SIGNAL PROCESSING IN SIGNAL PROCESSING IN COMMUNICATIONSCOMMUNICATIONS
Issues and TrendsIssues and Trends
Vincent PoorVincent Poor([email protected])([email protected])
UC, IrvineUC, IrvineFebruary 18, 2004February 18, 2004
Signal Processing in Communications
Communications in the 21st CenturyCommunications in the 21st Century
• High-Level Trends – Dramatic growth rates in capacity demands:
• wireless
• broadband
– Increase in shared (multiple-access, interference) channels:• cellular (IS-95, 3G)
• WiFi/Bluetooth/UWB (unlicensed spectrum)
• DSL (cross-talkers in twisted-pair bundles)
• Basic Resources– Bandwidth - tightly constrained – Power - tightly constrained – Diversity - exists naturally, and can be created – Intelligence - growing exponentially
Signal Processing in Communications
Signal Processing in CommunicationsSignal Processing in Communications
• Principal Roles – Source compression
– Mitigation of physical layer impairments • fading, dispersion, interference
– Exploitation of physical layer diversity • spatial, temporal, spectral
• Catchwords– Turbo - near-optimal, low-complexity iterative processing
– MIMO - multiple antennas at transmitter and receiver
– Cross-Layer - design across the PHY/MAC boundary
– Quantum - exploitation of quantum effects
Signal Processing in Communications
The Rest of This TalkThe Rest of This Talk
• Recent Results in ... – Turbo
– MIMO
– Cross-Layer
– Quantum
• Context: Multiuser Detection (MUD) – Unifies receiver processing in shared access systems
Signal Processing in Communications
MUDMUD
Signal Processing in Communications
Multiple-Access Channel (MAC)Multiple-Access Channel (MAC)
Modulator Channel010…
110…
SignalProcessing
110…Modulator
SignalProcessing 010…
......
......
MUD
Signal processing (MUD) is used to separate the users.Signal processing (MUD) is used to separate the users.
Multiuser Detection (MUD)Multiuser Detection (MUD)
......
Matched Filter,User 1
Matched Filter,User 2
DecisionLogic
MAC
110…
010…
MUD
OptimalOptimal, , linearlinear, , iterativeiterative & & adaptiveadaptive versions (more in a minute) versions (more in a minute)
MUD - Linear ModelMUD - Linear ModelK users, each transmitting B symbols, yields a linear model for inputs to the decision logic:
yy = = H bH b + + NN(0, (0, 22HH))
• y = KB-long sufficient statistic vector
• b = KB-long vector of symbols
• H = KBKB matrix of cross-correlations
The purpose of the decision logic is to fit this model.
MUD
MUD - VarietiesMUD - Varieties
yy = = H bH b + + NN(0, (0, 22HH))
• Optimal [Complexity O(2K); = delay spread] – ML: argmax l(y|b) – MAP: argmax p(bk,i|y)
• Linear [Complexity O((KB)3)]
– Decorrelator: sgn{H-1 y}
– MMSE: sgn{(H+ 22II)-1 y}
• Iterative [Complexity O(Knmax), etc.]
– Linear IC: Gauss-Siedel, Jacobi, conjugate-gradient– Nonlinear IC: the above with intermediate hard decisions– EM: symbols are stochastic– Turbo: symbols are constrained via channel coding, etc.
• Adaptive [Sampling, followed by LMS, RLS, subspace, etc.]
[Dai & Poor, T-SP’02]
MUD
TURBOTURBO
Signal Processing in Communications
Turbo ProcessingTurbo Processing
Inference Engine 2
(APP Calculator)
Inference Engine 1
(APP* Calculator)
{Prior, Observations, Constraints}1 {Prior, Observations, Constraints}2
{APP}1 {Updated Prior}2
{Updated Prior}1 {APP}2
Iterate until the APPs stabilize. Complexity Complexity (IE1)+ Complexity (IE2)
*APP = a posteriori probability Turbo
Convolutional Encoders
Interleavers MAC
Data for K Users Channel Input Channel Output
SISOMUD
K SISO Decoders
De-InterleaversInterleavers
Channel Output
Output Decision Soft-input/soft-output (SISO) Iterative Interleaving removes correlations
{Pdecoder(bk,i y)}
2KΔ +2νvs. 2KΔν
Turbo MUDTurbo MUD
{PMUD(bk, i y)}
Turbo
Turbo MUD Example [K = 4; Turbo MUD Example [K = 4; = 0.7] = 0.7]
Turbo
Rate-1/2 convolutional code; constraint length 5; 128-long random interleavers
Application to UWB SystemsApplication to UWB Systems
• K-user (impulse radio) UWB system transmits Nf
short pulses for each information symbol.
