Cooperation in Wireless Networks

Transcription

1 Cooperation in Wireless Networks Ivana Marić and Ron Dabora Stanford 15 September 2008 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 1

2 Objectives The case for cooperation Types of cooperation Performance measures Cooperation schemes Performance, limitations Building blocks Small networks, large scale networks Fundamental tradeoffs Introduce recent results Ivana Marić and Ron Dabora Cooperation in Wireless Networks 2

3 Outline Introduction Relaying strategies Conferencing and feedback Cooperation in networks with multiple communicating pairs Cooperation in fading channels Cooperation in large-scale networks Summary Ivana Marić and Ron Dabora Cooperation in Wireless Networks 3

4 Introduction Ivana Marić and Ron Dabora Cooperation in Wireless Networks 4

5 Introduction Motivation Basic measures Capacity Scaling laws Channel models Static channels Time-varying channels Diversity Ivana Marić and Ron Dabora Cooperation in Wireless Networks 5

6 Challenges Higher data rates and better coverage USIIA 2007, RIAA 2006 Dynamic nature: time-varying channel, users mobility, stochastically varying traffic Efficient spectrum allocation and coexistence of users Security and privacy Energy efficiency Operating large ad hoc networks Guaranteed rate (Quality-of-Service) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 6

7 Challenges Higher data rates and better coverage USIIA 2007, RIAA 2006 Dynamic nature: time-varying channel, users mobility, stochastically varying traffic Efficient spectrum allocation and coexistence of users Security and privacy Energy efficiency Operating large ad hoc networks Guaranteed rate (Quality-of-Service) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 6

8 Traditional Approach: A Network is a Collection of Point-to-Point Links Current wireless networks (cellular networks, Wi-Fi) are viewed as a collection of point-to-point links To increase data rates the point-to-point rate is increased What happens when this approach is exhausted (too expensive, approaching the fundamental limits)? Need to find methods to significantly increase data rate for the same PtP link performance Ivana Marić and Ron Dabora Cooperation in Wireless Networks 7

9 Current View: Interference is Harmful Wireless networks are inherently broadcast Any transmission is overheard by neighbouring nodes T 1 R 3 T 2 R 2 T 3 R 1 Interference is extremely harmful for existing wireless network designs Ivana Marić and Ron Dabora Cooperation in Wireless Networks 8

10 Addressing the Challenges via Cooperation Nodes which are not the source or destination of a given message help communicating the message Different types of cooperation Relaying Conferencing (iterative decoding) Feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 9

11 Addressing the Challenges via Cooperation Nodes which are not the source or destination of a given message help communicating the message Different types of cooperation Relaying Conferencing (iterative decoding) Feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 9

12 Addressing the Challenges via Cooperation Nodes which are not the source or destination of a given message help communicating the message Different types of cooperation Relaying Conferencing (iterative decoding) Feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 9

13 Addressing the Challenges via Cooperation Nodes which are not the source or destination of a given message help communicating the message Different types of cooperation Relaying Conferencing (iterative decoding) Feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 9

14 Addressing the Challenges via Cooperation Nodes which are not the source or destination of a given message help communicating the message Different types of cooperation Relaying Conferencing (iterative decoding) Feedback Future applications Ad-hoc networks Sensor networks Cooperation takes advantage of the broadcast nature of the wireless channel Ivana Marić and Ron Dabora Cooperation in Wireless Networks 9

15 Not Just Theoretical Dlink High Speed 2.4GHz (802.11g) Wireless Range Extender Under development for the (WirelessMAN/WiMAX) j - multihop relay specification m - advanced air interface Ivana Marić and Ron Dabora Cooperation in Wireless Networks 10

16 Let s begin Ivana Marić and Ron Dabora Cooperation in Wireless Networks 11

17 Memoryless Point-to-Point Channels Gaussian channel z i - bandlimited AWGN, i.i.d., E{ z i 2 } = N Ivana Marić and Ron Dabora Cooperation in Wireless Networks 12

18 Memoryless Point-to-Point Channels Gaussian channel z i - bandlimited AWGN, i.i.d., E{ z i 2 } = N Discrete channel: x i X, y i Y Ivana Marić and Ron Dabora Cooperation in Wireless Networks 12

19 The Memoryless Point-to-Point Channel Model A channel is characterized by the conditional distribution of its output at time i: i = 1,2,... p(y i y i 1,x i ), x i X and y i Y, Ivana Marić and Ron Dabora Cooperation in Wireless Networks 13

20 The Memoryless Point-to-Point Channel Model A channel is characterized by the conditional distribution of its output at time i: i = 1,2,... p(y i y i 1,x i ), x i X and y i Y, p(y i y i 1,x i ) takes into account all the effects of signal processing: time synchronization, frequency synchronization, PLL, equalizer,... A channel is called memoryless if p(y i y i 1,x i ) = p(y i x i ) X p 1 Y p3 p 2 q 1 q 2 q 3 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 13

21 The Memoryless Point-to-Point Channel: BSC X = 2, Y = 2 x i - BPSK signal Decoding takes place after a 2-level quantization at the receiver with threshold at zero Ivana Marić and Ron Dabora Cooperation in Wireless Networks 14

22 The Memoryless Point-to-Point Channel: BSC X = 2, Y = 2 x i - BPSK signal Decoding takes place after a 2-level quantization at the receiver with threshold at zero Binary symmetric channel X p p 1-p 1-p Y Ivana Marić and Ron Dabora Cooperation in Wireless Networks 14

23 Channel Capacity W Encoder X n p(y n x n ) Y n Decoder W ^ R denotes the information rate in bits/symbol In 1948 Claude E. Shannon showed that transmitting information over a (memoryless) PtP channel p(y x) can be done with an arbitrarily small probability of error as long as R max p(x) I(X;Y ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 15

24 Channel Capacity W Encoder X n p(y n x n ) Y n Decoder W ^ R denotes the information rate in bits/symbol In 1948 Claude E. Shannon showed that transmitting information over a (memoryless) PtP channel p(y x) can be done with an arbitrarily small probability of error as long as R max p(x) I(X;Y ) The capacity achieving code is characterized by the distribution p(x) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 15

25 Channel Capacity W Encoder X n p(y n x n ) Y n Decoder W ^ R denotes the information rate in bits/symbol In 1948 Claude E. Shannon showed that transmitting information over a (memoryless) PtP channel p(y x) can be done with an arbitrarily small probability of error as long as R max p(x) I(X;Y ) The capacity achieving code is characterized by the distribution p(x) Average probability of error: P (n) e = Pr(Ŵ W) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 15

26 Channel Capacity W Encoder X n p(y n x n ) Y n Decoder W ^ R denotes the information rate in bits/symbol In 1948 Claude E. Shannon showed that transmitting information over a (memoryless) PtP channel p(y x) can be done with an arbitrarily small probability of error as long as R max p(x) I(X;Y ) The capacity achieving code is characterized by the distribution p(x) Average probability of error: P (n) e = Pr(Ŵ W) Codebook: Generate 2 nr i.i.d. codewords Pr(x n ) = n i=1 p X(x i ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 15

27 Channel Capacity W Encoder X n p(y n x n ) Y n Decoder W ^ R denotes the information rate in bits/symbol In 1948 Claude E. Shannon showed that transmitting information over a (memoryless) PtP channel p(y x) can be done with an arbitrarily small probability of error as long as R max p(x) I(X;Y ) The capacity achieving code is characterized by the distribution p(x) (n) Average probability of error: P e = Pr(Ŵ W) Codebook: Generate 2 nr i.i.d. codewords Pr(x n ) = n i=1 p X(x i ) ɛ > 0 we can find n large enough s.t. at least one codebook for which P e (n) ɛ Ivana Marić and Ron Dabora Cooperation in Wireless Networks 15

28 Channel Capacity: Converse W Encoder X n p(y n x n ) Y n Decoder W ^ R max p(x) I(X;Y ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 16

