Cross-layer Design for Efficient Resource Utilization in WiMedia UWB-based WPANs

Transcription

1 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs RAED AL-ZUBI and MARWAN KRUNZ Department of Eectrica and Computer Engineering. University of Arizona. Utra-wideband (UWB) communications has emerged as a promising technoogy for high data rate wireess persona area networks (WPANs). In this paper, we address two key issues that impact the performance of a muti-hop UWB-based WPAN: throughput and transmission range. Arbitrary seection of routes in such a network may resut in reserving an unnecessariy ong channe time, and hence ow network throughput and high bocking rate for prospective reservations. To remedy this situation, we propose a nove cross-ayer resource aocation design. At the core of this design is a routing technique (caed RTERU) that uses the aocated channe time as a routing metric. RTERU expoits the dependence of this metric on the mutipe-rate capabiity of an UWB system. We show that seecting the route that consumes the minimum channe time whie satisfying a target packet deivery probabiity over the seected route is an NP-hard probem. Accordingy, RTERU resorts to approximate path seection agorithms (impemented proactivey and reactivey) to find near-optima soutions at reasonabe computationa/communication overhead. We further enhance the performance of RTERU by integrating into its design a packet overhearing capabiity. Simuations are used to demonstrate the performance of our proposed soutions. Categories and Subject Descriptors: I.6.0 [Simuation and Modeing]: Genera; G..6 [Numerica Anaysis]: Optimization Constrained optimization; G.2.2 [Discrete Mathematics]: Graph Theory Graph agorithms Genera Terms: Agorithms, Design, Performance Additiona Key Words and Phrases: Cross-ayer Design, OFDM-based UWB, Packet Overhearing, Routing, Sots Reservation. INTRODUCTION UWB has recenty emerged as an attractive technoogy for short range, high data rate wireess communications. Foowing the FCC s First Report and Order that permitted the depoyment of UWB devices [FCC 2002], efforts have been made to expoit the unique features of UWB in various appications, incuding wireess persona area networks (WPANs), wireess sensor networks, imaging and radar systems, and precision ocation tracking systems. Severa architectures for UWBbased WPANs have been proposed. One widey popuar proposa is based on mutiband OFDM. Industry advocates of this system formed an organization caed the Authors address: R. A-Zubi and M. Krunz, Department of Eectrica and Computer Engineering, University of Arizona, 230 East Speedway Bvd, Tucson, AZ , {azubi, krunz}@ece.arizona.edu. Permission to make digita/hard copy of a or part of this materia without fee for persona or cassroom use provided that the copies are not made or distributed for profit or commercia advantage, the ACM copyright/server notice, the tite of the pubication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to repubish, to post on servers, or to redistribute to ists requires prior specific permission and/or a fee. c 20YY ACM /20YY/ $5.00 ACM Journa Name, Vo. V, No. N, Month 20YY, Pages 0??.

2 2 R. AL-ZUBI and M. KRUNZ Muti-band OFDM Aiance (MBOA) [Muti-Band OFDM Aiance 2004], which eventuay evoved into a arge industria aiance known as WiMedia. WiMedia s UWB specifications have been adopted by the European Computer Manufacturers Association (ECMA) as a basis for an OFDM-based UWB standard [European Computer Manufacturers Association 2008]. This standard, caed ECMA-368, is used as a basis for the work in the underying paper. ECMA-368 defines 8 data rates, from 53.3 Mbps to 480 Mbps. It uses a TDMA channe access structure, whereby time is divided into msec intervas, caed superframes (see Figure ). Each superframe is further divided into 256 medium access sots (MASs), which form two parts of the superframe: a beaconing period (BP) and a data transfer period (DTP). The BP is used for contro and coordination purposes (e.g., bandwidth reservation, synchronization, device discovery). Each node is required to send a beacon at the beginning of each superframe (i.e., during BP) and must isten to the beacons of its neighbors. Nodes use information eements (IEs) in their beacons to exchange information. Data transmission is done in the DTP using one of two modes: random access and time-based reservation. The atter mode, known as the distributed reservation protoco (DRP), is particuary suitabe for rea-time streaming appications. According to DRP, devices that want to communicate with each other reserve their MASs from DTP MASs that are not aready reserved by neighboring nodes (see [European Computer Manufacturers Association 2008] and [Batra et a. 2004] for more detais). Beacon Period BP Fig.. Data Transfer Period MAS... Reservation via DRP Randomized Access Superframe structure in ECMA-368. BP One of the chaenges in UWB-based WPANs is how to maintain high throughput in dense topoogies. Most works that considered this probem (e.g., [Liu et a. 2008], [Radunovic and Boudec 2004], [Cai et a. 2008]) assume a fixed excusive region around the receiver of an active ink. No other transmissions can concurrenty take pace inside this region. The transmission rate over an active ink is, thus, adapted according to the interference from nodes outside the excusion region. One of the key issues in these works is how to determine the optima size of the excusion region for an arbitrary network topoogy. Another chaenge in UWB systems is the short transmission range. To overcome this probem, researchers have recenty considered the possibiity of mutihop transmissions, and consequenty investigated routing techniques for muti-hop UWB-based WPANs [Gao and Daut 2006]. Research in this area is sti in its infancy. Existing routing protocos for UWB (e.g., [Gao and Daut 2006] [Abdrabou and Zhuang 2006]) are based on hopcount and distance metrics. They do not account for resource utiization and throughput enhancement issues. In the context of a muti-hop UWB WPAN, route seection, rate assignment, and session throughput are a inter-reated issues. To see that, consider the exampe in Figure 2. In this exampe, there are two possibe paths between devices A and

