Maintaining communication and discovering new nodes using a dual transmitter approach implementing the Random Full or Half Speed, Random Speed, and

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1 Maintaining communication and discovering new nodes using a dual transmitter approach implementing the Random Full or Half Speed, Random Speed, and Random Direction channel hopping algorithms Institution:Carleton University Course: COMP 4905 Author: Michael Martino Supervisor: Dr. Michel Barbeau Date: November 22, 2013

2 Abstract The disparities between the usage of the regulated and unregulated bands are well noted. Work has been done to remedy the under usage of the regulated band. This project focuses on enhancing the work done by Barbeau et al. on three channel hopping algorithms known as Full or Half Speed, Random Speed, and Random Direction[1]. The idea for this project was to add an additional transmitter with the intention of using it to maintain communications with nodes discovered during a channel hopping search. The simulations are closely related to those performed in [1], allowing for direct comparisons to be made between the two. The simulation results illustrate that even with the added overhead of an additional transmitter, dual transmitter nodes implementing one of the three previously mentioned algorithms along with the Maintain Channel algorithm (developed for this project) outperform single transmitter nodes in every instance. Dual transmitter nodes discover their neighbours between 2 and 4 times as fast as their single transmitter counterparts.

3 Acknowledgements I would like to thank Dr. Barbeau for his guidance during this project and for allowing me to use his and his colleagues recent research on channel hopping algorithms as a basis for my research project. I would also like to thank Troy Hildebrandt for his unexpected contribution to the success of my project.

4 Contents 1 Introduction 1 2 Previous Work by Barbeau et al Full or Half Speed Algorithm Random Speed Algorithm Random Direction Algorithm Maintain Channel Algorithm 3 4 Simulation Model State Frame Model Consequences of a Successful Search Disadvantages of the Simulation Model Simulation Results 9 6 Conclusions 16

5 List of Figures 1 High level view of the state comparison model State comparison model of Full or Half Speed Algorithm[1] Example update after successful search Full or Half Speed Channel Hopping Algorithm (Dual Transmitter) Random Speed Channel Hopping Algorithm (10 nodes) Random Speed Channel Hopping Algorithm (20 nodes) Random Direction Channel Hopping Algorithm (10 nodes) Random Direction Channel Hopping Algorithm (20 nodes).. 15

6 1 Introduction The over usage of the unregulated radio spectrum and the under usage of the regulated radio spectrum have been examined and identified as challenges in a future where there are an increasing number of mobile and wireless technologies being developed. There is a significant amount of time where channels within the regulated band are unoccupied by primary users, being those users who have principal access to the band. These temporarily unoccupied channels could be used by secondary users. However, secondary users cannot depend on any single particular channel to be available at all times in these situations. This research project focuses on this problem; more specifically, it looks to add to the work done by Barbeau et al. in [1]. The authors propose a solution using channel hopping algorithms to allow for these secondary users to communicate on sets of commonly known channels. The three algorithms proposed are Random Full or Half Speed, Random Speed, and Random Direction. In [1], the time complexity of these algorithms is compared to other related algorithms such as the Jump-Stay Algorithm[2, 3] and the Random Channel Algorithm[4]. The authors also note their use of simulations to test the performance of these algorithms. There are a number of parameters to be accounted for, such as the number of secondary users in the network, the number of channels available to each user, and the number of commonly known channels between users. Barbeau et al. compare these algorithms via sets of simulations and conclude that in general, making abstraction of the guaranteed rendezvous property 1, random algorithms perform best.[1] The goal of this research project is to increase the speed with which secondary users are able to locate each other in the regulated spectrum. However, this project focuses on scenarios where there are more than two secondary users actively searching. Users, or more accurately nodes, in the previously mentioned algorithms only use one transmitter. In this project, nodes are created with two transmitters: a search transmitter and a maintain transmitter. The search transmitter executes one of Barbeau et al. s channel hopping algorithms. The maintain transmitter maintains previously established communications with any nodes discovered by the search transmitter. Nodes maintaining communication on the same channel are referred to as a neighbourhood throughout this paper. When two nodes discover each other, they determine the channel on which to maintain communications by exe- 1 An algorithm with a finite maximum Time to Rendezvous (TTR) is said to be guaranteed to rendezvous.[1] 1