29 Channel Capacity: Converse W Encoder X n p(y n x n ) Y n Decoder W ^ R max p(x) I(X;Y ) Conversely, if R > max p(x) I(X;Y ) then the average probability of error achieved by any code is bounded away from zero for any n Ivana Marić and Ron Dabora Cooperation in Wireless Networks 16

30 Channel Capacity: Converse W Encoder X n p(y n x n ) Y n Decoder W ^ R max p(x) I(X;Y ) Conversely, if R > max p(x) I(X;Y ) then the average probability of error achieved by any code is bounded away from zero for any n Definition: The Capacity of a channel is the maximal rate for which reliable communication can be achieved Ivana Marić and Ron Dabora Cooperation in Wireless Networks 16

31 AWGN Channel Capacity Let P be an average power constraint on the channel input: 1 n x i (w) 2 P, w W n i=1 The problem: Find the input distribution p(x) that maximizes I(X;Y) subject to average input power constraint P The solution: X CN(0,P) The capacity: ( C = log g 2 P ) bits/transmission N Ivana Marić and Ron Dabora Cooperation in Wireless Networks 17

32 Network Capacity A network is a collection of K nodes (sources, sinks) and directed edges (links). Ivana Marić and Ron Dabora Cooperation in Wireless Networks 18

33 Network Capacity A network is a collection of K nodes (sources, sinks) and directed edges (links). Assume symbol time synchronization of all elements in the network Analyze the network throughput for a block of n symbols Ivana Marić and Ron Dabora Cooperation in Wireless Networks 18

34 Network Capacity A network is a collection of K nodes (sources, sinks) and directed edges (links). Assume symbol time synchronization of all elements in the network Analyze the network throughput for a block of n symbols Let node k, k = 1,2,...,K send message W k W k The rate is Rk = log 2 W k n Ivana Marić and Ron Dabora Cooperation in Wireless Networks 18

35 Network Capacity A network is a collection of K nodes (sources, sinks) and directed edges (links). Assume symbol time synchronization of all elements in the network Analyze the network throughput for a block of n symbols Let node k, k = 1,2,...,K send message W k W k The rate is Rk = log 2 W k n Let D k be the set of nodes that decode W k Ŵ j k, j D k Ivana Marić and Ron Dabora Cooperation in Wireless Networks 18

36 Network Capacity A network is a collection of K nodes (sources, sinks) and directed edges (links). Assume symbol time synchronization of all elements in the network Analyze the network throughput for a block of n symbols Let node k, k = 1,2,...,K send message W k W k The rate is Rk = log 2 W k n Let D k be the set of nodes that decode W k Ŵ j k, j D k The probability of error for network transmission is K P e (n) } = Pr j {Ŵ k W k k=1 j D k Ivana Marić and Ron Dabora Cooperation in Wireless Networks 18

37 Network Capacity Region The capacity region is the set of all rate vectors (R 1,R 2,...,R K ) such that the probability of error P e (n) be made arbitrarily small by taking n large enough Why it is important? 1. It is the theoretical upper bound 2. Determines optimal communication strategies 3. Leads to practical designs can R 2 T 1 R 3 T 2 R 2 T 3 R 1 Very hard to find R 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 19

38 Multiuser Networks: The Multiple Access Channel The MAC: p(y x 1,x 2 ) p(x1, x 2 ) = p(x 1 )p(x 2 ) Introduced by Shannon in 1961 Capacity known for both discrete and Gaussian channels Capacity [Ahlswede 71, Liao 72] MIMO [Telatar 99] Fading [Gallager 94, Shamai & Wyner 97, Tse & Hanly 98] Ivana Marić and Ron Dabora Cooperation in Wireless Networks 20

39 Multiuser Networks: The Broadcast Channel The BC: p(y 1,y 2 x) Introduced by Cover in 1972 Capacity known only for special cases Degraded channels [Bergmans 73,74, Gallager 74] General BC with degraded message sets [Körner & Maron 77] MIMO BC [Weingarten, Steinberg & Shamai 06] Best achievable region due to Marton 79 Best upper bound due to Nair & El-Gamal 07 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 21

40 Multiuser Networks: The Relay Channel The relay channel: p(y,y 1 x,x 1 ) The most basic form of cooperation Introduced by van der Meulen in 1968 Capacity known only for special cases Physically degraded channels [Cover & El-Gamal 79] Gaussian relay channel with SNR [Kramer 05] Stochastically degraded relay channel with deterministic link [Zhang 88] Fundamental schemes introduced by Cover & El-Gamal 79 Decode-and-forward Compress-and-forward Ivana Marić and Ron Dabora Cooperation in Wireless Networks 22

41 Multiuser Networks: The Interference Channel The interference channel: p(y 1,y 2 x 1,x 2 ) The building block for multiple-pairs communication Introduced by Shannon in 1961 Capacity known only for special cases Strong interference [Carleial 75, Sato 81, Costa & El-Gamal 87] Gaussian IC with very weak interference [Shang, Kramer & Chen 08, Motahari & Khandani 08] Cognitive Gaussian IC No interference Best achievable region due to Han & Kobayashi 81 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 23

42 The Interference Channel: Strong Interference vs. Weak Interference Weak interference At least one of the cross-links is worse than the its respective direct link Tx 1 Rx 1 Strong interference The cross-links are better than the direct links Tx 1 Rx 1 Tx 2 Rx 2 Tx 2 Rx 2 Decoding W 1 at Rx 2 reduces the maximum rate of W 1 No single-letter expression for the capacity region Capacity known for special cases Decoding W 1 at Rx 2 does not constrain the maximum rate of W 1 The capacity achieving scheme is known [Sato 81], [Han and Kobayashi 81] The rates with weak interference are generally less than the rates with (very) strong interference Ivana Marić and Ron Dabora Cooperation in Wireless Networks 24

43 The Cut-Set Upper Bound A general tool for outer bounding the capacity region of a network Let V = {1,2,...,K} index the network nodes Let R ij denote the information rate from node i to node j A cut is a partition of V into two sets S and S = V \ S Theorem ( Aref 80) If the information rates { R ij} are achievable then there exists a joint distribution p ( x (1),x (2),...,x (K)) such that for every cut (S, S) R ij I (X ) (S) ;Y ( S) X ( S) i S,j S Ivana Marić and Ron Dabora Cooperation in Wireless Networks 25

44 Operating Regimes: Half-Duplex vs. Full-Duplex We shall compare results for different operating regimes In full-duplex the nodes receive and transmit simultaneously In half-duplex a node can either receive or transmit Often encountered in wireless systems in practice Ivana Marić and Ron Dabora Cooperation in Wireless Networks 26

45 Time-Varying Channels: Fast vs. Slow Fading When the channel is time varying, the received signal is given by y r,i = h tr,i x t,i + z i htr,i is the channel gain between the transmitter and receiver at time i h tr,i models a Rayleigh fading channel: h tr,i CN(0,1) There are three types of Rayleigh fading Fast fading: htr,i CN(0, 1), i.i.d., i = 1, 2,..., n block fading: htr,i = h tr, i = 1, 2,..., n Slow fading: htr,i = h tr Ivana Marić and Ron Dabora Cooperation in Wireless Networks 27

46 Time-Varying Channels: Fast vs. Slow Fading When the channel is time varying, the received signal is given by y r,i = h tr,i x t,i + z i htr,i is the channel gain between the transmitter and receiver at time i h tr,i models a Rayleigh fading channel: h tr,i CN(0,1) There are three types of Rayleigh fading Fast fading: htr,i CN(0, 1), i.i.d., i = 1, 2,..., n block fading: htr,i = h tr, i = 1, 2,..., n Slow fading: htr,i = h tr Ivana Marić and Ron Dabora Cooperation in Wireless Networks 27

