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Figure 11.9. Triangulation. (a) Remote positioning: The reference nodes exchange information between them to compute the position of the unknown node using the angle of arrival. (b) self-positioning: Where the unknown node estimates its angle to at least three reference nodes, the unknown node itself is able to compute its own position.

Figure 11.6. Flowchart of the joint scheduling and power control algorithm in Behzad and Co-workers [42, 43].

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A example of a probabilistic approach is proposed in reference 41. In this work, the error of the distance estimation is modeled as a normal random variable. When an unknown node receives a packet from a reference node, it can be in any place around the reference node with probabilities as depicted in Figure 11.10a. When

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Thus, any connected pair of nodes in the graph means that they cannot start transmissions simultaneously. With this interference graph, a distributed power control and scheduling algorithm is introduced. The scheduling policy decides whether two links can activate at the same time according to the graph, and the distributed power control algorithm nds the transmit power level for the scheduled links in the way similar to the one used in reference 40. The procedure of this cross-layer design is given in Figure 11.6. Fang and Rao [44] formulate the resource allocation (power) problem of maximizing the sum of transmitter utilities subject to a minimum and maximum data rate constraint per link and peak power level constraint per node in a wireless multihop network. The Additive Gaussian White Noise (AWGN) channel is assumed to be the channel model, so the system utilities de ned as functions of link rates enjoy the same properties as functions of transmission powers. Because the system utilities are functions of the transmit power levels of nodes, they propose a distributed power control algorithm based on the gradient method. The update of transmit power is as follows: Pi (t + 1) = Pi (t) L(P(t), qk ) Pi

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Figure 11.10. Probabilistic approach. (a) Probability of a node s position using one reference node: The unknown node has equal probability of being on around the reference node. (b) Probability when using two reference nodes: A pair of points with greater probabilities results from the system. (c) probabilities when using more than two references: A unique point with greater probability results from the system.

It has been argued that physical commodity products will find a fair value or an absolute value when they reach certain lows based on historical price comparisons and will never go to zero due to laws of supply and demand (Economics 101) Unlike stocks, commodities do not declare bankruptcy or go out of business The reason futures will always have some value is because they do not exist solely for traders to bet on price movement Producers and end users are also major participants in most futures markets as they use futures to reduce risk from adverse changes in price and to discover the current fair value for products they have to buy or sell to stay in business Traders in this category are referred to as commercials or hedgers.

Pmax (i) 0

Figure 11.10. (Continued)

where L(P(t), qk )/ Pi is the gradient of the objective function in each iteration, and is the step size The scheduling policy is a greedy degree-based scheduling algorithm, trying to limit the total interference at the receivers by scheduling a small number of transmitters around them Simulation results shows that this algorithm achieves signi cant throughput improvement 1132 Power Control: The Network Layer Problem Transmission power control can be considered as a network layer problem Transmission power control in MAC layer approach tries to send packets at the minimum necessary power such that the SINR at receiver is just above prede ned threshold for successful transmission, which leads to improvement of spatial reuse in wireless medium and energy saving for nodes However, the intended receivers of the transmission are determined by the network layer through routing protocols.

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