• Pulse positions change from pulse-to-pulse with a pseudorandom pattern, unique to each user.
• “Turbo” MUD Algorithm [Fishler & Poor, IEEE-SP]:– Iterate between two detectors, with intermediate
exchanges of soft information:
• “Pulse” detector: performs MUD on a pulse-by-pulse basis, ignoring the fact that multiple pulses contain the same symbol.
• “Symbol” detector: exploits the fact that multiple pulses contain the same symbol (“repetition decoder”).
Turbo
Nc = 20, Nf = 10, K = 20 (strong interferers, 6dB above user of interest)
Simulation - UWB Turbo DetectorSimulation - UWB Turbo Detector
Turbo
Turbo
Other ApplicationsOther Applications
• DSL [Dai & Poor, JSAC ’02]
• Powerline Comms. [Dai & Poor, Comm. Mag. ‘03]
• Channel Estimation (MCMC) [X. Wang, et al.]
MIMOMIMO
BS
MS
MS
MS
MS
Signal Processing in Communications
SPACE-TIME MUD SPACE-TIME MUD (The SIMO Case)(The SIMO Case)
BSMS
MSMS
MS
MIMO
Multipath SIMO MA ChannelMultipath SIMO MA Channel
€
r2 (t)
€
rP (t)
......
......
€
r1(t)User 1: 010…
User 2: 110…
User K: 011…
MIMO
Sufficient Statistic Sufficient Statistic (Space-Time Matched Filter Bank(Space-Time Matched Filter Bank))
As before, linear model with As before, linear model with optimaloptimal, , linearlinear, , iterativeiterative & & adaptiveadaptive versions. versions.
......
TemporalMatchedFilters
{k, l, p}
DecisionLogic
110…
010…
011…
BeamFormers
{k, l}
RAKEs{k}
€
r2 (t)
€
rP (t)
€
r1(t)
...... ...... ...... ......
KKLLPP KKLL KK
K Users; P Receive Antennas; L Paths/User/Antenna
[Wang & Poor, T-SP’99]
MIMO
MIMO MUDMIMO MUD
MS BS
MSMS
MS
Observation: MIMO MUD is the same as SIMO MUD, except for the decision algorithm - MI adds further constraints on b.
MIMO
Space-time Coded SystemsSpace-time Coded Systems
• Space-time Coded Systems
– Single-user Channels: • Encoding of symbols across multiple transmit antennas.
• ST block codes [Alamouti, Tarokh, et al.]; ST trellis codes [Tarokh,
et al.]; unitary ST codes [Hochwald, Marzetta, et al.].
– Multiuser Channels [Jayaweera & Poor, EJASP ‘02]: • Separation Th’m: “Full-diversity-achieving single-user ST trellis
codes also achieve full diversity in multiuser channels with joint ML detection & decoding (assumes large SNR, quasi-static Rayleigh fading, etc.).”
• Turbo-style iteration among ST trellis decoding & MUD achieves near-ML performance.
• Blind adaptive linear MUD for ST block coding via subspace tracking & Kalman filtering [Reynolds,Wang & Poor, T-SP’02]
MIMO
Turbo IC Space-Time MUD Turbo IC Space-Time MUD (MISO Case)(MISO Case)
MIMO
Performance (4 Performance (4 1; K=4) 1; K=4)
-5 0 5 1010-3
10-2
10-1
100Turbo IC-MMSE-ST-MUD Decoder FER Vs. SNR
Eb/N0
FER
it: 1
it: 2
it: 3
it: 4
16-states trellis space-time code
Turbo IC-MMSE-ST-MUD: rho=0.75, K=4, X Ants.=4Single User Bound
MIMO
BLAST-Type SystemsBLAST-Type Systems
• BLAST (Bell Labs Layered Space-Time Architecture)
– Basic BLAST [Foschini, et al.]: • Distributes symbols of a single user on multiple tx antennas.
• Uses MUD to separate different streams using spatial signature.
• Capacity (Rayleigh) linear in the min{#tx,#rx}antennae.
• Capacity gain degrades in interference-limited channels.