3 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 3 C: A C and A B C. Suppose that the traffic demand is 0 Mbps and the packet size is Kbyte. Given these vaues, the sum of MASs that shoud be reserved aong A C and A B C are 55 and 43, respectivey (an expanation of how these numbers are obtained is given in Section 3.). In this exampe, the 2-hop path A B C consumes 2 fewer MASs than the direct path A C, and is hence a better path. Note that because of device haf-dupicity, when path A B C is seected, MASs aocated aong the segment A B cannot overap with those aocated to B C. r = 60 Mbps r = 200 Mbps Device B 23 MASs 20 MASs Device A Source 55 MASs r = 53.3 Mbps Device C Destination Fig. 2. Exampe iustrating the inter-dependence of route seection, rate assignment, and session throughput in muti-hop UWB networks. Motivated by the above, in this paper we propose a new cross-ayer design for efficient resource utiization in WiMedia UWB-based WPANs. The structure of this design is shown in Figure 3. At the core of this design is a routing technique for efficient resource utiization (RTERU). RTERU expoits the fact that the higher the ink transmission rate, the smaer the number of MASs to be aocated, and hence the higher the number of free MASs that are avaiabe for other prospective reservations. At the same time, the transmission rate aso impacts the packet error rate (PER) over a ink: for a given ink quaity (i.e., SNR), the higher the transmission rate, the higher the PER. This paces an upper imit on the transmission rate that can be used to support a target PER. RTERU is designed to consider both metrics (i.e., number of MASs and PER). As shown in Figure 3, RTERU invoves interactions between different ayers. It takes as input the traffic demand γ (in bps) and a target end-to-end PER ε, which are provided by the appication ayer. It aso uses ink-quaity information, represented by PER-vs.-SNR curves, from the ink/physica ayer. The outputs of RTERU are an end-to-end path between a source and a destination, which is passed to the network ayer, the rate assignment aong the seected path, which is passed to the ink/physica ayer, and the number of required MASs over each ink aong the seected path, which is passed to the DRP protoco in the MAC ayer. To further improve its performance, RTERU optionay expoits an important feature of broadcast communications, namey packet overhearing (i.e., packets transmitted from a source to a destination are ikey to be overheard by non-intended nodes). This feature is expoited twice. First, during the session admission phase for the purpose of reducing the estimated end-to-end PER. This essentiay gives a spatia diversity gain, which is achieved by supporting mutipe paths to the destination. Secondy, packet overhearing is expoited during

4 4 R. AL-ZUBI and M. KRUNZ actua data transmission, where the IDs of overheard packets are announced so as to avoid reaying these packets by subsequent nodes aong the path. MASs that are aready aocated for reaying these overheard packets can now be reeased and used for other transmissions. Traffic Demand (bits/second) QoS Requirement : Maximum End-to-End PER Appication Layer RTERU (FBSA, RBSA, HSRA) Seect a Path and Assign Transmission Rates aong this Path End-to-End PER Network Layer Overhearing-Based HSRA DRP (Reserve/Reease MASs) Number of MASs over Each Link aong the Seected Path Temporariy Reeased Reservation MAC Layer Packet Overhearing with Feedback Fig. 3. Transmission Rate over Each Link aong the Seected Path PER vs. SNR Curves Link/Physica Layer Framework for cross-ayer design in WiMedia UWB-based WPANs. For each source-destination pair, RTERU aims at seecting a path and a rate assignment that minimize the sum of the aocated MASs whie at the same time satisfying the target end-to-end PER (ε). We show that this probem is NP-hard. Therefore, RTERU reies on a two-phase approximation. The first phase (pathsearch) outputs a set of candidate paths that is ikey to contain a near-optima path. By design, the size of this set is sma, so it can be inspected with sma computationa overhead. Examining this set is done in the second phase (rateassignment phase), in which the transmission rates over each candidate path are assigned such that the tota number of required MASs aong the path is minimized whie simutaneousy satisfying the constraint ε. Finay, the best feasibe path in the candidate set is seected. For the path-search phase, we propose two approximate agorithms: foodingbased search agorithm (FBSA) and rate-based search agorithm (RBSA). FBSA is a reactive approach, whereby the source node foods a route request (RREQ) throughout the network. Upon receiving the first RREQ, the destination node waits for a certain number of superframes in anticipation of receiving additiona RREQs. Because of the synchronized nature of the network (each RREQ propagates one hop per superframe), RREQs that arrive in different superframes carry information about different-ength paths. From these paths, the destination seects its candidate set.

5 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 5 RBSA is a proactive agorithm. For each transmission rate, the source constructs a graph, where the weight of each ink in this graph is a function of the ink PER and the number of MASs that required to satisfy the traffic demand γ. The source executes Dijkstra s agorithm to find the shortest path with respect to the ink weight. The output of RBSA is aso a set of candidate paths. In the rate assignment phase, the source node (in RBSA) or the destination node (in FBSA) performs rate assignment and the seection of a near-optima feasibe path. We show that this phase is equivaent to the mutipe-choice knapsack probem (MCKP), which is NP-hard. Therefore, we propose a heuristic soution, caed HSRA, for the rate assignment probem. The rest of the paper is organized as foows. Section 2 presents reated work. The probem setup and formuation are provided in Section 3. Section 4 presents RTERU, and Section 5 presents our proposed technique to expoit packet overhearing for the purpose of reducing the end-to-end PER. Section 6 presents the second approach for expoiting packet overhearing during data transmission. In Section 7, we use simuations to evauate the performance of our proposed cross-ayer designs. Concuding remarks are drawn in Section RELATED WORK Few works have addressed routing in muti-hop UWB-based WPANs. In [Gao and Daut 2006], the authors mainy focused on improving the performance of a common geographic routing approach, which is based on Eucidean distance. According to this approach, a node forwards packets to the neighbor that is geographicay cosest to the destination. The authors in [Gao and Daut 2006] noted that even if the above simpe strategy eads to a min-hop path, it may resut in seecting bad inks (i.e., inks with high PERs). Therefore, they proposed considering the ink quaity (i.e., PER) in choosing the next hop, so as to achieve a tradeoff between hopcount and ink quaity. For transmission rates 200 and 480 Mbps, the authors experimentay found the best transmission radii that achieve the tradeoff between hopcount and ink quaity. They concuded that the position-based greedy routing strategy with carefuy seected transmission radius works we in muti-hop UWB-based WPANs. However, they did not provide a specific mechanism for seecting the transmission radius for other transmission rates, and they did not address the rate assignment issue (they assumed a fixed transmission rate over a path, and did not provide a procedure to determine this rate). They aso did not account for the reationship among the number of reserved MASs, the end-to-end PER, and the transmission rate. As shown in our work, considering such reationship has a significant impact on the overa network performance. In [Abdrabou and Zhuang 2006], the authors proposed a position-based QoS routing protoco for UWB networks. Their protoco is based on the greedy perimeter stateess routing (GPSR). Different QoS parameters were considered, incuding the rate demand, PER, and end-to-end deay. Their simuation resuts showed that their protoco works we for muti-hop UWB networks. However, the authors did not account for the reationship between the number of reserved MASs, the endto-end PER, and the transmission rate. Furthermore, none of the aforementioned protocos expoited packet overhearing. Athough packet overhearing was used in

