WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. (2010) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/wcm.902

A cross-layer framework for multiple access and routing design in wireless multi-hop networks Tamer ElBatt1∗,† and Timothy Andersen2 1 2

Electronics and Communications Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt Wagner Associates, Inc., Hampton, VA 23669, U.S.A.

Summary In this paper we explore the inherent coupling between MAC and routing in wireless multi-hop networks attributed to interference. This is primarily motivated by the observation that shortest path routing could potentially lead to degrading the single-hop MAC throughput which constitutes an upper bound on the end-to-end multi-hop throughput. First, we formulate an optimization problem that maximizes the MAC throughput subject to path length, scheduling, SINR, and power constraints and establish bounds on the optimal performance. Second, we propose a novel crosslayer routing framework (set-based routing) that reduces problem complexity via resolving intra- and inter-set interference among sets of spatially close transmitters. Third, we propose joint routing, scheduling and power control (RSP) to solve the problem within each set. Finally, we show, through simulations, that set-based routing achieves not only 60% of the optimal performance for plausible scenarios but also up to 50% improvement over a generic reference system that represents a broad class of state-of-the-art protocol stacks and uses minimum hop (MH) routing and collision-free scheduling with no interaction. Copyright © 2010 John Wiley & Sons, Ltd.

KEY WORDS: wireless multi-hop networks; link scheduling; routing; cross-layer design; combinatorics; simulation

1.

Introduction

The problems of multiple access and routing have been extensively studied in the mobile ad hoc networks literature, yet in isolation. At one hand, major work has been devoted to maximizing spatial reuse while minimizing interference (collisions) that may arise at various receivers. MAC schemes for ad hoc networks can be broadly classified to random access and scheduled access. Under the former class, carrier sense multiple access (CSMA), CSMA/CA, ∗

and other collision avoidance mechanisms [1] have been studied and evaluated. In addition, busy tone multiple access [2] has attempted to solve the hidden terminal problem. Under the second class, scheduling non-conflicting transmissions in a distributed fashion has been the focal point of References [3,4]. However, the aforementioned schemes are confined to layer two in the International Standards Organization (ISO) Open Systems Interconnection (OSI) protocol stack and do not address the interaction with higher or lower layers.

Correspondence to: Tamer ElBatt, Electronics and Communications Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt. † E-mail: [email protected] Copyright © 2010 John Wiley & Sons, Ltd.

T. ELBATT AND T. ANDERSEN

On the other hand, the use of multi-hop paths to transport data between source and destination was shown to enhance the network capacity [5]. Research on multi-hop routing in wireless networks has been focused primarily along the following two thrusts: (i) efficient route discovery/maintenance under mobility conditions and topology changes [6,7] and (ii) modifying the routing metric to match a wide variety of objectives [8–14]. Most of the protocols developed under the former research thrust adopt the shortest path (SP) routing criteria widely employed in wireline networks [15]. Under the second research thrust, energy-efficient routing metrics have been proposed in References [16–20] to evenly distribute the network load among nodes according to their residual battery charges in order to increase the network life time. In Reference [21], the routing criteria has been modified to incorporate the received signal strength so that routes with stable links are favored over routes with vulnerable links. Finally, Reference [22] introduced a least resistance routing metric for frequency hopping ad hoc networks. However, References [21,22] do not consider the interference-induced coupling between MAC and routing decisions under investigation in this paper. Recently, the interaction between MAC and routing in wireless multi-hop networks has received considerable attention [23–33]. Reference [23] establishes bounds on the optimal throughput of interference-limited wireless multi-hop networks given the existence of an omniscient and omnipotent central entity. However, developing interferenceaware routing protocols was left as an open problem. Reference [24] proposes the expected transmission count routing metric (ETX) which incorporates the effects of link losses and interference among successive links of a path (intra-path interference). However, ETX does not incorporate interference explicitly through the SINR constraint. Moreover, it breaks one of the fundamental assumptions of this paper, namely transmit power is a controllable parameter. The problem of joint routing, scheduling and power control (RSP) has been recently addressed in References [25–29]. However, Reference [25] introduces joint routing and scheduling metrics to balance the energy-delay trade-off with no focus on interference. Unlike this work, a separate control channel is utilized to emphasize the interplay between MAC and routing through power control in Reference [26]. Reference [27] introduces a polynomial time approximation assuming no interference Copyright © 2010 John Wiley & Sons, Ltd.

between links in the same neighborhood sharing the same slot. Reference [28] focuses on the simple setting of symmetric one-dimensional multi-hop networks. Perhaps the work in Reference [29] is the closest to ours. However, it hinges on the Gaussian approximation for interference [34]. This assumption not only simplifies the joint scheduling-power control problem under low SINR regimes but also facilitates separating the MAC and routing portions of the problem. In this paper, we formulate an optimization problem and present a solution without making any assumptions about the structure of interference known to be non-Gaussian in the typical case of finite number of interferers. This work constitutes a step beyond our earlier work [30] to account for interference in the design of routing protocols. Our contribution in this paper is twofold: (i) a cross-layer routing framework (set-based routing) that scales via mitigating interference at two levels: within a set of spatially close transmitters and across different sets and (ii) introducing a joint hop-by-hop RSP solution within a set of interference-coupled transmitters. Given a set of sender–destination (S-D) pairs, we determine on a hop-by-hop basis, the RSP policies that balance the fundamental MAC throughputpath length trade-off subject to SINR among other constraints. Motivated by the complexity of characterizing the global optimal over the entire network, we propose a sub-optimal solution that solves the problem over ‘sets’ of spatially close transmitters and then resolve interference between sets. This is achieved through the following three steps: (i) construct interference-coupled transmitters sets, (ii) resolve intra-set interference, explicitly modeled, via the RSP algorithm, and (iii) resolve potential interference among overlapping sets via set coordination schemes. In this paper, we focus on the crosslayer solution framework and RSP algorithm which constitute our major contributions. Comprehensive design and analysis of the set construction and coordination components lie out of the scope of this work. The paper is organized as follows: In Section 2, the problem is motivated with the aid of simple examples. Afterwards, the joint MAC-routing problem is formulated and analyzed in Section 3. This is followed by a detailed description of the proposed solution along with the RSP algorithm in Section 4. Simulation results are given in Section 5 and conclusions are drawn in Section 6. Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

Fig. 1. Illustrating the MAC throughput-path length trade-off. The notation used in (b) for the transmission schedule S1 , S2 , I1 I2 implies that node S1 transmits in slot 1, node S2 transmits in slot 2 and nodes I1 and I2 transmit simultaneously in slot 3.

