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As is clear from the gure, this ooding mechanism is not very ef cient since various nodes can receive the same message multiple times In OLSR a more ef cient scheme for propagating routing information has been created Here each node assigns the task of propagating its LSAs only to a few of its one-hop symmetric neighbors These special nodes are selected in a way that ensures that the LSAs will reach all of its two-hop neighbors Those nodes selected for relaying the LSAs are MPRs For example, as shown in Figure 417, when node A transmits a routing update, it broadcasts it to each of its one-hop neighbors All of those nodes receive and process the message, but only the nodes that are MPRs for node A retransmit the message This reduces the number of retransmissions and hence the overhead generated by OLSR We next discuss the details of the OLSR routing protocol In OLSR, each node transmits hello messages periodically (eg every second) over each of the node s interfaces The main purpose of the hello message is to enable a node to discover its direct (one-hop) neighbors Hello messages are only broadcast to the one-hop neighbors and do not get transmitted past the one-hop neighborhood of a node The hello message contains the name of the originating node, the one-hop neighbors that the originating node has discovered so far, and the nodes that the originating node has selected to be its MPRs Once a node hears a hello message it checks whether the message originated from a new neighbor, and if so, it updates its one-hop neighborhood list The hello message is also very important for supporting the MPR concept Each node checks the hello messages received from its neighbors to see whether it has been selected to be an MPR by any of the neighbors If so, the node needs to ood the routing updates generated from such neighbors that have selected it to be their MPR Every node can also gure out which nodes are two hops away from it through the hello message, because each of its one-hop neighbors lists in the hello message all the nodes that are within one hop of them Each node selects its MPRs based on the two-hop neighborhood so that each of its two-hop neighbors can be reached through the MPRs.

As regards the estimate of the functional parameter, the preceding theorem can disappoint, which limits itself to proposing an estimate of integrals of a2 against the weight functions w To rebuild a pointwise estimator of a(t) starting from these integrals, a general method will be found in [IST 96] To understand the convergence speeds determined by Theorem 67, it is necessary to know that the convergences of the estimators reveal two types of error One comes from the central limit theorem and intervenes in the estimate of the rst-order parameters; we will call it stochastic error On the other hand, the second-order disturbance in the lter de ning the ltered white noise creates a distortion If H2 H1 > 1 , stochastic error is dominant over 2 distortion Otherwise, the convergence speed is imposed by distortion The estimate of the second-order factors (b, H2 ) is more dif cult because it necessitates that we build functions that do not depend asymptotically on the rst-order factors An example of such a functional is given by: V N 22H1 1 VN

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The intervention of the factor 22H1 1 is necessary to compensate for the in uence of the rst-order parameters exactly On the other hand, it must be estimated and for this we will use the convergence of: V N2

= 22H1 1

which is suf ciently rapid for the compensation to always take An estimator of the parameter H2 is thus obtained THEOREM 68 If the function: WN = V N

.

(663)

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the estimator: H2 (N ) = VN 2 /2 WN/2 1 1 log2 + log2 2 2 VN 2 WN (664)

converges as towards H2 when N + 6522 Identi cation of elliptic Gaussian random processes Although it is possible to directly identify the symbol of an elliptic Gaussian random process of the form: (t, ) = a(t)| | 2 +H1 + b(t)| | 2 +H2 + p( )

(665)

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