6 6 R. AL-ZUBI and M. KRUNZ severa previous works (e.g., [Hsu et a. 2006], [Biswas and Morris 2005], [Katti et a. 2008]), none of these works accounted for this feature during rate assignment or utiized the reserved channe time of overheard packets. Specificay, in [Hsu et a. 2006], packet overhearing was empoyed to reduce the overhead of route discovery, where routing information may be obtained in advance by anayzing overheard packets. The authors in [Biswas and Morris 2005] expoited packet overhearing to improve the performance of an opportunistic routing protoco. According to this protoco, one of the nodes that overheard the transmitted packet is chosen to forward the packet. The work in [Katti et a. 2008] is based on the fact that even when no node receives (overhears) a packet correcty, any given bit is ikey to be received (overheard) correcty by some nodes. Nodes that overhear a transmitted packet are aowed to forward parts of this packet, aowing the fina destination to recover the origina packet. 3. PROBLEM SETUP AND FORMULATION 3. Preiminaries As mentioned before, RTERU expoits the dependence among the muti-rate capabiity of an OFDM-based UWB system, the number of required MASs for a reservation, and the PER. Therefore, it is worth carifying such dependence. A given traffic demand γ (in bps) must first be packetized before being transported. et κ be the payoad portion of a packet (in bytes), ν the number of MASs that shoud be reserved in a superframe, and ξ the number of packets corresponding to the demand γ that shoud be sent per superframe. Then, γλsp ξ = () 8κ where λ sp = msec is the superframe interva. Let λ f be the amount of time needed to transmit these ξ packets. Then, λf ν = sots (2) λ ms where λ ms = 256 µsec is the MAS duration. Next, we expain how λ f is impacted by the transmission rate r. Note that λ f = ξ(λ p + SIPS) seconds, where SIPS = 0 µsec is the short inter-packet spacing and λ p is a packet transmission time. This λ p is given by λ p = λ m + λ h + λ u seconds, where λ m = µsec is the preambe interva (used for synchronization, carrier-offset recovery, and channe estimation), λ h = 3.75 µsec is the header interva, and λ u is the transmission time of a PHY service data unit. Note that λ m and λ h are fixed, and ony λ u varies with r. As given in the ECMA-368 standard, λ u can be expressed as: 8κ + 38 λ u = 6 λ sy sec (3) where λ sy = µsec is the symbo interva and is the number of information bits per 6 OFDM symbos, which depends on r, as shown in Tabe I. The above straightforward anaysis aows us to express ν as a function of r for various vaues of γ and κ, as shown in Figure 4. It can be seen that as γ increases, ν becomes more sensitive to r. Furthermore, for given γ and r (e.g., γ = 0 Mbps

7 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 7 Tabe I. Rate-Dependent Moduation and Coding Parameters in ECMA-368. r Mbps Moduation type Coding rate 53.3 QPSK / QPSK / QPSK / QPSK / QPSK 5/ DCM / DCM 5/ DCM 3/4 900 and r = 480 Mbps), ν expectedy decreases with κ, but in a sub-inear fashion. This can be expained by noting the noninear reationship between λ f and κ γ = 0 Mbps κ = 200 bytes κ = 600 bytes κ = 000 bytes ν γ = 2 Mbps r (Mbps) Fig. 4. ν versus r at different γ and κ. Next, we expore the reationship between r and the PER. Devices can estimate the probabiity of correct packet/bit deivery based on the received SNR or using historica data of the number of packets or bits sent and received over a ink. This information can then be used to obtain the PER-vs.-SNR curves [Stojmenovic et a. 2005]. In [Kuruvia et a. 2004], to reduce the computation time, the authors derived a reasonaby accurate yet simpe approximation of such curves. In our work, we assume that the PER-vs.-SNR curves are provided by the physica ayer. For our simuation purposes, to generate these curves, we extract the BER from the BERvs.-SNR curves given in [Nowak et a. 2008] (one curve for each transmission rate), and cacuate the PER as: PER = ( BER) 8κ (4) Note that Equation 4 assumes independence between bits in a packet. 3.2 Probem Formuation Consider an UWB WPAN. Its topoogy is represented by a graph G(N, L), where N is the set of nodes and L is the set of inks. A ink exists between two nodes