7 cuting the Maintain Channel algorithm (Algorithm 1). In these instances, a migration occurs where smaller neighbourhoods relocate, or more specifically switch channels to that of the larger neighbourhoods. Overall, by doubling the number of transmitters per node, we are also doubling the cost. Therefore, this project looks to determine if there is a higher cost-benefit ratio to using two transmitters versus one. Previous work relating to this project is described in Section 2. In Section 3, the details of the Maintain Channel algorithm used to determine the channel on which two nodes will maintain communications is discussed in detail. Section 4 and Section 5 present a simulation model, referred to as a State Frame Model, used in this project followed by an analysis of single and dual transmitter nodes executing the algorithms described in [1]. In Section 6, conclusions are drawn and potential improvements and future work in this area are proposed. 2 Previous Work by Barbeau et al. This project relies on work by Barbeau, Cervera, Garcia-Alfaro, and Kranakis described in the paper Common Channel Selection in a Multipoint Cognitive Radio Network[1]. In this paper, the authors discuss the importance of dynamic channel hopping algorithms for communication in the regulated band. Specifically, they analyze previous work on the subject [2, 3, 4] and develop another set of improved algorithms to solve this problem. These algorithms are Full or Half Speed, Random Speed, and Random Direction. Each of these algorithms chooses a random channel on which to begin searching at the start of each round. 2.1 Full or Half Speed Algorithm In this algorithm, a node selects a speed with which to hop from channel to channel. It hops in a clockwise 2 direction. The speed selected is either full or half speed. When a node has selected full speed, it broadcasts on a channel for 1 time unit. If it has selected half speed, it broadcasts on a 2 Each node has an array of available channels. Channels are sorted in either ascending or descending order. Clockwise traversal refers to stepping through the array from index 0 to n 1 where n is the number of channels. Counterclockwise would be the inverse direction. 2

8 channel for 2 time units. This speed is reselected every round 3. When nodes discover each other, it is referred to as a rendezvous. Upon rendezvous, the round terminates. 2.2 Random Speed Algorithm This algorithm is a generalization of the Full or Half Speed algorithm. A speed is chosen between 1 and 1 where k 2. When a node is hopping at a k rate of 1, that node broadcasts on a channel for k time units. k 2.3 Random Direction Algorithm Instead of the traversal speed, this algorithm varies the direction traveled being either clockwise or counterclockwise. This model requires that a dummy channel be added to the set of available channels when there are an odd number of channels available. This is done to ensure that rendezvous can occur. At the beginning of each round, a node selects a new direction of channel traversal until rendezvous occurs. 3 Maintain Channel Algorithm The central feature added by this project to work of Barbeau et al.[1] is the use of a secondary transmitter for maintaining communications as well as an algorithm to facilitate the selection of that channel. The secondary transmitter is only useful in situations where a node searches for multiple other nodes. The maintain transmitter remains inactive until a node s first discovery using the search transmitter. There are no benefits to using the algorithm proposed by this project in a two user scenario. In previous works [2, 3], a single transmitter method is used to allow nodes who have discovered each other to maintain communications thereafter. It is noted in [1] that in these multiple-users, multiple-hops scenarios, rendezvous is repeatedly applied between pairs which ensures a global rendezvous between multiple users. A set of parameters are exchanged between nodes. The largest set is adopted by both, allowing them to hop the same way. As previously stated, an algorithm determining the channel on which to maintain communications is implemented for the dual transmitter node in 3 Each round is based on the number of channels available to a node. The round begins by searching on the first channel, cycling through each channel until the last channel has been inspected. 3

9 this project. This algorithm is executed when two nodes discover each other. During this discovery, nodes exchange information regarding the channel on which they are currently maintaining communications and the size of the associated neighbourhood. Therefore, both nodes have access to the current search transmitter s channel (sch), each other s maintain transmitter s channel (mcha, mchb), and their respective number of neighbours (na, nb). These are used as parameters to the Maintain Channel Algorithm (Algorithm 1) to determine the channel on which to maintain communications. Algorithm 1 Maintain Channel 1: Given sch, mcha, mchb, na, nb. 2: 3: if (mcha and mchb are uninitialized) then 4: return sch 5: else if (mcha or mchb is uninitialized) then 6: return the initialized one of {mcha, mchb} 7: else if (mcha = mchb) then 8: return mcha 9: else if (na > nb) then 10: return mcha 11: else if (na < nb) then 12: return mchb 13: else 14: return (((mcha + mchb) mod 2) = 0)? mcha : mchb 15: end if The outcome of this algorithm generally causes smaller neighbourhoods to migrate towards larger neighbourhoods. However, there are several other possible scenarios. For example, as seen in line 3 of Algorithm 1, there is a situation where both nodes are finding their first neighbour. This means that their maintain transmitter is currently inactive (hence the uninitialized maintain channel). Therefore, both nodes switch their maintain transmitter to the current search channel, and their search channel is reselected as described by [1]. There is also a situation where nodes have the same number of neighbours (line 13 of Algorithm 1). In this case, one of the two maintain transmitter s channels are arbitrary chosen using the given information. In every situation, the two nodes generate the same output from the initial exchange of information. 4

