Network Formation and Power Control EEL6935: Wireless Ad Hoc Networks Network Formation and Power Control Presented by: Gustavo Vejarano

An example taken from [1]: EEL6935: Wireless Ad Hoc Networks An example taken from [1]:

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EEL6935: Wireless Ad Hoc Networks Another example (Two Radio WMN. In [2], a protocol for this scenario is proposed):

These properties are, but not limited to: Connectivity [3] EEL6935: Wireless Ad Hoc Networks From the examples, it can be observed that by controlling the range assignment of each node, some properties of the network can be optimized. These properties are, but not limited to: Connectivity [3] Energy conservation [3] Capacity [3] Coverage [3] Multicast throughput [4] Congestion control [5] Is this related to Cross Layer Design? From the examples, it can be observed that by controlling the range assignment of each node, some properties of the network can be optimized. These properties are, but not limited to: Connectivity [3] Energy conservation [3] Capacity [3] Coverage [3] Multicast throughput [4] Congestion control [5] Is this related to Cross Layer Design?

Optimization example (intuitive approach) EEL6935: Wireless Ad Hoc Networks Optimization example (intuitive approach)

Topology control: Definition and Taxonomy EEL6935: Wireless Ad Hoc Networks Topology control: Definition and Taxonomy Topology control is the calculation and assignment of each node's transmitting range such that one or more characteristics of the network are approximately optimized or completely optimized whenever this is possible. Topology control taxonomy [3] Homogeneous (i.e., CTR) Nonhomogeneous Location based RA, SRA, WSRA Energy efficient communication Direction based Neighbor based

EEL6935: Wireless Ad Hoc Networks Location based (RA) (1) The problem is to find a connecting range assignment function RA that guarantees strong connectivity and that minimizes the cost measure (1) For 1-D networks, the Optimal1DRA algorithm [6] finds the optimal RA. The complexity is O(n4). Example on the board. For 2-D and 3-D networks, the problem is NP-Hard. An approximate solution is finding an MST in the symmetric version of the maxpower graph. The exact solution is only 4-6% better [3]. In [6], it is proved that

EEL6935: Wireless Ad Hoc Networks Location based (RA) (2) This is an example for the 2-D case taken from [3].

Location based (SRA, WSRA) (1) EEL6935: Wireless Ad Hoc Networks Location based (SRA, WSRA) (1) The RA problem generates communication graphs with bidirectional and unidirectional edges. Many MAC (e.g., 802.11) and routing (e.g., AODV) assume that all edges are bidirectional. In [7], the overhead generated for taking into account unidirectional edges is discussed. The Symmetric RA (SRA) and the Weakly SRA (WSRA) problems have solutions whose graphs' edges are symmetric:

Location based (SRA, WSRA) (2) EEL6935: Wireless Ad Hoc Networks Location based (SRA, WSRA) (2) In [3], an algorithm for the 1-D SRA case is proposed (example on board). Its complexity is O(n log(n)). The SRA and WSRA problems for the 2-D and 3-D cases are still NP-Hard. In [3], the proof of this statement is developed, and approximate solutions are mentioned too. The previously mentioned MST approximate solution for the 2-D and 3-D RA cases is also valid for the corresponding WSRA cases. RA, SRA, and WSRA comparison:

Location based (energy efficient) (1) EEL6935: Wireless Ad Hoc Networks Location based (energy efficient) (1) The basic idea is to find a subgraph G' of the maxpower graph G that has an energy consumption close to the optimum one achieved in the G graph. This energy consumption is evaluated for two different cases: unicast and broadcast. In the unicast case, the problem is stated as follows: Find a good power spanner G' of G, where a subgraph G' of G is said to be a power spanner of G if ρG'  O(1). ρG' is defined as follows.

Location based (energy efficient) (2) EEL6935: Wireless Ad Hoc Networks Location based (energy efficient) (2) Distance spanners, which are also power spanners, have been already studied in Computational Geometry [8]. Some of these spanners are: Relative Neighborhood Graph (RNG), Gabriel Graph (GG), Delunay Triangulation (DT), Yao Graph c (Ygc). In [9], a distributed algorithm for building a GG graph is presented. The basic idea is to make each node broadcast its position (e.g., GPS) and receive its physical neighbors' positions. Based on this information, the node makes a list of its logical neighbors according to the GG requirement.