8 8 R. AL-ZUBI and M. KRUNZ if these nodes can communicate directy at the owest transmission rate r. Given the rate demand γ of a requested reservation and given a set of transmission rates R = {r, r 2,...,r M }, where M = R and r r 2... r M, each ink L is associated with two sets of parameters: n (r): minimum number of time sots that are required to estabish the requested reservation over ink at a transmission rate r, r R. e (r, SNR ): PER over ink when this ink is operated at a transmission rate r and the received SNR is SNR, r R. Let n(p) def = p n (r) be the sum of required MASs aong a path p. Given a source S and a destination D, a PER constraint ε, and γ, the probem is to find a path p and a rate assignment aong p such that: (i) e(p ) ε, where e(p ) = p ( e (r, SNR )) is the end-to-end PER over path p. (ii) n(p ) is minimized over a feasibe paths satisfying (i). In this paper, we use the terms feasibiity condition and optimization metric to refer to (i) and (ii), respectivey. Constraint (i) is a basic requirement for streaming appications. Note that other QoS requirements (i.e., rate demand and end-to-end deay jitter requirements) are being met. Specificay, the rate demand is met by reserving the required MASs in each superframe. Because of the TDMA structure, the end-to-end deay jitter (i.e., the maximum aowabe deviation from the nomina inter-packet time) experienced by a fow over a route cannot exceed the duration of one superframe ( 65 msec), which meets the jitter requirement of typica streaming appications. Remark 3.. In Constraint (i), we assume that the PERs over various inks are independent. This assumption can be justified as foows. The PER over a ink is determined by the channe quaity at the receiver of that ink, which depends on the SNR and transmission rate. In other words, packet errors depend on the receiver ocation. Two different receivers (incuding those of adjacent inks aong a path) experience independent fading, and hence their PERs are independent. Therefore, at a node, the PERs over incoming and outgoing inks are independent. For the optimization metric, we try to minimize the tota sum of sots aong a path, despite possibe MASs reuse aong such a path. The reason is expained in Figure 5. In this figure, there is a path p between nodes A and E (i.e., A B C D E). For a given rate assignment, the aocated MASs over each ink of this path are shown in the figure. The ink D E can reserve the same MASs reserved by A B. However, it is miseading to set n(p) = = 0 sots, because ink D E actuay prevents other inks (e.g., F G) from using the same two sots that are reserved for D E. In order to consider the actua impact of path reservation, the optimization metric shoud be cacuated without considering sot reuse (i.e., n(p) = 2 sots). In other words, despite the potentia for sot reuse, from a network-wide perspective reused sots do not come for free, as they potentiay impact the sot assignment in other contention regions. Note that the metric used in the feasibiity condition is a mutipicative metric. However, it can be transformed into an additive metric through a ogarithmic

9 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 9 2 sots 5 sots 3 sots 2 sots A B C D E G F Fig. 5. Exampe iustrating why sot reuse is not considered in the optimization metric. transformation: p og( e (r,snr ) og( ) ε ). With this transformation and under a given transmission rate, the probem reduces to minimizing an additive metric (i.e., number of sots) subject to a constraint on another additive metric. This is exacty the restricted shortest path (RSP) probem, which is known to be NP-hard [Ahuja et a. 993]. With the incusion of a rate assignment per ink, our probem is actuay more genera than RSP, so it is aso NP-hard. Therefore, approximate soutions with suboptima performance are needed. Such soutions must exhibit reasonabe computationa/communication overhead. 4. RTERU RTERU consists of two main phases: path search and rate assignment. In the first phase, a set of candidate paths is determined. The size of this set has to be sma enough such that its paths can be examined quicky during the second phase. In the second phase, transmission rates are assigned over various inks aong a given path such that the tota sum of sots aong the path is minimized whie at the same time the target end-to-end PER is satisfied. Finay, a near-optima path p is seected from the candidate set. 4. Path-Search Phase An exact soution to our probem requires examining every path between S and D. Because the number of paths grows exponentiay with the size of the network, this method is not practica. In the path-search phase, we aim at finding a near-optima soution at a ow computationa cost. To this end, we propose two path-search agorithms: fooding-based search agorithm (FBSA) and rate-based search agorithm (RBSA). FBSA is intended for reactive routing (simiar to AODV), whereas RBSA is intended for a proactive impementation. 4.. FBSA. Node S starts FBSA by broadcasting an RREQ as an IE in a beacon. The RREQ incudes the source ID, the destination ID, ε, γ, and the packet size κ. Every intermediate node U that receives the RREQ shoud first update the route sequence of the received path by adding its ID, and then incude the SNR vaue over the ast ink of the updated sequence. U then rebroadcasts the updated RREQ via a beacon during the beacon period of the upcoming superframe. If there exists a direct (-hop) path between S and U, U first checks if the SNR over at east one ink of the indirect path between S and D is ess than that of the direct path. If so, U discards the received RREQ. The rationa behind this mechanism can be carified by the foowing observation.

