Cooperation and Optimal Cross-Layer Resource Allocation in Wireless Networks

Transcription

1 Cooperation and Optimal Cross-Layer Resource Allocation in Wireless Networks Chris T. K. Ng Wireless Systems Lab PhD Orals Defense Electrical Engineering, Stanford University July 19, 2007

2 Future Wireless Networks Ubiquitous Communication Among People and Devices Wireless Internet access Nth generation Cellular Wireless Ad Hoc Networks Sensor Networks Wireless Entertainment Smart Homes/Spaces Automated Highways All this and more Hard Energy Constraints Hard Delay Constraints 2

3 Challenges in Wireless Communications Practical operating conditions Energy or power constraints. Real-time traffic Delay constraints. Time-varying channels Need to learn the channel condition or design to account for channel uncertainty. Broadcast medium Interference among neighboring nodes. Physical, MAC, network layers affect one another. Power allocation depends on all layers, and neighboring nodes. 3

4 Existing Wireless Network Architectures Network Layers Orthogonal Channels Application Network MAC Physical 4

5 Cross-disciplinary Wireless Network Design Communication Theory Signal Processing Estimation and Detection Cooperative Communications Optimization Separation/Interface Distributed implementation Cross-Layer Source-Channel Coding Computer Networks Routing, Scheduling Queueing Information Theory Asymptotic error-free communication 5

6 Cooperative Communications C 1 C 2 C 3 Capacity of wireless network is unknown. Cooperation. Exchange messages between nodes, process and relay information. E.g., multi-hop transmission. Wireless networks. Broadcast to all neighboring nodes: a wireless node may overhear nearby transmit signals. Simultaneous transmission by multiple nodes. Effective cooperation depends on topology, CSI, power allocation. 6

7 Cross-Layer Source-Channel Coding Ideal conditions: Separation between compression (source coding) and transmission (channel coding). C 1 Network Layers Application Network C 2 C 3 MAC Physical Does not exploit network topology, source correlation. 7

8 Assumptions on Wireless Channels Transmission Power Capacity = log SNR bits/second Channel Gain + noise Feedback: Channel State Information (CSI) Fading Channel E.g., Rayleigh fading Quantized CSI Fading States Channel Gain 2 Time 1 Assumptions: Point-to-point single user channel. No delay constraint. No complexity constraint. Optimal power control. Perfect CSI. 8

9 Part I: Cooperative Communications Fading Channel Channel Gain Transmission Power Time

10 Cooperation in Wireless Networks Cooperation in wireless networks can increase capacity. Wireless nodes can cooperate in different ways. E.g., transmitter vs. receiver cooperation. Depends on network geometry, CSI and power allocation assumptions. Benefits of cooperation: Capacity gain from transmitter and receiver cooperation. 10

11 Virtual MIMO: Two-Transmitter Two-Receiver Cooperation Orthogonal cooperation channels, assume G is large. Quasi-static phase fading, perfect CSI. To capture the cost of cooperation: Total network power constraint P. Bandwidth assumption 1): B r = B = B t = 1 Hz. Bandwidth assumption 2): B r + B + B t = 1 Hz. TX: dirty paper coding; RX: Wyner-Ziv compress-and-forward; TX-RX. Compare cooperation rates to capacity of non-cooperation, BC, MAC, and MIMO. 11

12 Transmitter-Receiver Cooperation Rates Low SNR (P = 0 db), BW 1) MIMO High SNR (P = 10 db), BW 1) BC/MAC Non-coop Small G : TX underperforms; RX better than NC. Large G :TX improves capacity. TX-RX cooperation useful when R TX is close to C BC. TX captures most benefits: TX outperforms RX; R TX close to R TX-RX. TX-RX cooperation useful when R TX is close to C BC. 12

13 Transmitter and Receiver Cooperation Node cooperation increases capacity. But not clear if transmitter cooperation or receiver cooperation offers greater benefits. Consider a wireless point-to-point link. Suppose a relay can be deployed either: Near the transmitter, or near the receiver. Which provides higher capacity improvement? Compare TX and RX cooperation rates. Cooperation strategy depends on channel state information (CSI) and power allocation assumptions. 13

14 System Model Transmitter and Receiver Cooperation Discrete-time AWGN relay channel. Channel power gain between TX and RX cluster is normalized to unity, but within cluster it is denoted by g. Average network power constraint P. 14