47 Time-Varying Channels: Channel State Information CSI is the knowledge a network node has on the channels Two types: transmitter CSI (CSIT) and receiver CSI (CSIR) Let H denote the random channel state and let the channel be defined by p(y x,h). There are four possible CSI configurations: CSIT CSIR Capacity No No max p(x) I(X;Y ) p(y x) = h p(y x,h)p(h) No Yes max p(x) I(X;Y H) Yes No varies Yes Yes E H {max p(x h) I(X;Y h)} Ivana Marić and Ron Dabora Cooperation in Wireless Networks 28

48 Time-Varying Channels: Outage Capacity Shannon s capacity measure is also called ergodic capacity Assumes that the channel is information stable (ex. i.i.d. fading) Application is delay tolerant For slow fading Rayleigh channels, the mutual information I(X;Y h) is a random variable depends on the channel realization h The channel is non-ergodic Note that for every R > 0, Pr (I(X;Y h) < R) > 0 The Shannon capacity is zero The event {h : I(X;Y h) < R} is called outage Outage capacity is the maximum rate that can be guaranteed for a given outage probability Pout: suppr(i(x;y h) < R) Pout R Ivana Marić and Ron Dabora Cooperation in Wireless Networks 29

49 Diversity Transmitting signals carrying the same information over different paths in time, frequency or space Cooperation diversity is achieved when nodes forward to other nodes information Enhance desired information Facilitate interference cancellation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 30

50 Diversity Transmitting signals carrying the same information over different paths in time, frequency or space Cooperation diversity is achieved when nodes forward to other nodes information Enhance desired information Facilitate interference cancellation Diversity reduces outage probability Ivana Marić and Ron Dabora Cooperation in Wireless Networks 30

51 Diversity Transmitting signals carrying the same information over different paths in time, frequency or space Cooperation diversity is achieved when nodes forward to other nodes information Enhance desired information Facilitate interference cancellation Diversity reduces outage probability Transmitter cooperation, receiver cooperation When the transmitters cooperate and also the receivers cooperate the system resembles a MIMO system Distributed MIMO Differences between MIMO and distributed MIMO: Messages known only at source nodes Cannot perform antenna power allocation Nodes may have half-duplex constraints Ivana Marić and Ron Dabora Cooperation in Wireless Networks 30

52 Time-Varying Channels: Finite-State Models Slow fading, fast fading are extreme cases An alternative model for time-varying channels with memory Correlated fading, multipath Filters (pulse shape, IF and RF filters) AGC, Timing, PLL, equalizer The finite-state channel (FSC) was introduced as early as 1953 [McMillan 53] Time variations are represented by correlated states Ivana Marić and Ron Dabora Cooperation in Wireless Networks 31

53 Finite-State Channels Memory is captured by the state of the channel at the end of the previous symbol s transmission Si is the channel state at time i s0 is the initial channel state p(y i, s i x i, x i 1, y i 1, s i 1, s 0 ) = p(y i, s i x i, s i 1 ) Si 1 contains all the history information for time i S is finite ISI channel: S i 1 = ( X i 1,X i 2,...,X i J ) x i h(k) y i k ISI Channel n i A/D Ivana Marić and Ron Dabora Cooperation in Wireless Networks 32

54 Analysis of Large Networks: Scaling Laws Finding the capacity region of even small networks is a very difficult task Many possibilities for cooperation Scaling laws allow us to obtain insights on the performance of large scale networks. Pioneering work of Gupta and Kumar 00 Notation f (n) = O(g(n)) f (n) limn < g(n) f (n) = Θ(g(n)) f (n) = O(g(n)) and g(n) = O(f (n)) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 33

55 Analysis of Large Networks: Scaling Laws Definitions: Assume a network that consists of n nodes that form m source-destination pairs. Let dl denote the distance between source and destination for pair l m The transport capacity is defined as C T = The transport capacity sup (R 1,R 2,...,R m) feasible m R l d l Provides a single number which summarizes what a network can deliver Follows a scaling law such as l=1 C T (n) = Θ( n), O(n) bit-meters/second Does not provide explicit information on the individual rates Ivana Marić and Ron Dabora Cooperation in Wireless Networks 34

56 Some Important Questions How to incorporate relaying into the design of a network? Compare performance of different schemes Under what conditions capacity is achieved What are the maximum rate gains we can expect from adding relays to the network? Different aspects of relaying that arise when considering multiple communicating pairs Do not exist in the classic relay channel Understand the fundamental performance tradeoffs associated with node cooperation Analysis of cooperation in large scale networks Ivana Marić and Ron Dabora Cooperation in Wireless Networks 35

57 Cooperative Strategies Ivana Marić and Ron Dabora Cooperation in Wireless Networks 36

58 In This Section... Decode-and-forward Compress-and-forward Amplify-and-forward Capacity upper bound Performance comparison Ivana Marić and Ron Dabora Cooperation in Wireless Networks 37

59 Cooperation in Wireless Networks T 1 R 3 T 2 R 2 T 3 R 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 38

60 Cooperation in Wireless Networks T 1 R 3 T 2 R 2 T 3 R 1 Traditional approach: multihop routing Many point-to-point links Intermediate nodes store and forward packets Ivana Marić and Ron Dabora Cooperation in Wireless Networks 38

61 Broadcast Wireless networks are inherently broadcast Any transmission is overheard by neighboring nodes Ivana Marić and Ron Dabora Cooperation in Wireless Networks 39

62 Broadcast Wireless networks are inherently broadcast Any transmission is overheard by neighboring nodes T 1 R 3 T 2 R 2 T 3 R 1 Interference is harmful for current wireless network designs Cooperative strategies exploit broadcast Ivana Marić and Ron Dabora Cooperation in Wireless Networks 39

63 Relay Channel Message W {1,...,M} sent at rate R Encoding at the source: X n 1 = f 1(W ) At the relay at time i: X 2,i = f 2,i (Y i 1 2 ), i = 2,...,n Decoding: Ŵ = g(y n 3 ) R = log 2 M/n Ivana Marić and Ron Dabora Cooperation in Wireless Networks 40

64 Decode-and-Forward Exploit broadcast transmission at the source Ivana Marić and Ron Dabora Cooperation in Wireless Networks 41

65 Decode-and-Forward Exploit broadcast transmission at the source Source and relay transmit simultaneously Ivana Marić and Ron Dabora Cooperation in Wireless Networks 41

66 Decode-and-Forward Exploit broadcast transmission at the source Source and relay transmit simultaneously Messages sent in blocks: w 1,w 2,...,w b,... Ivana Marić and Ron Dabora Cooperation in Wireless Networks 41

67 Decode-and-Forward Exploit broadcast transmission at the source Source and relay transmit simultaneously Messages sent in blocks: w 1,w 2,...,w b,... Two random codebooks: x1 n,xn 2 generated with p(x 2 )p(x 1 x 2 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 41

68 Superposition Coding Random codebooks x n 1,xn 2 generated with p(x 2)p(x 1 x 2 ) In block b: The source: x n 1 (h b(w b 1 ),w b ) The relay: x n 2 (h b(w b 1 )) block Markov encoding Ivana Marić and Ron Dabora Cooperation in Wireless Networks 42

69 Decode-and-Forward Strategies Irregular encoding, successive decoding Codebooks x n 1, x2 n have different sizes Regular encoding, sliding-window decoding Decoding over two block Regular encoding, backward decoding Decoding starts from the last received block Ivana Marić and Ron Dabora Cooperation in Wireless Networks 43

70 Decode-and-Forward R I(X 1 ;Y 2 X 2 ) R I(X 1 ;Y 3 X 2 ) + I(X 2 ;Y 3 ) = I(X 1,X 2 ;Y 3 ) R = max p(x 1,x 2 ) min{i(x 1;Y 2 X 2 ),I(X 1,X 2 ;Y 3 )} Ivana Marić and Ron Dabora Cooperation in Wireless Networks 44

71 Decode-and-Forward in AWGN Channels Choose: Gaussian p(x 1,x 2 ) E[ X1 2 ] = P 1, E[ X 2 2 ] = P 2, E[X 1 X 2 ] = ρ P 1 P 2 Superposition codebook: Gen. symbols: X 10 CN(0,(1 ρ 2 )P 1 ), X 2 CN(0,P 2 ) In block b: x n 10 (w b),x n 2 (w b 1) x n 1 (w b 1,w b ) = x n 10 (w b) + ρ P1 P 2 x n 2 (w b 1) Y 2 = h 12 X 1 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 45

