Grid-Based Channel Resource Allocation and Access Scheduling Using Latin Squares in Wireless Mesh Networks

Grid-Based Channel Resource Allocation and Access Scheduling Using Latin Squares in Wireless Mesh Networks Di Wu and Lichun Bao Donald Bren School of ICS, University of California, Irvine, USA Abstract Wireless communication channels are scarce shared resources in large scale wireless mesh networks (WMNs), and the network system performance is frequently plagued by hidden terminal interference in multi-hop scenarios. We propose a set of efficient channel resource allocation and access scheduling algorithms based on Latin squares for WMNs with multichannel communication capabilities, called (Grid-based channel Allocation and Access scheduling using Latin Squares). By forming grids over the WMN deployment area with nodal location information, maps Latin squares to the grids, and dynamically assigns multiple channels to the WMN grids for channel access scheduling purposes. The fairness of is analyzed in multi-flow multi-hop mesh networks with multichannel capabilities. The simulation results show that achieves much better performance than IEEE. DCF and other multi-channel access control protocols. I. INTRODUCTION Wireless mesh networks (WMNs) provide a cost-effective and performance-adaptive networking paradigm to deliver ad hoc and last-mile Internet access services. WMNs based on IEEE. standards [], also known as WiFi, have attracted special interests due to its simplicity of channel access control functions, low unit cost, flexibility for reconfigurations and wide acceptance in both -users and research communities. The medium access control (MAC) protocols in IEEE. standards [], such as DCF (distributed coordination function), all based on CSMA (carrier sensing multiple access) mechanisms. In mission critical applications, WMNs based on IEEE. protocol suite are unable to deliver the full channel capacity to the applications due to increasing channel overheads and severe interference caused by hidden terminals. One of the core issues is to address the channel resource sharing problem in distributed wireless environments. New coordination functions that compreh the various requirements of the wireless applications are long sought after. In this paper, we focus on the channel resource sharing problem under two research thrusts in wireless networks with single-radio multi-channel (SRMC) communication capability assumptions, ) the channel resource allocation problem, which asks for dynamic and adaptive conflict-free channel assignments to individual nodes or clusters in wireless networks in the macro-time scale; ) the multiple channel access control problem, which asks for collision-free packet transmissions in the micro-time scale. Such channel resource coordination functions are especially challenging due to inherent distributed nature of large scale wireless networks. This work was sponsored in part by the Raytheon Company under Grant No. RC-. ----//$. c IEEE The channel allocation and access scheduling problems have been extensively studied in the literature. MMAC used the beacon messages to synchronize the wireless nodes and negotiate the channel allocations []. The allocation and scheduling of partially overlapped channels in WMNs were discussed in []. WMNs with SRMC capabilities were addressed in []. Although beneficial for channel throughput, switching among multiple channels may results in disconnections in WMNs. Interference-aware topology control and QoS routing in multichannel wireless mesh networks were considered in []. In this paper, we propose a set of algorithms, called (Grid-based channel Allocation and Access scheduling using Latin Squares), that applies Latin squares [] on the aforementioned two research thrusts the channel resource allocation problem and the multiple channel access control problem in WMNs with SRMC communication capabilities. applies Latin squares in two time scales macrotime scale for the channel assignment, and micro-time for the channel access, both are deterministic due to the use of Latin squares. In addition, is capable of dynamic ondemand allocation of channel resources so as to improve the channel utilization efficiency. The basic ideas and contributions of include: To organize the network into grids and clusters according to location information; To guarantee the network connectivity using grid shifting; To achieve efficient channel utilization in each cluster using compact Latin square based channel access schedules; To guarantee fairness of the channel allocation to each grid point and each node. The rest of paper is organized as follows. Section II introduces the Latin squares concept. Section III describes the on-demand channel access scheduling mechanisms, and Section IV presents the channel allocation algorithm in WMNs, including grid infrastructure formation, channel allocation, channel access scheduling, network connection maintenance, and transmission schemes. Section V presents the simulation results of in WMNs with SRMC communication capabilities. Section VI concludes the paper. II. RELATED WORK A Latin square of order n is an n n square matrix that consists of n symbols {,,,n}, in which the symbols of each row and column are also distinct. Exting the Latin square concept, a k-dimensional Latin hypercube of order n is a k-dimensional array H k = [h i,i,,i k ] in which each row is a permutation of symbols,,,n []. Suppose n +

