Wireless Ad Hoc and Sensor Networks

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Distributed Power Control of Wireless Cellular and Peer-to-Peer Networks 201Defining xi() l = ei()l for each link, the SIR update equation for the entirenetwork can be represented in the vector form as Rl ( + 1) = Rl ( ) + vl (),where vl () =− Kxl () +η,with Rl (), vl (),K, xl (),γ , η represented as⎡R1()l ⎤⎢ ⎥⎢R2()l ⎥⎢ ⎥Rl () = ⎢.⎥ ,⎢ ⎥⎢.⎥⎢ ⎥⎢⎣Ri()l⎥⎦⎡v1()l ⎤⎢ ⎥⎢v2()l ⎥⎢ ⎥vl () = ⎢.⎥ ,⎢ ⎥⎢.⎥⎢ ⎥⎢⎣vi()l⎥⎦⎡k⎢ 1 000..0⎤⎥⎢0 k20 0 .. 0⎥⎢⎥K = ⎢. . . . . . . ⎥ ,⎢⎥⎢. . . . . . . ⎥⎢⎥⎢⎣0000..k⎥i ⎦⎡x1()l ⎤⎢ ⎥⎢x2()l ⎥⎢ ⎥xl () = ⎢.⎥ ,⎢ ⎥⎢.⎥⎢ ⎥⎢⎣xi()l⎥⎦⎡γ1 ⎤⎢ ⎥⎢γ⎥2⎢ ⎥γ = ⎢.⎥ ,⎢ ⎥⎢.⎥⎢ ⎥⎢ ⎥⎣γi ⎦⎡η1⎤⎢ ⎥⎢η2⎥⎢ ⎥η = ⎢.⎥⎢ ⎥⎢.⎥⎢ ⎥⎢⎣η⎥i ⎦(5.19)Using the SSCD or optimal power control approach presented in thispaper, the active links are always maintained active. Inactive links, aftersome time, get added into the network if they are admissible. They remainactive until the end of their transmission.We now consider a group of N + M links, such that originally the onesin the setA0 = {, 1 2, 3, … , N−1, N}(5.20)are active, whereas the ones in the setB0 = { N+ 1, N+ 2, N+ 3, … , N+ M− 1, N+M}(5.21)are inactive new links. We are mainly interested in whether the new linkswill eventually become active.THEOREM 5.3.1 (TOTALLY INADMISSIBLE NEW LINKS)Given that the network operates under the state-space-based or optimal powercontrol scheme, ifAl =A0 ≠φ and Bl = B0 ≠φ(5.22)
202 Wireless Ad Hoc and Sensor Networksfor everyl ∈{ 1, 2, 3 ,…},(time slots) then the following limits exist:*lim Rl ( ) = R
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Wireless Ad Hocand SensorNetworksPr
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18. Chaos in Automatic Control, edi
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CRC PressTaylor & Francis Group6000
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Table of Contents1 Background on Ne
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3 Congestion Control in ATM Network
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5.4.2 Distributed Power Controller
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7.3 Adaptive and Distributed Fair S
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9.2.2 Overview.....................
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the number of connections in each l
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y Maheswaran Thiagarajan, and tirel
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2 Wireless Ad Hoc and Sensor Networ
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10 Wireless Ad Hoc and Sensor Netwo
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2BackgroundIn this chapter, we prov
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Background 51u(k)x n (k + 1)x n (k)
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Background 53with x( 0)being the in
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Background 55with tr(.) the matrix
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Background 57nGiven a function ft (
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Background 592.3.2 Lyapunov Stabili
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Background 61as well as Jagannathan
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Background 63The subsequent example
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Background 65Evaluating this along
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Background 67Now, select the feedba
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Background 69is SISL if and only if
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Background 71L 1 (x)L(x, t)L 0 (x)0
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Background 73for some R > 0 such th
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Background 75Evaluating the first d
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Background 77Section 2.4Problem 2.4
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100 Wireless Ad Hoc and Sensor Netw
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4Admission Controller Design for Hi
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Admission Controller Design for Hig
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7Distributed Fair Scheduling in Wir
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Distributed Fair Scheduling in Wire
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8Optimized Energy and Delay-Based R
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Optimized Energy and Delay-Based Ro
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9Predictive Congestion Control for
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Predictive Congestion Control for W
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10Adaptive and Probabilistic Power
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Adaptive and Probabilistic Power Co
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Wireless Ad Hoc and Sensor Networks

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