72 DF Rate in AWGN Channels { ( R = max min log ρ h 12 2 (1 ρ 2 ) )P 1, N ( log h 13 2 P 1 + h 23 2 P 2 + 2Re{ρh 13h23 } )} P 1 P 2 N N N Signals coherently-combined Relay signal perfectly phase-aligned with the source signal Not practical Decoding constraint at the relay can be severe DF optimal for h 12 : source and relay act as two transmit antennas DF performs well when the relay is close to the source Ivana Marić and Ron Dabora Cooperation in Wireless Networks 46

73 Antenna-Clustering Capacity Generalizes to multiple relays Relays act as a multiple-transmit antenna Ivana Marić and Ron Dabora Cooperation in Wireless Networks 47

74 Classic Multihop { R = min T log 2 (1 + h 12 2 P 1 TN ), T log 2 (1 + h 23 2 } P 2 TN ) For α = 2, performs worse then using no relay at all Gains for α > 2 and for half-duplex relays α-path-loss exponent Ivana Marić and Ron Dabora Cooperation in Wireless Networks 48

75 DF in Half-Duplex Relay Channel All nodes know a priori when a relay listens/talks Ivana Marić and Ron Dabora Cooperation in Wireless Networks 49

76 DF in Half-Duplex Relay Channel All nodes know a priori when a relay listens/talks Mode modulation: data modulates listen/talk interval Ivana Marić and Ron Dabora Cooperation in Wireless Networks 49

77 DF in Half-Duplex Relay Channel All nodes know a priori when a relay listens/talks Mode modulation: data modulates listen/talk interval 4.5 cut set bound for a fixed slot strategy DF, random Rate [bit/use] DF, fixed relay off Pr(M 2 =L) for DF Pr(M 2 =L) for cut set bound d Ivana Marić and Ron Dabora Cooperation in Wireless Networks 49

78 Compress-and-Forward Relay does not decode the source message Relay quantizes Y n 2 into quantization codeword Ŷ n 2 By finding a jointly typical ŷ n 2 with received y n 2 Three codebooks: x n 1 (w b),ŷ n 2 (s b 1,z b ),x n 2 (s b 1) How does relay operate? In block b: knows s b 1, decides on z b thru quantization Obtains ŷ 2 (s b 1,z b ) What does it send? Binning: each z randomly assigned to bin s In block b + 1 : sends x 2 (s b ) such that z b s b Ivana Marić and Ron Dabora Cooperation in Wireless Networks 50

79 Compress-and-Forward Destination in block b + 1: Decodes s b Determines z b s b Knows ŷ 2 (s b 1,z b ),x 2 (s b 1 ) Decodes w b using (ŷ 2 (s b 1,z b ),y 3,b ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 51

80 Compress-and-Forward Destination in block b + 1: Decodes s b R Q I(X 2 ;Y 3 ) Determines z b s b Knows ŷ 2 (s b 1,z b ),x 2 (s b 1 ) Decodes w b using (ŷ 2 (s b 1,z b ),y 3,b ) R I(X 1 ;Ŷ2,Y 3 X 2 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 52

81 Compress-and-Forward Rate R = I(X 1 ;Ŷ2,Y 3 X 2 ) subject to I(Ŷ2;Y 2 Y 3 X 2 ) I(X 2 ;Y 3 ) for p(x 1 )p(x 2 )p(ŷ 2 x 2,y 2 )p(y 1,y 2 x 1,x 2 ) R is single-user rate when receiver has two antennas Ivana Marić and Ron Dabora Cooperation in Wireless Networks 53

82 Compress-and-Forward in AWGN Channels Choose: Ŷ 2 = Y 2 + Ẑ2 Ẑ 2 CN(0, ˆN 2 ) For smallest ˆN 2 choose: I(Y 2 ;Ŷ2 X 2 Y 3 ) = I(X 2 ;Y 3 ) ˆN 2 = N P 1( h h 13 2 ) + N P 2 h 23 2 ( R = log P 1 h 12 2 N + ˆN + P 1 h 13 2 ) 2 N Optimal for h 23 : relay and destination act as two-receive antenna CF performs well when the relay is close to destination Ivana Marić and Ron Dabora Cooperation in Wireless Networks 54

83 Antenna-Clustering Capacity Generalizes to multiple relays Relays act as a multiple-receive antenna Ivana Marić and Ron Dabora Cooperation in Wireless Networks 55

84 Antenna-Clustering Capacity Two closely spaced clusters: DF and CF Achieves optimal scaling behavior Ivana Marić and Ron Dabora Cooperation in Wireless Networks 56

85 Amplify-and-Forward In discrete channel: X 2,i = Y 2,i 1, Y X Ivana Marić and Ron Dabora Cooperation in Wireless Networks 57

86 Amplify-and-Forward In discrete channel: X 2,i = Y 2,i 1, Y X In Gaussian channel: X 2,i = a i Y 2,i 1 i = 1,...,n a i chosen to satisfy power constraint Ivana Marić and Ron Dabora Cooperation in Wireless Networks 57

87 Amplify-and-Forward In discrete channel: X 2,i = Y 2,i 1, Y X In Gaussian channel: X 2,i = a i Y 2,i 1 i = 1,...,n a i chosen to satisfy power constraint At the destination channel with ISI: Y 3,i = h 13 X 1,i + h 23 X 2,i + Z 3,i = h 13 X 1,i + ah 12 h 23 X 1,i 1 + Z 3,i Ivana Marić and Ron Dabora Cooperation in Wireless Networks 57

88 Amplify-and-Forward In discrete channel: X 2,i = Y 2,i 1, Y X In Gaussian channel: X 2,i = a i Y 2,i 1 i = 1,...,n a i chosen to satisfy power constraint At the destination channel with ISI: Y 3,i = h 13 X 1,i + h 23 X 2,i + Z 3,i = h 13 X 1,i + ah 12 h 23 X 1,i 1 + Z 3,i Waterfilling optimization of the spectrum of X n 1 Relay should not always transmit with maximum power In low-snr: bursty AF improves performance Ivana Marić and Ron Dabora Cooperation in Wireless Networks 57

89 AF Scaling Capacity Optimal scaling as number of relays increases Requires coherent combining of relay signals Ivana Marić and Ron Dabora Cooperation in Wireless Networks 58

90 Cut-Set Bound on Capacity Cut: partition of the set of nodes into two sets: (S, S) W (S)- set of messages with source in S and sink in S Choose encoders (inputs): P X. Denote as R(P X, S) set of rates that satisfies: R w I(X S ;Y S X S ) (1) w W(S) Cut-set bound for fixed P X : R(P X ) = S R(P X, S) Cut-set bound: R = PX R(P X ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 59

91 Cut-Set Bound Examples Point-to-point channel R = I(X;Y ) PX Relay Channel R = P X1 X 2 min{i(x 1 ;Y 2,Y 3 X 2 ),I(X 1,X 2 ;Y 3 )} Ivana Marić and Ron Dabora Cooperation in Wireless Networks 60

92 Performance Comparison 6 5 DF CF upper bound P 1 = P 2 = 10, N=1, α = 2 Rate [bit/use] AF relay off ρ for DF d Ivana Marić and Ron Dabora Cooperation in Wireless Networks 61

93 Cooperative Strategies: Summary DF: when relay is close to source CF: when relay is close to destination Generalize to multiple relays Capacity results are rare Ivana Marić and Ron Dabora Cooperation in Wireless Networks 62

94 Conferencing and Feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 63

95 In This Section... Cooperation via conferencing Feedback Fundamental results for memoryless channels Finite-state channels Summary Ivana Marić and Ron Dabora Cooperation in Wireless Networks 64

