Introduction to Wireless Networks Davide Bilò

Wired vs Wireless Wired Networks: data is transmitted via a finite set of communication links (physical cables) Wireless Networks: data is transmitted via etere using electromagnetic waves (radio and/or infrared signals)

Wireless Devices Advantages: portability mobility Disadvantage: limited energy supply

Types of Wireless Connections Wireless Personal Area Networks Bluetooth ZigBee Wireless Local Area Networks Wi-Fi Fixed Wireless Data Wireless Metropolitan Area Networks WiMax Wireless Wide Area Networks Mobile Device Networks Global System for Mobile Communications Personal Communication Service Digital Advanced Mobile Phone Service

Models of Wireless Networks

Cellular Networks wireless communication is based on the single-hop model

Radio Networks no fixed infrastructures are needed collection of homogenous devices radio transceivers equipped with processor some memory omnidirectional antennas useful for broadcast communications limited energy supply device can set their transmission power level all devices usually transmit at the same frequency communication is based on the multi-hop model to save energy to decrease interference to increase network lifetime

Models of Radio Networks Mobile high mobility of devices Static devices are stationary static ad-hoc radio networks static sensor networks main applications: emergency and disaster reliefs battlefield monitoring remote geographical regions traffic control …

Static Ad-Hoc Radio Networks wireless communication is based on the multi-hop model

Sensor Networks wireless communication is based on the multi-hop model staticdynamic

Signal Propagation in (Static) Radio Networks

Signal Attenuation The signal is a wave propagating in the open air. The signal intensity depends on: the transmission power level of the source environmental conditions: background noise interference from other signals presence of obstacles climatic conditions … the traveled distance

Transmission Power and Transmission Quality Transmission power: it is the amount of energy spent by a device to send a signal at some intensity. (thus energy consumption is proportional to signal intensity) Transmission quality: it is a threshold  >0 below which the signal intensity does not have to drop so that the msg it carries can be decoded correctly by any receiver

The Euclidean Model for (Static) Radio Networks Wireless devices are points on the Euclidean plane Given two points v 1 =(x 1,y 1 ),v 2 =(x 2,y 2 )  2, the distance d(v 1,v 2 ) between v 1 and v 2 is v 1 =(x 1,y 1 ) v 2 =(x 2,y 2 ) |x2-x1||x2-x1| |y2-y1||y2-y1|

If v 1 sends a msg M with power p(v 1 ), then the signal intensity perceived by v 2 is p(v 1 )/d(v 1,v 2 ) , where  1 is the distance-power gradient. The Euclidean Model for (Static) Radio Networks v1v1 v2v2

If v 1 sends a msg M with power p(v 1 ), then the signal intensity perceived by v 2 is p(v 1 )/d(v 1,v 2 ) , where  1 is the distance-power gradient. v 2 can decode msg M if p(v 1 )/d(v 1,v 2 )   (  >0 is the transmission-quality parameter) The Euclidean Model for (Static) Radio Networks v1v1 v2v2 signal intensity is <  signal intensity is 

If v 1 sends a msg M with power p(v 1 ), then every station in the transmission range of v 1 will receive the msg M The transmission range of v 1 is the disk centered at v 1 of radius The Euclidean Model for (Static) Radio Networks v1v1 signal intensity is <  signal intensity is 

When v 1 sends a msg M with power p(v 1 ), M is sent over all the transmission range of v 1 (broadcast transmission) in one round The transmission range of v 1 is the disk centered at v 1 of radius The Euclidean Model for (Static) Radio Networks v1v1 M M

Static Radio Networks are Synchronous Systems All devices share the same global clock So Devices act in rounds Message transmissions are completed within one round

Each device v transmits at power p(v)  0 ( p(v) may not be equal to p(u) ) The transmission range of all the devices uniquely determine a directed communication graph G=(V,E) V is the set of devices E={(v,u): u is in the transmission range of v} The Euclidean Model for (Static) Radio Networks

Broadcast Over Static Radio Networks (when all devices transmit at the same frequency)

u v v Message Collisions If v sends a msg M at round r, then all in-neighbors u of v receive M unless some other in-neighbors v of u sends a msg M at (the same) round r M M M (in this case u gets nothing) M M M

Collision Free Messages a node u receives a msg during round r iff exactly one of all its in-neighbors v sends a msg during round r M M M M M M

Broadcast Over Static Radio Networks Model: strongly connected directed graph G=(V,E) nodes know n=|V| (non-uniform) nodes have distinct identifiers in [n] (non-anonymous) ( id(v) is the identifier of node v ) (Observe that nodes do not know G as well as their neighborhood) Task: a source node s  V wants to inform all the other nodes of a msg M

Completion and Termination of the Broadcast Protocol Completion A protocol completes broadcast from s over G if there is a round r s.t. every node is informed about the source msg M Termination A protocol terminates if there is a round r s.t. any node stops any action within round r

A First Attempt Protocol Flooding ( description for node v at round r ) if node v is informed of M then v sends M else v does nothing s Flooding does not work!!! How can we avoid msg collisions?

