Cooperative Communications in Mobile Ad Hoc Networks - CiteSeerX

Scaglione, Dennis L. Goeckel, [ Anna and J. Nicholas Laneman]

Cooperative Communications in Mobile Ad Hoc Networks

© IMAGESTATE

[Rethinking the link abstraction]

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he motivation of this article is to clarify and help resolve the gap between the link abstraction used in traditional wireless networking and its much broader definition used in the context of cooperative communications, which has received significant interest as an untapped means for improving performance of relay transmission systems operating over the ever-challenging wireless medium. The common theme of most research in this area is to optimize physical layer performance measures without considering in much detail how cooperation interacts with higher layers and improves network performance measures. Because these issues are important for enabling cooperative communications to practice in real-world networks, especially for the increasingly important class of mobile ad hoc networks (MANETs), the goals of this article are to survey basic cooperative communications and outline two potential architectures for cooperative MANETs. The first architecture relies on an existing

clustered infrastructure: cooperative relays are centrally controlled by cluster heads. In another architecture without explicit clustering, cooperative links are formed by request of a source node in an ad hoc, decentralized fashion. In either case, cooperative communication considerably improves the network connectivity. Although far from a complete study, these architectures provide modified wireless link abstractions and suggest tradeoffs in complexity at the physical and higher layers. Many opportunities and challenges remain, including distributed synchronization, coding, and signal processing among multiple radios; modeling of new link abstractions at higher layers; and multiaccess and routing protocols for networks of cooperative links. INTRODUCTION Network architecture and the process of abstraction go hand in hand. For most wired networks, the notion of a link has been a

IEEE SIGNAL PROCESSING MAGAZINE [18] SEPTEMBER 2006

1053-5888/06/$20.00©2006IEEE

useful abstraction directly tied to the physical propagation medium. For wireless networks, especially the increasingly important class of MANETs, the classical notion of a link is more nebulous than in the wired case. Even so, two constraints are often imposed on network architectures to maintain it. These constraints include: ■ Constraint I: a functional physical layer communication link can originate from only one transmitter. ■ Constraint II: concurrent transmissions of multiple transmitters result in interference that, if not sufficiently attenuated by spatial or channel multiplexing, produces a collision, i.e., a level of distortion for the useful signal that is irreversible at the ultimate receiver. At various levels, many current MANET protocols attempt to create, adapt, and manage a network based on a maze of point-to-point links, all conforming to Constraints I and II. Multihop transmission combines several intermediate links among pairs of nodes using buffer space, power, and bandwidth to route their own data as well as data from other sources. Although an architecture based upon the classical link abstraction leads to many advantages that should not be underestimated, a number of issues arise in a wireless medium that hinder the classical link abstraction upon which these architectures are based. The emerging area of cooperation communications suggests that it is worthwhile to explore a broader solution space in which Constraint I and/or Constraint II are relaxed. COOPERATIVE COMMUNICATIONS: A TOP-DOWN MOTIVATION Multihop transmission as described above is a special case of a broader class of transmission protocols called cooperative communications that have recently received significant attention in various communities. Within prevalent models for cooperation, Constraints I and II correspond to additional constraints on the transmission protocols, imposed for practical or architectural reasons. Much of the work on cooperative communications demonstrates improved performance from largely physical layer perspectives; however, because many of the advantages essentially result from violating either of Constraints I or II, there is a great deal of room for design of network architectures that integrate cooperation, especially for MANETs. The goal of this article is to help bridge this gap by summarizing key ingredients of cooperative communications and illustrating two approaches for cooperative MANETs. A cooperative link consists of separate radios encoding and transmitting their messages at the physical layer in coordination; these nodes could be a single source and relay, or they can be a group or relays, or both. It has generally been physical layer researchers who have championed the use of cooperative diversity in wireless networks, arguing that nodes equipped with a single antenna, through physical layer coding and signal processing, could achieve similar diversity and coding gains to those of co-located multiantenna systems [27], while leveraging the distributed hardware and battery resources that are already

available. Such arguments are mostly based on link quality metrics, such as the average error probability and the outage probability. As indicated by the two network models described briefly in the next section, this point of view should be expanded because cooperative communications is inherently a network solution, and there are issues of protocol layering and crosslayer architecture that naturally must be explored jointly by a broad community of researchers. In addition to offering performance improvements in terms of network metrics such as connectivity, cooperation alleviates certain collision resolution and routing problems because it allows for simpler networks of more complicated links, rather than complicated networks of simple links. NETWORK MODELS As further developed in the sequel, we consider cooperative communications within two wireless network models. We focus the discussion on how the cooperative groups are activated and supported. Although this perspective is insufficient to claim that we specify an entire architecture, it does suggest tradeoffs between centralized and decentralized architectures as well as complexity among the physical, link, medium access, and network layers of the protocol stack. In “Cooperative Communications in Existing Network Architectures,” the first network model is a MANET with an existing clustered infrastructure, in which cooperative transmission is centrally activated and controlled by the cluster access points (AP). All terminals communicate through a cluster AP, which handles routing to other clusters. In the classical multihop architecture, each cluster is responsible for transmitting the message to a “gateway” node in the next cluster. In our cooperative network architecture, between clusters the AP uses multiple gateway nodes (Figure 1), which propagate the message providing cooperative gains compared to the single gateway solution. Better links translate into better network connectivity compared to multihop solutions. Relying on existing techniques to determine the clustering structure, our objective is to describe how the AP can select the cooperative nodes by means of matching algorithms and how this benefits the network connectivity. In “Cooperation for New Ad Hoc Architectures,” the second network model is a MANET in which a random source conveys extra control information and link parameters in the message to enable recipients to self-select and form a random cooperative cluster. The nodes recruited in this cluster can rely on the synchronization data available in the source packet. Within their estimation inaccuracies and propagation delays, the nodes can infer their transmission schedule. They can be ignorant of the codes chosen by the other nodes, but the resulting cooperative gains are close to those of a centralized scenario in which codes are explicitly assigned to the nodes. A small cluster of nodes can act as a source and recruit additional nodes to form a larger cluster, and so forth, to create multistage cooperation (Figure 2). We present two main ideas concerning this architecture. First, we show that, as in a traditional channel access problem,