2.

Motivation

In this section, we show, with the aid of simple examples, that handling routing and MAC decisions independently could lead to degrading the end-to-end (E2E) throughput. Consider a wireless network consisting of 13 stationary nodes with connectivity shown in Figure 1(a). Each node has a single radio and can detect at most one signal at a time, i.e., multi-user detection is not supported. For this example, we assume time is slotted and wireless channels are constant over a time slot. Moreover, we assume two source–destination pairs (S1 , D1 ) and (S2 , D2 ) with identical traffic demands. In addition, we assume that there is always a packet in the queue of each source node ready for transmission. We compare the average slot throughput and E2E throughput of three routing policies. The slot throughput is defined as the average number of successful transmissions per slot. In this section, the E2E throughput is defined as the average number of packets that are successfully transferred from each source to its respective destination over the period of d slots. First, we examine minimum hop (MH) routing which is a special case of SP routing when all links have unit metrics. From the network topology, it is straightforward to notice that the length of the MH route for each source–destination pair is two hops and there are two MH routes for each S-D pair. Consider the policy where the two source nodes choose node I0 as their next hop as shown in Figure 1(a) using dotted lines. It is evident that I0 constitutes an interference bottleneck at the MAC layer. This is a direct consequence of ignoring the interaction among the chosen paths through the amount of interference a certain path may introduce to others. We refer to this phenomenon as interferenceinduced congestion which constitutes a fundamental challenge unique to wireless networks. Thus, the two source nodes cannot simultaneously transmit to I0 in the same slot, and neither of them can transmit while I0 is transmitting. Moreover, I0 can forward only one packet to the destination at a time. This, in turn, yields average slot throughput of 1 transmission per slot. Copyright © 2010 John Wiley & Sons, Ltd.

Moreover, this policy consumes four slots for a single packet transfer from each source to its respective destination (referred to as the ‘Transmission Cycle’). Hence, we conclude that the above policy transfers d4 packets, from each source to its destination, over the course of d slots. Second, we consider the MH routing policy depicted in Figure 1(b). In this case, we assume that relay nodes I1 and I2 are spatially close enough to: (i) prevent simultaneous reception from the source nodes and (ii) prevent I1 from receiving while I2 is transmitting and vice versa. On the other hand, we assume that nodes D1 and D2 are spatially far to allow simultaneous reception of their packets from nodes I1 and I2 , respectively. It is evident that this policy should yield better performance due to choosing different next hops for S1 and S2 . However, the next hops are very close which still restricts spatial reuse. Hence, the transmission cycle becomes three slots, the average slot throughput improves to 4 d 3 and the E2E throughput improves to 3 packets. This suggests that resolving ties among MH routes should be guided by the MAC throughput, not simply random. Finally, we examine the performance of a routing policy that uses longer, yet spatially far, paths to avoid the interference bottleneck. Assume that S1 and S2 follow the 3-hop paths shown in Figure 1(c). In this case, we assume that paths are sufficiently separated to keep the SINR above the threshold necessary for successful reception on each path. Moreover, we assume that the SINR requirement allows the first and third hop transmissions of the same path to reuse the same slot. Thus, a simple scheduling scheme would pack same hop transmissions over the two paths in the same slot. This yields average slot throughput of 3 transmissions per slot, the transmission cycle becomes two slots and the E2E throughput becomes d2 packets.‡ This is twice

‡ If slot reuse along the same path is not allowed, then the transmission cycle becomes 3 slots, the average slot throughput = 2 transmissions per slot and the E2E throughput = d3 .

Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

T. ELBATT AND T. ANDERSEN

the throughput achieved under the MH routing policy in Figure 1(a) and 50% better than the best MH routing policy adopted in Figure 1(b). The above example confirms the fundamental role the MAC plays, along with the path length, in limiting the E2E routing throughput. Therefore, in the next section we formulate a cross-layer optimization problem that maximizes the single-hop MAC throughput subject to path length and SINR among other constraints. This formulation is justified by the following key observations: (i) the single-hop MAC throughput constitutes an upper bound on the E2E multi-hop throughput and (ii) maximizing the MAC throughput subject to path length constraints permits optimization over a short time horizon, precisely on a frame-byframe basis which fits perfectly with the hop-by-hop routing paradigm under consideration. This is in contrast to the more complex long-term objective of maximizing E2E throughput using multi-commodity flow models [23,29] and utility maximization formulations [33], typically studied over longer time horizons.

3. 3.1.