10 4 Simulation Model 4.1 State Frame Model The state comparison simulation model addresses the issue of nodes independently interacting with each other as well as accounting for random clock drift 4. This model is implemented using a single process. The main method of that process initializes a population of nodes, each selecting their own speed, direction, and other attributes based on the channel hopping algorithm[1] being implemented. Each node then generates an entire round of state frames which are sequentially added to a queue. These channel hopping algorithms can assign a new speed, start channel and direction at the end of each round. With this in mind, the simulation allows nodes to generate enough state frames to represent one round of searching. These state frames are the foundation of this model. The main process pops the head off of each node s queue and inspects each of these state frames. These frames represent one instant in time, and therefore, by comparing these frames, the process is able to determine if two nodes discover each other during this instant. If two nodes discover each other, there is a series of updates that are made; these are described in the next section. To illustrate this state model, Figure 1 depicts the queued state frames of four nodes. From a high level view of this model, each state frame is represented as a colored rectangle. Each color represents a node s search transmitter s channel. Each state frame represents its node s state during some fraction of a time unit (in Figure 1, a state frame covers 0.1 of a time unit). A state frame contains a reference to the node who created it and all of that node s relevant attributes at that given time unit. This includes the direction and speed it was traveling, it s search and maintain transmitter s channels, the total time that nodes has spent searching, and all of it s neighbouring node s IDs. For simplicity sake, Figure 1 only highlights a portion of each frame s attributes. When the simulation is initialized, each node chooses a random channel from some set of channels on which to begin its search. It also chooses its speed and direction as specified by a channel hopping algorithm in [1]. At this point, the main process discards a random number of state frames to offset the start times of each node. If a node has k frames discarded representing t time unit(s), then it means that this node has already occupied the regulated spectrum for t time units when the main process begins comparing state frames. Figure 1 illustrates four nodes who 4 Random clock drift refers to the phenomena that clocks do not run at exactly the same time as each other and over time drift farther apart. 5

11 Figure 1: High level view of the state comparison model have all chosen the same speed, traveling at 1 time unit per channel. When we closely examine the state frames of nodes 2 and 3, we can see that they discover each other after searching for 3 and 2.3 time units respectively. At this moment, both nodes have no neighbours which means that Algorithm 1 will return the current search channel as the channel that should be used by each node s maintain transmitter. While Figure 1 represent a generic representation of the node state model, Figure 2 illustrates an example of a state model generated using the Full or Half Speed algorithm[1]. In this example, we can see that nodes 2 and 3 are traveling at full speed as they produce five state frames per channel. In comparison, nodes 1 and 4 are traveling at half speed as they produce ten state frames per channel. 6

12 Figure 2: State comparison model of Full or Half Speed Algorithm[1] 4.2 Consequences of a Successful Search Once two nodes discover each other and determine a channel on which to maintain communications, the main process makes a series of updates to the simulation model. First, the remaining state frames of the two nodes who have discovered each other must be deleted. Each node resets it s total search time with that of the current frame being examined. As described in [1], a new round of searching is executed immediately after discovery. This means that a new speed, direction, and starting search channel are selected. Since a successful search occurred for each node during frames with time t and s respectively, these nodes need to generate new state frames representing new states after these specified times. In general, nodes never make direct contact with each other in the simulation; it is the main process that informs a node of the contact with another node. Therefore, when these independent timelines are compared, and they intersect (with respect to the channel), the remaining state frames are made obsolete. After executing Algorithm 1, nodes generate a round of output independently of nodes external to it s newly discovered neighbourhood. However, this discovery affects the other nodes in a neighbourhood (being those who are not under scrutiny by the main process) differently. Neighbourhoods that needs to migrate are informed by the node initially making contact. This migration does not affect the neighbouring node s current search execution state. Neighbours only need to update the size of their neighbourhood and the channel on which that neighbourhood is maintaining communications. As illustrated by Figure 3, state frames of these neighbours only need to have their maintenance related information updated; they do not need to generate another set of state 7