capacity region), improved reliability in terms of diversity gain, multistage cooperative access can be randomized, although not diversity-multiplexing tradeoff, and packet- or symbol-error quite in the same way as traditional random access. Second, we probabilities. The interest has therefore percolated to other show that in multicast applications this solution is considerably communities, and today there are many specific practical solumore power efficient than the multihop solutions. tions to harvest diversity from a network. Early examples are As we will see, the new ingredient of cooperative communica[2], [3], [11], [15], and [22] and tions suggests a rethinking of many more in more recent the link abstraction and creates A COOPERATIVE LINK CONSISTS OF years. Multipath diversity many opportunities and chalSEPARATE RADIOS ENCODING AND instead of antenna diversity was lenges from the physical layer to TRANSMITTING THEIR MESSAGES AT first exploited in [20]. higher layers. In the clustered THE PHYSICAL LAYER IN COORDINATION. We summarize the main elearchitectures, more work at the ments of cooperative communinetwork layer is necessary to cation protocols and illustrate their performance advantages. We support cooperation. In the distributed approach we describe, the assume that the cooperative nodes do not know the channel brunt of the work lies in the physical layer. response at the transmitter but that it can be estimated at the receiver; we assume that the estimate is without error. (The ELEMENTS OF COOPERATIVE COMMUNICATIONS channel parameters to be estimated grow with the number of Early formulations of general relaying problems appeared in cooperating nodes, and the effect of channel estimation errors the information theory community [5], [29] and were inspired can counterbalance the cooperative gains. For situations in by the concurrent development of the ALOHA system at the which the channel parameters can be made available at the University of Hawaii. The classical relay channel model is comtransmitter, through feedback or by duality, one can earn the prised of three terminals (Figure 3): a source that transmits performance advantages of beam-forming with bandwidth effiinformation, a destination that receives information, and a ciency equal to one. Multiple-input, multiple-output (MIMO) relay that both receives and transmits information to enhance gains prospected, for example, in [28] are attained only if the communication between the source and destination. More receivers process the data jointly. When, instead, the receivers recently, models with multiple relays have been examined [10], process the data independently the spectral efficiency is always [21]. Cooperation [11], [22] is a generalization of the relay ≤ 1 and, when the channel is known only at the receiver, for channel to multiple sources with information to transmit that blocks of finite size > 2, the spectral efficiency is always strictly also serve as relays for each other. Combinations of relaying less than one [27].) Receiver cooperation in the form of compress and cooperation are also possible and are often referred to and forward schemes [10] is not considered. generically as “cooperative communications.” Interestingly, all of these models fall within the broader class of channels with PHYSICAL LAYER MODEL FOR COOPERATIVE RADIOS generalized feedback [4], [9]. We assume that each radio has a baseband equivalent, discreteEven after 40 years of intense study, the relay channel capactime transmit signal X i [k], with average power constraint ity is not known in general. Although useful bounds on capacity K−1 2 have been obtained for various approaches (see, e.g., the sumk=0 |X i [k]| ≤ K Pi , where K is the duration of the signal, mary in [10]), it is thanks to our increased understanding of the and the received signal is Yi [k], i = 1, 2, ..., N. Hardware limitabenefits of multiantenna systems in wireless channels [27] that tions introduce the so called “half-duplex” constraint, namely, many have come to realize that multiple relays can emulate the the impossibility of concurrent radio transmission and recepstrategies designed for multiple transmit antenna systems and tion. Incorporating this constraint, considering narrowband offer significant network performance enhancements in terms transmission, we model the discrete-time received signal at of various metrics, including: increased capacity (or larger radio i and time sample k as [10].

Random Cooperative Cluster

Destination

Destination

AP AP

AP

Source Source

[FIG1] Cooperative gateways.

[FIG2] Randomized cooperation.


Yi [k] =  N  H X [k] + W [k], if radio i receives at time k i, j j i  j=i, j= i 0, if radio i transmits at time k, (1) where Hi, j captures the combined effects of symbol asynchronism, fading, quasi-static multipath fading, shadowing, and path-loss between radios i and j; Wi [k] is a sequence of mutually independent, circularly symmetric, complex Gaussian random variables with common variance N0 that models the thermal noise and other interference received at radio i. Note that Hi, j is assumed to be fixed during the block length. Radio i knows the realized Hi, j but not Hp, j, for p = i, and j = 1, 2, . . . , t. The Hi, j are modeled as independent complex-valued random variables for different j, which is reasonable for scenarios in which the radios are separated by a number of carrier wavelengths (in all cases, each transmitter has an independent random phase due to its local oscillator). Nodes that cooperate share a common message, which was transmitted previously by one or more nodes and received by the group of cooperating nodes. General relaying is done by mapping the message embedded in the received vector y i = (Yi [0], . . . , Yi [K − 1]) T onto a matrix code where each column is the new relay signal. Specifically, we can consider a portion or the entire decoded message as a vector of length M denoted by s = (S [0], . . . , S [M − 1]) T ; each one of the T cooperating relay nodes transmits a column x r = (X r[0], . . . X r[K − 1]) T of a K × T matrix code X = GK×T (s) (Figure 4). Denoting by log2 (|S |) the number of bits per symbol, (M/K ) log2 (|S |) is the spectral efficiency of the code. The number of columns T is the number of cooperating nodes. Different cooperative schemes correspond to different instantiations of the mapping s → G(s). Hence cooperative transmission is equivalent to a multi-input, single output system (MISO) with a per antenna power constraint.

