Distributed Protocols for Interference Management in Cooperative Networks

1 Distrib uted Protocols for Interference Management in Cooperati v e Networks Christopher Hunter , Student Member , IEEE, Ashutosh Sabharwal, Senior Member , IEEE Abstract In scenarios where de vices are too small to support MIMO antenna arrays, symbol-level cooperation may be used to pool the resources of distributed single-antenna de vices to create a virtual MIMO antenna array . W e address design fundamentals for distributed cooperati ve protocols where relays ha ve an incomplete vie w of network information. A key issue in distributed networks is potential loss in spatial reuse due to the increased radio footprint of flo ws with cooperativ e relays. Hence, local gains from cooperation hav e to balance against network level losses. By using a novel binary network model that simplifies the space ov er which cooperative protocols must be designed, we de velop a mechanism for the systematic and computational dev elopment of cooperativ e protocols as functions of the amount of network state information available at relay nodes. Through extensi ve network analysis and simulations, we demonstrate the successful application of this method to a series of protocols that span a range of network information availability at cooperati ve relays. Index T erms Cooperativ e communications, spatial reuse, network state information, distributed protocols. I . I N T RO D U C T I O N Symbol-le vel cooperation between neighboring wireless nodes is known to ha ve the potential for large data-rate gains in wireless fading channels [1]–[4, and references therein]. Howe ver , cooperativ e transmissions also lead to increased radio footprints due to multiple simultaneous transmissions by nodes which are spatially distributed (see Figure 1 as an example). Thus, it is possible that the increase in the throughput of one flo w comes at the expense of reduced spatial reuse. The actual tradeof f depends on C. Hunter and A. Sabharwal are with the Department of Electrical and Computer Engineering, Rice Uni versity , Houston, TX, 77005 USA e-mail: [chunter,ashu]@rice.edu. This work w as partially funded by NSF grants CNS-0551692, CNS-0619767, CNS-0923479 and CNS-1012921. 2 the form of inter -flow coordination protocols in the network, which determines the timing and form of nodes’ transmissions. In turn, the form of coordination depends on ho w much network state information is a vailable at each node. In this w ork, we systematically analyze the role of network state information and the associated design of random access protocols in the context of cooperati ve communication-based networks. S1 D1 S2 D2 R1 Fig. 1. Relays can decrease spatial reuse by adding interference. Our core contrib ution is a technique for protocol de velopment for cooperative relays. This technique applies for any subset of full network state information, which constitutes both the channel states of all links and node states. This contrib ution is framed by three key results. First, we propose a binary approximation for the netw ork, simplifying all random v ariables to two-state variables. The binary approximation is then used to create relay access policies where the relay has zero, one, or two hops of channel information about the rest of the network. For each case of channel state information (zero, one, and two hops), we also consider the impact of whether the relay adopts a conservati ve or greedy vie wpoint about the unknown network state information. These access policies serve as guidelines to design cooperativ e protocols for actual wireless channels. Second, we compare the partial information policies to the policy which has full information to quantify the performance impact of each piece of network state information. The six protocols ( { greedy or conserv ative } relay × { zero, one, or two } hops of channel kno wledge) quantify an intuitiv e result. If the relay is greedy and assumes the best case scenario about what is not known about the rest of the network, then gains can be significant for the cooperati ve flow but they come at the expense of significant loss for other flows in some topologies. In contrast, a conservati ve relay , which aims to cause no harm to other flo ws, requires a substantial amount of network information to provide any reasonable cooperati ve 3 gains. In short, a relay can be both helpful and socially responsible only if it has significant information about the state of the network. Otherwise, a conservati ve relay will end up staying silent in the bulk of unkno wn netw ork states in order to a void any harm to a neighboring flow . Lastly , we close the loop by translating the relay access policies from the binary approximation to SINR -based protocols and study their performance using hardware-accurate network simulations. This last step is possible for all but the single-hop knowledge policies because the binary collision model turns out to be too crude to predict the behavior in this case. For the other four protocols, our simulations re veal that the trends predicted by the binary model hold for the fading channels. The proposed “computational” mechanism for protocol design is inspired by the fact that designing medium access protocols with prov able performance is often analytically and/or computationally in- tractable due to lar ge state space. As a result, medium access protocols are often designed on a case-by- case basis with different amounts of network state information. As a notable exception, the authors in [5, and references therein] reverse engineer the exponential backof f structure of man y random-access MAC protocols as a solution to a non-cooperati ve game. Similarly , the authors in [6] present an optimization- based framew ork for automated protocol design that solves an example scheduling problem. These works pursue a different methodology to a similar high-level goal: the construction of protocols in a procedural fashion. Our methodology is similar in spirit to recent work on deterministic approximation information the- oretic analyses [7], where deterministic network models provide an insight into the design of Gaussian network models in man y , but not all, cases—for example, the deterministic