10 0 R. AL-ZUBI and M. KRUNZ Observation 4.. Let p be the direct path from S to D, and et q be a muti-hop path from S to D. If the SNR over at east one ink in q is ess than the SNR over p, then the sum of the required MASs aong q must be greater than the number of MASs aong p. In this case, there is no advantage in rebroadcasting the received RREQ at the intermediate node U. Further reduction in the fooding overhead can be achieved by preventing U from rebroadcasting the RREQ if the RREQ has previousy U. Foowing the receipt of the first RREQ, node D waits for up to K superframes to accumuate more RREQs, where K is a controabe parameter. RREQs received during the mth superframe, m =,...,K, wi contain information about m-hop paths from S to D. Let ψ m be the set that contains such m-hop paths. In the worst case, the size of ψ m grows exponentiay with N. If the topoogy is dense and K is arge, node D wi have to choose from a arge set of paths. To reduce the computationa cost, for m =,...,K, D randomy seects a smaer subset ω m ψ m from which it determines the best feasibe path gm among a ω m paths. The computation of gm is done during the rate assignment phase. This gm is added to the candidate set J. After computing ω m, node D needs to decide whether to terminate the agorithm or continue to wait for the (m+)th superframe. If n(g m ) m > 0, then D continues n(g m ) n (r M) n (r M) to wait. Otherwise, m = 0, and D terminates the agorithm. This criterion can be carified by the foowing observation. Observation 4.2. Let p be a path between S and D. For a given oad demand γ, the number of aocated MASs aong every ink p is n (r M ). Note that n (r M ) = n 2 (r M ) = ñ(r M ) for any two inks, 2 p. Then, p consists of at most n(p) ñ(r M) inks. Furthermore, if another path q between S and D such that n(q) n(p), then q aso consists of at most n(p) ñ(r M) hops. During superframe m, node D seects gm as the best path in the set ω m. Consider path gm+, which is seected in superframe m +. According to Observation 2, if n(gm+) n(gm), then the hopcount of gm+ cannot be greater than n(g m ) ñ(r hops. M) Therefore, during superframe m, node D knows that m and n(g m ) ñ(r M) are the current and maximum hopcounts of gm+, respectivey. Then, if n(g m ) ñ(r M) m > 0, D wi continue to wait for superframe m+. Otherwise, n(g m ) ñ(r M) m = 0, and D terminates the agorithm. Eventuay, D terminates the agorithm, after waiting for up to K superframes, and seects the optima path p from J. This seection is sent back to the source S. A pseudo-code of FBSA is shown in Agorithm. Compexity: FBSA has an execution compexity of O( ω m KC HSRA ), where C HSRA is the computationa compexity of the rate-assignment phase. Note that FBSA is distributivey executed over K superframes. Resut 4.3. (Bounds on the Path Returned by FBSA): For a source-destination pair, et h min and h opt be the hopcounts of the min-hop and optima paths, respectivey. Aso, et N opt and N FBSA be the sums of required MASs aong the

11 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs optima path and the one returned by FBSA, respectivey. Then, N opt N FBSA h min n (r ) h opt n (r N M) opt. Proof. Assume the destination waits for K superframes. Then, the destination seects the path in J that has the minimum number of MASs N FBSA (i.e., N FBSA = min{n(gm ), m =, 2,..., K}). We know that h optn (r M ) N opt h opt n (r ), N FBSA n(g ) h minn (r ), and N opt N FBSA. Therefore, h opt n (r M ) N opt N FBSA h min n (r ). This inequaity can be rewritten as h opt n (r M ) N opt N FBSA hminn (r ) N opt N opt. Aso, if we repace hminn (r ) N opt with hminn (r ) h optn (r M), then the inequaity is sti vaid. Therefore, N opt N FBSA hmin n (r ) h opt n (r N M) opt. Resut 4.3 shows that FBSA is a provabe approximation, i.e., there is a quantifiabe performance gap between this approximate soution and the optima one. Agorithm FBSA (executed at the destination D) Input: ψ m % set of paths received at D in the mth superframe Output: The feasibe path p that requires the minimum number of MASs, or faiure if no feasibe path can be found Initiaization: J = % set that wi incude candidate feasibe paths from which p wi be % seected decision = continue % wait for another superframe whie (decision == continue) Randomy seect a subset ω m from ψ m, where the size of ω m is a design parameter Using Agorithm 3, find the feasibe path gm that requires the minimum number of MASs among the paths in ω m Add gm to J if n(g m ) m > 0 n (r M ) decision = continue Wait one more superframe m = m + Get new ψ m during the new superframe ese decision = stop end end Among the paths in J, seect path p that requires the minimum number of MASs if p is found return p ese return no feasibe path found end

12 2 R. AL-ZUBI and M. KRUNZ 4..2 RBSA. In contrast to the reactive approach used in FBSA, RBSA foows a proactive approach, in which nodes exchange ink-state information using beacons. The source node S initiates RBSA by constructing a set of graphs Ω = {G, G 2,...,G M }, where M is the number of transmission rates. Each graph G i Ω, i =, 2,...,M, consists of the same set of nodes N and the set of inks L. The transmission rates over the inks in G i are not aowed to exceed r i. For L, et r be the maximum transmission rate that can be used over ink whie satisfying the target PER (ε). Then, the transmission rate over ink L in G i is set to r (i) = min{r i, r }. Figure 6 iustrates the process of assigning ink rates in G i. Then, each ink in G i is weighted by w (i), which is given by the foowing Lagrangian function (with Lagrangian mutipier equas ): w (i) = n (r (i) ) + og( e (r (i), SNR ). (5) ) A r * r * = 53.3 Mbps C r * = 320 Mbps B = 480 Mbps (a) Origina graph. A r () = 53.3 Mbps C () r () = 53.3 Mbps B r = 53.3 Mbps (b) Graph G (r = 53.3 Mbps). A r (7) r (7) = 53.3 Mbps r (7) C = 320 Mbps B = 400 Mbps (c) Graph G 7 (r 7 = 400 Mbps). Fig. 6. Exampe iustrating the process of constructing the set of graphs Ω in RBSA. Note that r (i) = min{r i, r }. Reca that we use the ogarithmic function to transform the mutipicative metric in the feasibiity condition to an additive metric. Now, for each graph G i, Dijkstra s agorithm is used to find the shortest S D path qi with respect to w(i). The set P = {q, q 2,..., q M } is then examined during the rate-assignment phase. Finay, S seects a near-optima path p from this set. A pseudocode for RBSA is shown in Agorithm 2. The rationae behind RBSA can be expained by considering the two extreme cases: G and G M. For G, the first term n (r () ) in the right-hand side of (5) is the argest among {n (r (i) ) : i =,...,M} for a inks. Furthermore, a inks in G wi have the same n (r () ) vaue. Simiary, the second term og( e (r (),SNR ) is the smaest among {og( ) e (r (i),snr ) : i =,...,M}, ) this vaue varies from one ink to another in the graph G, since it depends on SNR. Note that when Dijkstra s agorithm is executed, n (r () ) is the dominant factor when seecting a path among paths of different hopcounts. This is because n (r () ) og( ). However, in case of paths that have the same hopcount, the second term becomes dominant. Accordingy, q is the most feasibe e (r (),SNR ) min-hop path (i.e, the min-hop path that has the owest end-to-end PER). Now, consider the case of G M. The first term n (r (M) ) in the right-hand side of (5) is the smaest among {n (r (i) ) : i =,...,M} for a inks. Simiary, the