Destination Source Relay

[FIG3] Three-nodes model.

yi=

T

Hi,rx r + w i = Xh i + w i ,

(2)

r=1

where h i = (Hi,1 , ..., Hi,T) T is the vector of the relays’ fading coefficients. The simplest forms of cooperative diversity are the so-called amplify and forward (AF) and decode and forward (DF). In the AF strategy, for each transmit symbol S the nodes retransmit a scaled version of the samples received over orthogonal channels. This can be expressed in our general model by the following coding rule by having s = S and G(s)

i=1

X1 X2

S

+

X3

y

X4

[FIG4] Codes for cooperative transmission.

G(S) = diag(β1 Z1 , . . . , β T Z T) Pr H Z r = h r y r, β r ≤ , H E hH r y ry r h r

(3)

where y r in Z r = h H r y r is the received vector containing the symbol S of the message, and the constraints on the scaling coefficients β r guarantees that the node transmit power is Pr. For the DF strategy the nodes decode each symbol of the message and transmit the decoded symbol over orthogonal channels. The code matrix that corresponds to the DF is thus G(S) = diag

MODULATION AND CHANNEL CODING FOR COOPERATION The simplest setting possible to isolate the benefits of spatial diversity is that of frequency flat fading channels Hi, j[k] = Hi, jδ[k]. The received ector y i = (Yi [0], . . . , Yi [K − 1]) T is

4

y = ∑Hixi + W = G(s)h + w

G(s) = (x1, x2, x3, x4)

P1 Sˆ 1 , . . . ,

PT Sˆ T .

(4)

In both cases, it is assumed that each relay transmits in an orthogonal channel, so K =T and M = 1, resulting in a spectral efficiency equal to (1/ T ) log2 (|S |) that decreases with the number of nodes. Greater spectral efficiency can be achieved using space-time codes X = GK×T (s) (e.g., [1]) instead of AF or DF, which tend to attain diversity gains that are similar to those of DF but have both M and K growing in the same order. Note that in reality the relays will not transmit in perfectly orthogonal channel and timing offset and carrier frequency offset (CFO) need to be incorporated in the model. Time offset among the nodes produces signal dispersion analogous to that of a frequency selective channel. The effect can be modeled approximately with a complex-valued, possibly time-varying finite impulse response (FIR) filter of order D. If the code duration K is such that D ≤ 2K a received vector y i = (Yi [0], . . . , Yi [K − D − 1]) can be expressed as


yi =

T

H i,rx r + w i ,

(5)

r=1

where w is the additive white Gaussian noise vector and H i,r are (P − D ) × P Toeplitz convolution matrices for the channel between ith and rth terminal. Rearranging (5) as H i,rx r = T(x r)h i,r, with h i,r = (Hi,r[0], ..., Hi,r[D]) T and T(x r) Toeplitz: yi =

T

T(x r)h i,r + w i = X h i + w i ;

duplex operation in the relays. In the following γ s Ps/N0 , γ r Pr/N0 . Noncooperative Transmission: To be more precise, and for comparison with the results to follow, let us compute the outage probability of a system without cooperative diversity in the model (1) from radio s to radio d. In this case, the mutual information, in bits per channel use (all logarithms are taken to the base 2 unless indicated otherwise), viewed as a function of the fading coefficient Hd,s, satisfies [6] INC = log 1 + |Hd,s|2 γ s .

r=1

X (T(x1 ), . . . , T(x T)); T T T h i h i,1 , . . . , h i,T .

(6)

It can be easily recognized how similar (2) and (6) are, leading to the following conclusion: the dispersive medium effectively operates as an additional source of diversity that can be exploited by a judicious design of the matrix code X → X . This effect is exploited in cooperative multipath schemes, where relay nodes select a random delay and retransmit. Cooperative nodes also have distinct oscillators in their RF front-ends that cannot be perfectly tuned. The CFO introduces time variations that hinder the modeling done above in one aspect: the H i,r are actually (P − D) × P time-varying convolution matrices. As for a variety of wireless standards used today, neglecting ISI and/or CFO issues is a valid zero-order approximation to identify codes and trends; including the effect of an under-spread ISI channel is a good first order approximation of reality. PERFORMANCE BENEFITS Before discussing the use of cooperative links in MANET, we illustrate physical layer benefits brought by cooperation. For simplicity, we refer to the perfectly synchronous model, although via (6) several observations can be generalized. We consider as performance metrics the often-studied outage probability and average error probability. Outage probability allows for analysis of systems independent of a specific code design, because it is an information-theoretic framework based upon random coding. It gives an asymptotic bound on the rate of outage (packet loss) of a link at given spectral efficiency, where the limit is taken over the code length. Error probability allows for analysis and design of specific codes of limited coding block-lengths at a given spectral efficiency. Both frameworks can account for additional temporal or frequency diversity. OUTAGE PROBABILITY We study the outage probability [18] using the simple model in Figure 3 and use the indices s, d, and r to denote the source, the destination, and the relay nodes, respectively. Assuming that the channels are quasi-static over the transmission of each message, the channel mutual information becomes a random variable as a function of the fading coefficients, and the outage probability is then the probability that the mutual information random variable falls below the rate chosen a priori to encode the message. Focusing on outage probability allows us to easily account for the decreased spectral efficiency required by half-