is a prime number, and vectors A = [a i ] and B = [b i ] (i =,,,n) are two permutation arrays of symbol set {,,,n}, then a Latin square L n n =[l i,j ] of order n can be generated by multiplying the transpose of vector A, and vector B using the modulo multiplication operation: L n n = A T B, in which () l i,j = a i b j mod (n +), i,j {,,,n}. Although IEEE. DCF works in small networks, the BEB (binary exponential backoff) mechanism does not eliminate packet collisions due to its randomness in deriving the backoff intervals. MALS [] applied Latin square to calculate the backoff interval. In MALS, the rows of a Latin square are assigned to individual nodes, and the columns to time slots. A B C D A B C D A B C D A B C D t t t t Time Frame T Fig.. Channel Access Backoff Mechanism According to Latin Squares For instance, Fig. illustrates the Latin square assignments to nodes and time slots in a small network with four nodes A, B, C and D. In Fig., the time is structured by periodic time frames, which are further divided into time slots of period t i, i =,,,. In each time slot, the backoff intervals of each node for channel access (represented by the yellow hexagons) is equal to the Latin square symbol of the corresponding time slot. Because of the distinctiveness of Latin square symbols assigned to the nodes in each time slot, MALS eliminates potential packet collisions from different nodes. Using this mechanism, MALS can be implemented by simply replacing the backoff computation module in IEEE. DCF. In practice, the duration of a time frame can be around tens of milliseconds, and a time slot can last a few milliseconds. III. : CHANNEL ACCESS SCHEDULING A. Network Assumptions We consider wireless mesh networks (WMNs), in which each node knows enough location information of itself and its neighbors. In addition, we assume that each node in WMNs is equipped with a single radio and an omni-directional antenna, capable of switching between multiple channels, and each radio only works in half-duplex mode, i.e. may only receive or transmit at a time, but not both. In WMNs, we follow the protocol model discussed in [], and model the effective ranges of radio communications in three categories, namely the transmission range R tx, the carrier sensing range R cs and interference range R i. The carrier sensing range R cs is an adjustable parameter in the physical layer modules, and is usually set to to. times R tx []. Therefore, the two-hop distance in WMNs is a good approximation of the carrier sensing range, and node activation scheduling usually requires all neighbors of a node within two hops be silent when the node transmits. time B. On Demand Channel Access Scheduling It is usually the case that only a subset of the network nodes require channel access for data forwarding purposes. Hence, instead of assigning a Latin square row to each node in the wireless networks, we map the Latin square rows to different colors, and in turn assign colors to nodes with traffic forwarding demands using graph coloring algorithms. The graph coloring is to achieve conflict-free color assignments to nodes within two hops of each node. For coloring purposes, each node maintains a coloring table, denoted by ctab, consisting of the following information: Node ID, denoted by nodeid, which is usually the MAC address of the node. Color assigned to node i, denoted by mycolor i. When a node has no color assigned, its mycolor i =. The color bitmap of node i s one-hop neighbors, denoted by onehop. Expiration time. Each coloring tuple is refreshed when the tuple is updated by the corresponding node. The basic mechanism of the conflict-free color assignment is to exchange one-hop neighbor colors between adjacent nodes by piggybacking the color tuple (nodeid, mycolor i, onehop i ) information in every data frame sent by node i. Fig.. MAC Header mycolor onehop bits bits Payload Packet Format with Coloring Information. Fig. illustrates the coloring information included in the header of data frames in. As we see beside the normal MAC header and payload fields, the colors are represented using two bitmaps, one for the transmitting node itself, and the other for its one-hop neighbors. Assuming that two-hop neighborhood has less than nodes active for data packet transmissions, the coloring bitmap is set -bit long, in which each bit represents a color that has been taken or not by setting the bit to or, respectively. The color assignment algorithm consists of two parts at the transmitter and the receiver, respectively. Algorithm : Piggybacking Color Information on Outgoing Packets Input: node i s color table ctab, and an outgoing packet p Output: Outgoing packet p with color information p.mycolor ctab[i].mycolor; p.onehop ; for j ctab do if j p.dst then p.onehop p.onehop ctab[j].mycolor; S p; Algorithm specifies the steps to attach coloring information on the outgoing data frame at a node. On line, the packet registers the transmitter s own color information. On lines -, the transmitter finds all the colors of its onehop