The Joint MAC-routing Problem Assumptions

We consider a wireless multi-hop network consisting of n nodes with unique IDs indexed from 1 to n. Each node is equipped with a single radio and an omni-directional antenna. All nodes share the same frequency channel and time is divided into equal slots that are grouped into frames. Each frame is of fixed length and accommodates d data slots. The transmit power is the only radio parameter that we control in this work. Other radio parameters, e.g., link bit rate, coding rate, etc. are assumed to be fixed throughout the paper. The slot duration is assumed to be larger than packet duration by an interval called the ‘guard band’. These bands are essential for synchronization in order to compensate for arbitrary delays due to signal propagation and/or clock drifts. For an arbitrary node x, we assume that node y is a single-hop neighbor of x if it successfully receives its transmission under two conditions: (i) Node x uses maximum power and (ii) Node x is the only node transmitting, i.e., no interference. In this case, successful reception is guaranteed if the SNR at y is greater than a threshold. We refer to this topology as the basic topology since successful communication over some links may be impossible in the presence of interference. However, it serves the purpose of defining the set of neighbors of node x, denoted N(x), which is instruCopyright © 2010 John Wiley & Sons, Ltd.

mental in specifying the next hop decision space for our cross-layer framework. We incorporate interference awareness mechanisms on top of hop-by-hop table-based routing protocols based on distributed Bellman-Ford [15]. Thus, we assume that route information are available to all nodes in the network. Incorporating interference-awareness into on-demand routing is out of the scope of this paper. The transmit power is assumed to decay nonlinearly with distance, i.e., Pr (z) = Pt ∗ z−α , where Pt is the transmitted power, z is the distance between transmitter and receiver and α is the path loss exponent. The transmit power per node cannot exceed a maximum power level, Pmax . We primarily focus on fixed multi-hop wireless networks (e.g., mesh and access networks) and, hence, mobility is not a major design driver and is not modeled in this work. However, this assumption can be relaxed to the class of low mobility access networks where the link gain matrix changes over a time scale much larger than the time scale over which the proposed algorithm operates, namely a frame. We adopt a packet model, as opposed to user flow models in References [23,33], to formulate the crosslayer MAC-routing problem. A source node generates packets according to a Poisson process with rate λ packets/s. We assume that each packet is intended for a single destination, i.e., unicast. We adopt an interference model that explicitly accounts for interference caused by transmitters who are spatially close. Otherwise, interference is handled indirectly through set coordination in Section 4.4. This model circumvents the limitations of the unit disc abstraction where no interference is caused beyond a certain range. Moreover, it is more realistic than models which assume all nodes in the network interfere with each other [30]. Those models yield a fully connected mesh which complicates the design, especially for scalable scenarios. 3.2.

Problem Formulation

In this section we formulate a cross-layer optimization problem that is inspired by the following key observations: (i) the single-hop MAC throughput constitutes an upper bound on the E2E multi-hop throughput and (ii) maximizing the MAC throughput subject to path length constraints permits optimization on a frameby-frame basis which fits perfectly with the packet model and hop-by-hop routing paradigm under consideration. This is in contrast to the more complex long-term objective of maximizing E2E throughput Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

using multi-commodity flow models and utility maximization formulations. Given a set of K sender–destination pairs at the beginning of frame i, denoted SD(i) = {(S1 , D1 ), (S2 , D2 ), . . . , (SK , DK )}, the hop-byhop RSP problem is formulated as a multi-objective optimization problem [35] with the MAC throughput and path length as the objective functions. In order to reflect the hop-by-hop and frame-by-frame nature of the problem formulation, we emphasize that ‘senders’ in this context could imply original sources of packets as well as intermediate relays. We adopt the -constraint (or Trade-off) method whereby one of the objectives is chosen as the primary objective to optimize (MAC throughput in this case) and the other objective (path length) is reformulated as a constraint. Next, we introduce the notation used in the formulation. ηmac is the single-hop MAC throughput measured in the number of successful links per slot. N(Sk ) is the set of neighbors of node Sk . NH = {NH(S1 ), NH(S2 ), . . . , NH(SK )} is the vector of next hop nodes for all senders where a packet can progress at most one hop in each frame. Lk is the length of the path from Sk to Dk passing through NH(Sk ) measured in number of hops. k is an upper bound on the length of the path from Sk to Dk . SL = {SL1 , SL2 , . . . , SLK } is the vector of slot indices assigned to various links. Pt = {Pt1 , Pt2 , . . . , PtK } is the vector of transmit powers of various senders to their next hops. SINRk is the signal-to-interference-and-noise ratio at the receiver of Pt G Sk , namely NH(Sk ). It is given by Sk k k 2 , where INH(S

k)

+σ

Gk is the link gain from node Sk to its next hop, σ 2 is Sk is the interference power the noise power and INH(S k) at the next hop from transmitters other than Sk sharing the same slot. Finally, γ is a minimum requirement on the SINR that is dictated by the upper bound on the BER necessary for successful reception. Thus, the problem is formulated as a constrained optimization problem: ηmac max NH, SL, Pt s.t. (i) NH(Sk ) ∈ N(Sk ) ∀Sk (ii) Lk ≤ k ∀k (iii) SLk = SLj ⇒ NH(Sk ) = Sj , NH(Sj ) = Sk ∀k, j (iv) SLk = SLj ⇒ NH(Sk ) = NH(Sj ) ∀k = j (v) SINRk ≥ γ, ∀Sk (vi) 0 ≤ Ptk ≤ Pmax ∀Sk Copyright © 2010 John Wiley & Sons, Ltd.

(1)

Constraints (i) and (ii) are related to routing where the first implies that the next hop of any sender should be among its neighbors whereas the second limits the routing policy space to include paths of length no greater than k for all k. This represents the path length contribution in the problem which eliminates the hard MH requirement adopted in most MANET routing protocols. In addition, the routing policy space is constrained to include only loop-free paths. Constraints (iii) and (iv) are related to scheduling and they simply eliminate the possibility of self interference and multiple simultaneous transmissions to the same receiver (common receiver) in a generated schedule. Constraints (v) and (vi) are related to power control where they represent the condition for successful reception and peak power constraint, respectively. 3.3.

