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Andrea Goldsmith Stanford University DAWN ARO MURI Program Review U.C. Santa Cruz Oct 5, 2009 Joint work with Y. Chang, R. Dabora, D. Gunduz, I. Maric, Y. Xie Space: The Final Frontier

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Introduction Multiple antennas add a new degree of freedom in MIMO wireless network design MIMO increases capacity as well as tradeoff regions available to higher protocol layers We investigate capacity, performance regions, and cross-layer design to optimize tradeoffs

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Crosslayer Protocol Design Application Network Access Link Throughput Delay Diversity (T*,D v *,D l *) In MIMO MANETs Results will lead to optimal layering and insight into layer interfaces

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Technical Approach Capacity via cooperation: Investigate strategies where node cooperation exploits degrees of freedom from multiple antennas Capacity with cognition: Extend overlay cognitive techniques to exploit MIMO Diversity-multiplexing-delay tradeoffs: Investigate these tradeoffs for multihop MIMO networks. End-to-end performance optimization: Optimize end-to-end performance in MIMO MANETs using joint source/channel coding and wireless network utility maximization (WNUM)

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Cooperation in MIMO Wireless Networks Many possible cooperation strategies: Virtual MIMO, generalized relaying and interference forwarding, one-shot/iterative conferencing, others “Easy” to extend virtual MIMO to MIMO nodes Impact of extra antennas on other techniques unclear Practical issues: Overhead, forming groups, dynamics, synch,…

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Generalized Relaying (SISO) Relaying strategies: Relay can forward all or part of the messages Much room for innovation Relay can forward interference To help subtract it out TX1 TX2 relay RX2 RX1 X1X1 X2X2 Y 3 =X 1 +X 2 +Z 3 Y 4 =X 1 +X 2 +X 3 +Z 4 Y 5 =X 1 +X 2 +X 3 +Z 5 X 3 = f(Y 3 )

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Achievable Rates The strategy to achieve these rates is: - Single-user encoding at the encoder 1 to send W 1 - Decode/forward at encoder 2 and the relay to send message W 2 This region equals the capacity region when the interference is strong and the channel is degraded for any distribution p(p(x 1 )p(x 2,x 3 )p(y 1,y 2 |x 1,x 2,x 3 ) dest1 dest2 encoder 1 encoder 2 relay

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Beneficial to forward both interference and message

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New Outer Bound via a Genie Parameters chosen so RX1 obtains less noisy information about W 2 then RX2: relay Y 1g Y1Y1 Y2Y2 X1X1 Y 1g = d 1 X 1 +d 2 X 2 + d r X 3 +d 3 Z 1 +d 4 Z 1 ’ where var(Z e )≤var(Z 2 ) X2X2 X3X3 → Receiver 1 can decode (W 1,W 2 ) Currently extending to MIMO multihop networks

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Extension to MIMO and Multihop Open Questions Which nodes should cooperate What (partial) interference should be forwarded How should interference be cancelled: spatially or via detection The questions apply to ad-hoc and cellular infrastructures

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Cognitive Radio Paradigms Underlay Cognitive radios constrained to cause minimal interference to noncognitive radios Interweave (Dynamic Spectrum Access) Cognitive radios find and exploit spectral holes to avoid interfering with noncognitive radios Overlay Cognitive radios overhear and enhance noncognitive radio transmissions Knowledge and Complexity Cognitive radios sense environment to support new users without hurting legacy users

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Capacity of Cognitive MIMO Networks Coexistence conditions: Noncognitive user unaware of secondary users Cognitive user doesn’t impact rate of noncognitive user Encoding rule for the cognitive encoder: Generates codeword for primary user message Generates codeword for its message using dirty paper coding Two codewords superimposed to form final codeword NC TX C TX NC RX C RX RX1 RX2 CR NCR

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Achievable rates (2 users) For MISO secondary users, beamforming is optimal Maximum achievable rate obtained by solving Closed-form relationship between primary/secondary user rates.

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MIMO cognitive users (2 Users) Propose two (suboptimal) cognitive strategies D-SVD Precode based on SVD of cognitive user’s channel P-SVD Project cognitive user’s channel onto null space between C TX and NC RX, then perform SVD on projection

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Multi-user Cognitive MIMO Networks Achievable rates with two primary users Cognitive MIMO network with multiple primary users Extend analysis to multiple primary users Assume each transmitter broadcasts to multiple users Primary receivers have one antenna Secondary users are MISO. Main Result: With appropriate power allocation among primary receivers, the secondary users achieve their maximum possible rate.

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Diversity-Multiplexing Tradeoffs in MIMO Use antennas for multiplexing: Use antennas for diversity High-Rate Quantizer ST Code High Rate Decoder Error Prone Low P e Low-Rate Quantizer ST Code High Diversity Decoder How should antennas be used? Depends on end-to-end metric.