15 CSI and Power Allocation Assumptions We consider two models of CSI: Each node has full CSI (allows carrier synchronization between TX and Relay). Receiver CSI only (no synchronization). Also two models of power allocation: Optimal power allocation: TX has power constraint, and relay ; needs to be optimized. Equal power allocation. Combination results in 4 separate cases. 15

16 Cooperation Strategies Capacity of the relay channel is an open problem. The cut-set bound provides a capacity upper bound. Achievable schemes: [Cover&El Gamal 79]: Decode-and-forward (DF) and Compress-and-forward (CF). [Kramer,Gastpar&Gupta 05]: DF is close to optimal when relay is close to TX. CF performs well when relay is close to RX. Cooperation strategies DF for transmitter cooperation. CF for receiver cooperation. No cooperation: capacity of a single-user channel. 16

17 Cooperative Capacity Gain Comparison The optimized capacity bounds are in descending order for g > 2. 17

18 Effective Cooperation Strategies Equal Power Allocation with Full CSI TX co-op Optimal Power Allocation with Receiver CSI RX co-op RX cut-set bound TX cut-set bound Capacity gain is only realized with the right cooperation strategy. Under equal power allocation with full CSI, TX cooperation is superior. Under optimal power allocation with receiver CSI, RX cooperation is superior. 18

19 Necessary Conditions for Capacity Gain from TX and RX Cooperation Equal Power Allocation with Receiver CSI Non-coop capacity TX & RX cut-set bounds With equal power allocation and RX CSI, cooperation offers no capacity gain. Capacity upper bounds: MISO channel: No capacity gain over SISO without CSI at transmitter. SIMO channel: No capacity gain under equal power allocation. 19

20 Conferencing Relay Channel Relay and receiver cooperate via orthogonal conference links with total capacity C. Allocation of conferencing resources in each direction: a in [0,1]. A conference is permissible: total cardinality of communications does not exceed capacity. Possibly sent over multiple rounds (iterative). In practice the conference links may be realized via orthogonal channelization with sufficiently long coding blocks. Transmit power constraint: P. Every node has perfect CSI. 20

21 One-Shot vs. Iterative Cooperation One-shot DF or CF Two-round Iterative Conferencing (First CF, then DF) Relay channel gain Relay channel gain P = 10 Conference link capacity One-shot DF is capacityachieving when g is large relative to C. One-shot CF is better than DF when C is large relative to g. Conference link capacity When the relay has a weak channel (g < 1): One-shot CF outperforms iterative. Iterative conferencing outperforms one-shot cooperation for large g and C. 21

22 Effective Cooperation Strategies Different strategies for cooperation: Virtual MIMO Relaying with TX or RX cooperation. Iterative conferencing. Capacity gain is only realized with the right cooperation strategy. With full CSI, TX cooperation is superior. With optimal power allocation and RX CSI, RX cooperation is superior. With equal power allocation and RX CSI, cooperation offers no capacity gain. 22

23 Part II: Cross-Layer Source-Channel Coding

24 Source-Channel Coding Ideal conditions: Separation between compression (source coding) and transmission (channel coding). 24

25 Layered Transmission with Successive Refinement ??????? Superposition Coding Refinement Layer 111 Base Layer 1010 How to allocate transmission power among the layers? 25

26 Motivation Real-time communication systems Delay-constrained traffic. Difficult for the transmitter to learn the channel condition. Performance metrics: distortion as defined by applications instead of channel capacity. E.g., satellite voice communication systems. Broadcasting Users experience different channel conditions. Uncertainty in channel estimation 26

27 Source-Channel Coding without CSI at the Transmitter Transmission of Gaussian source without CSIT. Quasi-static block fading. Decoding is delay-limited. Channel is non-ergodic: separation is suboptimal. Transmitter knows the fading distribution. Minimize expected distortion E H [D] of reconstruction. Power constraint P. Bandwidth ratio: b channel uses per source symbol. 27

28 Layered Broadcast Coding with Successive Refinement Layered broadcast coding: Superposition coding: one layer for each fading state. Receiver decodes the layers supported by the channel realization. Undecodable layers are treated as noise. Successive decoding is capacityachieving for single-antenna Gaussian broadcast channel. Gaussian source is successively refinable: Each layer successively refines the description in the lower layer. 28

29 Two-Layer Power Allocation Optimization Superposition coding: Karush-Kuhn-Tucker (KKT) optimality condition: Power Allocate power to the higher layer: Base Layer Refinement Layer Up to a fixed power ceiling that depends only on the fading distribution. 29