Protocol Round Robin (description for node v at round r of phase i) (a phase consists of n consecutive rounds) if node v is informed of M and id(v)=r then v sends M else v does nothing

Analysis of Protocol Round Robin Let L i ={v  V: the hop-distance from s to v is  i} Lemma: At the end of phase i, all nodes in L i will be informed of the source msg M. Proof: By induction on i. Fact: At the beginning, only L 0 ={s} is informed of the source msg M Base case i=1 : no msg collision occurs at round id(s) of phase 1 where only s sends M. Inductive case i>1 : Consider any v  L i. Let u  L i-1 s.t. (u,v)  E. Hypothesis: At the end of phase i-1, u is informed of M. No msg collision occurs at round id(u) of phase i where only u sends M. Thus, v will be informed of M at the end of phase i. s u  L i-1 vLivLi

Analysis of Protocol Round Robin Let L i ={v  V: the hop-distance from s to v is  i} Lemma: At the end of phase i, all nodes in L i will be informed of the source msg M. Corollary: Let  be the (unkown) source eccentricity, i.e., the minimum over all the integers i s.t. L i =V. Then  phases suffice to inform all the nodes of the source msg M. Lemma: Protocol Round Robin completes broadcast in O(  n) rounds.

Analysis of Protocol Round Robin Let L i ={v  V: the hop-distance from s to v is  i} Lemma: At the end of phase i, all nodes in L i will be informed of the source msg M. Corollary: Let  be the (unkown) source eccentricity, i.e., the minimum integer i such that L i =V. Then  phases suffice to inform all the nodes of the source msg M. Lemma: Protocol Round Robin completes broadcast in O(  n) rounds. What about termination? (  n-1 as G is strongly connected) (Thus nodes can decide to stop after n-1 phases)

Analysis of Protocol Round Robin Theorem: Protocol Round Robin completes broadcast in O(  n) rounds terminates broadcast in O(n 2 ) rounds

Can We Do Better Than Protocol Round Robin ? Yes if the in-degree  of nodes is “not too large” completion in O(  log n) termination in O(n  log n) (most of “good” networks have small value of  ) Observation: protocol Round Robin does not exploit parallelism at all Goal: Select parallel transmissions  =max{  v :v  V} where  v =|{u  V:(u,v)  E}|

A Way of Selecting Parallel Transmissions Definition: Let n and k be two integers with k  n. A family F of subsets of [n] is (n,k) -selective if, for every non empty subset X of [n] with |X|  k, there exists a set F  F s.t. |F  X|=1. A trivial example… F ={{1},{2},…,{n}} is (n,k) -selective for any k  n How can selective families be used for broadcast? (Assumption: nodes know  )

Protocol Select Set-up: all nodes know the same (n,  ) -selective family F ={F 1,…,F t } (description for node v at round r of phase i ) (a phase consists of t consecutive rounds) if node v is informed of M and id(v)  F r then v sends M else v does nothing

Analysis of Protocol Select : A First (Wrong) Attempt Let L i ={v  V: the hop-distance from s to v is  i} Lemma: At the end of phase i, all nodes in L i will be informed of the source msg M. Proof: By induction on i. Fact: At the beginning, only L 0 ={s} is informed of the source msg M Base case i=1 : no msg collision occurs at the first round r of phase 1 s.t. id(s)  F r where only s sends M. Inductive case i>1 : consider any v  L i. Let N v ={id(u):(u,v)  E and u  L i-1 }. Hypothesis: At the end of phase i-1, N v is informed of M. Since N v  [n] and |N v | , there exists r s.t. N v  F r ={id(u)}. No msg collision occurs at v during round r of phase i where u sends M. Therefore, v will be informed of M at the end of phase i.

What’s wrong? Inductive case i>1 : consider any v  L i. Let N v ={id(u):(u,v)  E and u  L i-1 }. Hypothesis: At the end of phase i-1, N v is informed of M. Since N v  [n] and |N v | , there exists r s.t. N v  F r ={id(u)}. No msg collision occurs at v during round r of phase i where u sends M. we are not considering the impact of nodes id( w)  L i \ L i-1 s.t. (w,v)  E and id(w)  F r 1. if w is informed at beginning of round r of phase i, then it creates msg collision at v (Is this a solution? we may add id(w) to N v )

What’s wrong? Inductive case i>1 : consider any v  L i. Let N v ={id(u):(u,v)  E and u  L i-1 }. Hypothesis: At the end of phase i-1, N v is informed of M. Since N v  [n] and |N v | , there exists r s.t. N v  F r ={id(u)}. No msg collision occurs at v during round r of phase i where u sends M. we are not considering the impact of nodes w  L i \ L i-1 s.t. (w,v)  E and id(w)  F r 1. if w is informed at beginning of round r of phase i, then it creates msg collision at v (Is this a solution? we may add id(w) to N v ) NO 2. if w is not informed at beginning of round r of phase i, then no msg is sent to v

How to Adapt Protocol Select IDEA: Only nodes that have been informed of M at the end of phase i-1 will be active during phase i Proof of Lemma now works if N v ={id(u):(u,v)  E and u is informed at the end of phase i-1 } completion time is O(  | F |) (to minimize completion time, we need minimum-size selective family) Theorem: For sufficiently large n and k  n, there exists an (n,k) -selective family of size O(klog n). (and this is optimal!!!)  for protocol Select, | F |=O(  log n)

Analysis of Protocol Select Theorem: Protocol Select completes broadcast in O(  log n) rounds terminates broadcast in O(n  log n) rounds

If you want to know more… Algorithmic problems for radio networks S. Schmid and R. Wattenhofer, Algorithmic models for sensor networks T. Locker, P. von Rickenbach, and R. Wattenhofer, Sensor networks continue to puzzle: selected open problems Both papers can be downloaded from Broadcast over radio networks A.E.F. Clementi, A. Monti, and R. Silvestri, Distributed broadcast in radio networks of unknown topology