model in [7] is not a useful approximation of the MIMO channel. Information theoretic analyses of cooperative communication have a sizable body of literature [1], [2], [8, and references therein]. These works generally assume perfect network knowledge and centralized coordination to establish performance bounds on cooperativ e networks. In practice, global network kno wledge at ev ery node is often infeasible and/or not scalable as the size of the netw ork increases. In contrast, we study distributed cooperativ e protocols. The work in [9] studies the effects of interference and cooperative networks from the opposite perspectiv e of our work. Whereas [9] studies the implications of interference on the performance of a cooperativ e flow , we design protocols that address the implications of increased interference by cooperativ e flows on the rest of the network. Network-layer distributed cooperati ve protocols hav e a considerably more sparse presence in the literature. A survey of the current state-of-the-art [10] highlights the spatial reuse issue as an open problem. The protocols in [11]–[15] rely on non-simultaneous transmissions, and hence are a form of 4 opportunistic routing. W e are interested in protocols where the source and relay transmit simultaneously within the same bandwidth since these simultaneous transmission schemes achiev e higher rates [16] and simplify transceiv er design [17], [18] compared to their non-simultaneous counterparts. The protocols in [19], [20] use R TS/CTS packet exchanges to mitigate interference caused by relaying on surrounding flo ws. R TS/CTS is disabled by default in the majority of 802.11 chipsets because of the overhead suffered on e very transmission. In contrast, we study r eactive N A CK-based cooperativ e protocols that do not require preemptiv e handshak es to coordinate cooperation. While not specifically targeting cooperation applications, there exists a sizable body of literature on managing interference in ad hoc netw orks. These varied strate gies range from altering carrier-sense thresholds according to netw ork dynamics [21], to modifying the N A V structure of 802.11 to be less conserv ative [22], [23], and finally to using out-of-band b usy tones to enhance channel reservations [24]. T o address the main challenge in managing relay-induced interference, we ha ve chosen to base our protocol design on standard CSMA/CA access mechanisms like the IEEE 802.11 DCF . Conceptually , we belie ve that the prior literature can be le veraged in the conte xt of cooperati ve interference management by using the proposed framew ork. The rest of the paper is or ganized as follows: In Section II, we describe our signal, decoding, and carrier-sense model. In Section III, we construct a binary approximation of this model and de velop relaying policies for dif ferent amounts of network state information. W e ev aluate the relativ e performance of these relaying policies by considering their propensity to assist or harm the network. In Section IV, we translate these policies into SINR -based protocols and ev aluate their performance using a custom network simulator . I I . S Y S T E M M O D E L In this section, we describe our signal model, decoding model, and carrier-sensing model. W e then discuss physical layer relaying schemes and define the desired relaying policies. 1) Signal Model: W e assume a slow f ading model on the propagation of wireless signals. The reception of a transmission from a source node S at a destination node D in the presence of interferers is represented by y D = h SD x S + X i ∈ I h i D x i + z D , (1) 5 where y D represents the receiv ed signal at D and x S represents the transmitted signal from S . The multiplicati ve fade h ij between nodes i and j remains constant for at least the duration of x . 1 The additi ve noise z D is assumed to be circularly symmetric complex Gaussian random variable that is drawn i.i.d. for ev ery sample of x i . The set I contains all other simultaneously transmitting sources in the network that act as interferers to S . 2) Decoding Model: W e further assume an SINR -based decoding model that allows D to correctly decode a pack et from S if and only if H SD E [ | x S | 2 ] P i ∈ I H i D E [ | x i | 2 ] + E [ | z D | 2 ] ≥ γ DEC , (2) where H ij = | h ij | 2 = | h j i | 2 represents the instantaneous, path-symmetric po wer of the fading channel, E [ · ] represents an expected value over the duration of the transmission x S , and γ DEC is an SINR detection threshold. 3) Carrier-sensing Model: When a node S is backlogged with packets to send and is currently recei ving, it will pause the state of its backoff counter when the total received energy exceeds a threshold, or X i ∈ I H i S E [ | x i | 2 ] + E [ | z D | 2 ] ≥ γ CS , (3) where γ CS is a carrier -sensing power threshold. 4) N ACK-based Relaying Pr otocols: Many schemes for cooperati ve signaling have been proposed. For example, the two most common methods for signaling that can improv e di versity in reception o ver direct transmission are the Amplify-and-F orward (AF) and Decode-and-Forward (DF) schemes 2 [1]. In our prior w ork, we designed and implemented a N A CK-based cooperati ve MA C layer [17] alongside a DF-capable cooperati ve PHY transceiv er [25] in a real-time FPGA-based prototyping platform and sho wed large improvements in throughput and bit-error-rate. W e use this implementation as the basis for the MA C layer protocol de velopment in this paper . In principle, howe ver , the discussion throughout this work can easily be extended to incorporate other signaling methods that are deri ved from AF and DF . In a N A CK-based cooperativ e MA C protocol, the relaying phase of cooperation is only engaged when a direct transmission between source and destination fails due to insufficient channel quality [10]. 1 In this formulation, we make no assumptions on the distribution from which h ij is drawn. In Section IV we will ev aluate the protocols in a Rayleigh fading environment, but our proposed methodology applies to other channel distributions. 2 In many of the works in the information theoretic literature (e.g. [1]), these signaling schemes are referred to as protocols. In our work, we reserve the protocol terminology for higher -layer MA C behaviors and refer to these signaling methods as schemes. 