(7)

The outage probability for rate R, in bits per channel use, is then given by [18] 2 R −1 . p NC out := Pr[INC ≤ R] = Pr |Hd,s| ≤ (2 − 1)γ s

(8)

Note that if radios s and d transmit and receive, respectively, in only L out of the K channel uses, the mutual information random variable becomes INC = (L/K) log 1 + (K/L)|Hd,s|2 γ s .

(9)

Because the number of channel uses is reduced by the factor (L/K), radio s can increase its transmitted power per channel use by the factor (K/L) and remain within its average power constraint for the entire block. (More details can be found in [18].) This observation is useful for studying half-duplex relaying. Cooperative Transmission: Outage results for cooperative transmission can be obtained by extending similar results for MIMO systems [28]. The simplest AF algorithm for a single source and relay produces an equivalent one-input, two-output complex Gaussian noise channel with different noise output levels. As [13] details, the mutual information random variable conditioned to the channel is 1 IAF = log 1 + 2|Hd,s|2 γ s 2

+ f(2|Hr,s|2 γ s, 2|Hd,r|2 γ r)

(10)

as a function of the fading coefficients, where f(x, y) := xy(x + y + 1)−1 .

(11)

For the simplest selection DF algorithm with repetition coding [13], the mutual information random variable is

IRDF

1 log(1 + 2|Hd,s|2 γ s),   2 if 12 log(1 + 2|Hr,s|2 γ s) ≥ R = 1 2 2   2 log(1 + 2|Hd,s| γ s + 2|Hd,r| γ r),  1 2 if 2 log(1 + 2|Hr,s| γ s) > R.

(12)

The two cases in (12) correspond to the relay’s not being able to decode and being able to decode, respectively. More sophisticated


d(outage)

− log pout (SNR) . log SNR SNR→∞ lim

100 10−1

10−2 Pout

space-time coding can be employed (see e.g., [12]). For comparison, we show their outage probability in Figure 5 (labeling them as STCDF), but leave a detailed analysis for brevity. The outage probabilities p AF out := Pr[IAF ≤ R ] for (8) and p RDF out := Pr[IRDF ≤ R ] for (12) can be evaluated numerically (Figure 5). The term diversity order that we have so far used informally, is defined as the negative slope of a plot of log-outage versus signal to noise ratio (SNR) in decibels

Noncooperative Rep. DF, One Relay AF, One Relay STC DF, One Relay Rep. DF, Two Relays AF, Two Relays STC DF, Two Relays

10−3

10−4

It is the sum of the SNR random variables 10−5 |Hi, j|2 Pj/N0 in (8) and (12) that leads to diversity gains when compared to (7). In fact, even for such 10−6 simple relaying algorithms, one can often show 0 5 10 15 20 25 that full diversity order 2 can be achieved [13]. SNR (dB) Figure 5 illustrates example outage performance for noncooperative transmission and cooperative [FIG5] Outage performance of noncooperative and cooperative transmission. Path-loss exponent α = 3; i.i.d. Rayleigh fading; relays placed at the midpoint transmission with up to two relays for no coopera- between the source and destination, spectral efficiency R = 1/2; uniform power tion (7), AF (12), repetition DF (14), and allocation. parallel/space-time DF (STC-DF, see e.g., [12]). We observe from Figure 5 that cooperation increases the outage uct of the eigenvalues of (G(sk) − G(s i ))∗ h (G (sk) − G(s i )) for diversity order, and provides full spatial outage diversity in the all possible message pairs are those that are expected to provide number of cooperating nodes (source plus the relays). Although the best coding gain, since they minimize (14). The generalizathe two forms of DF have similar performance for the case of tion to the frequency selective channel case is straightforward one relay for the particular network geometry, path-loss expousing the model in (6), since (6) and (2) look exactly alike. nent, and spectral efficiency considered, for two relays the advantages of STC-DF are apparent in Figure 5. COOPERATIVE COMMUNICATIONS IN EXISTING NETWORK ARCHITECTURES PROBABILITY OF ERROR In a cluster-based MANET, all terminals communicate through a As done in [27], cooperative diversity gains can be demonstrated cluster head or access point (AP). In such scenarios, the AP can using a probability of error metric. For links affected by gather information about the state of the network, e.g., the path Rayleigh flat fading h ∼ CN (0, h ) , using (2) the following losses among terminals, select a cooperative mode based upon some network performance criterion, and feed back its decision Chernoff bound on the pairwise error probability holds: on the appropriate control channels. Here cooperative diversity P(sk → s i ) ≤I + SNR/4(G(sk) lives across the medium-access control, and physical layers; −1 routing is not considered. Each cluster involved in the route is − G(s i ))∗ h (G(sk) − G(s i )) . (13) responsible for getting the signal to a destination “gateway” node, serving as the source node for the next cluster. Figure 1 illustrates how the APs communicate information Hence, denoting by d is the number of nonzero eigenvalues of (G(sk) − G(s i ))∗ h (G(sk)− between terminals in different clusters. In our cooperative netthe combined matrix G(s i )) we have P(sk → s i ) = O(SNR−d ) for SNR>>1. Using work model the gateways between clusters are cooperative links. In this context, the cost of cooperation compared to using a (13) it is easy to argue that the error-rate diversity is noncooperative gateway amounts to a loss in spectral efficiency, that depends on the code selection s → G(s), and also to the − log Pe(SNR) d(Pe) lim → d(Pe) additional cost of the AP control overhead. The architectural log SNR SNR→∞ benefits expected are similar to those of a two-tier network that ∗ = min rank (G(sk) − G(s i )) h (G(sk) − G(s i )) . k,i offers more reliable and longer range connections for interclus(14) ter communications but uses point-to-point communications within the limits of the cluster. Below we describe some approaches that the AP can use to match terminals and activate Note that the maximum diversity order is equal to the number of cooperative links given an existing clustered infrastructure. cooperating nodes d ≤ T. Code matrices that maximize the prod-