Problem Complexity

In this section, we discuss two fundamental challenges which motivate the set-based routing concept: (i) the challenge of interference-aware link metrics and (ii) computational complexity. 3.3.1. The challenge of interference-aware link metrics Under SP routing, the path length (which depends on the link metric) is the only factor that decides the best route between any source–destination pair. Various examples of link metrics in the literature, namely Euclidean distance, residual battery charge, and buffer occupancy, depend solely on the two nodes forming the link. They are independent of the existence of other source–destination pairs or their SPs. On the contrary, Equation (1) incorporates multi-user interference into the routing decision via the MAC throughput objective and the SINR constraint. These two factors depend on the existence of other senders and their spatial separation. Hence, the routing decision of a given source–destination pair becomes coupled to the routing decision of other pairs. Accordingly, the notion of a link metric that incorporates interference becomes challenging since the interference introduced to the receiver of a link (to compute its metric) depends on the next hops of other links which, in turn, depends on the interference caused by the transmitter of the link of interest. The above observation can be illustrated using the following example: Assume node a is transmitting to next hop b and node u is transmitting to next hop v as shown in Figure 2(a). The amount of interference Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

T. ELBATT AND T. ANDERSEN

|A| =

d+1 



C(K; t1 , t2 , . . . , tm )

(2)

m=2 t1 , t2 , . . . , tm :

m

t j=1 j

Fig. 2. The challenge of defining an interference-aware link metric: interference introduced to link uv depends on the routing decision of node a which, in turn, depends on the interference caused by node u.

at node v from transmitters other than u is given by Ivu = Pab ∗ z−α av . However, if node a was transmitting to a different next hop (say c) as shown in Figure 2(b), then the amount of interference seen at node v would be Ivu = Pac ∗ z−α av . Thus, the interference introduced to link uv depends on the routing decision of transmitter a which, in turn, depends on the routing decision of transmitter u. Hence, there is a fundamental hurdle towards defining link metrics that explicitly account for interference. This leads us to the novel concept of set-based routing, presented in Section 4, where the MAC and routing decisions are taken jointly for a set of spatially close transmitters (as opposed to link-based routing decision which is taken for each transmitter independently). 3.3.2.

Computational complexity

The complexity of Equation (1) stems from the fact that routing and scheduling multiple pairs concurrently are combinatorial in nature. For instance, the cardinality of the next hop decision space R grows exponentially with
 the number of  S-D pairs (K) as  K N(Sk ) . Even though the given by |R| = O k=1 path length constraint in Equation (1) reduces the number of neighbors who are eligible next hops, the exponential growth of the routing policy space with the number of sources still persists. On the other hand, the scheduling policy space A accommodates all policies that partition the set of K links over a number of slots that is less than or equal to d. If links can be scheduled over a subset of d slots, then this schedule or part of it can be repeated in order to utilize the remaining slots. We account for all combinations of partitioning K transmissions into m slots each supporting tj transmissions where 2 ≤ m ≤ d + 1, 0 ≤ tj ≤ K, 1 ≤ j ≤ m. Hence, it turns out that for K ≥ d,§

§ If K < d, partitioning the K transmissions would be limited to K instead of d slots.

Copyright © 2010 John Wiley & Sons, Ltd.

=K

where C(K; t1 , t2 , . . . , tm ) is the multinomial coefficient that gives the number of possible combinations of partitioning K elements into m groups each having tj elements and is given by C(K; t1 , t2 , . . . , tm ) =

K! t1 ! t2 ! . . . tm !

(3)

Notice that |A| is not only a combinatorial function of the number of senders, K, but also grows with the number of data slots per frame, d. The difficulty of the problem is further aggravated by the lack of a tractable mathematical structure. This leads us to two essential steps: (i) bound the optimal performance in the next section and (ii) introduce set-based routing in Section 4. 3.4.

Performance Bounds

Motivated by the complexity of characterizing the optimal, we establish an upper bound on the optimal MAC throughput ηmac . Unlike the asymptotic capacity bounds in Reference [5], we bound the MAC throughput for a network of any size n. This is important to judge the performance of sub-optimal set-based routing proposed in Section 4 and assess the open room for improvement. The upper bound is obtained by a genie-aided policy which has access to global network information. In order to account for different node placements, network topologies and transmit powers, the upper bound on ηmac is obtained when nodes are optimally placed so that best next hops can be reached using minimum powers and same hop transmissions of all K S-D pairs can successfully share the same slot. Notice that K is generally a function of n as determined by the communication scenario. Thus, the maximum number of single-hop transmissions per slot is given by K if we do not consider the possibility of slot reuse on each individual path. Spatial reuse of slots on the same path is subject to the self-interference, common receiver and SINR constraints. If nodes are optimally placed, we consider the best case where every other hop on the same route can share the same slot (i.e., hops 1, 3, 5, . . . on the same route can share the same slot whereas hops 2, 4, 6, . . . can share another slot). Thus, for a single path of length L hops, the maximum number of Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

single-hop transmissions that can share a slot would   be cL2 where c2 = 2. This implies that the maximum number of single-hop transmissions for K paths (upper   bound) is given by KL where L is the average path c2 length. It is evident that for finite n, the upper bound is dominated by the constant c2 and the dependence of K and L on the number of nodes n which is determined by the topology and spatio-temporal traffic patterns. A lower bound on ηmac can be simply established using a scenario where all nodes are close enough to yield very low SINR, even in the presence of a single interferer. This yields a maximum of 1 transmission per slot which may constitute a tight or loose bound depending on the topology and scenario as shown in Section 5. In Section 5.3.2, we compare the upper bound to the MAC throughput achieved by a number of cross-layer set-based routing policies.

4. 4.1.