96 Conferencing Rx 1 Y n 1 Tx C 21 C 12 n Y 2 Rx 2 Conferencing refers to two users interactively helping each other decode their messages: The transmission over the wireless medium is typically received by users in the vicinity of the target user Users have dedicated (orthogonal) links between them, over which they communicate Ivana Marić and Ron Dabora Cooperation in Wireless Networks 65

97 Multi-Step Conferencing Rx 1 Rx 1 Rx 1 W ^ 1 W 12 (1) W 12 (2) W 12 (K) Tx W 21 (1) W 21 (2) W 21 (K) ^ W 2 Rx 2 Rx 2 Rx 2 Step 1 Step 2 Step K A conference can span several cycles At each cycle receivers use more refined knowledge on the other receiver s channel output Decoding takes place after the last cycle Admissible conference: the total rates of the conference messages is less than the capacity of the conference links 1 n K k=1 log 2 W (k) ij C ij, (i,j) { (1,2),(2,1) } Ivana Marić and Ron Dabora Cooperation in Wireless Networks 66

98 A Conference: Formal Definition Rx 1 Rx 1 Rx 1 W ^ 1 W 12 (1) W 12 (2) W 12 (K) Tx W 21 (1) W 21 (2) W 21 (K) ^ W 2 Rx 2 Step 1 Rx 2 Step 2 Rx 2 Step K An (C 12,C 21 )-admissible K-cycle conference between Rx 1 and Rx 2 consists of K message sets from node i to node j, (i, j) = { (1, 2), (2, 1) } W (k) ij = K pairs of mapping functions } {1, 2,..., 2 nr(k) ij, k = 1, 2,..., K. h (k) 12 : Y1 n W (1) 21 W(2) 21 W(k 1) 21 W (k) 12 h (k) 21 : Y2 n W (1) 12 W(2) 12 W(k) 12 W(k) 21 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 67

99 Full Cooperation Rx 1 Y n 1 Tx C 21 C 12 n Y 2 Full cooperation: When each receiver sends his channel output to the other receiver Y n 1 becomes available at Rx 2 Y n 2 becomes available at Rx 1 Rx 2 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 68

100 Full Cooperation Rx 1 Y n 1 Tx C 21 C 12 n Y 2 Full cooperation: When each receiver sends his channel output to the other receiver Y n 1 becomes available at Rx 2 Y n 2 becomes available at Rx 1 Full cooperation can be achieved with a single cycle if C12 = H(Y 1 Y 2 ) and C 21 = H(Y 2 Y 1 ) Rx 2 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 68

101 Full Cooperation Rx 1 Y n 1 Tx C 21 C 12 n Y 2 Full cooperation: When each receiver sends his channel output to the other receiver Y n 1 becomes available at Rx 2 Y n 2 becomes available at Rx 1 Full cooperation can be achieved with a single cycle if C12 = H(Y 1 Y 2 ) and C 21 = H(Y 2 Y 1 ) In one step Rx 2 can send to Rx 1 enough information that will allow Rx 1 to recover Y n 2 Using a scheme by Slepian & Wolf 73 Rx 2 Rate I(X; Y1, Y 2 ) is achievable at Rx 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 68

102 Full Cooperation Rx 1 Y n 1 Tx C 21 C 12 n Y 2 Full cooperation: When each receiver sends his channel output to the other receiver Y n 1 becomes available at Rx 2 Y n 2 becomes available at Rx 1 Full cooperation can be achieved with a single cycle if C12 = H(Y 1 Y 2 ) and C 21 = H(Y 2 Y 1 ) In one step Rx 2 can send to Rx 1 enough information that will allow Rx 1 to recover Y n 2 Using a scheme by Slepian & Wolf 73 Rx 2 Rate I(X; Y1, Y 2 ) is achievable at Rx 1 We will focus on results for partial cooperation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 68

103 Conferencing: MAC The encoders exchange messages prior to transmission The capacity region [Willems 83] R 1 I(X 1 ;Y X 2,U)+C 12 R 2 I(X 2 ;Y X 1,U)+C 21 R 1 + R 2 min { I(X 1,X 2 ;Y U)+C 12 + C 21,I(X 1,X 2 ;Y) } for p(u)p(x 1 u)p(x 2 u) This is achieved with a single conference step Ivana Marić and Ron Dabora Cooperation in Wireless Networks 69

104 Conferencing: MAC The encoders exchange messages prior to transmission The capacity region [Willems 83] R 1 I(X 1 ;Y X 2,U)+C 12 R 2 I(X 2 ;Y X 1,U)+C 21 R 1 + R 2 min { I(X 1,X 2 ;Y U)+C 12 + C 21,I(X 1,X 2 ;Y) } for p(u)p(x 1 u)p(x 2 u) This is achieved with a single conference step Ivana Marić and Ron Dabora Cooperation in Wireless Networks 69

105 Conferencing: Relay Channel Compare two schemes (C = C rd + C dr ): Single step (classic relaying, Cdr = 0) Single cycle with Step 1: CF from destination to relay Step 2: DF from relay to destination Ivana Marić and Ron Dabora Cooperation in Wireless Networks 70

106 Conferencing: Broadcast Channel I(X;Y 1) R 2 I(X;Y 2)+C12 I(X;Y 2) C 12 R 1 I(X;Y 1) When the channel is physically degraded, a single conference step achieves capacity x p(y 1 x) p(y 2 y 1 ) y 1 It is enough to let the strong receiver assist the weak receiver y 2 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 71

107 Conferencing: Broadcast Channel I(X;Y 1) R 2 I(X;Y 2)+C12 I(X;Y 2) C 12 R 1 I(X;Y 1) When the channel is physically degraded, a single conference step achieves capacity x p(y 1 x) p(y 2 y 1 ) y 1 It is enough to let the strong receiver assist the weak receiver For the general BC It is still an open question whether higher rates can be achieved with multiple steps Can design a K-cycle conference using K 1 CF cycles and a final DF step Ivana Marić and Ron Dabora Cooperation in Wireless Networks 71 y 2

108 Feedback PtP channel: the receiver sends back information to the transmitter Allows transmitter to adapt its signal to the channel X i = f i (W,Y i 1 ) Network: the wireless medium is a broadcast medium Signals received at nodes in the vicinity of the destination are correlated with the signal at the destination node Ivana Marić and Ron Dabora Cooperation in Wireless Networks 72

109 Feedback in Multiuser Scenarios In Multiuser scenarios feedback facilitates both direct and indirect cooperation Direct: Feedback sent from the destination receiver Indirect: Feedback sent from neighbouring receivers Consider for example the BC Feedback from one receiver can increase the rate to both receivers Ivana Marić and Ron Dabora Cooperation in Wireless Networks 73

110 Memoryless Multiuser Scenarios Sometimes feedback does not help The PtP DMC (p(y n x n ) = n i=1 p(y i x i )) The physically degraded DMBC [El-Gamal 78,81] x p(y 1 x) p(y 2 y 1 ) y 1 y 2 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 74

111 Memoryless Multiuser Scenarios Sometimes feedback does not help The PtP DMC (p(y n x n ) = n i=1 p(y i x i )) The physically degraded DMBC [El-Gamal 78,81] x p(y 1 x) p(y 2 y 1 ) y 1 y 2 Feedback does help in the following scenarios: The discrete, memoryless MAC [Gaarder & Wolf 75] The discrete, memoryless relay channel Feedback achieves the cut-set bound [Cover & El-Gamal 79] The general BC [Ozarow 79] Including the stochastically degraded channel Ivana Marić and Ron Dabora Cooperation in Wireless Networks 74

112 Channels with Memory: Finite-State Channels The memory for time i is represented by the state S i 1 The PtP-FSC: p(y i, s i x i, x i 1, y i 1, s i 1, s 0 ) = p(y i, s i x i, s i 1 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 75

