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In this section we focus on the dynamic source routing (DSR) described in [53] DSR is a reactive routing protocol Thus, routes get created only when they are needed and there is no periodic routing traf c for creating or maintaining routes DSR also makes use of source routing In source routing, when a node originates a data packet it puts in the header of the packet all the hops that the packet needs to traverse to get to the destination DSR has two main components: route discovery and route maintenance Route discovery is used by nodes for discovering new routes when they do not have routes to destinations they need to communicate with Route maintenance is used for discovering routes that have been broken due to node movements or failures When a route is broken, either a different existing (less optimal) route may be used or the node may initiate

From this we deduce that, if F is not a polynomial, then: 1) (aj ) belongs to l1 (N) if and only if a > 1 or (a = 1 and d > 0); 2) (aj ) belongs to l2 (N) if and only if a > 1 or (a = 1 and d > 1 ) 2 Consequently, 1 |aj | = + and 1 |aj |2 < + if and only if a = 1 and d ] 1 , 0] Let us consider a transfer function of the form (81) with 2 2 1 |aj | < + , meaning that either F is a polynomial, or: a > 1 or a = 1 and d > 1 2 (83)

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Let us suppose now that if ( k , dk ) 2 , then the conjugated factor (1 k z)dk will appear in the right-hand side part of (81) Then, (aj ) is a real sequence If ( n ) is a white noise, the process de ned by:

aj (n j)

.

(84)

.

is a second order stationary process, with zero-mean, linear and regular, with a spectral J density proportional to f ( ) = | j=1 (1 j exp(i ))dj |2 Moreover, if ( (n)) is an iid sequence, (X(n)) is strictly stationary and ergodic This process admits an autoregressive development of in nite order:

Under the following conditions: 1) | j | 1 for all j {1, , J}; 2) if | j | = 1, then Re(dj ) ] 1 , 1 ], 2 2 when n tends towards in nity, we have: 1) an = O(a n ) and bn = O(b n ) when > 1; 2) an = O(n d 1 ) and bn = O(n 1 ) when = 1, with b = min{| j | 1 , dj N} and = max{Re(dj ), | j | = 1} The coef cients (aj ) are the solution of the af ne linear difference equation of order J:

(n k)qk pk 1 an k = 0,

(85)

with aj = 0 if j < 0 and a0 = 1 The pj and qj are respectively the coef cients of the two relatively prime polynomials P and Q de ned by Q(0) = 1 and: F (z) = F (z)

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