neighbors, and maps them to the bitmap p.onehop using the logic OR operation, denoted by on line. Line calls the S function to transmit the packet. Note that, on Algorithm line, the one-hop color map excludes a special one-hop neighbor the destination of the packet. This is because the bitmap p.onehop is used by the destination to search for its own color and resolve possible color assignment collisions. If the destination has no color assignment, it will use the coloring information from all its one-hop neighbors to find an unused color for itself. Otherwise, if it finds that it own color has been used in the color bitmap of the received packet, it finds a color assignment collision, and has to look for another color, again. Algorithm : Node Coloring Using Received Packet Input: node i s color table ctab, and received packet p Output: node i s color // Broadcast destination? if p.dst then if ctab[i].mycolor then // Mask out node i s color. p.onehop p.onehop & ctab[i].mycolor; // unicast packet to node i? else if p.dst i then if ctab[i].mycolor then if ctab[i].mycolor & p.onehop then conflict true; // unicast packet to other nodes? else if p.dst i and ctab[i].mycolor then p.onehop p.onehop & ctab[i].mycolor; // Record coloring information in ctab RecordColor(p.src, p.mycolor, p.onehop); if conflict then // Search for a new color. RecomputeColor(i); Algorithm specifies the coloring conflict resolution process once a node i receives a packet p. Several logic operation notations are used in the algorithm, such as binary negation of a binary number using the overline, and operation using &. The broadcast address is represented using all s, which is equal to. Two functions, RecordColor(i) and RecomputeColor(i), are not provided but explicit and simple enough to implement easily. In Algorithm, lines - and - simply record the coloring information of packet p after masking off node i s own color. If packet p is destined to node i itself, then the existence of the same color as node i s in packet p s onehop color map indicates a coloring conflict with node i, as shown on lines -, which invokes the re-computation of node i s color assignment on lines -. If packet p is destined to other nodes, node i simply records the coloring information after masking off its own color on lines -. Once the color assignment to each node is derived, the Latin square row assignments to different nodes is automatically achieved according to color to Latin square row mapping. In multi-hop wireless networks, the color assignment happens when a routing path is established between a source and its destination. That is, when a unicast RREP (route reply) message is sent from the destination to the source. While in the first phase of route discovery that uses RREQ (route request) broadcast messages, color assignments are learned but not assigned to the nodes along the source to destination path. IV. : GRID-BASED CHANNEL ALLOCATION IEEE. DCF has implemented several collision avoidance mechanisms, such as RTS, CTS and ACK handshaking to avoid hidden terminal problems. However, due to the different impact ranges of wireless transmissions, i.e., the ranges for transmission, carrier sensing and interference, These mechanisms occasionally fail to avoid hidden terminal problems in multi-hop wireless networks. Instead, a grid-based spatial division multiple access scheme has to be applied in, and CSMA scheme has to be limited within individual grids. A. Network Grid Formation Similar to the channel allocation scheme in cellular networks, we allocate channel resources in a grid formation. Fig.. Network Grid Formation The left-hand side of Fig. shows the -cell clustering scheme, which is applied in channel reuse by the cells with the same number assignments. Similarly, we organize WMNs by the grid and the grid cluster. For simplicity, we choose a square grid formation scheme with -grid clusters as shown on the right-hand side of Fig.. Given multiple channels in a multi-hop wireless network, we will apply the same channel assignment results to all the -grid clusters. We assume the wireless nodes have the same transmission range. Similar to cellular technology, each grid edge is set to be twice the transmission range so that the distance between two nearby grids with the same channel allocation is about three times the side length. Such a separation of the same channel allocation guarantees interference freedom for concurrent transmissions over the same channel. B. Channel Allocation In WMNs, especially those based on IEEE. standards, we have limited number of channels for a full and conflict-free channel assignment to the wireless grids. These limited amount of channels have to be time-shared among all the network