6 Synchronizing cooperative transmission to this event at both the source and relay simultaneously is solved by explicit N ACK broadcast from the destination [17]. 5) Relaying P olicies: W e refer to the instantaneous snapshot of network dynamics as network state information ( NSI ). Consider a network of nodes represented by the set N . T wo key components frame NSI , NSI := n H | N | ( | N |− 1) 2 , X | N | o , (4) where H := { H ij |∀ i, j ∈ N , i 6 = j } (5) X := { X i |∀ i ∈ N } (6) represent the sets of channel states and transmission states in the network respecti vely . Note that the cardinality of H is | N | ( | N |− 1) 2 if self-channels are disallo wed and channel gains are assumed to be path symmetric. Since the cardinality of X is | N | , the cardinality of NSI grows with the cube of the number of nodes in the network, or O ( | N | 3 ) . Giv en a half-duplex constraint, a node i can either be transmitting or receiving at any gi ven point in time 3 , or X i ∈ { Tx , Rx } . Let R ∈ N represent a node in the netw ork that is capable of acting as a cooperativ e relay for a flow of traf fic in the same network and X R represent its instantaneous transmission state. Additionally , let [ NSI ⊂ NSI represent a subset of network state information av ailable to the relay and ψ ∈ [ NSI represent a particular netw ork state from the perspecti ve of the relay . W e define a r elaying policy as the mapping of a known NSI state at R onto the transmission state of the relay , or X R := f ( ψ ) , (7) where f : d NSI → { Tx , Rx } . W e distill the task of cooperativ e polic y design do wn to determining this functional mapping for a particular objectiv e: to maximize the rate of a cooperativ e flow while minimizing any rate degradations in noncooperati ve flo ws of the network. In other w ords, we aim to minimize the spatial reuse de gradation that can be caused by cooperativ e relays by eliminating relay transmissions in cases where doing so would harm a nearby flo w . 3 W e limit the discussion to devices that can only transmit and recei ve. Our approach can easily be employed to consider applications such as sensor networks where devices may have additional states such as being idle. 7 I I I . B I NA RY A P P R OX I M A T I O N A N D P O L I C Y D E S I G N In the model described in Section II, NSI contains channel fades that are supported o ver a continuum of values. In this section, we de velop a binary model, NSI B , as an approximation of the full NSI , for the fiv e node, two-flo w network in Figure 1. W e sho w that the states in this model can be explicitly classified by the effect that relay transmission would ha ve on the network if the relay were to transmit in such states. W e then define relaying policies that operate with incomplete d NSI B ⊂ NSI B and e valuate their relativ e performances using the binary approximation. A. Network Model Appr oximation W e approximate the signal and detection models presented in Section II in tw o fundamental ways. First, we consider a binary approximation of instantaneous channel f ades where H B ij ∈ { 0 , 1 } is a Bernoulli random v ariable with parameter p H B ij . In ef fect, p H B ij acts as a proxy for SNR ij where high SNR ij ( p H B ij → 1 ) makes a high gain channel ( H B ij = 1 ) very likely . Additionally , node state X i ∈ { 0 , 1 } is a Bernoulli random v ariable with parameter p X i where a X i = 0 represents reception and X i = 1 represents transmission. Collision No Collision No Collision Tx Node Rx Node H ij =1 Fig. 2. Nodes form vertices and channel fades form edges in the network graph. Second, we approximate the SINR -based detection model in Section II with a graph-based collision model illustrated in Figure 2. In this model, nodes form vertices that are interconnected by the instanta- neous edges formed by H B ij . If two nodes m and n are both in transmit states X m = X n = 1 , and are linked to a common recei ver l with H B ml = H B nl = 1 , then a collision occurs and neither transmission is decodable. W e note that the binary collision model, without the probability law on the links, is commonly used in medium access layer protocol design [26]. In Section IV, we remov e both of these assumptions and translate the policies generated using the binary approximation into SINR -based cooperativ e protocols. 8 S1 D1 S2 D2 R1 (a) 15 network state elements. S1 D1 S2 D2 R1 (b) 8 network state elements. Fig. 3. The highlighted links and nodes represent network elements that can take on activ e or inactiv e states The shift to binary-valued network states reduces the uncountably infinite number of states that make up NSI to a finite number . That said, the cardinality of NSI B still grows with the cube of the number of nodes in the network just like its continuous-valued counterpart in Equation (4). F or tractability , we limit our study to the case of the two-flow , five node network graph shown in Figure 3. The node R1 represents a relay node that is a priori paired with source S1 . Figure 3(a) sho ws that 15 possible random v ariables (10 channel states + 5 node states) make up any giv en snapshot of the network. Since each of these 15 bits can take on one of two v alues, there are a total of 2 15 = 32768 possible network states. T o reduce this state space to a more manageable size, we limit the scope of the discussion to relay policies designed for the N A CK-based cooperativ e protocols discussed in Section II. This reduction allo ws us to focus on a r elay-centric network model that ignores all interactions that are unaffected by relay activity . The goal of this study is to determine the conditions under which the relay should transmit (i.e. when X R1 = Tx ). Let ψ B ∈ NSI B represent a single state of the network. This state is formed by the H B ij ∈ N and X i ∈ N bits present in the two-flo w network. W e need not consider the value of X R1 in the construction of ψ B because the goal is to determine X R1 as a function of the other elements. Second, by assuming a N A CK-based protocol where the relay is only ev er requested to transmit under the condition that its source is unable to communicate to its destination, we can further