1

0.1

0.1 Direct

Average Pr[Outage]

Average Pr[Outage]

1

0.01

0.001 Random

0.0001

0.001 Random

0.0001

Greedy Minimal

10−5

Direct 0.01

Greedy Minimal

10−5

10−6

10−6 0

10

20 SNR (dB) (a)

30

40

0

10

20 SNR (dB) (b)

30

40

[FIG6] Outage probability versus SNR for different matching algorithms (averaged over 100 random trial networks uniformly distributed in a square of side 2,000 m, with the base-station/access point located in the center). Fading variances are computed using a d−a path-loss model, with a = 3. The weight between a pair of nodes is the average of the outage probabilities for one terminal using the other as a relay, and vice versa. The received SNR for direct transmission averaged over all the terminals in the network is normalized to be the horizontal axis. (a) N = 50, (b) N = 100.

CENTRALIZED PARTITIONING FOR INFRASTRUCTURE NETWORKS In this section, we consider grouping terminals into cooperating pairs. Additional studies of grouping algorithms appear for example in [14]. Choosing pairs of cooperating terminals is an instance of a more general set of problems known as matching problems on graphs [19]. The minimal weighted matching problem is to find a matching of minimal weight [19]. [There are several alternatives to the weighted matching approach. For example, we can randomly partition the terminals into two sets and utilize bipartite weighted matching algorithms, with lower complexity (albeit in the same order) than the matching approaches in [19]. Also suitable for decentralized implementation, we can randomly partition the terminals into two sets and use so-called stable marriage algorithms.] Other matching algorithms, with lower complexity, are possible. Specifically, we consider the following: ■ Minimal weighted matching: These algortihms are well studied and readily available in, e.g., [19]. The algorithms have cubic complexity in the number of nodes [19]. ■ Greedy matching: In this low-complexity alternative algorithm, we randomly select a free node and match it with its best remaining partner. The process continues until all of the vertices have been matched. The complexity is quadratic in the number of nodes. ■ Random matching: An alternative with linear complexity is to match nodes randomly. The rewards for the added complexity of solving the matching problems are the enhanced physical layer performance and the reduction by half of the order of the networking problem. To illustrate the performance benefits, Figure 6 shows a set of example results from the various matching algorithms described above and for AF

cooperation [c.f. (12)]. From the results in Figure 6, we observe that all the matching algorithms exhibit full outage diversity gain of order two with respect to direct transmission. As we would expect, random, greedy, and minimal matching perform increasingly better but only in terms of SNR gain. The relative SNR gain does improve slightly with increasing network size, especially for the greedy matching, suggesting that optimal matching is crucial to good performance in small networks, offering fewer choices among a small number of terminals. CONNECTIVITY IN CLUSTERED NETWORKS WITH COOPERATIVE GATEWAYS Whereas capacity measures the aggregate amount of information that can be sent across a wireless network, the connectivity of a network identifies the pairs of nodes between which information can be transferred (i.e., those that can exploit a portion of that capacity). Since it depends upon link metrics and channel access is not considered, connectivity is usually simpler to determine than the network capacity. It can be measured in various senses, depending on the criterion that determines if a link is available or not. In this section, we indicate to what degree cooperative transmission in a clustered network can improve connectivity. We assume that all transmissions are affected by a deterministic path loss and random independent fading such that two identical signals transmitted simultaneously from the same distance result in a signal that has twice the average power. A link is available if the receive average SNR is above a fixed threshold (SNR ≥ τ ). Note that the cooperative link SNR accumulates all contributions from the previous relays, in violation of Constraint I. For comparison, the next


section highlights results on connectivity that apply to classical point to point MANET.

CONNECTIVITY IN CLUSTERED NETWORKS WITH COOPERATION In cooperative networks, clustering can help connectivity by essentially increasing the area in which to search for new neighbors, as shown in Figure 7. In fact, if not all nodes are isolated, there will be nodes in a connected cluster that the AP can recruit in finding new neighbors. As a result, it is intuitive that the necessary condition in [8] need not be satisfied for the cooperative network to be fully connected with high probability. To prove it, we assume that the cooperative signals add up in power and that the SNRs at the receiver can be calculated. We assume that the link is symmetric, although in practice an AF algorithm should be used in the reverse link from the far away node to the cluster. Such a simple model does not account for the fact that cooperation can bring diversity and lower the SNR∗ threshold necessary to attain a certain outage or average error rate probability; however, it is amenable to large scale analysis and provides bounds to the connectivity that can be expected from diversity-achieving schemes.