Location based (energy efficient) (3) EEL6935: Wireless Ad Hoc Networks Location based (energy efficient) (3)

Location based (energy efficient) (4) EEL6935: Wireless Ad Hoc Networks Location based (energy efficient) (4) In the broadcast case, the problem is stated as follows: Find a good broadcast spanner G' of G, where a subgraph G' of G is said to be a broadcast spanner of G if βG'  O(1). βG' is defined as follows: This is an NP-Hard problem. An approximate solution is the Broadcast Incremental Power algorithm [3]. The idea is to find a spanning tree at each node, and then, to define the edges of the approximate G' (GBIP) as the set equal to the union of all the edges found at each node. The approximation ratio is between 13/3 and 12.

Topology Control Algorithms (1) EEL6935: Wireless Ad Hoc Networks Topology Control Algorithms (1) So far, the algorithms have been centralized. Although they gave us a general picture of Topology Control, they are not suitable for many real world applications. By definition, MANETs lack a centralized authority. Therefore, distributed algorithms are definitely necessary. In a distributed environment no node is aware of the complete network. They are aware only of their surroundings. The topologies generated are only approximate solutions to the optimal ones. It must be kept in mind that some of the optimization problems to be addressed by the algorithms have conflicting goals. Therefore, some relaxation of the problem specifications should be allowed in order to come up with practical solutions.

Topology Control Algorithms (2) EEL6935: Wireless Ad Hoc Networks Topology Control Algorithms (2) Design guidelines [3]: Be fully distributed and asynchronous Be localized Rely on bidirectional links only Rely on “low quality” information (neighbors' position: GPS, direction: directional antennas, distance: power estimation) Preserve connectivity (worst case connectivity, connectivity w.h.p.) Generate a topology with small physical node degree (worst case: n-1 physical neighbors, w.h.p.: bounded number of physical neighbors)

Location based algorithm (1) EEL6935: Wireless Ad Hoc Networks Location based algorithm (1) The R&M algorithm: All to one algorithm suitable for WSNs. The problem is to find the reverse spanning tree of minimum energy cost rooted at the master node. R&M is based on the enclosure and neighbor set for minimizing the energy consumption. The idea is to distributively build the enclosure graph, and then to execute the Bellman- Ford algorithm for finding the minimum reverse spanning tree.

Location based algorithms (2) EEL6935: Wireless Ad Hoc Networks Location based algorithms (2) The Local MST (LMST) algorithm: It is a distributed algorithm for estimating the MST. The objective is to achieve the good characteristics of the MST in a distributed way. The algorithm: Each node broadcasts at max power its ID and position Each node builds its local MST on its visible neighbors The set of edges in the communication graph is the union of all the one-hop connections in every node's local MST. The communication graph is made symmetric by finding the symmetric supergraph or the symmetric subgraph. The LMST algorithm preserves connectivity in the worst case, so the number of physical neighbors could reach n-1. Also, the algorithm has a maximal logical node degree equal to 6.

Direction based algorithms (1) EEL6935: Wireless Ad Hoc Networks Direction based algorithms (1) The CBTC algorithm: It makes use of directional antennas for estimating the neighbors' angle of arrival (AoA). The algorithm: Each node broadcasts its ID and TX power and ACKs every received broadcast with its ID and TX power. This is done with increasing power until there is at least one physical neighbor in the cone of angle ρ when this is swept all around the node. The final graph is made symmetric. It guarantees connectivity, but it generates a high number of messages. Other versions of the algorithm take advantage of the directional antennas for setting only the necessary power in each direction and are also able to guarantee k-connectivity.

Direction based algorithms (2) EEL6935: Wireless Ad Hoc Networks Direction based algorithms (2) Finding the transmission power in the CBTC algorithm: The DistRNG algorithm: It is a distributed algorithm for finding the RNG from the maxpower graph. The goal is to achieve the good characteristics of the RNG: relatively low logical node degree, hop diameter is not too large, the average RA is low.