reduce the follo wing states as follows: • X S1 ≡ 1 : A N A CK from D1 triggers simultaneous transmissions at S1 and R1 . If it decides to transmit, R1 will o verlap transmission with S1 . • X D1 ≡ 0 : If the cooperation request is signaled by D1 via a NA CK, then D1 kno ws that a cooperative transmission is to follo w and it will not initiate any transmissions. • X D2 ≡ 0 : In general, D2 can potentially generate transmissions in the form of ACK/N A CK control packets meant for S2 . T o reduce the number of states that must be considered, we assume that this cannot occur . In Section IV, we broaden the policies generated by this model to include arbitrary number of flo ws among an arbitrary number of nodes. Since flo ws can be bidirectional, this ef fectively 9 also captures the case of interference caused by control packets and thus relaxes this assumption. • H B S1D1 ≡ 0 : In a reacti ve cooperati ve protocol, relay transmissions only occur when the corresponding source transmission fails due to insuf ficient channel gain. Thus, we can assume that this channel is disconnected 4 . • H B S1R1 ≡ 1 : Giv en the decode-and-forward physical layer operating at the relay , the link between S1 and R1 must be connected for the relay to transmit. Figure 3(b) sho ws that this conditional model reduces the number of state elements in the network to only 8, lea ving a f ar more manageable total of 2 8 = 256 possible states. B. State Classification A relay transmission can have a number of ef fects on the network as a whole. W e classify these effects into three sets A , B , and C . Set A contains all states where a relay transmission assists the S1 - D1 flo w in recov ering a packet. Set B contains all states where S2 is forced to defer a back off while receiving when it otherwise would not because of R1 triggering a carrier -sense. Finally , set C contains all states where D2 f ails to decode a message from S2 because of a collision caused by R1 . Formally , A ∈ { ψ B | H B R1D1 X S2 H B S2D1 = 1 } (8) B ∈ { ψ B | X S2 H B R1S2 H B S1S2 = 1 } (9) C ∈ { ψ B | X S2 H B S2D2 H B R1D2 H B S1D2 = 1 } (10) where the o verline represents a logical complement. Figure 4 highlights three example netw ork states ψ B that occupy the subsets A , B , and C . Since e vents B and C correspond to mutually e xclusive ev ents ( S2 reception and transmission respectiv ely), these subsets are also mutually exclusi ve. Using Equations (8) through (10), we label each network state ψ B with its membership in these subsets, or ψ B ∈ { A , B , C , A ∩ B , A ∩ C , D } , (11) where D represents a set of states where relay transmission has neither positiv e nor neg ative impact on the network. In Appendix A, we classify each possible network state. 4 A relaying phase is triggered by an explicit NA CK broadcast from destination to source and relay . Hence, an assumption that H B S1D1 = 0 appears dissatisfying since the N ACK must be communicated ov er this channel back to the source. In practice, N ACKs can be coded at far lower rates and thus be far more resilient to channel outages than data payloads. Thus, H B S1D1 = 0 represents the case the channel gain is low enough to not support a full data payload yet high enough to support a N ACK. 10 S1 D1 S2 D2 R1 (a) Assist Example ( A ). S1 D1 S2 D2 R1 (b) Backoff Example ( B ). S1 D1 S2 D2 R1 (c) Collision Example ( C ). Fig. 4. Every state can be labelled with membership in the A , B , and C subsets. C. Relaying P olicies with P artial NSI In the pre vious section, we showed that network states can be classified according to the relay’ s effects on the network. Gi ven these labels, relaying policies can be deri ved that govern whether a relay should transmit as a function of the current state of the network ( X R1 = f  ψ B  ). In this section, we first define relaying policies assuming that the relay is fully aware of the current global network state ψ B . W e then consider relaying policies where the relay has incomplete network state information ( d NSI B ). 1) Full NSI: When a relay has access to full NSI B , it can accurately determine the current state of the network ψ B . As such, the relay knows perfectly what effect transmission during this state will have on the netw ork as a whole. W e can define a relay polic y that minimizes negati ve impact on a surrounding flo w by disallowing transmission when ψ B is labelled with ev ents B or C since these reduce spatial reuse by interfering with the operations of the other flow: X R1 =              0 if ψ B ∈ B ∪ C 1 if ψ B ∈ A ∩  B ∪ C  Z otherwise , (12) where Z represents a “don’t care” where neither a relay transmission nor the lack thereof will impact the network in any way . Counting the number of states that are members of B or C in Appendix A, we see that 48 of the 256 total states represent conditions where the relay should av oid transmitting. One can write the Boolean expression that ties the values of the individual network state elements to the behavior of the relay X R1 (the relay avoiding transmission). One can employ standard Boolean reduction techniques to con v ey this behavior more simply than the sum-of-products form of 48 cases, or X FNSI R1 = X S2 H B S2D2 H B R1D2 H B S1D2 | {z } ¬ + X S2 H B R1S2 H B S1S2 | {z }  (13) 11 S1 D1 S2 D2 R1 (a) X FNSI R1 = 0 since ψ B ∈ A . S1 D1 S2 D2 R1 (b) X FNSI R1 = 1 since ψ B ∈ C . Fig. 5. If H R1D2 is unknown, the relay cannot distinguish between these two states. In this expression, we use the FNSI acronym as representation of the “Full NSI” policy . There are tw o critical components to this beha vior . The ¬ term addresses the potential for the relay to cause a packet drop due to a collision with a transmission from S2 . Specifically , the relay should avoid transmitting when S2 is transmitting and S2 would not collide with a transmission from S1 b ut would collide with a transmission from R1 . The  term addresses the potential for the relay to cause unnecessary backof f deferrals at S2 . The relay should av oid transmitting when S2 is recei ving and no link is present between S1 and S2 but a link is present between S1 and R1 . This beha vior establishes the baseline performance of a relaying policy that has access to all of the elements required to calculate Equation (13). The power of this methodology lies in the fact that we can also determine the relay behavior for any arbitrary subset of NSI B . 