CONNECTIVITY IN POINT-TO-POINT NETWORKS Connectivity has been well studied for ad hoc networks in the limit of an infinite number of nodes placed randomly on a twodimensional surface. Assuming that the path loss is a monotonic increasing function of the distance dij between two nodes i and j (e.g., d−α ij ) and denoting by A the circular area centered at a node i , where all nodes j ∈ A have SNR(dij) ∝ d−α ij above the threshold set for connectivity SNR(dij) > τ , any two nodes that are within a distance from each other that is smaller than the radius of A are connected. The graph obtained by drawing a line between any two nodes of separation less than the radius of A reveals sets of nodes that can communicate with each other directly or through a path consisting of multiple hops, and such a set is termed a cluster. In such a setting, there have been two separate definitions of what it means for a network to be connected. In the sparse network setting, the network is defined as connected if a cluster containing an infinite number of nodes (termed the infinite cluster) is present in the network. In the dense network Multihop Cooperative Cluster setting, the network is defined as being Link Range A connected once all pairs of nodes can communicate with one another. We will refer to the latter definition as the network’s being fully connected. Both definitions are intrinsic properties of the network graph, and in clustered multihop networks the edges of this graph are used to communicate. α 2 In the large sparse network analyα+2 A ≥ N−1 log (N) + c(N) (log log N + log2)α+2 A ≥ N−1 4π(4log N) ses, nodes are generally distributed on (a) (b) the infinite two-dimensional plane with some density λ. The connectivity [FIG7] Connectivity with cooperative radios in a cluster. is amenable to analysis via percolation theory [16]. Clearly increasing λ must improve the connectiviIn the sparse network case, it can be shown through simula(coop) ty. Interestingly, there exists a node density λ0 (termed the pertion (see Figure 8) that the percolation threshold λ0 is sig(noncoop) = 4.5 of colation threshold’) such that, for λ < λ0 , networks with nificantly reduced from the value of λ0 noncooperative networks [24]. In dense networks, it can be density λ will exhibit an infinite cluster almost never, whereas shown that the cooperative network can be fully connected for λ > λ0 , networks with density λ will exhibit an infinite cluswith high probability without satisfying the necessity condition ter almost surely [16]. for full connectivity in the noncooperative network. The proof For dense networks, analysis is generally performed for N construction relies on subdividing the network region into nodes distributed randomly on a surface of unit area. The semismall sections, all of which are likely to have a large cluster of nal work by Gupta and Kumar [8], considering large N on a unit nodes within the area A with high probability. These clusters disk, provides a necessary and sufficient condition to guarantee can connect not only with all nodes within the section but also full connectivity of the network: the area of radio coverage of with clusters in neighboring sections, thus fully connecting the each node should be at least A(noncoop) = N −1 [log N + c(N)], network. The required radio coverage area of a given node for where lim inf c(N) = +∞. The condition is necessary in the such connectivity is given by Theorem 6 of [24] sense that a network with nodes communicating with coverage area < N −1 [log N + c(N)] (where lim sup c(N) < +∞), is α 2 A(coop) ≥ N −1 4π(4 log N) α+2 (log log N + log 2) α+2 , (15) proven to be almost surely not fully connected. Critical to the proof of the above result is the powerful theorem that, asymptotically, the probability that the network is not fully connected where α is the path-loss exponent. Comparing (15) with the is dominated by the probability of an isolated node. result in [8] we have a gain in required power for connectivity of


ers. In this section, we illustrate one way in which these operations can become distributed, describing the second architecture shown in Figure 2.

Probability of Infinite Component

1 0.9 0.8 0.7

α = 2.0

α = 3.5

α = 2.5

α = 4.5

0.6 0.5 0.4 0.3 0.2 0.1 0 0.8

1

1.2 1.4 1.6 1.8 2 2.2 2.4 Normalized Node Density (πr2 = 1)

2.6

[FIG8] Probability of the existence of an infinite cluster versus node density for collaborative networks with path-loss exponent α of size d by d.

RANDOMIZED COOPERATIVE CODING Let us assume that there are T cooperating nodes. In the presence of a central control, like the cluster AP, each of the cooperative nodes is assigned to transmits a column xl ∈ X of a predetermined code matrix X = GK×T(s). This section shows how the code assignment can be randomized, when the nodes are unaware of how many nodes are going to cooperate and there is not central code assignment. A randomized coding rule targets a fixed maximum diversity order L, which is independent of the actual number of nodes cooperating. In randomized cooperation [26] each node projects the rows of the code matrix X = GK×L(s) over a random, independently generated, L × 1 vector r r , r = 1, . . . , T, generating a randomized code x˜ r = Xr r = GK×L(s)r r . Like in (5), the received vector is the mixture of these randomized codes convolved with their respective channel impulse response:

yi =

T j=1

H i, j G(s)r j + w i x˜ j

⎛ ⎞ L T ⎝ = H i, j rj,l ⎠ xl + w i j=1

l=1

=

L

˜ i,l xl + w i , H

(17)

l=1

[FIG9] BER of T = 3 cooperative nodes using Alamouti code (L = 2) [1] for different distributions of R.