grids. There are two methods to assign channels, namely the one based on Latin square and the other based on Latin cube. Fig. (a) shows a sample Latin square of size, which is generated by prime number as illustrated in Eq. (), for channel allocation purposes. In this example, we assume there are available channels. In order to assign these channels into each -grid cluster, we map the grids to the rows of the Latin square, and the time slots to the columns. (a) Latin Square Based Allocation Fig.. T TTT C C C C C C C C C C T TTT T T G G G G G G G G G G N/A (b) Latin Cube Based Allocation Channel Allocation in. For each grid cluster, channels,,, will be allocated to grids that have been assigned with Latin square symbols,,, during every time slot, correspondingly. For instance in Fig. (a), in time slot T, gridsg, G, and G are allocated with channel C, C, C, respectively. However, when we apply the Latin square in the -grids cluster, the required Latin square symbols may appear on the last row of the Latin squares in some time slots, which does not map to any existing grids. In this case, we swap the required Latin square symbols on the th row with the Latin square symbol located on other rows, so as to map the corresponding channels to the existing grids. Fig. (b) shows another way of allocating the channels to grids of each -grid cluster using Latin cubes. The Latin cube used in Fig. (b) was generated by prime number too. The grids, channels and time slots are mapped to the columns, rows and layers of the Latin cube. In each time slot, the channels are allocated to individual grids if the grid has a symbol on the corresponding rows. Similar to Latin square based channel allocation, the symbol may appear on the last column, which maps to none of the grids in our scenario. In this case, we shift the channel mapping by skipping the rows that give no channel allocations. For instance, because row does not map symbol to any of the existing grids, the channel mapping skips over row and maps channel to row in Fig. (b). In other cases, the number of channels may be more than that of the grids. It can be resolved by taking a modulo operation on the number of channels by the number of grids, and the remainder number of channels still follows the same channel allocation algorithms as illustrated in Fig. (a) and (b). As for the other channels which are multiples of the number of grids, we evenly allocate them over all the grids. However, the utilization of multiple channels with each grid is a separate issue, not addressed in this paper. Once a grid is assigned a channel, the wireless nodes inside the grid can communicate using the channel access protocol, specified in Section II. While wireless nodes that are inside grids without any channel allocated have to remain silent during the corresponding time slots. C. Grid Shifting Note that time slot for channel allocation is different from the time slot for channel access. In order to explain the temporal relationship between the time units for channel access scheduling and channel allocation, we introduce the notation: Denote t acc and T acc as the time slot and time frame durations for channel access schedules, respectively, and t all and T all for channel allocation schedules. In addition, denote the size of the Latin square for channel access scheduling as L acc, and that for channel allocation as L all. Then the relations between these components are: T acc = t acc L acc, () t all = T acc, () T all = t all L all = t acc L acc L all. () The reason that each channel allocation time slot includes four access time frames T acc in Eq. () is due to the grid shifting operation to maintain network connectivities. This is because when different channels are allocated to the grids in the virtual grid based mesh network, wireless nodes that belong to different grids and channels cannot communicate with each other, thus potentially breaking the existing network connections. In order to guarantee the network connectivity, we have to apply a grid shifting algorithm so as to ensure that every pair of neighbor nodes have a chance to stay in the same channel to communicate. (a) (b) Step : Right (c) Step : Down Fig.. (d) Step : Left Four-Step Grid Shifting for Channel Allocations (e) Step : Up We schedule channel access periods in four steps, as shown in Fig.. In each step, the grid coordinate origin shifts in four directions consecutively, which are right, down, left and up directions, respectively. During each step, the grid only shifts half of the grid size. Because nodes may belong to different grids of a grid cluster in the four steps, every node needs to re-calculate its channel number in each step. In practice when we build a WMN using IEEE. devices, a reasonable configuration about the temporal relations between channel access and channel allocation periods is to set t acc =ms, T acc =ms, t all = ms and T alloc =.s, when the Latin square size for channel access is L acc =, and L all =. That is, the longest interval for activating a grid