13 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 3 Agorithm 2 RBSA (executed at the source S) Input: G(N, L) R = {r, r 2,..., r M} % set of transmission rates S and D % source and destination nodes n (r) and e (r,snr ) for a L and r R % the number of MASs and the PER over ink at transmission rate r, respectivey Output: The feasibe path p between S and D that requires the minimum number of MASs or faiure if no feasibe path can be found Initiaization: P = % set that wi incude candidate feasibe paths from which p wi % be seected for a r i R for a L Compute r (i) = min{r i, r } % the transmission rate that wi be assigned % over each ink in G i Use r (i) Assign w (i) in equation (5) to compute w (i) to ink in graph G i end For graph G i, use Dijkstra s agorithm to find the shortest path qi with respect to w (i) between S and D Record qi in P end Among the paths in P, seect path p that requires the minimum number of MASs if p is found return p ese return no feasibe path found end second term og( e (r (M),SNR ) is the argest among {og( ) e (r (i),snr ) : i = ),...,M}. Therefore, qm is the optima path in terms of the number of MASs (if qm is feasibe, then it is the optima soution). In that sense, as r i increases, the probabiity of satisfying the feasibiity condition decreases whie the probabiity of satisfying the optimization metric increases. RBSA tries to find a compromise between the two extreme cases. Compexity: RBSA has a computationa compexity of O(M( N og( N ) + L +C HSRA )), where N og( N )+ L is the computationa compexity of Dijkstra s agorithm and C HSRA is the computationa compexity of the rate-assignment phase. Observation 4.4. If qi is infeasibe, then qj is aso infeasibe for i j, since e(qi ) e(q j ). The above observation can be used to further reduce the computationa compexity of RBSA by aowing it to sequentiay determine qi, i =, 2,..., M. Bounds on the Path Returned by RBSA: Foowing simiar anaysis to the

14 4 R. AL-ZUBI and M. KRUNZ one used in determining the bounds for FBSA (see Section 4..), it can be shown that N opt N RBSA hmin n (r ) h opt n (r N M) opt, where N RBSA is the number of MASs aong the path returned by RBSA (other parameters are defined in Section 4..). 4.2 Rate Assignment Phase Definition 4.5. Rate-Assignment Probem: Consider an h-hop path between S and D. Let R j be the set of transmission rates that can be assigned to the jth ink on that path. Each rate r x R j corresponds to an optimization metric n j (r x ) and a feasibiity metric og( e j(r x,snr j) ). The rate-assignment probem is to choose one transmission rate for each ink such that the sum of the vaues of optimization metric is minimized whie the sum of feasibiity metric does not exceed a predefined vaue. The rate-assignment probem is reated to the we-known Mutipe-Choice Knapsack probem (MCKP). Definition 4.6. Mutipe-Choice Knapsack Probem (MCKP) [Pisinger 995]: Given y casses C, C 2,..., C y of items to pack a knapsack. Each item i C j has a profit f ij and a weight w ij. The probem is to choose one item from each cass such that the profit sum is maximized whie the weight sum does not exceed a predefined vaue. If we et the casses of items in MCKP be the sets of transmission rates, the knapsack in MCKP be a path, and the profit and weight of each item in MCKP be the optimization and feasibiity metrics of each transmission rate, respectivey, then an instance of MCKP can be converted into an equivaent instance of the rate-assignment probem. Because MCKP is NP-hard [Dudzinski and Waukiewicz 987], the rate-assignment probem is aso NP-hard. Accordingy, we propose a heuristic soution for the rateassignment probem (HSRA). HSRA starts by assigning the highest possibe transmission rate over each hop of a given path p in order to minimize the tota number of MASs aong p. However, a high transmission rate over a ink means a high PER, which may ead to an end-to-end PER arger than ε. Therefore, unti the feasibiity condition is satisfied, HSRA graduay reduces the end-to-end PER such that the corresponding increase in the tota number of MASs aong the path is maintained as sma as possibe. The operationa detais of HSRA are as foows. As mentioned above, the first step in HSRA is to seect r M for each ink in p. If this rate assignment satisfies the feasibiity condition, then it is optima. Otherwise, the agorithm examines h different rate assignments, each being created by repacing r M over one ink by r M. For exampe, if the first rate assignment over a 3-hop path is {r 8, r 8, r 8 } and it is infeasibe assignment, then HSRA wi examine three other rate assignments: {r 7, r 8, r 8 }, {r 8, r 7, r 8 }, and {r 8, r 8, r 7 }. The best feasibe one among them wi be seected. If none of them is feasibe, the second step is initiated with a new rate assignment that is created by repacing r M by r M over ony the ink that has the highest PER under the first rate assignment. For exampe, under the first rate assignment {r 8, r 8, r 8 }, if the third ink has the highest PER, then the second step wi be initiated with {r 8, r 8, r 7 }. In other words, the second step of HSRA is