2) Incomplete NSI: One can use exactly the same full NSI B table in Appendix A to construct incomplete NSI B policies by recognizing that eliminating knowledge is equiv alent to binning network states into coarser delineation. Figures 5(a) and 5(b) show two network states where the full NSI policy enables and disables relay transmission respecti vely . Howe ver , the only difference between the network states is the H R1D2 state element. If this state element is unknown to the relay , the two states are binned together creating a conflict set where the lack of knowledge yields ambiguity in what the relay should do; the relay is unable to determine whether the current state of the network is in an assist classification A or also in a collision classification C . In dealing with these conflict sets that arise with incomplete kno wledge av ailable to the relay , we consider two approaches to this problem: Conservati ve V iew: When a relay is unable to distinguish between multiple states, it may assume the worst about the state elements it does not know . This assumption yields a disabled relay ( X R1 = 0 ) in the case that any state within the conflict set demands a disabled relay . 12 Greedy View: Adopting the best-case vie wpoint about unkno wn states, a relay can enable transmission ( X R1 = 1 ) when any state within the conflict set demands relay transmission. These approaches apply to any arbitrary subset of the full NSI B kno wledge, so a remaining task is to determine what subsets of full NSI B to consider . A useful way of sorting NSI B is considering the hop-distance of the NSI B elements from the relay . This approach allows a quantitativ e description of how “local” a node’ s vie w of the network is [27]. Let d NSI B ( n ) represent the set of NSI elements no further than n hops aw ay from the relay . In our two-flo w network, these sets are defined as d NSI B (2) = { H B S1S2 , H B R1S2 , H B S1D2 , H B S2D2 , H B R1D2 , H B R1D1 , H B S2D1 } (14) d NSI B (1) = { H B R1S2 , H B R1D2 , H B R1D1 } (15) d NSI B (0) = {∅} . (16) In the case of d NSI B (2) , all wireless channels are at least two hops aw ay so the relay kno ws full NSI B with the notable e xception of the transmission state of S2 (i.e. X S2 ). In the following sections we use the notation Cons ( n ) to identify policies that use the conservati ve mapping with n hops of knowledge. Similarly , the notation Greed ( n ) is used to identify policies that use the greedy mapping. Conservati ve P olicies: Using the same Boolean reduction techniques as before, conserv ative relaying policies can be identified for different numbers of hops of information made a vailable to the relay . X Cons (2) R1 = H B S2D2 H B R1D2 H B S1D2 + H B R1S2 H B S1S2 (17) X Cons (1) R1 = H B R1S2 + H B R1D2 (18) X Cons (0) R1 = 1 . (19) In the full NSI B case in Equation (13), the X S2 acts as a kind of switch to determine whether the relay’ s behavior is dominated by collision av oidance or backof f deferral av oidance. In Equation (17), this switch is missing and both terms apply because the two-hop polic y does not ha ve access to the node state. In Equation (18), the relay is only able to base its decision of whether to transmit on the set d NSI B (1) . Acting conserv ativ ely , the relay is only able to transmit when the links between R1 and both S2 and D2 are disconnected. The relay guarantees that it cannot cause a backoff deferral at S2 or a collision at D2 . 13 Finally , the relay in Equation (19) is nev er able to transmit since it can nev er guarantee that it will not harm another flo w . Greedy Policies: Greedy relaying policies can be identified for different numbers of hops of information made av ailable to the relay . X Greed (2) R1 = H B S2D2 H B R1D2 H B S1D2 · H B R1S2 H B S1S2 + H B R1D1 (20) X Greed (1) R1 = H B R1D1 (21) X Greed (0) R1 = 0 . (22) The key dif ference between Equations (13) and (20) is that if only one condition (collision or backof f deferral) instructs the relay to halt, it is assumed that the unknown X S2 state element would hav e disabled that term. In other words, the relay only halts transmissions when either a B or C event would occur regardless of the X S2 state. Additionally , another case for disabling the relay appears when R1 and D1 are disconnected since the relay cannot assist the cooperati ve flow in this case. In Equation (21), the relay only disables transmission when it knows that it will not be able to help. In these cases, there is only an opportunity to harm the network, so ev en the greedy relay disables transmission. Finally , the relay in Equation (22) kno ws nothing about the network and greedily transmits whene ver it is requested. D. Discussion of Pr otocol Overhead The binary model-based relay policies dictate the behavior of the relay given elements of NSI. In this section, we discuss how such information might be collected in actual protocols, noting that complete protocol implementation is out of scope of this paper . The amount of overhead for collecting this information is determined by two factors: (i) the rate of change of NSI and (ii) ho w much knowledge is desired. First, the rate of change of NSI depends on the amount of mobility in the system. For lo w-mobility , slo w-fading en vironments such as the indoor W i-Fi, channel coherence times can be many tens or hundreds of packet intervals. As such, NSI knowledge at the relay need only be updated on the timescales of these coherence times. Second, the amount of o verhead required differs from one NSI element to the next. For instance, the one-hop NSI states may be logged passi vely (with zero overhead) at the relay by simply ov erhearing surrounding transmissions. In fact, e ven some two-hop kno wledge may be acquired without additional o verhead. Assuming the non-cooperati ve flo w employs the same N A CK-based protocol as the 14 cooperati ve flo w , the relay can infer the link quality between the non-cooperati ve source and destination by overhearing A CKs and NA CKs generated by the non-cooperati ve destination. E. P erformance Evaluation As a mechanism to compare the