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SIGNAL PROCESSING IN COMMUNICATIONS Issues and Trends Vincent Poor (poor@princeton.edu) UC, Irvine February 18, 2004 Signal Processing in Communications

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Communications 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

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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

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The 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

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MUD

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Multiple-Access Channel (MAC) Modulator Channel 010… 110… Signal Processing 110… Modulator Signal Processing 010…...... MUD Signal processing (MUD) is used to separate the users.

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Multiuser Detection (MUD)... Matched Filter, User 1 Matched Filter, User 2 Decision Logic MAC 110… 010… MUD Optimal, linear, iterative & adaptive versions (more in a minute)

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MUD - Linear Model K users, each transmitting B symbols, yields a linear model for inputs to the decision logic: y = H b + N (0, 2 H) 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

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MUD - Varieties y = H b + N (0, 2 H) Optimal [ Complexity O(2 K ); = delay spread] – –ML : argmax (y|b) – –MAP: argmax p (b k,i |y) Linear [ Complexity O((KB) 3 )] – –Decorrelator : sgn {H -1 y } – 2 I –MMSE : sgn {(H+ 2 I) -1 y } Iterative [ Complexity O(Kn max ), 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-SP02] MUD

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TURBO Signal Processing in Communications

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Turbo 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 (IE 1 )+ Complexity (IE 2 ) *APP = a posteriori probability Turbo

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Convolutional Encoders Interleavers MAC Data for K Users Channel Input Channel Output SISO MUD K SISO Decoders De-InterleaversInterleavers Channel Output Output Decision Soft-input/soft-output (SISO) Iterative Interleaving removes correlations vs. Turbo MUD Turbo

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Turbo MUD Example [K = 4; = 0.7] Turbo Rate-1/2 convolutional code; constraint length 5; 128-long random interleavers

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Application to UWB Systems K-user (impulse radio) UWB system transmits N f 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

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N c = 20, N f = 10, K = 20 (strong interferers, 6dB above user of interest) Simulation - UWB Turbo Detector Turbo

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Other Applications DSL [Dai & Poor, JSAC 02] Powerline Comms. [Dai & Poor, Comm. Mag. 03] Channel Estimation (MCMC) [X. Wang, et al.]

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MIMO BS MS Signal Processing in Communications

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SPACE-TIME MUD (The SIMO Case) BS MS MIMO

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Multipath SIMO MA Channel...... User 1: 010… User 2: 110… User K: 011… MIMO

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Sufficient Statistic (Space-Time Matched Filter Bank ) As before, linear model with optimal, linear, iterative & adaptive versions.... Temporal Matched Filters {k, l, p} Decision Logic 110… 010… 011… Beam Formers {k, l} RAKEs {k}............ KLP KL K K Users; P Receive Antennas; L Paths/User/Antenna [Wang & Poor, T-SP99] MIMO

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MIMO MUD MS BS MS Observation: MIMO MUD is the same as SIMO MUD, except for the decision algorithm - MI adds further constraints on b. MIMO

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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 Thm: 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-SP02] MIMO

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Turbo IC Space-Time MUD (MISO Case) MIMO

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Performance (4 1; K=4) MIMO

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BLAST-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-WC04] : MUD restores the BLAST capacity gain in interference channels. MIMO

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CROSS-LAYER Signal Processing in Communications

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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 Higher-Layer Functionality Cross-Layer

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Wireless Multi-Hop Network Network Diameter = maximum number of hops to reach any node Network Diameter = maximum number of hops to reach any node Connectivity between nodes depends on PHY (e.g., node-layer processing) Connectivity between nodes depends on PHY (e.g., node-layer processing) Cross Layer [Comaniciu & Poor, T-WC04]

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N = number of nodes that can be supported in the network D = network diameter (maximum number of hops to reach any node) L = spreading gain (BW fixed) Target SIR = 5 Ad-hoc Network Capacity v.Diameter Cross Layer

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Competition in Multiple- Access 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., Allerton03]

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Game Theoretic Framework Throughput: T k = R k f( k ), where f( k ) is the frame success rate, and k is the received SIR of user k. Game: G = [{1, …, K}, {A k }, {u k }] K: total number of users A k : set of strategies for user k u k : utility function for user k Cross-Layer

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Large-System Analysis Consider random CDMA with spreading gain N. As K, N with K/N = ; Nash equilibria: Two mechanisms: power pooling power pooling interference reduction interference reduction Cross-Layer

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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 Example Cross-Layer

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QUANTUM MUD Signal Processing in Communications

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010… Modulator Channel Physical Measurement Decision Logic 010… 110… Modulator Physical Measurement Quantum MAC Measurements may not be compatible No cloning theorem Instrument and detector must be designed jointly Quantum

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2-User Example: Error Probabilities Counter: ML MUD based on photon counts in each mode. Optimal: Optimal quantum MUD 30 photons (average) per user. Source: Concha & Poor, IT04 Quantum

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Conclusion 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

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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)

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