15 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 5 to reduce the transmission rate (or PER) over the worst ink of the given path (i.e., the ink that has the highest PER among a inks of the given path). We beieve this is a ogica approach because the transmission rate over the worst ink has a significant impact on the end-to-end PER. This procedure continues unti the feasibiity condition is satisfied. A pseudocode for HSRA is shown in Agorithm 3. Agorithm 3 HSRA Input: Path p with h inks R = {r, r 2,..., r M} n (r) and e (r,snr ) for a p and r R ε Output: The feasibe rate assignment C that resuts in minimum number of MASs aong path p or faiure if no feasibe rate assignment can be found Initiaization: C = [r M, r M,..., r M], C =h % assign the maximum transmission rate r M over each ink of p n(p) = % set the number of MASs aong p to for step = to Mh if C is feasibe % C resuts in end-to-end PER ess than ε return C % this is the best feasibe rate assignment break end for i = to h % examine h rate assignments that are constructed by reducing the % transmission rates in C over each ink of p one at a time C o = C % record a copy of C C(i) = next highest transmission rate % e.g., r M is repaced by r M n(p) (C) = tota number of MASs aong p at rate assignment C if C is feasibe and n(p) (C) < n(p) C = C % this is the best feasibe rate assignment n(p) = n(p) (C) % this is the minimum number of MASs aong p end C = C o % return a copy of C that is stored in C o end if C is found return C % this is the best feasibe rate assignment break end % construct a new rate assignment for the second step, as foows: C( ) = next highest transmission rate over the ink, where p is the ink that has the highest PER at C. If the transmission rate over the ink equas r, then is the ink that has the next highest PER end return no feasibe rate-assignment found Compexity: The worst-case computationa compexity of HSRA occurs when both of the foowing events take pace: () Assigning the minimum rate (i.e., r ) over each ink in path p is the ony feasibe rate-assignment, and (2) e i (r ) e i+ (r M )

16 6 R. AL-ZUBI and M. KRUNZ for every two adjacent inks i and i+, where i =, 2,...,h. In this case, the agorithm wi run M h steps. In each step, it examines h rate assignments. Therefore, the worst-case computationa compexity of HSRA is O(Mh 2 ). 5. OVERHEARING-BASED HSRA An important feature of broadcast communications is that packets transmitted from a source to a destination are ikey to be overheard by other non-intended nodes. In this section, we expoit this feature to enhance the performance of HSRA. Our proposed technique for expoiting packet overhearing is based on the fact that packet overhearing increases the packet deivery rate over a given path by supporting mutipe paths to the destination. Such spatia diversity gain aows the use of higher transmission rates aong the given path, eading to a decrease in the tota number of required MASs, and hence an increase in the number of admitted fows. To iustrate, consider the exampe in Figures 7 (a)-(b). In Figure 7 (a), rate assignment over each ink on the path A B C is done ignoring the fact that the packet sent from A to B is ikey to be overheard by C. Using the equation of end-to-end PER used in section 3.2, the end-to-end PER is and the tota number of required MASs aong the path is 43 sots. However, as shown in Figure 7 (b), by considering packet overhearing, there are two possibe paths to deiver the packet from A to C: A B C and A C. Assume that the PER over ink A C at rate R = 60 Mbps (the rate used over ink A B) is 0.0. Then, the end-to-end PER (not shown in the figure) wi decrease to This reduction in PER can be expoited to increase the transmission rate over the inks aong the path A B C whie at the same time satisfying the target end-to-end PER of Accordingy, the tota number of required time sots aong the path is reduced to 35 sots (see Figure 7 (b)). R = 60 Mbps PER=0.03 Number of sots= 23 R = 200 Mbps PER=0.04 Number of sots= 20 R = 200 Mbps PER=0.08 Number of sots= 20 R = 320 Mbps PER=0.0 Number of sots= 5 Device B Device B End-to-end PER= Tota number of sots=43 End-to-end PER= Tota number of sots= 35 Device A Source Device C Destination Device A Source Device C overhears packets sent from A to B PER=0.30 Device C Destination (a) Without Expoiting Packet Overhearing. (b) With Expoiting Packet Overhearing. Fig. 7. Exampe that iustrates the expoitation of packet overhearing to improve resource utiization. To expain how we obtained the end-to-end PER in the above exampe, consider a 3-hop path between a source S and a destination D, as shown in Figure 8. In this case, considering packet overhearing resuts in 4 possibe paths: S A D, S A B D, S B D, and S D. Let PER SD and E XY respectivey denote

17 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 7 the end-to-end PER and the event that a packet is successfuy deivered over a ink X Y. Then, PER SD = Pr[(E SA E AD ) (E SA E AB E BD ) (E SB E BD ) (E SD )]. Note that the union terms in this expression represent the events of successfu packet deivery over the various paths, e.g., (E SA E AD ) represents the event that a packet is successfuy deivered over the path S A D. According to the set theory, evauating PER SD requires that the dependency between these events shoud be accounted for. This dependency can be easiy handed by understanding the physica meaning of the various combinations. As an exampe, the term Pr[(E SA E AD ) (E SA E AB E BD )] refects the probabiity of receiving the packet over S A D and S A B D, which means a successfu reception over a inks of the two paths. Therefore, Pr[(E SA E AD ) (E SA E AB E BD )] = Pr[E SA E AD E AB E BD ]. Other combinations (e.g., (E SA E AD ) (E SA E AB E BD ) (E SB E BD )) can be recursivey computed using previousy cacuated combinations (e.g., Pr[(E SA E AD ) (E SA E AB E BD ) (E SB E BD )] = Pr[E SA E AD E AB E BD E SB ]). In genera, computing the probabiity of a union of events is an NP-hard probem [Ba and Provan 988]. Severa approximate soutions were proposed to sove this probem (e.g., [Ba and Provan 988], [Frigessi and Verceis 985]), which can be used to determine an estimate of PER SD. In practica WPANs, the path engths are imited to a few hops, which aows cacuating the exact soution with manageabe processing overhead using the exact agorithm presented in [Mier 968]. S A B D Fig. 8. Exampe iustrating packet overhearing in a 3-hop path. Impementation: Our proposed technique for expoiting packet overhearing can be integrated into any given routing scheme (e.g., min-hop and shortest-distance). Specificay, to integrate our packet overhearing technique into RTERU, we modify the cacuation of the end-to-end PER done by HSRA. Aso, our technique requires that once a data packet is received by a node, the packet wi not be discarded even if the target of the packet is not this node. 6. PACKET OVERHEARING WITH FEEDBACK We now want to present a new technique to expoit the reserved channe time (i.e., MASs) of overheard packets. In this technique, the fina destination node D of a given h-hop path p announces the IDs of the packets that overheard by itsef during a given superframe m to avoid unnecessary reaying of these packets in superframe m+. During superframe m+, nodes are aowed to utiize the reserved reaying time of the overheard packets by using the prioritized contention access (PCA) protoco [European Computer Manufacturers Association 2008]. To iustrate, consider the exampe in Figure 9. In this exampe, assume that after appying our RTERU mechanism aong with our technique that discussed in Section 5, the seected path between the source A and destination C is A B C. Further,