13 frames. In this example, nodes 1 and 2 find each other using their search transmitters. Node 2 is already part of a neighbourhood which includes node 4. Therefore, when the main process updates the model, both nodes 1 and 2 generate a new round of state frames and node 4 updates it s maintenance information. This state frame generation and comparison repeats until all nodes are communicating. Once global rendezvous occurs, the total search time of the last node to begin its search is used as the total execution time of that simulation. Figure 3: Example update after successful search 4.3 Disadvantages of the Simulation Model The state frame simulation model is relatively easy to implement, monitor, and understand, but while it is generally straight forward, it has several 8

14 disadvantages. For instance, when two nodes discover each other, their interactions are instantaneous. This model does not account for any handshaking time 5. This model does not require any message exchange and therefore avoids having additional time loss associated with message creation, the acknowledgement of messages between two parties, retransmission of lost messages, etc. These factors can also lead to situations where nodes occupying the same channel are not guaranteed to make contact with each other. However, in the state frame model, two nodes occupying the same channel are guaranteed to make contact. Another disadvantage of this model is the arbitrary partitioning of time represented by each state frame. When this model executes a simulation using the Full or Half Speed Algorithm[1] for example, nodes will hop channels at a rate of either full or half speed. When nodes hop at full speed, they produce 5 state frames per channel, and when nodes hop at half speed, they produce 10 state frames per channel. While the concept of partitioning time into smaller pieces appeared to be logical, the appropriate size of a partition (of 5 and 10 in this case) was not as evident. It is clear that a finer partition results in greater accuracy, but the specifics of a reasonable partition size was an unclear. Therefore, the choice to produce 5 and 10 states frames for the Full or Half Speed Algorithm[1] simulation was made arbitrarily. This question of accuracy was also an issue with regards to a reasonably sized k in the Random Speed Algorithm[1]. In this algorithm, nodes hop channels at a speed of 1. Again, in an arbitrary fashion, a random value of k where k 1 k < 10 was chosen. Therefore, nodes traveling at a speed of, 1, and produce 10, 4, and 2 state frames per channel. 5 Simulation Results In order to generate comparable simulations to those appearing in [1], a similar set of parameters is used to run sets of tests. Each test measures the Time To Rendezvous(TTR) in population sizes of 10 and 20 nodes, each hopping over 10 to 100 different channels. The nodes share a percentage of common channels ranging between 10% and 100%. Each of these combinations is evaluated by taking the average execution time over 500 rounds. These values and methods are the same as those used in [1]. For the single and dual transmitter models to be equivalent, the dual model must discover 5 This is the time required to exchange parameters between the two nodes, setting up before the intended communication occurs. 9

15 nodes twice as fast as its single transmitter counterpart as it bears approximately twice the cost with a second transmitter. Figure 4 illustrates the global Time To Rendezvous (TTR) of two population sizes of 10 and 20 nodes implementing the Full or Half Speed Algorithm. It has no equivalent simulation in [1], so no comparisons can be drawn between the two bodies of work. However, comparisons can be drawn between simulations executing the generalized version of this algorithm as depicted by Figure 5 and 6. In these figures, there are noticeable differences between simulations executing the Random Speed Algorithm on single and dual transmitter nodes. Figure 5 depicts simulations on a population size of 10. In this scenario, dual transmitter nodes increasingly outperform their single transmitter counterparts. However, to recount, dual transmitter nodes cost twice as much. With access to 10 channels, the cost-benefit ratio between the two types of nodes is nearly equivalent. As nodes gain access to more channels, the dual transmitter models have higher cost-benefit ratios compared to their counterparts; however, the difference is marginal. Looking at Figure 6 representing a population size of 20 nodes, the cost-benefit ratio is significantly better as nodes gain access to more channels. If we compare the simulations of nodes accessing 100 channels where 50% to 100% of those channels are the same, dual transmitter nodes achieve a global rendezvous approximately 4 times faster than their counterparts. Stated another way, dual transmitter nodes are twice as efficient as single transmitter nodes in a population of 20 nodes. Similar results are depicted by Figures 7 and 8 when we compare the single and dual transmitter models executing the Random Direction Algorithm in population sizes of both 10 and 20 nodes. Some results are inconceivable. For example, when the Random Direction Algorithm is implemented (with either 10 or 20 nodes) with 10 of the same channels, each node is able to detect all its neighbours in 1 time unit. This fact is easily explained by the following. At first, nodes occupy 10 channels (only the search transmitter is active). There is almost certainly a single discovery during this initial moment. If only two nodes detect each other, these two nodes will activate their maintain transmitters and all nodes will occupy a total of 11 channels (10 searching + 1 maintaining). As nodes continue to discover each other, they activate their maintain transmitters and they occupy two channels. A maintain transmitter s channel must be occupied by at least two nodes, but it may be occupied by all ten nodes as well. So, while there are a variety of situations that may occur, it is guaranteed that at least one discovery is being made during each round of 10