A(noncoop) A(coop) 2 α+2 log N = . log log N

Cooperative − Gain =

(16)

COOPERATION FOR NEW AD HOC ARCHITECTURES “Cooperative Communications in Existing Network Architectures” illustrates how cooperative communications can serve MANET, clustered in the traditional sense, as a tool to improve performance. However, cluster heads were required to perform two additional operations: 1) the encoding strategy for the cooperating nodes and 2) deciding which nodes are involved in a given cooperative transmission. Both issues add complexity at the physical, multiple access, and network lay-

˜ l , l = 1, . . . , L are the where in the last equation, denoting by H equivalent convolution matrices. One can clearly see that the received vector is equivalent to that of L cooperative nodes, each transmitting a column xl ∈ X, like in the centralized matching scheme and where each link is characterized by the effective ˜ l , l = 1, ..., L; the latter is the randomized channel response H mixture of the true channel responses H j, j = 1, . . . , T. The diversity that can be obtained through this scheme depends on the statistics of the resulting equivalent channels ˜ l , l = 1, . . . , L and on the particular selection of the code G(s) H just as it does for the deterministic assignment discussed earlier. For channels that are frequency flat: y = G(s)Rh + w = G(s)h˜ + w

T h˜ = H˜ i,1 . . . H˜ i,L T = (r1 . . . r T) Hi,1 , . . . Hi,T = RL×Th.

(18)

(19)

Under the assumption of Rayleigh fading h ∼ CN (0, h ), as shown in [26] (see Figure 9), there are several options for the randomization matrix R to achieve the full diversity L of the code G(s) when the number of nodes exceeds L even by only one extra node, i.e., if T = L + 1. If T ≤ L the same random selection rules


give a diversity that is O(T). The main observation in [26] is that for several distributions for R the error rate diversity

modulate (transmitter) demodulate and decode (receiver) the data to the D/A and from the A/D converters (IF or baseband) interfacing the RF front end. The buffers connected to the T if L ≥ T + 1 receiver contain decoded data. A message that contains a d(Pe) = (20) L if L ≤ T − 1. request for cooperation is stored in the relay buffer, whose transmission is synchronized by the preamble sequence received in the message containing the request. The upper layDesigns that use linear combinations of ST-codes are discussed, ers need to be informed about the state of the relay buffer. The for example in [7] and [30], which do not require prior knowldashed lines going to the upper layers indicate a control that edge of the number of nodes active; [26] generalizes a number of can enable or inhibit the transother designs that are fully mitter and receiver modules decentralized including cooperBETTER LINKS TRANSLATE INTO BETTER (and can therefore reject a ative multipath covered by havNETWORK CONNECTIVITY COMPARED cooperation request). In genering G(s) a Toeplitz matrix and TO MULTIHOP SOLUTIONS. al, the half-duplex constraint the vectors r r being a selection mandates that the receiver be vector. Finally, note that this inactive when the transmitter is busy. But the upper layers can framework provides a means to trade off diversity performance also prevent cooperative transmission for other reasons, exerwith receiver complexity. The cost in performance is a potential cising network and access control as needed to manage the network. loss of diversity compared to the centralized rule, with the probaLet us denote by S the cooperating group. The group cannot bility of such a loss decreasing with increasing L [26]. There are rely on an AP to forward its message as mentioned earlier. benefits and drawbacks in targeting large or small degrees L of Instead, it can repeat the request for cooperation and recruit a diversity. Having large degrees of diversity allows harvesting the second group and so on. To avoid cycles, the selection rule greatest gains if the nodes cooperating are T > L, but if T < L, should exclude from the set S[k] at the kth iteration all points because the maximum diversity attainable is in the order of T, that have been in previous sets (xj, yj) ∈ S[i], i < k. Using the coding for large L requires an investment in complexity, increased bandwidth, and latency that are disincentives for same definition of connectivity as described earlier, so that the choosing a large L. node is connected to receive a message in the kth iteration if the receiver SNRk(xj, yj) > τ , a broadcast scheme could use all RANDOMIZED CLUSTERING such nodes to cooperate, and the set S[k] is IN PHYSICAL LAYER COOPERATION This section overviews a method for forming cooperative groups in S[k] = {(xj, yj) : {(SNRk(xj, yj) > τ ) ∩ }; a distributed and randomized fashion based upon source requests. k = (xj, yj) ∈ / ∩ S[i] , (21) In an infrastructure-less network a source can include an i=0 appropriate preamble sequence to provide a request for cooperation as well as the sync signal. The key differences in layering where only nodes whose receive SNRk(xj, yj) > τ retransmit, the transmission functions are: 1) the relay traffic should be and the additional condition simply verifies that the node has stored in a separate buffer and due to the timing restrictions not transmitted before (since this condition is always present, necessary for coordinating the transmission with other nodes, we omit it in the following discussion). the control of the relay traffic buffer is primarily at the physical layer and timed through the synchronization preUpper Layers amble in the cooperative request message; 2) the network layer, based on Local parameters relevant to the traffic flow, Output Traffic enables or inhibits cooperation for relay Buffer State Cooperative traffic that identifies a specific Transmitter source/destination pair, and 3) the link Relay and multiple access sublayers can RF Traffic Buffer Front End inhibit or enable cooperation, can mandate a different coding rule for different Local Input cooperating radios, but cannot change Cooperative Traffic Buffer the schedule. Figure 10 represents a Receiver functional block diagram for the physiSync cal layer that reflects these points. The two cooperative transmitter and receiver modules respectively encode and [FIG10] Physical layer of a cooperative radio.


Ps = 10, Pr = 2, τ = 1, ρ = 0.5

20 15

15

10

10

5

5

0

0

−5

−5

−10

−10

−15

−15

−20 −20

−15

−10

−5

0 (a)

5

10

Ps = 10, Pr = 2, τ = 2.5, ρ = 0.5

20

15

20

−20 −20

−15

−10

−5

0 (b)

5

10

15

20

[FIG11] Asymptotic shape of the cooperative groups in the limit for a centralized assignment of orthogonal cooperation channels under free space path loss ( 1/d 2 , d is the node distance). Ps is the power of the source, Pr the power of each relay and τ is the SNR threshold. A phase transition is observed: in the figure on the left the concentric annuli increase in area while they shrink in the right figure. In the second case the threshold is too high for connectivity.

