower bounds   Interference channel   Scaling laws   Achievable rates for small networks Biggest Open Ques4on: How to manage interference? Par4al answer: exploited it via coopera4on and cogni4on Coopera4on in Wireless Networks   Many possible coopera4on strategies:   Virtual MIMO , generalized relaying, interference forwarding, and one-­‐shot/itera4ve conferencing   Many theore4cal and prac4ce issues:   Overhead, forming groups, dynamics, synch, … Capacity Gain with Virtual MIMO (2x2) x1
G
G
x2
  TX coopera4on needs large coopera4ve channel gain to approach broadcast channel bound   MIMO bound unapproachable General Relay Strategies TX1 Y3=X1+X2+Z3 TX2 
RX1 Y4=X1+X2+X3+Z4 X1 relay X3= f(Y3) X2 Y5=X1+X2+X3+Z5 RX2 Can forward message and/or interference 
Relay can forward all or part of the messages 

Much room for innovaGon Relay can forward interference 
To help subtract it out Beneficial to forward both interference and message In fact, it can achieve capacity Analog network coding and the MAC cutéset boun
10
S
P3
Ps
D
P2
P4
R [bits/channel use]
P1
P1 = 2P =100
P3 = 4P =10
hij = 10, for all i,j
9
8
7
MAC cutéset bound
6
analog network coding
5
4
3
2
amplified noise power
1
0
0
50
100
150
200
source power
P
s
•
For large powers Ps, P1, P2, analog network coding
approaches capacity
250
300
MIMO in Ad-­‐Hoc Networks •  Antennas can be used for mulGplexing, diversity, or interference cancellaGon • Cancel M-­‐1 interferers with M antennas •  What metric should be opGmized? Cross-­‐Layer Design Cogni4ve Radio Paradigms  Underlay   Cogni4ve radios constrained to cause minimal interference to noncogni4ve radios  Interweave   Cogni4ve radios find and exploit spectral holes to avoid interfering with noncogni4ve radios  Overlay   Cogni4ve radios overhear and enhance noncogni4ve radio transmissions Knowledge and Complexity Underlay Systems   Cogni4ve radios determine the interference their transmission causes to noncogni4ve nodes   Transmit if interference below a given threshold NCR IP NCR CR CR   The interference constraint may be met   Via wideband signalling to maintain interference below the noise floor (spread spectrum or UWB)   Via mul4ple antennas and beamforming Interweave Systems   Measurements indicate that even crowded spectrum is not used across all 4me, space, and frequencies   Original mo4va4on for “cogni4ve” radios (Mitola’00)   These holes can be used for communica4on   Interweave CRs periodically monitor spectrum for holes   Hole loca4on must be agreed upon between TX and RX   Hole is then used for opportunis4c communica4on Compressed sensing reduces A/D and processing requirements Overlay Cogni4ve Systems   Cogni4ve user has knowledge of other user’s message and/or encoding strategy   Can help noncogni4ve transmission   Can presubtract noncogni4ve interference CR NCR RX1 RX2 Similar ideas apply to cellular overlays and cogni4ve relays Performance Gains from Cogni4ve Encoding outer bound
our scheme
prior schemes
Only the CR
transmits
Cellular Systems with Cognitive Relays
Cognitive Relay 1
Coding Scheme data
Source
Cognitive Relay 2
  Enhance robustness and capacity via cognitive relays
  Cognitive relays overhear the source messages
  Cognitive relays then cooperate with the transmitter in the
transmission of the source messages
  Can relay the message even if transmitter fails due to congestion,
etc.
  Strictly improves capacity over BC alone or cognitive nodes alone
Is a capacity region all we need to design networks? Yes, if the application and network design can be decoupled
Application metric: f(C,D,E): (C*,D*,E*)=arg max f(C,D,E)
Capacity
(C*,D*,E*)
Delay
Energy
Some capacity ques4ons   How to parameterize the network capacity region   Power/bandwidth   Channel models and CSI   Outage probability   Security/robustness   Defining capacity in terms of asympto4cally small error and infinite delay has been highly enabling   Has also been limi4ng 
Unconsummated union in networks and IT   What is the alterna4ve? Must be fundamental and useful
MANET Metrics
New Paradigms
for Upper
Bounds
Constraints
Capacity and Fundamental Limits
Capacity
Upper
Bound
Achievable Rates
for Layerless
Networks
Delay
Lower
Bound
Degrees of
Freedom
Energy
Generalized
Network
Inferface
New Theory Needed
Models and
Dynamics
Network and Application
Optimization
Capacity
(C*,D*,E*)
Delay
Utility=U(C,D,E)
Energy/SNR
Metrics
Problem Definition
Application Metrics
Some Rela4vely New Theory   Upper Bounds   Network equivalence   Strong converses   Achievable rates for layerless dynamic networks   Noisy network coding   Analog network coding   Network interface and op4miza4on   Dynamic network u4lity maximiza4on Summary   Capacity of wireless single-­‐user and mul4user channels fairly well defined   Impact of feedback, outage, energy unknown   Cellular system and ad hoc networks have limited capacity results and even problem formula4ons   Understanding impact of applica4ons on problem formula4ons limited Tutorial References Newer Results: Capacity I. Maric, R. Dabora and A. Goldsmith, An Outer Bound for the Gaussian
Interference Channel with a Relay, 2009 ITW, Taormina, Italy, Oct. 2009
Newer Results: Networks