Cross-layer Set-based Routing Solution Outline

In this section, we present a novel sub-optimal solution based on the concept of set-based routing. As shown in Figure 3, set-based routing relies on tight cross-layer interactions among the lower three layers of the OSI stack. These interactions are essential to exchange information necessary for solving the crosslayer problem and putting the solution into action. In our problem setting, performance metrics (meters) are passed up the stack to formulate and solve the

Fig. 3. Cross-layer set-based routing interactions. Copyright © 2010 John Wiley & Sons, Ltd.

problem while decision variables (knobs) are passed down the stack to put the solution into execution. The meters in formulation (1) are the SINR and ηmac measured by the PHY and MAC layers, respectively and passed to the network layer where the set-based routing problem is being solved. On the other hand, the knobs are the next-hop (routing), scheduling and power control decisions decided at layer 3 and passed down to the MAC and PHY layers, respectively for execution. Under the set-based routing framework, interference is resolved at two levels, namely among a set of interference-coupled transmitters and across different sets. Accordingly, set-based routing consists of three major building blocks: (i) constructing small sets of interference-coupled transmitters, (ii) joint routing, scheduling and power control (RSP) algorithm to solve Equation (1) within each set, and (iii) set coordination schemes to combat inter-set interference. In this paper, we focus on the detailed design and analysis of RSP which constitutes a major contribution of this work. We present considerable performance gains even with simple solutions for set construction and coordination and leave their optimized design and detailed analysis for future research. 4.2.

Set Construction

The problem of grouping transmitters depending on their interference coupling exhibits similarity to the problem of clustering in mobile ad hoc and sensor networks [36]. In contrast to the known motivations for clustering (e.g., local processing and communications for scalability and reduced overhead), the prime motivation here is interference. For instance, Reference [29] groups transmitters in a pre-specified geographical region in the same cluster. However, intercluster interference is approximated as static ambient noise. Alternatively, we adopt a simple topology-based criteria for defining interference-coupled transmitters (ICT) sets, such that transmitters within H hops from a specific transmitter belong to the same ICT set. Otherwise, they belong to different sets. Despite its simplicity, the topology-based criteria enables dynamic control of the set size (i.e., number of transmitters per set), depending on the number of transmitters and their spatial separation, via adapting the parameter H. A simple technique to construct ICT sets according to a pre-specified parameter H is described next. Given a set of K S-D pairs at the beginning of a frame, the nodes Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

T. ELBATT AND T. ANDERSEN

proceed in a distributed fashion in an ascending order of their IDs, where nodes who have nothing to transmit in the current frame skip their turn. On the other hand, nodes who wish to transmit in the current frame disseminate their IDs to their H-hop neighbors via Hhop flooding. By the completion of this process, each node in the network would have a list of up to H-hop away transmitters. Nodes who have nothing to transmit simply ignore their respective lists whereas transmitter k considers its H-hop transmitters list as ICTk set and becomes the leader of this set. Thus, the above algorithm constructs K ICT sets, one per transmitter. This leads to overlapping among most of the constructed sets (i.e., transmitters who belong to multiple ICT sets at the same time). Coordination schemes for handling set overlapping are discussed in Section 4.4. Next, we quantify the number of control messages generated per frame by the ICT set construction algorithm. As described above, each transmitter floods a control message over H hops in a contention-free manner. Hence, the total number of broadcast messages sent per transmitter is given by the sum of a geomet2 H−1 , where N is the ric series: 1 + N + N + . . . + N average number of single-hop neighbors. Accordingly, the control overhead associated with set construction H 
would scale as O K N −1 where K is the number N−1 of transmitters (whether original sources or intermediate relays) at the beginning of the frame. Notice the linear growth of the control overhead with K and the exponential growth with the parameter H. This clearly demonstrates that minimizing the control overhead dictates small values of H which implies small set sizes. 4.3. Joint Routing, Scheduling and Power Control (RSP) In this section, we introduce the novel RSP algorithm which is executed at the ICT set leader and attempts to find a sub-optimal solution for Equation (1) within each ICT set. The objective is threefold: first, determine the hop-by-hop routing decision (i.e., next hop). Second, decide which link should be activated in which slot. Third, specify the set of powers needed in order to satisfy the SINR requirements at respective receivers. Next, we highlight the main features of the proposed algorithm followed by a detailed description of the operation and interaction of various parts of the algorithm. Given a small number of links within an ICT 

This becomes an upper bound if the broadcast tree is pruned due to common neighbors. Copyright © 2010 John Wiley & Sons, Ltd.

set, the essence of RSP is to search for a routing and scheduling policy that achieves shortest possible path (not necessarily the shortest path) and near-optimal MAC throughput, respectively while guarantee convergence of the iterative distributed power control (DPC) algorithm to the minimum power vector in all slots [37]: Ptj (T + 1) = min Pmax ,

γ Ptj (T ) (4) SINRj (T )

where Ptj is the power transmitted from node j to its next hop neighbor, SINRj is measured at the receiver of node j and T is the iteration number. Next, we address the following RSP design questions:


How to speed up the routing and scheduling search process?


What are the major cross-layer interactions between routing, scheduling and power control?