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DMT at High SNR ‡ Define family of block codes {C(SNR)} of length T with rate R(SNR)~r log SNR Define diversity and multiplexing gains asymptotically ‡ Zheng/Tse 2002

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Optimizing Diversity vs. Multiplexing Closed-form solution at high SNR Optimal d*(r*) diversity/multiplexing point minimizes D T d*(r*) DTDT For nonasymptotic regime, Use optimization

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DMT in MIMO Multihop Networks Quasi-static Rayleigh fading channel Channel state known only at the receivers

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DMT for Full-duplex Relays The relay can receive and transmit simultaneously The DMT for (M1,M2,M3) full-duplex system is The hop with the minimum diversity gain is the bottleneck Achieved by decode-and-forward relaying with block Markov structure Follows easily since DF achieves capacity

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Dynamic Decode-and-Forward in Half-duplex In half-duplex system, TX and RX must share time DDF introduced by Azarian et al. (IT’05) to optimize this sharing Relay listens until decoding complete, then transmit DDF achieves the best known DMT for half-duplex relay channels, yet short of the upper bound We show: Achieves optimal DMT in multi-hop relay channels Not piece-wise linear, no general closed form expression Can be cast into a convex optimization problem Extended to multiple relays

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Multiple full-duplex relays: DMT dominated by hop with minimum diversity gain. Multiple half-duplex relays: Odd and even numbered relays transmit in turn. DDF (with time limitation for successive hops) is DMT optimal. DMT dominated by 2 consecutive hops with min. diversity gain Multiple Relay Networks

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End to End Distortion Use antennas for multiplexing: Use antennas for diversity High-Rate Quantizer ST Code High Rate Decoder Low-Rate Quantizer ST Code High Diversity Decoder We optimize the point on the DMT tradeoff curve to minimize distortion

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What about delay? Retransmissions add time diversity at the cost of delay Extends DMT to diversity-multiplexing-delay tradeoff ARQ can be done on each link and/or end-to-end. The diversity-multiplexing-delay (DMDT) tradeoff has been characterized for point-to-point links: Want to extend this to multihop networks End-to-end distortion can be optimized over the DMDT. ARQ 1 D R D R ARQ 2 ARQ 3 H1 H2H3 Infinite Queue Delay:k1 Delay:k2Delay:k3 ARQ E2E

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DMDT for MIMO Relay Networks M i antennas on ith node End-to-end ARQ: L max ARQ rounds, per hop L i max ARQ rounds, sum L i = L. Delay sensitive data: end-to-end delay constraint k, per hop k i delay constraint: sum k i = k. Messages: come and leave a node Poisson Process (in equilibrium), exponential “service” time with mean L i Transmission outage has two causes Used all ARQ rounds but still cannot decode Missing a deadline due to queueing and transmission delay ARQ L1 D R D R ARQ L2ARQ L3 H1 H2H3 Messages Poisson rate mu Messages Received Infinite Queue Delay:k1 Delay:k2Delay:k3

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Optimal Multihop ARQ Transmission outage probability: P(ARQ error) + P(Delay > k) Finite but high SNR: P(ARQ error) use DMDT, P(Delay > k) derived from stationary distribution of random delay Optimal ARQ and k i allocation that minimizes the transmission outage probability Larger L i has smaller P(ARQ error) but larger P(Delay > k), vice versa Quasi-convex optimization problem, global optimal solution can be solved

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Optimal ARQs For point-to-point MIMO (4,2), L = 10, SNR 20dB As deadline constraint is relaxed, optimal ARQ converges to maximum allowable (L = 10) Similar effect for (4,2,2) multihop MIMO relay network Conclusion Under an end-to-end delay constraint, using the maximum number of ARQ rounds L is not necessarily optimal Contrasts with prior ARQ results without a delay constraint Point-to-point (4,2) 2 hop (4,2, 2) Open question: Is ARQ best use of 1 bit feedback

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What about Interference Cancellation? Antennas can be used for multiplexing, diversity, or interference cancellation Cancel M-1 interferers with M antennas What metric best captures the tradeoff? Diversity/Multiplexing/SINR -1 ?

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Minimizing End-to-End Distortion Source rate: bR bits per source sample Channel rate: R bits per channel use Expected end-to-end distortion: At high SNR Source distortion D(R)=2 -R R=rlog(SNR) P out SNR -d(r) E[D] SNR -(br) +SNR -d(r) E[D] minimized for br=d(r) Use optimization at moderate SNR

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Layered Source Coding We extend these ideas to layered SCs By prioritizing source bits, can reduce E[D] Use either a time-division or broadcast strategy Optimize power allocation across layers

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Distortion Results Broadcasting layered source codes hits upper bound for MISO/SIMO For MIMO, we can achieve the upper bound with 1 bit of feedback Complex systems don’t have closed-form solns; need optimization (NUM)

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Interference in End-to-End Distortion Interference exploitation at the physical layer improves end- to-end distortion We have proved a separation theorem for a class of interference channels Separate source and channel coding optimal We found the operating point on the DMT multihop region for minimal distortion Under delay constraints, optimization needed Investigating new notions of capacity, distortion, and separation optimality Incorporate notions of outage and expectation in capacity and end-to-end distortion Future work will apply these notions to MIMO multihop networks

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Summary and Open Questions MIMO improves MANET capacity as well as diversity- multiplexing-delay-interference cancellation tradeoffs Much room for innovation in generalized relaying and cognitive techniques for MIMO nodes Capacity and tradeoff regions still largely uncharacterized New tools for optimizing the tradeoff region operating point to maximize end-to-end performance metrics are needed Open questions in MIMO MANET design How to best use limited feedback Cross-layer design for cognitive MIMO nodes Protocol layering, separation, and interfaces Throughput Delay Diversity (T*,D v *,D l *)

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