113 Channels with Memory: Finite-State Channels The memory for time i is represented by the state S i 1 The PtP-FSC: The FS-MAC: p(y i, s i x i, x i 1, y i 1, s i 1, s 0 ) = p(y i, s i x i, s i 1 ) p(y i, s i x 1,i, x 2,i, x i 1 1,1, xi 1 2,1, yi 1, s i 1, s 0 ) = p(y i, s i x 1,i, x 2,i, s i 1 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 75

114 Channels with Memory: Finite-State Channels The memory for time i is represented by the state S i 1 The PtP-FSC: The FS-MAC: p(y i, s i x i, x i 1, y i 1, s i 1, s 0 ) = p(y i, s i x i, s i 1 ) p(y i, s i x 1,i, x 2,i, x i 1 1,1, xi 1 2,1, yi 1, s i 1, s 0 ) = p(y i, s i x 1,i, x 2,i, s i 1 ) The FSBC: p(y i, z i, s i x i, x i 1, y i 1, z i 1, s i 1, s 0 ) = p(y i, z i, s i x i, s i 1 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 75

115 Finite-State Channels Can model effects beyond the physical propagation medium Filters, loops Example: to incorporate the effect of a K-tap equalizer, the state S i 1 can also be a function of Y i 1 i K Si 1 = f (Y i 1 i K ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 76

116 Finite-State Channels Can model effects beyond the physical propagation medium Filters, loops Example: to incorporate the effect of a K-tap equalizer, the state S i 1 can also be a function of Y i 1 i K Si 1 = f (Y i 1 i K ) Useful for analyzing correlated fading between the two extremes of fast (i.i.d.) and slow Ivana Marić and Ron Dabora Cooperation in Wireless Networks 76

117 Finite-State Channels Can model effects beyond the physical propagation medium Filters, loops Example: to incorporate the effect of a K-tap equalizer, the state S i 1 can also be a function of Y i 1 i K Si 1 = f (Y i 1 i K ) Useful for analyzing correlated fading between the two extremes of fast (i.i.d.) and slow Notation: Directed Mutual Information I(X n Y n ) = n I(X i ;Y i Y i 1 ) i=1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 76

118 Finite-State Channels Can model effects beyond the physical propagation medium Filters, loops Example: to incorporate the effect of a K-tap equalizer, the state S i 1 can also be a function of Y i 1 i K Si 1 = f (Y i 1 i K ) Useful for analyzing correlated fading between the two extremes of fast (i.i.d.) and slow Notation: Directed Mutual Information I(X n Y n ) = n I(X i ;Y i Y i 1 ) }{{} H(X i Y i 1 ) H(X i Y i ) i=1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 76

119 Finite-State Channels: Capacity of the PtP-FSC The capacity of a channel with memory is usually given by a limiting expression as the blocklength n We must verify that the limit exists and is finite Otherwise the channel does not support reliable communication in the Shannon sense We assume no CSI Capacity without feedback [Gallager 68] C = lim max n s 0 S p(x n ) min 1 n I(X n ;Y n s 0 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 77

120 Finite-State Channels: Capacity of the PtP-FSC The capacity of a channel with memory is usually given by a limiting expression as the blocklength n We must verify that the limit exists and is finite Otherwise the channel does not support reliable communication in the Shannon sense We assume no CSI Capacity without feedback [Gallager 68] C = lim max n s 0 S p(x n ) min 1 n I(X n ;Y n s 0 ) Capacity with feedback [Permuter, Weissman & Goldsmith 08] C FB = lim n 1 n max min i=1 p(x i x i 1,y i 1 ) s 0 S n I(X n Y n s 0 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 77

121 Remark Capacity without feedback [Gallager 68] C = lim Capacity with feedback C FB = lim n max n s 0 S p(x n ) min 1 n I(X n ;Y n s 0 ) 1 n max min i=1 p(x i x i 1,y i 1 ) s 0 S n I(X n Y n s 0 ) Feedback increases the capacity of the PtP-FSC [Permuter et al. 08] In contrast to the DMC Ivana Marić and Ron Dabora Cooperation in Wireless Networks 78

122 The Finite-State Broadcast Channel with Feedback and Cooperation B Y i-1 D Y i Decoder 1 ^ W 0 ^ W 1 W 1 W 0 W 2 Encoder X i Broadcast Channel p(z,y,s x,s ) Z i-1 D C Z i Decoder 2 ^ ^ W 0 W 2 A Z i-1 D 8 possible configurations Switch C facilitates full cooperation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 79

123 The Finite-State Broadcast Channel with Feedback and Cooperation: Conclusions When all switches are open FSBC without feedback/cooperation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 80

124 The Finite-State Broadcast Channel with Feedback and Cooperation: Conclusions When all switches are open FSBC without feedback/cooperation When the FSBC is physically degraded capacity is achieved using a superposition codebook with memory Ivana Marić and Ron Dabora Cooperation in Wireless Networks 80

125 The Finite-State Broadcast Channel with Feedback and Cooperation: Conclusions When all switches are open FSBC without feedback/cooperation When the FSBC is physically degraded capacity is achieved using a superposition codebook with memory Feedback can help the physically degraded FSBC Although it does not help the physically degraded DMBC Ivana Marić and Ron Dabora Cooperation in Wireless Networks 80

126 The Finite-State Broadcast Channel with Feedback and Cooperation: Conclusions When all switches are open FSBC without feedback/cooperation When the FSBC is physically degraded capacity is achieved using a superposition codebook with memory Feedback can help the physically degraded FSBC Although it does not help the physically degraded DMBC When switch C is closed the channel behaves as a physically degraded channel Capacity is achieved with a superposition codebook for all feedback configurations Ivana Marić and Ron Dabora Cooperation in Wireless Networks 80

127 The Finite-State Broadcast Channel with Feedback and Cooperation: Conclusions When all switches are open FSBC without feedback/cooperation When the FSBC is physically degraded capacity is achieved using a superposition codebook with memory Feedback can help the physically degraded FSBC Although it does not help the physically degraded DMBC When switch C is closed the channel behaves as a physically degraded channel Capacity is achieved with a superposition codebook for all feedback configurations When switch C is open and feedback comes from one user only Capacity achieved if the channel is physically degraded and the strong user is sending feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 80

128 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

129 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node For the MAC a single cycle achieves capacity Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

130 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node For the MAC a single cycle achieves capacity For the physically degraded BC a single step achieves capacity Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

131 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node For the MAC a single cycle achieves capacity For the physically degraded BC a single step achieves capacity For the relay channel: When C/g is high single CF step When C/g is low single DF step For intermediate values of C/g iterative decoding Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

132 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node For the MAC a single cycle achieves capacity For the physically degraded BC a single step achieves capacity For the relay channel: When C/g is high single CF step When C/g is low single DF step For intermediate values of C/g iterative decoding Feedback allows the transmitter to adapt its transmission according to the received signal Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

133 Summary Conferencing helps by successively refining the knowledge each node has on the received signal at the other node For the MAC a single cycle achieves capacity For the physically degraded BC a single step achieves capacity For the relay channel: When C/g is high single CF step When C/g is low single DF step For intermediate values of C/g iterative decoding Feedback allows the transmitter to adapt its transmission according to the received signal Finite-state channels allow modelling of propagation as well as implementation aspects Ivana Marić and Ron Dabora Cooperation in Wireless Networks 81

134 Summary In general, feedback is useful in network scenarios For PtP-DMC feedback does not help Ivana Marić and Ron Dabora Cooperation in Wireless Networks 82

135 Summary In general, feedback is useful in network scenarios For PtP-DMC feedback does not help When the channel has memory feedback is, in general, useful also for PtP links Ivana Marić and Ron Dabora Cooperation in Wireless Networks 82

136 Summary In general, feedback is useful in network scenarios For PtP-DMC feedback does not help When the channel has memory feedback is, in general, useful also for PtP links In broadcast scenarios with full cooperation Capacity achieving schemes can be derived both with and without feedback Ivana Marić and Ron Dabora Cooperation in Wireless Networks 82