16 Figure 4: Full or Half Speed Channel Hopping Algorithm (Dual Transmitter) (a) 10 Nodes (b) 20 Nodes inspections on a set of state frames. In general, the dual transmitter graphs have a steadily increasing trend for set of tests which appears similar in shape to the graphs of the single transmitter data. This correlation is satisfying as it appears that our simulations follow a similar trend to that of [1] s simulation data. 11

17 Figure 5: Random Speed Channel Hopping Algorithm (10 nodes) (a) Dual Transmitter (b) Single Transmitter (Reproduced with permission of the copyright owner from [1]) 12

18 Figure 6: Random Speed Channel Hopping Algorithm (20 nodes) (a) Dual Transmitter (b) Single Transmitter (Reproduced with permission of the copyright owner from [1]) 13

19 Figure 7: Random Direction Channel Hopping Algorithm (10 nodes) (a) Dual Transmitter (b) Single Transmitter (Reproduced with permission of the copyright owner from [1]) 14

20 Figure 8: Random Direction Channel Hopping Algorithm (20 nodes) (a) Dual Transmitter (b) Single Transmitter (Reproduced with permission of the copyright owner from [1]) 15

21 6 Conclusions With these positive results in mind, there are a few areas of this topic that could be examined by future work on this subject. For example, dual transmitter nodes could have both transmitters implementing a channel hopping algorithm (instead of restricting one transmitter to serve as a means of maintaining communications as suggested by this project). Another interesting idea would be to create nodes with n transmitters and determine the number of transmitters a node should activate given a certain environment (number of channels available, number of nodes required to terminate search, etc.) to optimize the speed/power ratio for a node to discover k nodes. One could potentially tune a node to activate and deactivate transmitters dynamically with respect to that node s surrounding environment in order to ensure optimal functionality. There are also aspects of this project that could be modified to attain better results. As noted earlier, a node currently does not use it s maintain transmitter until it has discovered another node. This transmitter could initially be used to execute a one of the channel hopping algorithms until the first discovery is made at which point it would be used to maintain communications. One could also partition more state frames per channel to increase the accuracy of this simulation model. While this may not increase the speed with which a group of nodes discover each other, it will certainly be a more accurate representation of reality. However, I would suggest that if state frames begin to represent more specific moments in time, the total number of frames produced in one function call should also represent a smaller period of time. In conclusion, dual transmitter nodes outperform single transmitter nodes when implementing either the Full or Half Speed, Random Speed, or Random Direction[1] algorithms alongside the Maintain Channel algorithm (Algorithm 1) proposed earlier. The results of these simulations suggest that as single and dual transmitter nodes are equally assigned greater numbers of channels as well as being assigned to larger neighbourhoods, dual transmitter nodes increasingly outperform single transmitter nodes. In general, the results suggest that dual transmitter nodes discover their neighbours 2 to 4 times as fast as their single transmitter counterparts. 16

22 References [1] M. Barbeau, G. Cervera, J. Garcia-Alfaro, and E. Kranakis. Common Channel Selection in a Multipoint Cognitive Radio Network. June [2] Z. Lin, H. Liu, X. Chu, and Y.-W. Leung. Jump-stay based channelhopping algorithm with guaranteed rendezvous for cognitive radio networks. In Proceedings of IEEE INFOCOM, pages , April [3] H. Liu, Z. Lin, X. Chu, and Y.-W. Leung. Jump-stay rendezvous algorithm for cognitive radio networks. IEEE Transactions on Parallel and Distributed Systems, 23(10): , [4] N. Theis, R. Thomas, and L. DaSilva. Rendezvous for cognitive radios. Mobile Computing, IEEE Transactions on, 10(2): ,