18 8 R. AL-ZUBI and M. KRUNZ assume that the reservations for the inks A B and B C are as shown in the figure and the number of transmitted packets during each reservation is 5 packets. As indicated in the figure, during the first superframe of the session, A sends the maximum possibe number of packets during A B reservation. In the second superframe, C announces the IDs of overheard packets by using IE in its beacon. This announcement shoud be considered by node B to avoid retransmitting the overheard packets and aow other nodes (e.g., D and E) to utiize (if they need) the reaying time of these packets for other communications, e.g., transmitting a text fie from a computer to a printer. Expoiting the retransmission time of overheard packets to print a fie Device D Device B Device E Sent packets: Device A Source Device C overhears packets sent from A to B Device C Destination Superfarme Device C announces the overheard packets BP A B B C BP A B B C BP... SST Sent packets: Overheard packets: 5 2 Sent packets: Sent packets: 4 3 BP: Beacon period SST: Session start time A B: time reservation for the ink A B B C: time reservation for the ink B C Fig. 9. Exampe iustrating the idea of expoiting packet overhearing with feedback. Impementation: To aow the destination of a given path to overhear packets transmitted aong the path, the destination needs to switch to the receive mode during the MASs that reserved aong this path. Aso, any announcement of overheard packets by the destination of the path shoud be considered by the nodes that receive it. If the node participates in the path, it shoud avoid reaying the announced overheard packets. Otherwise, the node has the choice to use the reserved reaying time of overheard packets. Note that the node needs the reserved reaying time of the announced overheard packets if there is no sufficient MASs avaiabe. Remark 6.. In the aforementioned technique, we do not consider packets overheard by the intermediate nodes of a path p, i.e., we ony consider packets overheard by the fina destination. The reason behind this can be expained as foows. If an

19 Cross-ayer Design for Efficient Resource Utiization in WiMedia UWB-based WPANs 9 intermediate node of path p forwards the packets without considering the packets overheard by the next intermediate node of path p, this wi resut in mutipe paths to the destination, which is required by our technique discussed in Section PERFORMANCE EVALUATION 7. Simuation Setup In this section, we study the performance of RTERU and contrast it with three routing techniques: min-hop, shortest-distance, and LOAD [Kim et a. 2007]. The reason behind choosing these protocos for the comparison can be expained as foows. In our work, we mainy focus on the path seection component of the routing soution (not on the route discovery component). This is because the beaconing process defined by ECMA-368 is fundamenta to any route discovery mechanism used in WPANs, where the path ength is imited to a few hops. Therefore, our work aims at deveoping a new path seection agorithm and compare it with commony used path seection schemes (e.g., min-hop and shortest-distance). These schemes are commony impemented by severa we known routing protocos (e.g., AODV and DSR). Note that the min-hop and shortest-distance schemes choose arbitrariy among the different paths of the same ength, ignoring ink quaity, thus not necessariy finding the best routes. One version of AODV (caed LOAD) was proposed to consider ink quaity in seecting the routes. Its routing metric is composed of the hop count (HC) and the number of weak inks (WL) aong the path. Specificay, the path cost is the tupe (WL, HC). Paths are ordered exicographicay according to this tupe. A path with cost (WL, HC ) is said to be better than a path with cost (WL 2, HC 2 ) if WL < WL 2, or if WL = WL 2 and HC HC 2. A weak ink is a ink whose quaity (i.e., received SNR) is ess than a given threshod. Our resuts are based on simuation experiments conducted using CSIM programs (CSIM is a C-based process-oriented discrete-event simuation package [CSI ]). The determination of interference and noise is done according to the physica (SINR) mode. We consider a muti-band UWB WPAN, where N nodes are uniformy paced within 20 x 20 meter 2 fied (Uness stated otherwise). This size is representative of reaistic depoyment scenarios (e.g., indoor offices, apartments, etc.). Nodes are randomy paired. For a given source-destination pair, the session ength is randomy seected in the range [0, 60] seconds. Once the session terminates, a new session is immediatey initiated with a newy seected duration. For a sessions, the traffic oad γ (in bps) of a reservation is a controabe parameter and is taken to be the same for a sessions. For simpicity, data packets are assumed to be of a fixed size ( KB). Other parameter vaues used in the simuation are given in Tabe II. These vaues correspond to reaistic hardware settings [Batra et a. 2004] [European Computer Manufacturers Association 2008]. 7.2 Resuts We mainy focus on five performance metrics: () network throughput (i.e., goodput), (2) PER, (3) Jain s fairness index (i.e., throughput fairness) (5) bocking rate, and (5) deficiency. To expain these metrics, we first carify the procedure for estabishing a session between two nodes. The source node starts by checking the avaiabe channe time, i.e., unreserved MASs in the superframe. If adequate