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Optical ampli ers amplify incident light through stimulated emission, the same mechanism as used with lasers. These ampli ers are the same as lasers without feedback. Optical gain is achieved when the ampli er is pumped either electrically or optically to realize population inversion. There are semiconductor laser ampli ers, Raman ampli ers, Brillouin ampli ers, and erbium-doped ber ampli ers (EDFAs). Certainly the EDFAs show the widest acceptance. One reason is that they operate near the 1.55-mm wavelength region, where ber loss is at a minimum. Reference 11 states that it is possible to achieve high ampli er gains in the range of 30 dB to 40 dB with only a few milliwatts of pump power when EDFAs are pumped by using 0.980-mm or 1.480-mm semiconductor lasers. Figure 9.31 is a block diagram of a low-noise EDFA. In Figure 9.31, optical pumping is provided by ber-pigtailed semiconductor lasers with typically 100 mW of power. Low-loss wavelength division multiplexers ef ciently combine pump and signal powers and can also be used to provide a pump by-pass around the internal isolator. The EDFA has an input stage that is codirectionally pumped and an output stage that is counterdirectionally pumped. Such multistage EDFA designs have simultaneously achieved a low noise gure of 3.1 dB and a high gain of 54 dB (Refs. 10 and 11). The loops of ber should be noted in Figure 9.31. These are lengths of ber with a dopant. The length of erbium-doped ber required for a particular ampli er application depends on the available pump power, doping concentration, the design topology, and gain and noise requirements.

where by assumption the two groups have a common variance, 2 . As mentioned, Cohen (1977) de ned a large effect as something that is visible to the naked eye and concluded that for two normal distributions having a common variance, small, medium, and large effect sizes correspond to = .2, = .5, and = .8, respectively. Given , the sample sizes

By either modifying the objective function or relaxing one of the constraint functions, the preceding problem formulation can be reduced to several datagathering optimization problems considered in the literature Byers and Nasser [54] consider the optimization problem of maximizing the overall utility of sensor networks during the system lifetime, subject to an energy constraint The energy constraint is expressed as a high-level cost on sensing, transmission, reception, and aggregation Chang and Tassiulas [61] devise a routing solution to maximize the system lifetime of sensor networks under the given source rate of nodes and subjected to ow conservation and energy constraints1 Without considering the node capacity constraint, the problem reduces to a linear programming problem Sadagopan and Krishnamachari [56] use an iterative approximation algorithm to solve a similar linear programming problem except by changing the objective function from maximizing the system lifetime to maximizing the data extraction rate.

It can be shown that in this case, = 2wmax, so this assignment also has a span of at most c0 /2 = c0wmax Thus, in either case, f2 has span at most c0wmax The two assignments f1 and f2 are then combined by adding cR + c0 to every channel in f2, and then merging the channel sets assigned by f1 and f2 at each node This gives a final assignment of span at most (cR c0) + c0wmax + c0 Using the lower bounds (52) and (53), it can be shown that the performance ratio of the algorithm is as claimed If c0 < 2c1, Algorithms B and C can be combined into a linear time approximation algorithm with performance ratio 1 + 1/(n 1), where n is the number of nodes in the cycle The combination algorithm is formed as follows.

Duarte-Melo et al [41] formulate a nonlinear programming problem that jointly considers the datacompression and data-dissemination problem to maximize the number of snapshots generated from the network, or equivalently maximize the system lifetime Chen et al [55] rst transform the optimization problem (Eqs (153) (156)) to a convex programming problem, by linearizing the energy constraint (Eq (155)) This is done by properly setting the value of the system lifetime in advance and controlling the data rate of a node (and hence its total energy consumption rate) so as to sustain its battery lifetime longer than the speci ed lifetime Given the transformed problem, they then derive a distributed solution with the use of the dual optimization problem and the pricing mechanism given in ref [53].

First, find the assignment f1 computed by Algorithm C for (G, w ) where w (v) = wmin for every node v Then, find the assignment f2 computed by Algorithm B for (G, w ) where w (v) = w(v) wmin Finally, combine the two assignments by adding cRwmin + c0 to each channel of f2 and then merging the channel sets assigned by f1 and f2 Using bound 16, it can be shown that the algorithm has performance ratio 1 + 1/(n 1) as claimed..

They devise a simple nodecapacity estimation method to measure the node capacity (which changes with the traf c load and nodal distribution, but is needed in the optimization problem) on-line, and incorporate optimization results in selecting routes to further increase the overall utility..

April Sales revenue Food cost Gross profit Payroll and related expense Supplies and other expense Utilities expense Rent expense Advertising Income before depreciation Depreciation Net Income $30,000 ( 12,000) $18,000 $9,000 1,500 500 1,000 500 $10,500 1,750 750 1,000 500

Fundamentals of Telecommunications. Roger L. Freeman Copyright 1999 Roger L. Freeman Published by John Wiley & Sons, Inc. ISBNs: 0-471-29699-6 (Hardback); 0-471-22416-2 (Electronic)