– Turbo BLAST [Dai, Molisch & Poor, T-WC’04]:
• MUD restores the BLAST capacity gain in interference channels.
MIMO
CROSS-LAYERCROSS-LAYER
Signal Processing in Communications
• Use of advanced signal processing at the
nodes of a wireless network has effects at the
MAC layer.
• Examples using MUD include effects on:
– Capacity: users-per-dimension - cellular [Tse & Hanley;
Yao, Poor & Sun; Comaniciu & Poor] & ad hoc [Comaniciu
& Poor] networks
– Utility: bits-per-joule [Meshkati, et al.]
Effects of MUD on Wireless Effects of MUD on Wireless Higher-Layer FunctionalityHigher-Layer Functionality
Cross-Layer
Wireless Multi-Hop NetworkWireless Multi-Hop Network
• Network DiameterNetwork Diameter = maximum number of hops to reach any node = maximum number of hops to reach any node• ConnectivityConnectivity between nodes depends on PHY (e.g., node-layer processing) between nodes depends on PHY (e.g., node-layer processing)
Cross Layer[Comaniciu & Poor, T-WC’04]
NN = number of nodes that can be supported in the network = number of nodes that can be supported in the networkDD = network diameter (maximum number of hops to reach any node) = network diameter (maximum number of hops to reach any node)LL = spreading gain (BW fixed) = spreading gain (BW fixed)Target SIR = 5Target SIR = 5
Ad-hoc Network Capacity v.DiameterAd-hoc Network Capacity v.Diameter
Cross Layer
Competition in Multiple-Competition in Multiple-Access NetworksAccess Networks
• Consider a multiple-access network.
• User terminals are like players in a game,
competing for network resources; each would like to
maximize its own utility.
• The action of each user affects the utility of others.
• Can model this as a non-cooperative game.
Cross-Layer[Meshkati, et al., Allerton’03]
Game Theoretic FrameworkGame Theoretic Framework
€
uk = utility =throughput
transmit power=
Tk
pk
bits
Joule ⎡ ⎣ ⎢
⎤ ⎦ ⎥
Throughput: Tk = Rk f(k), where f(k) is the frame success
rate, and k is the received SIR of user k.
Game: G = [{1, …, K}, {Ak}, {uk}]
K: total number of users
Ak: set of strategies for user k
uk: utility function for user k
Cross-Layer
Large-System AnalysisLarge-System Analysis
€
uk
=R
kf (γ * )
γ *σ 2h
kΓ where
Γ MF = 1−α γ * for α <1
γ *
Γ DE = 1− α for α < 1
Γ MMSE = 1− α γ *
1+ γ * for α < 1+
1γ *
with h k
= hkp
2
p=1
P
∑ and α =α
P
• Consider random CDMA with spreading gain N.• As K , N with K/N = ; Nash equilibria:
Two mechanisms:Two mechanisms:• power poolingpower pooling• interference reductioninterference reduction
Cross-Layer
• Multiuser detectors achieve higher utility and can
accommodate more users compared to matched filter.
• Significant performance improvements are achieved when
multiple antennas are used compared to single antenna case.
Numerical ExampleNumerical Example
Cross-Layer
QUANTUMQUANTUM
MUDMUD
Signal Processing in Communications
010…Modulator Channel
PhysicalMeasurement
DecisionLogic 010…
110…Modulator
PhysicalMeasurement
Quantum MACQuantum MAC
• Measurements may not be compatible
• “No cloning” theorem
• “Instrument” and detector must be designed jointly
Quantum
2-User Example: Error Probabilities2-User Example: Error Probabilities
CounterCounter: ML MUD based on photon counts in each mode.: ML MUD based on photon counts in each mode.OptimalOptimal: Optimal quantum MUD: Optimal quantum MUD
30 photons (average)30 photons (average)per user.per user.
SourceSource: Concha & : Concha & Poor, Poor, IT’04IT’04
Quantum
ConclusionConclusion
• Signal processing is central to the enablement of higher communications capacity, especially for shared access channels.
• Things to watch: – Turbo – MIMO – Cross-Layer– Quantum
Signal Processing in Communications
THANK YOU!THANK YOU!
Signal Processing in Communications
Two New Books:
• Wireless Communication Systems: Advanced Techniques for Signal Reception (with X. Wang; Prentice-Hall, 2004)
• Wireless Networks: Multiuser Detection in Cross-Layer Design (with C. Comanciu and N. Mandayam; Kluwer, 2004)