For nodes that know their own location, the criterion can include network layer parameters limiting the region where the nodes could cooperate, for example, S[k] = {(xj, yj) : (|yj| < W/2) ∩ (0 ≤ xj ≤ D) ∩ (SN R(xj, yj) > τ )},

(22)

where it is assumed that, without loss of generality, the source is located at point (0,0) and the destination of the message is within a certain strip of length D and width W (parameters that are all conveyed in the source message). Under the new reference model in Figure 10, random access policies can resolve contention between groups that carry uncorrelated data. In other words, the contention and the collision models in Constraint II still stand, but it applies between groups. Perhaps the most dramatic change of this clustering model in MANET is that individual relays are treated as physical layer resources rather than network layer entities; the network and multiple access layers can deal with each group of cooperative nodes as a single entity, and this actually simplifies their decisions. This new abstraction of “link,” how to model it, how to adjust the medium access control and routing algorithms, are questions for the networking community to consider. CONNECTIVITY IN RANDOMIZED COOPERATION Randomized cooperation can also be shown to improve connectivity, as

demonstrated in the asymptotic analysis of the cooperative network first introduced in [25]. The limit nearly corresponds to the dense scenario discussed previously, i.e., infinite node density, but here normalizing the relay power per unit area [25]. Specifically, denoting by Pr the relay power and by N the total number of nodes in a region of area A, it is assumed that lim lim

N→∞ Pr→0

Pr N = lim lim Prρ = P¯ r < ∞. ρ→∞ Pr→0 A

(23)

The analysis highlights a phase transition [25, thrm. 2], illustrated in Figure 11: only for τ < (π ln 2) P¯ r do all nodes receive the message, otherwise the areas Ak progressively shrink. For a given threshold we can use the result in [25, thrm. 2] to calculate the minimum power density necessary for connectivity P¯ r−min = τ (π ln 2)−1 resulting in a total power expenditure to cover an area A equal to P(coop) = AP¯ r−min = Aτ (π ln 2)−1 . Unfortunately, the classical connectivity results for sparse and dense networks discussed earlier cannot be directly compared with this result because our node density is infinite, while the power density is finite. To have a comparison with multiR hop networks, we resort to the following argument: we consider the optimal r hexagonal tessellation shown in Figure 12, as the multihop solution to broadcast the message throughout the network using the centers of the hexagons and compare the total power spent in this case. For hexagons of radius r, the number of nodes needed to cover the area A is the ratio between A and the [FIG12] Multihop broadcast.


area of the√shaded triangular shape in Figure 12, i.e., Nr = 2A/(r2 3). If both networks are set to meet the same SNR threshold constraint τ . Ignoring the interference from nearby Pr ≥ τ r2 . Thus nodes, each hexagon-center node has to transmit √ (noncoop) 2 = Nr Pr−min = Nrτ r = 2Aτ/ 3 . The percentage P gain of P(coop) versus P(noncoop) approaches 50%. CONCLUSIONS This article illustrates two options for including cooperative designs in MANET and shows that incorporating cooperation at the physical layer offers a number of advantages in flexibility over standard MANET that go beyond simply providing a more reliable physical layer link. Studies on the diversity of cooperative links are numerous and will continue to develop practical schemes with improved performance. We argue that since cooperation is essentially a network solution, instead of a point-topoint solution, finding the appropriate link abstraction for cooperative transmission raises a number of important but nontraditional research problems for networking and physical layer researchers to investigate further. AUTHORS Anna Scaglione ([email protected]) received her Laurea (M.Sc.) degree in 1995 and Ph.D. degree in 1999 from the University of Rome, “La Sapienza.” She is currently an associate professor in electrical and computer engineering at Cornell University, where she was an assistant professor from 2001 to 2006 and, in the year 2000–2001, at the University of New Mexico. She received the 2000 IEEE Signal Processing Transactions Best Paper Award; she has also received the 2002 NSF Career Award, and she is corecipient of the Ellersick Best Paper Award (MILCOM 2005). Her expertise is in the broad area of signal processing for communication systems. Her current research focuses on cooperative networks and sensors’ systems. Dennis L. Goeckel ([email protected]) split time between Purdue University and Sundstrand Corporation from 1987–1992, receiving his B.S.E.E. from Purdue in 1992. He received his M.S.E.E. and Ph.D. degrees in 1993 and 1996, respectively, from the University of Michigan. Since 1996, he has been with the Electrical and Computer Engineering department at the University of Massachusetts, where he is currently an associate professor. His research interests are in the design of digital communication systems, particularly for wireless communications applications. J. Nicholas Laneman ([email protected]) received B.S. degrees in electrical engineering and computer science from Washington University in 1995. He earned the S.M. and Ph.D. degrees in electrical engineering from the Massachusetts Institute of Technology in 1997 and 2002, respectively. Since 2002, he has been an assistant professor in the Department of Electrical Engineering, University of Notre Dame, where his current research interests lie in wireless communications, information theory, and networking. He received the 2006 NSF CAREER Award, the 2003 ORAU Ralph E. Powe Junior Faculty Enhancement Award, and the MIT EECS Harold L. Hazen Teaching Award in 2001.

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