30 Two-Layer Optimal Power Allocation and Minimum Expected Distortion Small : power allocation increases with channel condition. Large : power allocation decreases. Expected distortion dominated by the bottom layer. Expected distortion is same as one layer with effective channel gain and effective probability. Two layers can be represented by a single aggregate layer. 30

31 Aggregate Layer with Effective Channel Gain and Probability Power 1 Base Layer Refinement Layers Recursively apply the two-layer optimization step between an aggregate layer and the next lower layer. 31

32 Multiple-Layer Optimal Power Allocation Discretized Rayleigh fading: 25 layers. SNRs P = 0, 5, 10 db. As SNR increases, power allocation is extended down to the lower layers. No power allocated beyond = 1. Bandwidth ratios: b = 0.5, 1, 2. Higher b (more channel uses per source symbol): Spreads power allocation. 32

33 Multiple-Layer Minimum Expected Distortion Low SNR: Negligible improvement from having more layers. High SNR: Distortion dominated by outage probability. Low SNR: Quantized CSIT nearly as good as perfect CSIT. High SNR: Quantized CSIT marginally better than no CSIT. 33

34 Continuous Fading Distribution Limiting process as the spacing between two layers tends to 0. Optimal power distribution for a continuum of infinite layers. Solution given by a set of first-order linear differential equations: : pdf of the fading distribution Optimal power distribution: : cumulative power allocation Power allocated to layer and above 34

35 Optimal Power Distribution Power distribution converges to the one that maximizes expected capacity as b 0. 35

36 Reducing Distortion: CSIT vs. Diversity CSI at the Transmitter:? CSI Feedback Diversity: Multiple antennas to combine independent fading paths. Fading Channel Channel Gain Time 36

37 Benefits of Diversity vs. CSIT Optimal power distribution for different diversity order L. Distortion exponent: At high SNR performance benefit from diversity exceeds that from CSIT, especially when b is large. 37

38 Optimal Resource Allocation in Cross-Layer Source-Channel Coding Transmission of a Gaussian source without CSIT. Layered broadcast coding with successive refinement source coding. Optimized power allocation for minimum expected distortion. Two-layer power allocation: Allocate power to higher layer up to a power ceiling. Multiple layers: Recursively apply two-layer optimization. Continuous fading distribution: Limiting process as spacing between layers tends to 0. Minimum expected distortion: At high SNR, large benefits from diversity. 38

39 Hybrid Digital-Analog Communications Digital Channel Fading Analog Channel Side Information Combine digital transmission with analog transmission. The analogy side information is correlated with the digital description. The digital transmitter does not know the fading realization of the analog channel. 39

40 Source Coding with Uncertain Analog Side Information Encoder: rate constraint. Decoder: side information over uncoded analog channel subject to slow fading. Decode knows fading realization but encoder knows only distribution. Motivation: E.g., wireless sensor network. Minimize expected distortion: Optimally allocate rate among the layers (fading states) in the Heegard- Berger rate-distortion function. 40

41 Minimum Expected Distortion with Uncertain Side Information Rate-distortion (no side information) Convex Optimization Problem Wyner-Ziv (constant side Information channel) Discretized Rayleigh fading: Convex optimization problem. Optimal rate allocation concentrates at lowest layer: R * 1 = R X. When the source coding rate is large: Uncertain side information is almost no more useful than no side information. Wireless system design: Reduce analog channel uncertainty. 41

42 Future Work Iterative cooperation. Hybrid digital-analog transmission. Optimal rounds of iterations. Digital: Analog: Network cooperative compression and transmission. Multiple sources and destinations. Correlated source data streams.?? 42

43 Conclusions Cooperative communications Virtual MIMO, relaying, conferencing, etc. Performance gain is only realized with the right cooperation strategies. Need CSI for transmitter cooperation; need power allocation for receiver cooperation. Optimal resource allocation in source-channel coding Improvement in end-to-end user performance metrics. Optimal resource allocation by jointly considering compression in the application layer, and transmission in the physical layer. Future wireless networks Hybrid analog-digital transmission, network coding, distributed compression, iterative cooperation. 43