is up to. seconds using our grid-based channel allocation scheme in the worse case scenario. Lemma : The four-step grid shifting algorithm guarantees that each and every network connection can be activated on the same channel. Proof: We prove the lemma using a heuristic by throwing sticks into the grids, as shown in Fig.. The length of a stick is the transmission range of the wireless nodes in WMNs. Because each grid in Fig. represents an area in which all wireless nodes have the same channel assignment, the fact that the stick crosses none of the grid boundaries proves that the points of the stick can communicate over the same channel within one of the four steps in the grid shifting algorithm. In Section IV-A, we have designed the grid formation such that the edge length of each grid is twice the transmission range of wireless nodes. In addition, the grid shifting algorithm has applied grid shifting steps by half of the grid size, which is exactly the transmission range of wireless node. Therefore, we have these intermediate conclusions: The grids are symmetric, which means that the analysis about any grid applies to all other grids. Fig.. ) ) ) ) Stick contained in a grid. ) ) ) ) Stick contained after the first shift. ) ) ) ) Stick contained after two shifts. Network Connection Activation in One of the Grid Shifting Steps. The stick, representing the spatial one-hop neighbor relation, has only three ways of placement in a grid: ) completed contained in a grid, ) crossing boundary of two adjacent grids, and ) crossing two boundaries of adjacent grids, which are represented in Fig.. Figure shows that all the three possible placements of sticks can be contained within a grid in one of the four-step grid shifts. Otherwise, the length of stick would have to be longer than half the grid size. D. Channel Transmission Scheduling Because the channels are allocated and accessed according to grids in, the neighbors of a node may not always be on the same channel as the node. Therefore, the node needs to carefully schedule in which time slot(s) to transmit a packet, and how many times the packet has to be transmitted. If the node transmits a broadcast packet, it has to schedule the transmission of the broadcast packet for up to times in order to reach each and every one-hop neighbor. If the node transmits a unicast packet, it has to schedule the packet transmission while the node and its one-hop destination are located within the same grid. If the packet is unicast, the packet only has to be sent once to the correct receiving one-hop neighbor in the corresponding time slot, when the two neighbors are in the same grid point. If the packet is broadcast or multicast, the packet has to be resent in multiple time slots so that the corresponding neighbors could receive the packet. One way to implement such multi-channel packet transmission scheduling is to maintain a separate packet buffer for each channel. Data packets are placed in a channel buffer on a node if the one-hop neighbor will join the the same channel as the node itself in the nearest future. V. PERFORMANCE EVALUATIONS In order to evaluate the effectiveness of mechanism in more practical scenarios, we implemented in NCTUns v. []. The channel access scheduling problem is completely indepent of the routing protocols. Therefore, we use AODV to test our algorithms, and compare the performance of our protocols with other existing solutions. The performance of, compared with. DCF and MMAC, is evaluated in two simulation scenarios. The first is in a fully connected network scenarios with multiple CBR (constant bit rate) flows, and the second is in a multi-hop multi-flow networks with SRMC communication capabilities. The Latin squares are assigned using graph coloring. In our simulations, the transmission range of each node is set to m and the carrier sense range is m. The packet size of the CBR traffic is set to bytes, and the link bandwidth for each channel is Mbps. We assume that nine non-overlapping channels are available for SRMC operations. A node may be the source and destination for multiple flows. Each simulation was carried out for a duration of seconds, and the delay, jitter and network throughput performance metrics are collected in each run. A. Fully Connected Network In fully connected networks, we placed nodes in a m m area and created CBR flows between random pairs of nodes. All nodes are within each other s transmission range. Such a scenario is rather to examine the performance of channel access scheduling protocols by comparing with IEEE. DCF protocol. Fig. shows the average -to- CBR traffic performance. Because adopts the CSMA scheme as well as a deterministic backoff function based on Latin square assignments, and removes the control overhead on RTS/CTS and ACK frames, provides about % higher throughput, % lower average delay and % lower delay jitters than IEEE. DCF under different network loads in -node network scenarios. B. Multi-hop Multi-flow Network In order to evaluate the performance of in multihop multi-channel WMNs, we simulated another multichannel access control protocol, MMAC [], along with and IEEE. DCF. Unfortunately, the only available MMAC implementation was programmed in NS