Which problem, routing or scheduling, should be given precedence in the search process? To address the first question, the routing search process commences with the MH policy since minimizing the average path length is still a desirable feature of the solution. If there are multiple MH paths, we resolve the tie via random selection. The natural question that arises next is: In what order should the routing policies be examined? The significance of this question stems from the fact that neighbors of a sender differ in the length of the path on which they reside and the amount of interference they are exposed to. Thus, we argue that neighbors who satisfy constraint (ii) in Equation (1), and are loop-free, should be ordered according to their path lengths to destination so that neighbor(s) on shorter path(s) are examined first. This ranking, in conjunction with the ranking of scheduling policies, should speed up the search process to find paths shorter than the  constraint and guarantee high ηmac . The scheduling search process commences with the ‘All Transmissions in a Single Slot’ (ATSS) policy followed by policies that tend to distribute transmissions evenly among slots in the frame. The rationale behind this is to pack as many transmissions as possible in a slot in order to maximize the MAC throughput. If this leads to empty slots in the frame, then the generated schedule, or part of it, could be repeated using next packets in the queues ready for transmission. To address the second question, Figure 4 shows a flowchart that demonstrates the interaction of the major modules of RSP. As illustrated before, the Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

Fig. 4. Flowchart of the RSP algorithm.

algorithm starts with examining MH routing and ATSS scheduling as directed by the set leader. Accordingly, all transmitters in the set send control information to the set leader, possibly in a contention-free manner, that defines the set of links. This is essential to solve the self-interference and common receiver problems. Accordingly, the set leader examines constraints (iii) and (iv) in Equation (1) for all slots in the frame. If one or both constraints are violated, the scheduling algorithm defers conflicting transmissions to a future slot using the heuristic in Reference [30] which examines the two constraints in sequence and defers users’ transmissions to resolve any conflicts. Otherwise, the algorithm proceeds to the power control portion Copyright © 2010 John Wiley & Sons, Ltd.

with a set of single-hop links along with their slot assignments. The DPC algorithm examines the power admissibility of the set of single-hop links in each slot judged by the convergence of Equation (4). If all slots turn out to be power admissible, then the algorithm exits with the solution for the current frame. Otherwise, another routing and/or scheduling policy is examined for power admissibility. If a solution is not found after searching all eligible routing and scheduling policies, RSP falls back to MH routing which forms a set of single-hop links that are passed on to the scheduling and power control portions, irrespective of the level of ηmac this set of MH links can achieve. Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

T. ELBATT AND T. ANDERSEN

Finally, we address the third question. We first note that routing can circumvent the negative impact of interference, which limits the single-hop MAC throughput, without deferring transmissions to future slots. Hence, we propose to give precedence to examining routing over scheduling policies. More specifically, for a given scheduling policy, all routing policies that satisfy constraints (i) and (ii) in Equation (1) are examined until either a solution is found or another scheduling policy is examined. This choice is based on the premise that routing could reduce interference, just like scheduling, yet without sacrificing the MAC throughput. Notice that a new scheduling policy is generated from an existing one via deferring the link(s) with minimum SINR [30] in the last DPC iteration of violating slot(s) in an attempt to lower the level of interference. This could allow the remaining links to converge to the minimum power vector quite fast. 4.4.

Set Coordination

It is evident from Section 4.2 that ICT sets could be overlapping, i.e., one or more transmitters may belong to multiple ICTs. Set overlapping gives rise to the so-called inter-set interference which leads to coupling different ICT sets. Executing the RSP algorithm for these sets simultaneously is problematic since source (or relay) node(s) in the overlapped regions would be set leaders and still receive conflicting orders from other set leaders as well. This is equivalent to merging the sets, yet, without any coordination among the set leaders. One way to circumvent this hurdle is to enable the merged sets to somehow detect the overlap and then elect a new leader for the larger set who runs a single RSP algorithm. However, this would be achieved at the expense of two major drawbacks: first, executing RSP for larger sets implies higher computational complexity. Second, it contradicts one of the fundamental premises of this paper that spatially far transmitters, whose mutual interference is negligible, should belong to different sets. In this section, we embrace an alternative approach that avoids set merging via the notion of set scheduling (or coordination). Thus, the problem boils down to coordinating the execution of the RSP algorithm for different ICT sets such that: (i) it is executed for overlapping ICT sets at different times and (ii) executed simultaneously for non-overlapping ICT sets. The problem of determining the minimum length set schedule subject to the above two constraints is a combinatorial problem that requires global information about set overlapping at a central controller. Copyright © 2010 John Wiley & Sons, Ltd.

In order to examine the viability and effectiveness of the set-based routing framework, we adopt simple sequential coordination that satisfies the first constraint above only. Simulation results confirm the profound impact that RSP and sequential coordination have on performance. Accordingly, the RSP algorithm is executed for all ICT sets sequentially, in an ascending order of leader IDs, irrespective of their overlap. A sender that belongs to multiple ICT sets determines its RSP decisions through the RSP execution of the set reaching its turn first. Afterwards, its solution is handled as a constraint during the RSP execution of other sets. The key feature of this simple scheme is to resolve inter-set interference without the need to merge overlapped sets. It can be shown that the control overhead of sequential coordination grows exponentially with H since each set leader is responsible for flooding its set solution over H hops in order for the leaders of overlapped sets to utilize such information in solving their respective sets.

5. Performance Evaluation and Discussion 5.1.

Simulation Setup

In this paper, we conduct simulation experiments using the ns-2 simulator. We consider a uniform network topology where n = 64 fixed nodes are placed across a square area of length 1000 m. The square is split into 64 smaller squares where the location of each node is selected randomly within each of these squares. The number of data slots per frame is d = 5 where each slot is of duration 6 ms. A source node generates packets of length 512 bytes according to a Poisson process with rate λ packets/s. We assume that each node has a queue of arbitrarily large size since our objective is to capture packet losses attributed to interference. The maximum radio transmit power is set to 20 dBm which translates to a range of approximately 300 m in the absence of interference. The path loss exponent α = 4 and the SINR threshold for successful reception at a receiver (γ) = 5 dB. The receiver thermal noise power is assumed to be −90 dBm. The maximum number of iterations in the DPC algorithm is set to 20. We consider three source–destination pairs where source nodes are separated from their respective destinations by approximately 1000 meters on the average in order to emphasize intra-path interference contributed by intermediate relays. As simulation progresses, it Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

should be noted that these three flows give rise to an increasing number of effective packet sources from frame to frame, on the average, since next hop nodes act as sources of forwarded packets. Motivated by the computational complexity of solving DPC for large number of links along with the exponential growth of control overhead per frame with H, we limit H to a small value (H = 2) in this set of experiments. This only limits ICT sets to include transmitters that are within 2-hops away as discussed in Section 4.2. The length of paths from source to destination could be arbitrary as shown in Figure 6. The network load is varied via increasing the packet arrival rate per source node (λ) from 10 to 360 packets/s. Each simulation run is carried out for the duration of 900 s. 5.2.

