TABLE OF CONTENTS Prove that every contraction mapping satisfies the Synchronous Convergence Condition of the Asynchronous Convergence Theorem.
Given that the Standard Interference Function is a pseudocontraction, prove the following:
(a) That it has a unique fixed point.
(b) Synchronous adaptations converge to the fixed point.
(c) Synchronous adaptations are stable.
Consider a network consisting of three terminals and an access node with noise power of 80 dBm implementing TPC with a statistical spreading gain of 64. Suppose gains to the access node 1, access node 2, and access node 3 are 10, 15 and 20 dB, respectively, and each node would like to achieve a target SINR of 8 dB. Assume each radio's set of transmit power levels is convex:
(a) Determine whether these target SINRs are feasible.
(b) If these SINRs are feasible, solve for the operating power vector.
(c) Based on the discussion in this chapter, what conditions are necessary to ensure convergence?
(d) Is this operating power vector stable? How do you know?
Repeat question 3, assuming target SINR for the access node 1, access node 2, and access node 3 are 6, 8, and 10 dB, respectively.
Repeat question 3, assuming the radios operate with discrete power levels.
Consider a pair of cognitive radio local area networks (LANs) where each LAN is attempting to maximize its network capacity. Each LAN must make a one-time choice of frequencies { f 1, f 2, f 3}. If the two LANs choose the same frequency, the...