performance of dif ferent policies, we ev aluate the probability of the network entering a particular event subset while simultaneously considering whether a relaying policy transmits. In other words, a relaying policy can be penalized for transmitting within the B or C event subsets and re warded for transmitting in A . The probability of a relay transmitting in e vent A is P r { X R1 ∩ ψ B ∈ A } = X ψ B ∈ A X R1  ψ B  · P r { ψ B } , (23) where P r { ψ B } can be calculated by the product of the Bernoulli parameters. Similar expressions for e vent spaces B and C can be deri ved. It is useful to consider a particular application scenario where the R1 node is geographically near the S1 node. This models a usage case where one user owns both the relay and source nodes and both devices are located near the user . Furthermore, let us simplify the discussion of these systems by considering a single dominant parameter: flo w separation. Specifically , let p H B S1S2 = p H B S1D2 = p H B R1S2 = p H B R1D2 = p where p represents a single parameter that acts as a proxy for flo w separation. As p → 1 , the flo ws are topologically connected with high probability , and as p → 0 , the flows are disconnected with high probability . For simplicity of discussion, assume e very other state element probability is 1 2 . Using Equation (23), we compute expressions that determine the propensity of each policy to transmit in the A , B , and C subsets as a function of the single independent parameter p . T ABLE I P E R F O R M A N C E E V A L UATI O N O F R E L A Y I N G P O L I C I E S Policy P r { X R1 ∩ ψ B ∈ A } P r { X R1 ∩ ψ B ∈ B } P r { X R1 ∩ ψ B ∈ C } FNSI 5 p 2 − 5 p +6 16 0 0 Cons (2) 3 p 4 − 6 p 3 +10 p 2 − 7 p +2 16 0 0 Cons (1) 3 p 2 − 6 p +3 8 0 0 Cons (0) 0 0 0 Greed (2) − p 4 +2 p 3 − p +3 8 − p 4 +2 p 3 − 3 p 2 +2 p 16 − p 4 +2 p 3 − 2 p 2 + p 8 Greed (1) 3 8 − p 2 + p 4 − p 2 + p 8 Greed (0) 3 8 − p 2 + p 2 − p 2 + p 4 15 T able I summarizes the performance of each of the six pre viously described relaying policies. Of note, the full NSI B policy and the conservati ve incomplete NSI B policies ne ver transmit in the subsets where doing so could potentially cause a collision or backof f deferral e vent. As such, the probability of harming the other flo w by transmitting on these occasions is zero. The greedy policies, ho wev er , allo w some degradation in the other flo w in order to improve the policies’ abilities to assist their o wn flows. 0 0.1 0.2 0.3 0.4 0 1 2 FNSI n Probability Greed Cons. (a) Probability of assisting. 0 0.0375 0.0750 0.1125 0.1500 0 1 2 FNSI n Probability Greed Cons. (b) Probability of causing backoff de- ferral. 0 0.0175 0.0350 0.0525 0.0700 0 1 2 FNSI n Probability Greed Cons. (c) Probability of causing collision. Fig. 6. Conservati ve relaying behavior requires substantial NSI before cooperativ e gain is observed. Consider the case that p = 1 2 . Figure 6 sho ws the performance of each policy as a function of NSI B av ailable to R1 . In general, the trend is that more d NSI B kno wledge results in less harm to another flow since the relay kno ws more about the network it needs to protect. Like wise, increasing d NSI B kno wledge allo ws conservati ve relays to assist their flo w more and e ventually con ver ge with their greedy counterparts. Incrementally , the jump from zero hops of kno wledge to one hop of kno wledge has very little effect on the conservati ve policies—the improvement seen in performance of the cooperative flow is marginal. For the greedy policies, ho wev er , ha ving e ven a single hop of information pro vides a substantial drop in the amount of harm the relay will impart on the neighboring flow . Conserv ative policies require large amounts of NSI before cooperativ e gains can be seen. Figure 7 plots the expressions in T able I as functions of p . In Figure 7(a), we plot the probability of each scheme transmitting during the states where a relay is able to help its paired flo w . The greedy policies all improv e performance o ver the full NSI B policy since they transmit during cases where the full NSI B policy halts relay transmission in accordance with minimizing negati ve impact on the neighboring flow . The conserv ati ve policies decrease performance over the full NSI B policy since they av oid transmitting in states where the full NSI B policy would because they are unable to distinguish these states from those where the relay should be halted. The Cons (1) polic y in particular exhibits an unusual beha vior in that it is able to help only as p → 0 . This is due to the fact that, gi ven only one hop of NSI B kno wledge, 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 p Likelihood 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p 0.05 L i ke l i h o o d 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Greed(0), Greed(1) Greed(2) Cons(2) FNSI Cons(0) Cons(1) Probability 0.0 (a) Probability of assisting. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 p Likelihood 0.02 0.04 0.06 0.08 0.10 0.12 0.14 L i ke l i h o o d 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p Greed(0) FNSI , Cons(2) ,Cons(0), Cons(1) Greed(2) Greed(1) Probability (b) Probability of causing backoff de- ferral. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 p Likelihood 0.01 0.02 0.03 0.04 0.05 0.06 0.07 L i ke l i h o o d 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p Greed(0) FNSI , Cons(2) ,Cons(0), Cons(1) Greed(2) Greed(1) Probability (c) Probability of causing collision. Fig. 7. Each policy exhibits different behaviors in terms of the relay’ s propensity to transmit in the ev ent subspaces. a relay is unable to align its transmissions to source interference that would be present anyway since it has no idea what the link qualities are between its source and other nodes in the network. In Figures 7(b) and 7(c), we see the impact of the relay policies on the probability of the neighboring flo w deferring and colliding, respectively . As stated previously , the full NSI B and conservati ve incomplete NSI B policies cause no deferrals or collisions. The greedy incomplete NSI policies, ho wev er , allow degradations in the interest of increasing the probability of assisting the cooperati ve flo w . I V . P R OT O C O L D E