Reference System (REF)

In this section, we describe the reference system (REF) which represents a wide class of state-of-the-art protocol stacks for multi-hop wireless networks. It is used as a benchmark to gauge the performance gains of set-based routing. First, we assume the transmission power is fixed at Pmax and there is no provision for dynamic adaptation. Second, we assume that the routing and MAC decisions are taken in isolation. A table-based routing protocol is executed on a hop-by-hop basis using the MH routing criteria. Ties between multiple MH paths are resolved via random selections. Once the routing decision is made at the beginning of a frame, then it is the responsibility of the scheduling algorithm to resolve the contention among the constructed links. Scheduling is based on the conservative maximal slot scheduling in Reference [3] which attempts to create collision-free schedules via satisfying the following constraints: (i) a node is not allowed to simultaneously transmit and receive in a slot, (ii) a node is not allowed to receive from more than one transmitter in the same slot, and (iii) A receiver should not be a neighbor of any other transmitter. 5.3.

Performance Results

In this section, we compare the throughput achieved by the joint design of MAC and routing to the reference system and the upper bound established in Section 3.4. 5.3.1.

Comparison to the REF system

The performance metric used to compare the two systems is the E2E throughput measured as the Copyright © 2010 John Wiley & Sons, Ltd.

long-run average number of data packets that reach their respective final destinations successfully per second. In order to better understand the trade-offs involved, we examine three routing policies. These policies are generated via appropriately configuring set-based routing to widen the scope of the next hop decision space depending on the scenario (intense of interference, average path length, and flow dynamics). This configuration mechanism constitutes the operational manifestation of, and has a direct one-to-one correspondence to, the path length constraint k in the mathematical problem formulation in Equation (1). Recall that the routing search process in the RSP algorithm ranks MH paths in the highest rank and the rank decreases as the path length increases. Accordingly, the first policy, referred to as ‘Highest Rank Paths Only’ (HRPO), limits search in the routing policy space to neighbors residing on MH paths. This policy may show performance gains only if there are multiple MH paths between some S-D pairs, which is typical in many networks with moderate connectivity. The second policy, referred to as ‘Second Rank Paths Also’ (SRPA), widens the search scope to accommodate MH paths in the highest rank along with longer path(s) in the second rank. This policy trades path length for MAC throughput in an attempt to improve the E2E throughput. Finally, the third policy, referred to as ‘All Rank Paths’ (ARP), is an extreme that considers neighbors on all possible paths between the source and destination as potential next hops, irrespective of their associated path lengths. Accordingly, MH routing and ARP policies can be viewed as the extremes. At one end of the spectrum, MH routing attempts to minimize path lengths irrespective of the MAC throughput. At the other end, ARP attempts to maximize the MAC throughput irrespective of path lengths. Simulation results confirm that neither extreme constitutes a favorable design choice. First, we compare the long-run average number of successful packet transmissions per slot under the four schemes. The importance of this experiment stems from the fact that this parameter reflects the MAC Throughput. It can be easily noticed from Figure 5 that the reference system yields the lowest MAC throughput due to ignoring the negative impact MH routing may have on the MAC performance. On the contrary, the HRPO and SRPA policies show considerably higher MAC throughput. Notice that HRPO improves the MAC throughput of REF by a factor of 25% at heavy loads. It is crucial to notice that this is achieved while preserving the MH routing criteria since the HRPO policy attempts to exploit the spatial separation of next Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

3 2.8

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Copyright © 2010 John Wiley & Sons, Ltd.

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hop nodes to pack as many transmissions as possible in each slot. Moreover, it can be noticed that as the path length constraint in Equation (1) is relaxed, the SRPA policy improves the MAC throughput of REF by a factor of 38% at heavy loads. This is attributed to widening the routing search space which creates more room for spatially separating the paths of various S-D pairs. Under the ARP policy, the MAC throughput increases at low to moderate loads and then starts to decrease under high loads. We attribute this to routing based solely on MAC throughput which could lead to forwarding packets to directions far from destination. This leads to following arbitrarily long paths, as shown later, which imposes higher load on the network. Next, we compare the long-run average path length under the four policies as shown in Figure 6. This measure reflects the price paid for improving the MAC throughput. It is straightforward to notice that the reference system yields the lowest average path length due to adopting the MH routing criteria. Moreover, policies that improve the MAC throughput, namely HRPO and SRPA, has average path lengths similar or longer than the reference system. In addition, the ARP policy has the longest path length on the average as expected. Figures 5 and 6 confirm that the interplay between MAC throughput and path length is what determines the net E2E throughput. Figure 7 shows the E2E throughput performance under the four policies. First, we notice that the reference system yields low performance due to ignoring the trade-off between MAC throughput and path length. Second, the HRPO and SRPA policies give the highest E2E throughput due to improving the MAC through-