137 Summary In general, feedback is useful in network scenarios For PtP-DMC feedback does not help When the channel has memory feedback is, in general, useful also for PtP links In broadcast scenarios with full cooperation Capacity achieving schemes can be derived both with and without feedback In multiuser scenarios feedback from a neighbouring node can help other nodes to communicate Ivana Marić and Ron Dabora Cooperation in Wireless Networks 82

138 Summary First Half Ivana Marić and Ron Dabora Cooperation in Wireless Networks 83

139 Summary First Half Cooperation is an important tool for coping with the design challenges of future wireless networks Ivana Marić and Ron Dabora Cooperation in Wireless Networks 84

140 Summary First Half Cooperation is an important tool for coping with the design challenges of future wireless networks Channel models Discrete, AWGN Fading: fast, block, slow Diversity Finite-state: correlated time variations Ivana Marić and Ron Dabora Cooperation in Wireless Networks 84

141 Summary First Half Cooperation is an important tool for coping with the design challenges of future wireless networks Channel models CSI Discrete, AWGN Fading: fast, block, slow Diversity Finite-state: correlated time variations Ivana Marić and Ron Dabora Cooperation in Wireless Networks 84

142 Summary First Half Cooperation is an important tool for coping with the design challenges of future wireless networks Channel models CSI Discrete, AWGN Fading: fast, block, slow Diversity Finite-state: correlated time variations Performance metrics Channel Capacity Transport capacity Scaling laws Ivana Marić and Ron Dabora Cooperation in Wireless Networks 84

143 Summary First Half Relaying Decode-and-forward Compress-and-forward Amplify-and-forward Ivana Marić and Ron Dabora Cooperation in Wireless Networks 85

144 Summary First Half Relaying Decode-and-forward Compress-and-forward Amplify-and-forward Conferencing Interactive decoding Ivana Marić and Ron Dabora Cooperation in Wireless Networks 85

145 Summary First Half Relaying Decode-and-forward Compress-and-forward Amplify-and-forward Conferencing Interactive decoding Feedback Cooperation between transmitters and receivers Useful in network scenarios Feedback does not have to come from the target receiver Ivana Marić and Ron Dabora Cooperation in Wireless Networks 85

146 Networks with Multiple Source-Destination Pairs Ivana Marić and Ron Dabora Cooperation in Wireless Networks 86

147 In This Section... Differences when relaying for multiple pairs Cooperation in interference channel with a relay Cooperation in cognitive radio networks Ivana Marić and Ron Dabora Cooperation in Wireless Networks 87

148 Relaying Relay strategies well developed decode, compress, amplify -and-forward Capture broadcast No interference One flow Ivana Marić and Ron Dabora Cooperation in Wireless Networks 88

149 Relaying for Multiple Sources? The smallest network: interference channel with a relay Ivana Marić and Ron Dabora Cooperation in Wireless Networks 89

150 Relaying for Multiple Sources? The smallest network: interference channel with a relay Simple approach: multihop routing Relay time-shares in helping sources Ivana Marić and Ron Dabora Cooperation in Wireless Networks 89

151 Multihop Ivana Marić and Ron Dabora Cooperation in Wireless Networks 90

152 Multihop Ivana Marić and Ron Dabora Cooperation in Wireless Networks 90

153 Multihop How can we do better? No combining of bits, symbols or packets at the relay Ivana Marić and Ron Dabora Cooperation in Wireless Networks 90

154 Generalized Relaying Joint encoding and forwarding of multiple data streams Ivana Marić and Ron Dabora Cooperation in Wireless Networks 91

155 Network Coding Butterfly network: Routing achieves (R 1,R 2 ) = (β,1 β), for any β [0,1] Ivana Marić and Ron Dabora Cooperation in Wireless Networks 92

156 Network Coding Butterfly network: Routing achieves (R 1,R 2 ) = (β,1 β), for any β [0,1] Network coding: relay combines packets. Achieves (R 1,R 2 ) = (1,1) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 92

157 Joint Encoding of Messages Network Coding idea: Generalized relaying: Ivana Marić and Ron Dabora Cooperation in Wireless Networks 93

158 Encoding Elements From... Relay channel: generalized amplify, quantize, decode -and-forward MAC channel: interference cancellation Interference channel: rate-splitting Broadcast channel: binning, dirty paper coding Many encoding strategies can be applied Evaluation is difficult Goal: Develop strategies that can be applied to larger networks and can bring gains Ivana Marić and Ron Dabora Cooperation in Wireless Networks 94

159 Simple Joint Encoding Strategies: Gaussian Channel Y 3 = h 13 X 1 + h 23 X 2 + Z 3 3 Y j = h ij X i + Z j i=1 Amplify-and-Forward (analog network coding): X 3 = cy 3 = c(h 13 X 1 + h 23 X 2 + Z 3 ) Decode-and-Forward: X 3 = P 3 ( cv 1 (W 1 ) + cv 2 (W 2 )) Can outperform time-sharing Ivana Marić and Ron Dabora Cooperation in Wireless Networks 95

160 DF with Network Coding Y 1 = h 31 X 3 + Z 1 Y 2 = h 32 X 3 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 MAC to relay, BC to sources Ivana Marić and Ron Dabora Cooperation in Wireless Networks 96

161 DF with Network Coding Y 1 = h 31 X 3 + Z 1 Y 2 = h 32 X 3 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 MAC to relay, BC to sources Relay broadcasts: For R 1 = R 2 : x n 3 (w 1 w 2 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 96

162 DF with Network Coding Y 1 = h 31 X 3 + Z 1 Y 2 = h 32 X 3 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 MAC to relay, BC to sources Relay broadcasts: For R 1 = R 2 : x3 n(w 1 w 2 ) For R 1 R 2 : x3 n(w 11,w 12 w 2 ) where he splits w 1 = (w 11,w 12 ) at (R 1,R 2) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 96

163 DF with Network Coding Y 1 = h 31 X 3 + Z 1 Y 2 = h 32 X 3 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 MAC to relay, BC to sources Relay broadcasts: For R 1 = R 2 : x3 n(w 1 w 2 ) For R 1 R 2 : x3 n(w 11,w 12 w 2 ) where he splits w 1 = (w 11,w 12 ) at (R 1,R 2) AF: x 3 = a(h 13 x 1 + h 23 x 2 + z 3 ), under power constraint Ivana Marić and Ron Dabora Cooperation in Wireless Networks 96

164 DF with Network Coding Y 1 = h 31 X 3 + Z 1 Y 2 = h 32 X 3 + Z 2 Y 3 = h 13 X 1 + h 23 X 2 + Z 3 MAC to relay, BC to sources Relay broadcasts: For R 1 = R 2 : x3 n(w 1 w 2 ) For R 1 R 2 : x3 n(w 11,w 12 w 2 ) where he splits w 1 = (w 11,w 12 ) at (R 1,R 2) AF: x 3 = a(h 13 x 1 + h 23 x 2 + z 3 ), under power constraint x3 n(w 1,w 2 ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 96

165 Differences when Relaying for Multiple Sources Ivana Marić and Ron Dabora Cooperation in Wireless Networks 97

166 Differences when Relaying for Multiple Sources Joint relaying of multiple data streams Interference: Sources create interference Relaying one message increases interference to other users Ivana Marić and Ron Dabora Cooperation in Wireless Networks 97

167 Interference Channel No relay Capacity region unknown Ivana Marić and Ron Dabora Cooperation in Wireless Networks 98

168 Interference Channel No relay Capacity region unknown except... Ivana Marić and Ron Dabora Cooperation in Wireless Networks 98

169 In Strong Interference Gaussian channel: Y 1 = X 1 + ax 2 + Z 1 Y 2 = bx 1 + X 2 + Z 2 Cross-link is stronger than direct: a, b 1 Optimal: jointly decode both messages Multiaccess channel to each receiver Gains from interference cancellation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 99

170 In General: Rate-Splitting If interference not strong: unwanted messages cannot be decoded To reduce interference: partial decoding An encoder splits message into two messages Decoder decodes one unwanted message and cancels interference Ivana Marić and Ron Dabora Cooperation in Wireless Networks 100

