Cross-Layer Design of MIMO Wireless Networks

1. Cross-Layer Design of MIMO Wireless Networks Space: The Final Frontier Andrea Goldsmith Stanford University Joint work with Y. Chang, R. Dabora, D. Gunduz, I. Maric, Y. Xie DAWN ARO MURI Program Review U.C. Santa Cruz Oct 5, 2009

2. 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

3. Crosslayer Protocol Design In MIMO MANETs • Application • Network • Access • Link Throughput (T*,Dv*,Dl*) Delay Diversity Results will lead to optimal layering and insight into layer interfaces

4. 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)

5. 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,…

6. RX1 TX1 X1 Y4=X1+X2+X3+Z4 relay Y3=X1+X2+Z3 X3= f(Y3) Y5=X1+X2+X3+Z5 X2 TX2 RX2 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

7. encoder 1 dest1 relay encoder 2 dest2 Achievable Rates for any distribution p(p(x1)p(x2,x3)p(y1,y2|x1,x2,x3) • The strategy to achieve these rates is: • - Single-user encoding at the encoder 1 to send W1 • - Decode/forward at encoder 2 and the relay to send message W2 • This region equals the capacity region when the interference is strong and the channel is degraded

8. Beneficial to forward bothinterference and message

9. New Outer Bound via a Genie Y1 X1 • Parameters chosen so RX1 obtains less noisy information about W2 then RX2: Y1g= d1X1 +d2X2+ drX3 +d3Z1 +d4Z1’ Y1g X3 relay X2 Y2 • where var(Ze)≤var(Z2) • → Receiver 1 can decode (W1,W2) Currently extending to MIMO multihop networks

10. 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

11. Cognitive Radio Paradigms Cognitive radios sense environment to support new users without hurting legacy users • 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

12. Capacity of Cognitive MIMO Networks NCRX NCR NCTX RX1 NCRX NCRX RX2 CR CTX CRX • 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

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

14. 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 CTX and NCRX, then perform SVD on projection

15. Multi-user Cognitive MIMO Networks • 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. Cognitive MIMO network with multiple primary users Achievable rates with two primary users

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

17. 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

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

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

20. 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

21. 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

24. Multiple Relay Networks • 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

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

26. D 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 E2E ARQ 1 Infinite Queue Delay:k1 ARQ 3 ARQ 2 Delay:k2 Delay:k3 H1 H2 H3 R R D

27. D DMDT for MIMO Relay Networks • Miantennas on ith node • End-to-end ARQ: L max ARQ rounds, per hop Li max ARQ rounds, sum Li = L. • Delay sensitive data: end-to-end delay constraint k, per hop ki delay constraint: sum ki = k. • Messages: come and leave a node Poisson Process (in equilibrium), exponential “service” time with mean Li • Transmission outage has two causes • Used all ARQ rounds but still cannot decode • Missing a deadline due to queueing and transmission delay ARQ L1 ARQ L2 ARQ L3 Infinite Queue Delay:k1 Delay:k2 Delay:k3 H1 H2 H3 R R D Messages Poisson rate mu Messages Received

28. 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 ki allocation that minimizes the transmission outage probability • Larger Li has smaller P(ARQ error) but larger P(Delay > k), vice versa • Quasi-convex optimization problem, global optimal solution can be solved

29. Optimal ARQs Point-to-point (4,2) • 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 2 hop (4,2, 2) Open question: Is ARQ best use of 1 bit feedback

30. 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?

31. 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)  PoutSNR-d(r) • E[D] SNR-(br) +SNR-d(r) • E[D] minimized for br=d(r) • Use optimization at moderate SNR

32. 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

33. 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)

34. 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

35. 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 (T*,Dv*,Dl*) Delay Diversity