Nodes ( CBR Flows) Nodes ( CBR Flows) Nodes ( CBR Flows)....... Average Delay (s).. Delay Jitter... Throughput (KBps)............... Load Rate (Mbps) Load Rate (Mbps) Load Rate (Mbps) (a) End-to-End Delay (b) End-to-End Delay Jitter (c) End-to-End Throughput Fig.. Average End-to-End Attributes in -Node Scenario with CBR Flows Nodes ( CBR Flows) Nodes ( CBR Flows) Nodes ( CBR Flows) Normalized Delay (ratio)... MMAC Normalized Jitter (ratio)... MMAC Normalized Throughput (ratio)..... MMAC Packet Arrival Rate per flow (packet/sec) Packet Arrival Rate per flow (packet/sec) Packet Arrival Rate per flow (packet/sec) (a) End-to-End Delay (b) End-to-End Delay Jitter (c) End-to-End Throughput Fig.. Performance Comparisons in -Node Multi-hop Wireless Networks with CBR Flows. simulator [], and a side-by-side direct comparison between MMAC, and IEEE. DCF is impossible. Fortunately, both NCTUns and NS simulators have implemented IEEE. protocols for ad hoc and wireless mesh networks, enabling us to use the performance of IEEE. DCF in the respective simulators as a baseline for overall comparisons. That is, we run the same simulation scenarios, which is to place = nodes over an area of size m m, and to use channels and create CBR flows in the multi-hop wireless networks. After the delay, jitter and throughput metrics are collected, we compare the performance of the three protocols, relative to the corresponding performance of IEEE. DCF. Therefore, the performance of. is normalized to be in every metric. Such an approach eliminates a lot of non-critical simulation assumptions, such as the network data rate, packet size, wireless signal propagation models etc., and keeps only the critical information about the relative advantages or disadvantages of different protocols. In addition, normalization based on a reference protocol also allows to compare different simulation results in fewer figures. Fig. shows the relative performance of and MMAC, normalized on the corresponding performance of IEEE. DCF. As we can see, provides the lowest delay and jitter and the highest network throughput under most network loads, while IEEE. DCF performs the worst. VI. CONCLUSION We have presented, a novel grid-based medium access protocol using Latin squares for channel allocation and channel access scheduling purposes in wireless mesh networks with multiple channel communication capabilities. In, the network is organized into grids and clusters according to location information, and guarantees the network connectivity using the grid shifting algorithm. The channel access efficiency and fairness were achieved by using compact Latin square based channel access and channel allocation schedules. Especially, we have applied Latin squares to the IEEE. DCF backoff algorithm to avoid the hidden terminal problem in multi-hop WMNs. Our simulation results show that has strong advantages over IEEE. DCF and MMAC, in fully connected network and in multi-hop multi-flow WMNs with SRMC capabilities. REFERENCES [] IEEE Std.. Wireless LAN Medium Access Controlf (MAC) and Physical Layer (PHY) Specifications. Technical report, IEEE, Jul.. [] E. Aryafar, O. Gurewitz, and E.W. Knightly. Distance- Constrained Channel Assignment in Single Radio Wireless Mesh Networks. In INFOCOM,. [] L. Bao. MALS: Multiple Access Scheduling Based on Latin Squares. In Proc. IEEE MILCOM, Monterey, CA, Oct. - Nov.. [] P. Gupta and P.R. Kumar. The capacity of wireless networks. IEEE Transactions on Information Theory, :,. [] C.E. Laywine and G.L. Mullen. Discrete Mathematics Using Latin Squares. Wiley-Interscience,. [] A.H. Mohsenian and V.W.S. Wong. Partially Overlapped Channel Assignment for Multichannel Wireless Mesh Networks. In ICC,. [] J. So and N. H. Vaidya. Multi-channel MAC for ad hoc networks: Handling multichannel hidden terminals using a single transceiver. In MOBIHOC, pages,. [] J. Tang, G. Xue, and W. Zhang. Interference-Aware Topology Control and QoS Routing in Multi-Channel Wireless Mesh Networks. In MOBIHOC,. [] S.Y. Wang, C.L. Chou, C.H. Huang, C.C. Hwang, Z.M. Yang, C.C. Chiou, and C.C. Lin. The Design and Implementation of the NCTUns. Network Simulator. Computer Networks, ():, Jun.. [] NS- web site. availabe at http://www.isi.edu/nsnam/ns/. [] K. Xu, M. Gerla, and S. Bae. How effective is the IEEE. RTS/CTS handshake in ad hoc networks? In GLOBECOM, pages,.