171 Interference Forwarding Relay observes signals from both sources Relay can use some of its power to forward interference Increase interference to cancel it Ivana Marić and Ron Dabora Cooperation in Wireless Networks 101

172 Special Case Scenario No source1-relay link Can forwarding interference W 2 help both receivers? Increases rate R 2 but increases interference at destination 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 102

173 Encoding No rate-splitting nor binning Block-Markov, regular encoding Decoding: sliding-window or backward Ivana Marić and Ron Dabora Cooperation in Wireless Networks 103

174 Gaussian Channel Y 1 = X 1 + h 12 X 2 + h 13 X 3 + Z 1 Y 2 = h 21 X 1 + X 2 + h 23 X 3 + Z 2 Y 3 = h 32 X 2 + Z 3 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 104

175 No Relaying No relay: strong interference regime 0.8 Rate Regions of Gaussian Channels without relay R h 12 = 1,h 2 21 = 2,h2 23 = 0.15,h2 32 = 12 R 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 105

176 Relaying No relay: strong interference regime With relay, no interference forwarding 0.8 Rate Regions of Gaussian Channels with relay, h 13 =0 0.5 without relay R h 12 = 1,h 2 21 = 2,h2 23 = 0.15,h2 32 = 12 R 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 106

177 Relaying and Interference Forwarding No relay: strong interference regime With relay, and interference forwarding 0.8 Rate Regions of Gaussian Channels with relay, h 13 =2 with relay, h 13 =0 0.5 without relay R h 12 = 1,h 2 21 = 2,h2 23 = 0.15,h2 32 = 12 R 1 Ivana Marić and Ron Dabora Cooperation in Wireless Networks 107

178 Interference Forwarding Relay can... help decoder by interference forwarding Interference cancelation hurt decoder by increasing interference Interference rate becomes too large Interference forwarding: through decode,compress -and-forward More general schemes Ivana Marić and Ron Dabora Cooperation in Wireless Networks 108

179 Virtual (Distributed) MIMO No dedicated relay Transmitter cooperation Transmitters need knowledge about each other s messages Obtained through: 1. Cooperative strategies 2. Dedicated orthogonal links; conferencing 3. Feedback 4. Cognition Ivana Marić and Ron Dabora Cooperation in Wireless Networks 109

180 Gains From Virtual MIMO Orthogonal links for cooperation Expected sum rates (bps) CMIMO CBC, CMAC RTX-RX RTX RRX CNC Cooperation channel gain G (db) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 110

181 Cognitive Radio Networks Motivation: bandwidth gridlock Wireless spectrum is crowded Licensed band not efficiently used Its inefficient use led to spectrum holes From slides by B. Brodersen, BWRC cognitive radio workshop Ivana Marić and Ron Dabora Cooperation in Wireless Networks 111

182 Cognitive Radios Co-exist with oblivious users without impacting their service Sense the environment Use the obtained side information to adaptively transmit Ivana Marić and Ron Dabora Cooperation in Wireless Networks 112

183 Interweave (Opportunistic) Approach From slides by B. Brodersen, BWRC cognitive radio workshop Dynamic spectrum access Sense the environment Transmit in a spectrum hole Ivana Marić and Ron Dabora Cooperation in Wireless Networks 113

184 Underlay Approach Share the bandwidth; created interference below a threshold Ivana Marić and Ron Dabora Cooperation in Wireless Networks 114

185 Cognition and Cooperation Why not use obtained information for cooperation? In cooperation: a helper needs knowledge about relayed message Assistance of the source node Listening to the channel Cognitive node can obtain similar information through cognition Overlay paradigm: share the band and compensate for interference by cooperation Ivana Marić and Ron Dabora Cooperation in Wireless Networks 115

186 Overlay Approach What is the optimal cognitive strategy? Ivana Marić and Ron Dabora Cooperation in Wireless Networks 116

187 It All Hinges on...side Information Interweave: users activity Underlay: channel gains Overlay: channel gains, codebooks and (partial) messages Ivana Marić and Ron Dabora Cooperation in Wireless Networks 117

188 How Can Side Information be Obtained? Interweave: users activity Detection of spectrum holes Holes common to the transmitter and receiver Underlay: channel gains If there is a channel reciprocity or feedback Overlay: channel gains, codebooks and (partial) messages Codebooks: through protocol Messages via: retransmission; cooperation; decoding Ivana Marić and Ron Dabora Cooperation in Wireless Networks 118

189 Cognitive Radio Channel Model Two messages: W k {1,...,M k } sent at rates R k Encoding: X n 1 = f 1(W 1,W 2 ), X n 2 = f 2(W 2 ) Decoding: Ŵ k = g k (Y n k ) Ivana Marić and Ron Dabora Cooperation in Wireless Networks 119

190 Elements of Cognitive Encoding Strategy Opportunistic approach: interference avoidance Ivana Marić and Ron Dabora Cooperation in Wireless Networks 120

191 Elements of Cognitive Encoding Strategy Opportunistic approach: interference avoidance Utilize techniques developed from many canonical models 1. Cooperative strategies To increase rate at oblivious receiver 2. Rate-splitting To allow oblivious decoder to cancel part of interference 3. Precoding against interference To eliminate interference at cognitive receiver Ivana Marić and Ron Dabora Cooperation in Wireless Networks 120

192 Cooperation To increase rate for the oblivious receiver Cognitive radio acts as a relay X1 n = f 1(W 1,W 2 ) Dedicates some power to transmit the other user s message Increases interference to its own receiver Ivana Marić and Ron Dabora Cooperation in Wireless Networks 121

193 Rate-Splitting To reduce interference Without cognition: interference channel Ivana Marić and Ron Dabora Cooperation in Wireless Networks 122

194 Precoding against Interference To eliminate interference at cognitive receiver Full cognition: MIMO broadcast channel Strategy: precoding against interference [Gel fand and Pinsker, 1979] Gaussian channels: Dirty-paper coding (DPC) [Costa, 1981] Achieves capacity Ivana Marić and Ron Dabora Cooperation in Wireless Networks 123

195 Capacity Results for Gaussian Channels Y 1 = X 1 + ax 2 + Z 1 Y 2 = bx 1 + X 2 + Z 2 a weak strong inteference inteference Wu et.al b Regions for which capacity is known: Strong interference, a > b > 1 Cooperation achieves capacity Weak interference, b 1 Dirty paper coding and cooperation achieve capacity Ivana Marić and Ron Dabora Cooperation in Wireless Networks 124

196 Insights 1. Orthogonalizing transmissions is suboptimal 2. Canceling strong interference is beneficial 3. Rate-splitting can be used for partially canceling interference Ivana Marić and Ron Dabora Cooperation in Wireless Networks 125

197 Insights Side information in cognitive radio networks can be used for: Cooperation Precoding against interference In considered network: cooperation and GP precoding capacity-achieving in some regimes Delay should be considered Ivana Marić and Ron Dabora Cooperation in Wireless Networks 126

198 Relaying for Multiple Sources Jointly encode messages Exploit broadcast Relays forward messages and interference Create virtual MIMO W 1 exploit W 2 broadcast W 3 joint encoding f(w 1, W 3 ) interference forwarding joint encoding Ivana Marić and Ron Dabora Cooperation in Wireless Networks 127

199 Cooperation in Fading Channels Ivana Marić and Ron Dabora Cooperation in Wireless Networks 128

200 In This Section... Examples Diversity-multiplexing tradeoff for the PtP MIMO channel DMT for cooperative systems Summary Ivana Marić and Ron Dabora Cooperation in Wireless Networks 129

201 Fading Channels Rayleigh fading: Many scatterers, no LOS Communication in dense urban areas Rician Fading: Many scatterers with LOS Satellite communications 2 K = 5 0 Relative Power, db, Relative to RMS Time, seconds Ivana Marić and Ron Dabora Cooperation in Wireless Networks 130