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put subject to a constraint on the path length. Third, the ARP policy yields the worst throughput performance due to following spatially far, yet excessively long, paths from source to destination. Finally, we notice that the HRPO policy outperforms the reference system by a factor of 50% at heavy loads and decreases to 35% at moderate loads. On the other hand, the SRPA outperforms the reference system by a factor of 34% for moderate and heavy loads. Notice that although the SRPA policy is inferior to HRPO, it still outperforms the reference system. Referring to the relative performance of HRPO, SRPA and ARP we conclude that there is a turning point in the behavior of the RSP algorithm, that is directly related to the path length constraint. Under HRPO and SRPA, where routing is restricted to MH and slightly longer paths, there could be room for overall performance improvement as demonstrated. On the Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm

CROSS-LAYER MULTIPLE ACCESS AND ROUTING DESIGN FOR WIRELESS NETWORKS

other hand, as we approach the ARP policy (via relaxing the path length constraint), improving the MAC throughput becomes out weighed by the lengthy paths followed from source to destination. Thus, we conclude that by appropriately configuring the scope of the set-based routing policy space depending on the node arrangement, flow dynamics and interference intense, the proposed cross-layer framework could achieve significant performance improvements over the state-ofthe-art.

5.3.2.

Comparison to the upper bound

So far, we have made a strong case for the benefits of cross-layer set-based routing over the reference system (REF) which treats MAC and routing decisions in isolation. However, this does not reveal how close/far the proposed solution is to/from the optimum. Therefore, we conclude this section with a stronger argument that shows the potential of set-based routing. Recall from Section 3.4 that the upper bound on ηmac   is given by KL c2 , where K = 3 is the number of S-D pairs in our simulations and L is average path length if the nodes are optimally placed. However, nodes in this scenario are randomly placed as described in Section 5.1. We circumvent this hurdle via using the average MH path length for the simulated deployment from Figure 6 (approx. 6.3 hops) with the understanding that this yields a looser upper bound than the one if nodes are optimally placed. c2 represents the spatial reuse density on each path, which is set to 2 when nodes are optimally placed. This yields the following upper bound   which is 10 transmissions/slot. Notice on ηmac : 3∗6.3 2 that this upper bound assumes packets are always available in the queues. However, the average MAC throughput of HRPO and SRPA in Figure 5 are only 2.6 and 3 transmissions/slot at high loads. This large performance gap from the upper bound is attributed to two factors: (i) a tighter upper bound is obtained if L corresponds to optimally placed nodes and (ii) c2 = 2 is very aggressive since it corresponds to every other hop reusing a slot. In fact, this has never happened for the simulated node deployment. Instead, we observed more conservative patterns of slot reuse per path that yield c2 = 3.8 on the average and a tighter upper bound of 5. Comparing to this new bound, it is straightforward to conclude that the SRPA policy achieves about 60% of this bound. In conclusion, this result not only confirms the strong potential for cross-layer setbased routing but also opens ample room for further improvements. Copyright © 2010 John Wiley & Sons, Ltd.

6.

Conclusion

In this paper we introduce a cross-layer framework for solving the multiple access and routing problems in interference-limited wireless multi-hop networks. Our main contribution is to formulate an optimization problem, establish bounds on its optimal performance, incorporate interference into the routing decision and reduce problem complexity via the cross-layer set-based routing framework. Moreover, we introduce a novel joint RSP algorithm that handles intra-set interference. We conduct a simulation study that compares the cross-layer MAC and routing framework to a reference system where MAC and routing decisions are taken in isolation. Results exhibit performance improvement up to 50% for a variety of routing policies. In addition, set-based routing is shown to achieve 60% of the upper bound on optimal. This opens ample room for exploring further refinements within the framework, e.g., distributed minimum-time set coordination schemes and interference-aware on-demand routing.

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Authors’ Biographies Tamer ElBatt received the B.S. and M.S. degrees in Electrical Engineering from Cairo University, Giza, Egypt, in 1993 and 1996, respectively, and the Ph.D. degree in Electrical and Computer Engineering from the University of Maryland at College Park, MD, in 2000. From 1993 to 1996, he was a Teaching Assistant with the Department of Electronics and Communications, Faculty of Engineering, Cairo University, Giza, Egypt. From 1996 to 2000, he was a Research Assistant in the Department of Electrical and Computer Engineering, University of Maryland at College Park, MD. From 2000 to 2006, he was with HRL Laboratories, LLC, Malibu, CA as a Research Scientist in the Information and System Sciences Laboratory. From 2006 to 2008, he was with San Diego Research Center as a Senior Research Staff Member. From 2008 to 2009, he was with the Advanced Technology Center (ATC) of the Lockheed Martin Space Systems Company, Sunnyvale, CA as a Senior Research Scientist and Communications and Networking R&D Group Lead. In July 2009 he joined the Department of Electronics and Communications, Faculty of Engineering, Cairo University, Giza, Egypt as an Assistant Professor. He is a recipient of HRL Achievement Award in 2002, 2004. He has over 35 publications in refereed journals and international conferences, holds five U.S. patents and five more applications pending. He is a Senior Member of the IEEE, currently serves on the editorial board of the Wiley International Journal of Satellite Communications and Networking, and has served on the program committees of major IEEE and ACM conferences, e.g., INFOCOM, MOBIHOC, MOBICOM, ICC, IPSN, SECON, and VANET. His research interests lie in the broad areas of performance analysis and design of wireless networks with emphasis on clean-slate networking architectures, cross-layer optimization, MAC, MIMO networking, sensor and vehicular networks. Timothy Andersen received his B.S. degree in Computer Science from the University of Texas Austin in 2002 and worked as a research assistant on topics in wireless networking at HRL Laboratories from 2001 to 2003. He received his M.S. and Ph.D. degrees in Mathematics from Rensselaer Polytechnic Institute in 2005 and 2007, respectively. He has been a Senior Analyst at Daniel H. Wagner Associates Inc. in Hampton, VA since 2007. Wirel. Commun. Mob. Comput. (2010) DOI: 10.1002/wcm