Wireless Ad Hoc and Sensor Networks

440 Wireless Ad Hoc and Sensor NetworksEquation 9.5, then the mean estimation error of the variable along with themean error in queue utilization converges to zero asymptotically, if the parameterθ i is updated asˆ ( ) ˆ ( ) ( ) ( )θ iθ k+ 1 = θ k + λ ⋅u k ⋅ e k+1i i i fi(9.10)provided(a) λ ui( k ) 2 2< 1 and(b) K fvmax < 1/ δ , where δ = 1/[ 1 −λ∗| ui( k)| ],K fvmax is the maximum singular value of K fv , λ, the adaptation gain,and efi( k) = fi( k) − fˆ i ( k ) , the error between the estimated value and theactual one.The rate selected by the preceding algorithm in Equation 9.5 does nottake into account the fading channels whether an adaptive scheme isemployed or not for traffic estimation. It only detects the onset of congestionby monitoring the buffer occupancy. Under the fading wireless channels,the transmitted packets will not be decoded and dropped at thereceiver, thereby requiring retransmissions as the effects of fading channelsare not explicitly considered. To mitigate congestion due to channelfading, the selected rate from Equation 9.5 has to be reduced when thetransmission power calculated by the DPC scheme exceeds the transmitternode’s capability (greater than maximum transmission power). This isaccomplished by using virtual rates and backoff interval selection. Selectingthe backoff interval for a given node is a difficult task because itdepends upon the backoff intervals of all neighboring nodes, which arenormally unknown. Therefore an adaptive scheme is proposed to estimatethe backoff interval of a given node.9.3.2 Backoff Interval SelectionBecause multiple nodes in a wireless sensor network compete to accessthe shared channel, backoff interval selection for nodes plays a criticalrole in deciding which node gains access to the channel. Thus, the proposedrate selection is implemented by suitably modifying the backoffintervals of the nodes around the congested node to achieve the desiredrate control. In the case of contention-based protocols, it is difficult toselect an appropriate backoff interval because of multiple nodes competingfor the channel. For a given node, a relationship between transmissionrate and backoff interval depends upon the backoff intervals of all nodeswithin a sensing range of a transmitting node in the CSMA or CA paradigm.To calculate this relationship, a node needs to know the backoffintervals of all its neighbors, which is not feasible in a wireless networkbecause of a large traffic overhead resulting from communication.Therefore, we propose using a distributed and predictive algorithm toestimate backoff intervals, such that a target rate is achieved. The main