Neighbor based algorithms (1) EEL6935: Wireless Ad Hoc Networks Neighbor based algorithms (1) The KNeigh algorithm: It is a distributed protocol that assures connectivity w.h.p. based on the results found for the solution of the CNN problem. The Critical Neighbor Number (CNN) problem: n nodes are randomly distributed according to certain distribution in a region of area R. What is the minimum number of physical neighbors such that the network is connected w.h.p.? The solution [3]:

Network based algorithms (2) EEL6935: Wireless Ad Hoc Networks Network based algorithms (2) The KNeigh algorithm: Every node transmits at its ID at max power Based on this information, every node finds its k closest neighbors. K is a common parameter determined according to the previously presented table. Every node broadcasts its list of k neighbors at max power Every node erase from its list the neighbor nodes that are not connected to it (i.e., symmetric subgraph is established) Every node sets its power so that it can reach its farthest neighbor KNeigh is resilient to errors in the neighbor distance estimation [3]. It has a bounded limited number of physical neighbors. It does not require additional hardware.

The Range Assignment and Multicast Throughput [4] (1) EEL6935: Wireless Ad Hoc Networks The Range Assignment and Multicast Throughput [4] (1)

The Range Assignment and Multicast Throughput [4] (2) EEL6935: Wireless Ad Hoc Networks The Range Assignment and Multicast Throughput [4] (2) The problem is stated as follows: This is an optimization problem that the authors solve by dividing the problem in two independent optimization problems. One of them is at the physical layer (i.e., range assignment problem), and the other one is at the network layer (i.e., multicast routing problem). Based on the problems' solutions, an algorithm is proposed.

EEL6935: Wireless Ad Hoc Networks Conclusions The topology control was presented as the calculation of the transmitting range of the nodes in the network such that one or more characteristics are optimized. The taxonomy of topology control was reviewed, and the nonhomogeneous classification was covered. Algorithms for the RA, SRA, and WSRA problems were presented. The energy efficient unicast and broadcast communication was studied. Distributed algorithms were presented for the location, direction, and neighbor based approaches. An example for the design of a distributed algorithm for optimizing multicast throughput was presented.

Note: This presentation is mainly based on the work reported in [3]: EEL6935: Wireless Ad Hoc Networks Note: This presentation is mainly based on the work reported in [3]: P. Santi, Topology Control in Wireless Ad Hoc and Sensor Networks, John Wiley and Sons, Chichester, UK, July 2005.

References (1) EEL6935: Wireless Ad Hoc Networks [1] R. Hincapie, J. Sierra, R. Bustamante, "Remote Locations Coverage Analysis with Wireless Mesh Networks based on IEEE 802.16 Standard," in IEEE Commun. Mag., vol. 45, no. 1, pp. 120-127, Jan. 2007. [2] J. J. Huei and I. Rubin, "Backbone Topology Synthesis for Multiradio Mesh Networks," IEEE J. Sel. Areas Commun., vol. 24, no. 11, pp. 2116–2126, Nov. 2006. [3] P. Santi, Topology Control in Wireless Ad Hoc and Sensor Networks, John Wiley and Sons, Chichester, UK, July 2005. [4] J. Yuan, Z. Li, W. Yu, and B. Li, "A Cross-Layer Optimization Framework for Multihop Multicast in Wireless Mesh Networks," IEEE J. Sel. Areas Commun., vol. 24, no. 11, pp. 2092–2103, Nov. 2006. [5] M. Chiang, "Balancing transport and physical layers in wireless multihop networks: Jointly optimal congestion control and power control," IEEE J. Sel. Areas Commun., vol. 23, no. 1, pp. 104–116, Jan. 2005.

EEL6935: Wireless Ad Hoc Networks References (2) [6] L. Kirousis, E. Kranakis, D. Krizanc, and A. Pelc, "Power consumption in packet radio networks," 2000 (available at http://citeseer.ist.psu.edu/cache/papers/cs/27548/http:zSzzSzwww.scs.carleton. cazSz~kranakiszSzPaperszSztcs.pdf/power-consumption-in-packet.pdf) [7] M. Marina and S. Das, "Routing performance in the presence of unidirectional links in multihop wireless networks," Proc. ACM Mobihoc 02, Lausanne, pp. 12– 23. (available at http://www.cs.pitt.edu/~mosse/3510/routing-unidr.pdf) [8] J. Goodman and J. O'Rourke, Handbook of Discrete and Computational Geometry. CRC Press, New York, 1997. [9] W. Song, Y. Wang, X. Li, and O. Frieder, "Localized algorithms for energy efficient topology in wireless ad hoc networks," Proc. ACM MobiHoc, Tokyo, pp. 98–108. 2004