44 Publications Journal Papers 1. Chris T. K. Ng, Deniz Gündüz, Andrea J. Goldsmith and Elza Erkip, Optimal Power Distribution and Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement, submitted to IEEE Transactions on Information Theory, Chris T. K. Ng and Andrea J. Goldsmith, The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies, submitted to IEEE Transactions on Information Theory, Chris T. K. Ng, Nihar Jindal, Andrea J. Goldsmith and Urbashi Mitra, Capacity Gain from Two-Transmitter and Two-Receiver Cooperation, accepted for publication in IEEE Transactions on Information Theory, Conference Papers 1. Chris T. K. Ng, Chao Tian, Andrea J. Goldsmith, Shlomo Shamai (Shitz), Minimum Expected Distortion in Gaussian Source Coding with Uncertain Side Information, to appear at IEEE Information Theory Workshop (ITW), September 2 6, 2007, Lake Tahoe, CA. 2. Chris T. K. Ng, Deniz Gündüz, Andrea J. Goldsmith and Elza Erkip, Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement, IEEE International Symposium on Information Theory (ISIT), June 24 29, 2007, Nice, France. 3. Deniz Gündüz, Chris T. K. Ng, Elza Erkip and Andrea J. Goldsmith, Gaussian Source over Gaussian Relay Channel with Correlated Relay Side Information, IEEE International Symposium on Information Theory (ISIT), June 24 29, 2007, Nice, France. 4. Chris T. K. Ng, Deniz Gündüz, Andrea J. Goldsmith and Elza Erkip, Recursive Power Allocation in Gaussian Layered Broadcast Coding with Successive Refinement, IEEE International Conference on Communications (ICC), June 24 27, 2007, Glasgow, Scotland. 44

45 Publications (cont) 5. Chris T. K. Ng and Andrea J. Goldsmith, Capacity and Cooperation in Wireless Networks, Information Theory and Applications (ITA) Workshop, February 6 10, 2006, La Jolla, CA. (Invited) 6. Chris T. K. Ng, Ivana Maric, Andrea J. Goldsmith, Shlomo Shamai (Shitz), Roy D. Yates, Iterative and One-shot Conferencing in Relay Channels, IEEE Information Theory Workshop (ITW), March 13 17, 2006, Punta del Este, Uruguay, pp (Invited) 7. Chris T. K. Ng, J. Nicholas Laneman and Andrea J. Goldsmith, The Role of SNR in Achieving MIMO Rates in Cooperative Systems, IEEE Information Theory Workshop (ITW), March 13 17, 2006, Punta del Este, Uruguay, pp Chris T. K. Ng and Andrea J. Goldsmith, Capacity and Power Allocation for Transmitter and Receiver Cooperation in Fading Channels, IEEE International Conference on Communications (ICC), June 11 15, 2006, Istanbul, Turkey, pp Chris T. K. Ng and Andrea J. Goldsmith, Capacity Gain from Transmitter and Receiver Cooperation, IEEE International Symposium on Information Theory (ISIT), September 4 9, 2005, Adelaide, Australia, pp Chris T. K. Ng and Andrea J. Goldsmith, Transmitter Cooperation in Ad-Hoc Wireless Networks: Does Dirty- Payer Coding Beat Relaying? IEEE Information Theory Workshop (ITW), October 24 29, 2004, San Antonio, TX, pp (Invited) 11. Chris T. K. Ng and Andrea J. Goldsmith, Capacity of Fading Broadcast Channels with Rate Constraints, Forty- Second Annual Allerton Conference on Communication, Control and Computing, September 29 October 1, 2004, Monticello, IL, pp

46 Acknowledgements Prof. Goldsmith, Prof. Cioffi, Prof. Paulraj, Prof. Gill. Co-authors: Prof. Laneman, Ivana Maric, Prof. Shamai, Prof. Yates, Deniz Gunduz, Prof. Erkip, Chao Tian, Prof. Jindal, Prof. Mitra. WSL group members and visitors; Stanford classmates: Prof. Cui, Xiangheng, Taesang Yoo, Yifan Liang, Sachin Adlakha, Prof. Aghajan, Tim Holliday, Ron Dabora, Kazuhide Kawabe, Dong-Wook Roh, Sung Ho Moon, Prof. Romero, Prof. Paris, Grace Gao, Rajiv Agarwal, Hyunok Lee, Chan-Soo Hwang, Moshe Malkin, David Yu, Stephanie Pereira, Almir Mutapcic, Haim Permuter, Ritesh Madan, Rui Zhang, and others. Joice DeBolt, Pat Oshiro, Bernadette Aguiao. Friends. My family. 46