S I G N A N D S I M U L A T I O N The policies presented in Section III operate on binary network state information. No w , we translate the preceding two-flo w policies into n -flow protocols. These protocols are then implemented in a custom network simulator and are e valuated in realistic fading en vironments. A. Pr otocol T ranslation The binary network model abstracts from reality in tw o key w ays. First, only two unidirectional flo ws are considered, whereas arbitrary networks can potentially have many bidirectional flo ws. Second, channels take on only binary states whereas actual channels span a continuum of po wers. W e now translate the aforementioned policies into cooperativ e protocols that ov ercome these limitations of the model. Specifically , we can directly translate the Cons (2) , Cons (0) , Greed (2) , and Greed (0) policies. The one- hop policies, ho wev er , highlight a limitation in the binary network model when it applies to SINR-based protocol design. Consider the policy stated in Equation (18). The relay transmits when its links to the other flow are disconnected. As defined by the binary collision model, the relay is able to guarantee that no collision or deferral e vent can take place in these states. This policy does not translate to an 17 SINR -based scenario, where the measurement of a single link quality is insuf ficient to guarantee that a collision or deferral ev ent will not take place. Even if the relay measured the instantaneous channel between itself and another destination as being very weak, it is still possible that a transmission will cause a collision if the channel supporting the other flow is also very weak. Despite this limitation, we are able to conclusiv ely sho w that the remaining policies not only are capable of being translated into SINR -based protocols, b ut their r elative performance in realistic fading en vironments is accurately predicted by our analysis of the binary model. Conservati ve Protocols: The Cons (2) and Cons (0) policies can be directly translated into protocols that operate on instantaneous SINR measurements. Consider a network N consisting of N nodes. Protocol 1: Cons (2) N = { 0 , 1 , 2 , . . . , N − 1 } X Cons (2) R = Tx f or i ∈ N \ { S , D , R } do f or j ∈ N \ { i, S , D , R } do if ( BO S i and BO SR i ) or ( COL S ij and COL SR ij ) then X Cons (2) R = Rx Protocol 1 formally specifies the Cons (2) beha vior . The collision and backof f terms are COL S ij =  P t L ij | h ij | 2 P t L S j | h S j | 2 + z < γ DET  COL SR ij =  P t L ij | h ij | 2 P t L S j | h S j | 2 + P t L R j | h R j | 2 + P k ∈ I 1 P t L kj | h kj | 2 + z < γ DET  BO S i =  P t L S i | h S i | 2 + z ≥ γ CS  BO SR i = " P t L S i | h S i | 2 + P t L R i | h R i | 2 + X k ∈ I 2 P t L ki | h ki | 2 + z ≥ γ CS # where [ · ] represents the Iverson bracket. Additionally , P t is a constant representing transmission power , L ij is a multiplicati ve factor that reduces po wer according to path loss between nodes i and j , z is a constant representing the thermal noise power in each radio, γ DET represents a threshold for the minimum SINR required to decode a reception, and γ CS represents a power threshold for carrier-sensing. Finally , 18 the I subsets represent other potential transmitters in the network (including other relays) as defined by I 1 = N \ { S , D , R , i, j } I 2 = N \ { S , D , R , i } . The Cons (0) protocol can simply be stated as X Cons (0) R = Rx since the relay ne ver transmits. These protocols ensure that the relay is disabled whene ver it would cause a deferral or collision event in surrounding flo ws. As such, the y guarantee zero reduction in spatial reuse. Greedy Protocols: Similarly , the Greed (2) and Greed (0) policies can be directly translated into protocols that operate on instantaneous SINR measurements. Protocol 2: Greed (2) N = { 0 , 1 , 2 , . . . , N − 1 } X Greed (2) R = Tx f or i ∈ N \ { S , D , R } do f or j ∈ N \ { i, S , D , R } do if ( BO S i and BO SR i and COL S ij and COL SR ij ) or COL SRD then X Greed (2) R = Rx Protocol 2 formally specifies the Greed (2) beha vior . The collision and backof f terms are COL SRD =  P t L SD | h SD | 2 + P t L RD | h RD | 2 z < γ DET  COL S ij =  P t L ij | h ij | 2 P t L S j | h S j | 2 + z < γ DET  COL SR ij =  P t L ij | h ij | 2 P t L S j | h S j | 2 + P t L R j | h R j | 2 + z < γ DET  BO S i =  P t L S i | h S i | 2 + z ≥ γ CS  BO S , R i =  P t L S i | h S i | 2 + P t L R i | h R i | 2 + z ≥ γ CS  where all components share the same definitions. The Greed (0) protocol can simply be stated as X Greed (0) R = Tx since it makes no effort to defer any of its transmissions. The greedy protocols will increase the rate of the cooperative flo w b ut will do so at some cost to surrounding flows. 19 B. Custom Simulator T o ev aluate the distrib uted protocols, we construct a custom network simulator based on the well-kno wn ns-2 simulation en vironment. The 802.11 extension to ns-2 contributed a number of enhancements for wireless applications [28]. W e hav e added significant extensions to include a cooperativ e PHY module and a path-symmetric Rayleigh fading channel module. Using our real-time FPGA implementations of cooperati ve protocols [17], [18], we ha ve verified the accuracy of this simulator with actual over -the-air and channel emulator measurements. C. P erformance Evaluation In T able II, we specify the key simulation parameters. All other parameters in the experiment including T ABLE II S I M U L A T I O N P AR A M E T E R S Header Rate BPSK (1/2 rate code) Payload Rate 16-QAM (3/4 rate code) Path loss Exponent 3 F ading Correlated Rayleigh Doppler Fr eq. ( f d ) 15Hz R TS/CTS Disabled T raffic CBR Packet Size 1470 bytes SINR thresholds for packet decoding are identical to the default values specified in [28]. In Section III, we e valuated the various policies with a single parameter p that affects the likelihood of the cooperati ve flow being connected to the other flo w in the netw ork. In this section, the analogous parameter is the distance between the relayed and non-relayed flow as sho wn in the simulation topology in Figure 8. The cooperativ e flo w has a large source-destination distance in order to place that flo w in a fading- dominated