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where R is the transmission rate, L is the packet length and BER is the bit error rate which is a function of the SINR seen by j. As the modeled game has an in nite horizon, a CRN implemented in this manner will exhibit convergent behavior if: (1) some mechanism exists for broadcasting the desired operating vector, the discount factor, and the punishment strategy; (2) there is full knowledge of the environment so the radios can differentiate deviant behavior from fades and jammers external to the CRN; (3) there is knowledge of the action chosen by each radio at each stage. 16.6.1.3 S-modular games Altman and Altman [71] examines the application of super-modular games to distributed power control. Thus the objective functions for this game are characterized by Equations (16.8) and (16.9). Herein each game follows a general updating algorithm (GUA), which is actually a best response dynamic. Thus if these network games have a unique NE, behavior converges to the NE from any initial p. For a CRN which satis es this characterization, the conditions for convergence are: (1) The adaptation algorithms must incorporate perfect knowledge of the objective function. (2) The network must have a unique steady state. (3) Some method must exist for measuring current performance and for sensing relevant environmental parameters. Depending on the particular adaptation algorithm, it might be necessary to know the number and type of other radios in the network. Altman and Altman [71] assert that the classes of power control algorithms considered in by Yates [75] are S-modular games. Yates examines power control in the context of the

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turns the parent and children of each item The class looks like this:

To define a constructor you create a method with no return type, whose method name is identical to the class name The constructor is the method that the code calls to create an instance of the object In this case, the constructor takes the first name and the last name as parameters, allowing the programmer to specify these names when instantiating the Employee object Listing 517 is an example of how to call a constructor

public class PersonTreeContentProvider extends ArrayContentProvider implements ITreeContentProvider { public Object[] getChildren(Object parentElement) { Person person = (Person) parentElement; return personchildren; } public Object getParent(Object) { Person person = (Person) element; return personparent; } public boolean hasChildren(Object) { Person person = (Person) element; return personchildrenlength > 0; } }

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class Program { static void Main() { Employee employee; employee = new Employee("Inigo", "Montoya"); employeeSalary = "Too Little"; ConsoleWriteLine( "{0} {1}: {2}", employeeFirstName, employeeLastName, employeeSalary); } // }

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uplink of a cellular system under ve scenarios: (1) xed assignment where each mobile is assigned to a particular base station; (2) minimum power assignment where each mobile is assigned to the base station where its SINR is maximized; (3) macro diversity where all base stations combine the signals of the mobiles; (4) limited diversity where a subset of the base stations combine the signals of the mobiles; and (5) multiple connection reception where the target SINR must be maintained at a number of base stations. In each scenario, each mobile, j, tries to achieve a target SINR j as measured by a function, I (p). I (p) is the standard effective interference function which has the following properties: (1) positivity, e.g. I (p) > 0; (2) monotonicity, e.g. if p p*, then I (p) I ( p*); (3) scalability, e.g. for all > 1, I (p) > I ( p), where the convention that p > p* means that pi > pi * i N . Single-cell target SINR games are also ordinal potential games. To prove it, consider a modi ed game where the action sets are the received power levels at the base station. A received power level for mobile j, r j , is the product of its path loss to base station k, h j,k , and its transmitted power level. Then the objective functions of a target SINR game can be expressed as

hierarchy) Individual runs of text may have different styles as-

Figure 5-11