regime (i.e. a significant number of the packet losses suffered by the destination are due to inadequate channel capacity between S1 and D1 ). The non-cooperati ve flow is in an interference- dominated regime where v ery few of its transmissions are lost due to fades. This topological selection emphasizes the negati ve impact of the relay on the non-cooperativ e flo w and allows clear differences between the distrib uted cooperativ e protocols to be seen. 20 D1 S2 D2 S1 R1 55m 27.5m Flow Separation Fig. 8. W e vary the flow separation distance as the independent variable for the simulation. A useful metric for e valuating the performance of a protocol is to compare the throughput of each flo w when a relay is present in the network with the throughput of each flo w when there is no relay . W e consider this change in throughput when a relay is present in the network. Figure 9 shows the measured throughput difference when a relay is present and when it is not for each pre viously described protocol. Figure 9(a) focuses on the impact of cooperation on the cooperativ e flo w . Of note, the Cons (0) protocol provides no improvement over the case where the relay is absent from the netw ork because the Cons (0) protocol ne ver uses it. All other protocols, ho wev er , pro vide throughput improvement. In particular , the Greed (0) protocol (that always uses the relay) provides the most improv ement at all flow separation distances. This fact is predicted by the binary network model and was shown in Figure 7(a). 0 50 100 150 200 250 300 − 1 0 1 2 3 4 5 6 x 10 6 Flow Separation (m) ! Throughput (bps) Performance of Flow with Relay 0 50 100 150 200 250 300 Flow Separation (m) -1 0 1 2 3 4 5 6 Change in Throughput (Mbps) G re e d (2 ) G re e d (0 ) C o n s(2 ) C o n s(0 ) (a) Cooperativ e Flow Performance. 0 50 100 150 200 250 300 − 10 − 8 − 6 − 4 − 2 0 2 x 10 5 Flow Separation (m) ! Throughput (bps) Performance of Flow without Relay 0 50 100 150 200 250 300 Flow Separation (m) -1 -.8 -.6 -.4 -.2 0 .2 Change in Throughput (Mbps) 0 50 100 150 200 250 300 − 1 0 1 2 3 4 5 6 x 10 6 Flow Separation (m) ! Throughput (bps) Performance of Flow with Relay 0 50 100 150 200 250 300 F l o w Se p a ra t i o n (m) -1 0 1 2 3 4 5 6 Change in T h ro u g h p u t (Mb p s) Greed(2) Greed(0) Cons(2) Cons(0) (b) Non-cooperativ e Flow Performance. Fig. 9. The relay can assist the flow with which it is paired and harm the flo w with which it is not. These effects can be balanced with protocol selection. Figure 9(b) shows the impact of relaying on the non-cooperative flow . Since the relay can only increase the footprint of the cooperati ve flo w , this means that spatial reuse can only degrade and not improv e the 21 performance of the non-cooperati ve flow . Again, the Cons (0) protocol ne ver uses the relay so it nev er degrades the throughput of the non-cooperativ e flow . Greed (0) , howe ver , has two distinct regions where the harm on non-cooperati ve flo w reaches local maxima. The reason there are two regions is that the locations where collisions and backoff deferrals each create the most impact are not necessarily the same; they depend on the many parameters specific to the simulation. Reg ardless, the Cons (2) protocol av oids any harm just as the corresponding policy predicts in Section III. In Figure 7, each policy was analyzed as a function of a proxy for flo w separation. Noting the similarities with the actual flow separation comparisons in Figure 9, this confirms the binary model as a robust mechanism for the procedural generation of cooperati ve protocols. V . C O N C L U S I O N S Physical layer cooperation shows tremendous potential for performance improv ement in wireless links that are able to use cooperati ve relays. Howe ver , for links that are unable to use relays, cooperation is a threat to their own performance due to the loss of spatial reuse caused by additional transmitters in the shared wireless medium. In this work, we ha ve presented a policy design methodology that allo ws the systematic study of relay beha vior for arbitrary amounts of network knowledge at the relay . Through extensi ve network simulations, we demonstrate the successful application of this method to distributed protocols that operate in fading en vironments. 22 A P P E N D I X A S T AT E C L A S S I FI C AT I O N I N B I NA RY M O D E L Recalling that H B ij and X i are binary v alued, let ψ B = H B R1D2 · 2 0 + H B R1D1 · 2 1 + H B R1S2 · 2 2 + H B S2D1 · 2 3 + H B S2D2 · 2 4 + H B S1S2 · 2 5 + H B S1D2 · 2 6 + X S2 · 2 7 . Each network state is labelled in the follo wing table. ψ B Label ψ B Label ψ B Label ψ B Label ψ B Label ψ B Label ψ B Label ψ B Label 0 D 32 D 64 D 96 D 128 D 160 D 192 D 224 D 1 D 33 D 65 D 97 D 129 D 161 D 193 D 225 D 2 A 34 A 66 A 98 A 130 A 162 A 194 A 226 A 3 A 35 A 67 A 99 A 131 A 163 A 195 A 227 A 4 B 36 D 68 B 100 D 132 D 164 D 196 D 228 D 5 B 37 D 69 B 101 D 133 D 165 D 197 D 229 D 6 A ∩ B 38 A 70 A ∩ B 102 A 134 A 166 A 198 A 230 A 7 A ∩ B 39 A 71 A ∩ B 103 A 135 A 167 A 199 A 231 A 8 D 40 D 72 D 104 D 136 D 168 D 200 D 232 D 9 D 41 D 73 D 105 D 137 D 169 D 201 D 233 D 10 A 42 A 74 A 106 A 138 D 170 D 202 D 234 D 11 A 43 A 75 A 107 A 139 D 171 D 203 D 235 D 12 B 44 D 76 B 108 D 140 D 172 D 204 D 236 D 13 B 45 D 77 B 109 D 141 D 173 D 205 D 237 D 14 A ∩ B 46 A 78 A ∩ B 110 A 142 D 174 D 206 D 238 D 15 A ∩ B 47 A 79 A ∩ B 111 A 143 D 175 D 207 D 239 D 16 D 48 D 80 D 112 D 144 D 176 D 208 D 240 D 17 D 49 D 81 D 113 D 145 C 177 C 209 D 241 D 18 A 50 A 82 A 114 A 146 A 178 A 210 A 242 A 19 A 51 A 83 A 115 A 147 A ∩ C 179 A ∩ C 211 A 243 A 20 B 52 D 84 B 116 D 148 D 180 D 212 D 244 D 21 B 53 D 85 B 117 D 149 C 181 C 213 D 245 D 22 A ∩ B 54 A 86 A ∩ B 118 A 150 A 182 A 214 A 246 A 23 A ∩ B 55 A 87 A ∩ B 119 A 151 A ∩ C 183 A ∩ C 215 A 247 A 24 D 56 D 88 D 120 D 152 D 184 D 216 D 248 D 25 D 57 D 89 D 121 D 153 C 185 C 217 D 249 D 26 A 58 A 90 A 122 A 154 D 186 D 218 D 250 D 27 A 59 A 91 A 123 A 155 C 187 C 219 D 251 D 28 B 60 D 92 B 124 D 156 D 188 D 220 D 252 D 29 B 61 D 93 B 125 D 157 C 189 C 221 D 253 D 30 A ∩ B 62 A 94 A ∩ B 126 A 158 D 190 D 222 D 254 D 31 A ∩ B 63 A 95 A ∩ B 127 A 159 C 191 C 223 D 255 D R E F E R E N C E S [1] J. 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