multiobjective distributed power control algorithm fro...

Multiobjective Distributed Power Control Algorithm for CDMA

Wireless Communication Systems

PWSN Article Summation

• Article written by:

M. Elmusrati1,2, R. Jännti1,2, H. N Koivo1 1: Control Engineering Laboratory, Helsinki University of Technology

2: Department of Computer Science, University of Vaasa

• IEEE Transactions on Vehicular Technology

March 2007 (Vol. 56, No. 2)

PWSN Course 2011, Martin Jakobsson (mjakobbs at kth.se)

Background (wireless (RF) communication)

• Code Division Multiple Access (CDMA)

– Setting where several users share the same channel.

– Other strategies are TimeDMA and FrequencyDMA.

• CDMA requires good power control.


The Power Problem

• SINR: Signal to Interference plus Noise Ratio

• 𝑃𝑖: power of user 𝑖

• 𝐺𝑖𝑗: Gain from user 𝑖 to receiver 𝑗

• 𝛿 𝑡 : Random noise

• SINR is a measure of the Quality of Service (QoS). SINR -> probability that message is received


The Power Problem

• Typically: Minimize power spent while guaranteeing a minimum QoS, e.g.,

min 𝒑𝑠. 𝑡. 𝑄𝑜𝑆 ≥ 𝑄𝑜𝑆min

• Optimal p is (centrally) computable through a system of linear equations. However, the full matrix Q must be known centrally. This is not practical.

• Distributed Power Control (DCP). Most algorithms assume (quasi)static channel gain (snapshot analysis)

PWSN Course 2011, Martin Jakobsson

(mjakobbs at kth.se)

Idea of Paper • “The preferred power control is that one that can achieve an

accepted QoS level (i.e., a level that is between minimum and supremum QoS levels) very fast at low power consumption.”


Idea of Paper • In this paper: Multiobjective optimization

Minimize p and “Maximize” QoS

↝


Deriving the Algorithm

• Each user should minimize its error funciton:

(Other objectives than these, such as throughput, could be included.)

• The problem could consider several timesteps by optimizing

In the algorithm however, N=1.


• The error function can be simplified as:

• Assume P is described by an autoregressive model.




• Inserting

and

into

gives

or with



• Necessary condition for optimality:

• This can be written (solving for w)

𝜕

𝜕𝒘J(P)=0



are known from least-squares techniques

Rx and Rxx can be calculated recursively. By using the matrix inversion lemma, this avoids inverting Rxx.

• In the simplest case, 𝛾=0 and n=1,

• This means only one old value of P is saved (n=1), and the algorithm is unaffected by events in the past (𝛾=0)


• For this simple case, the algorithm becomes:

• When 𝜆𝑖,1 = 0 (optimize SINR regardless of power), the algorithm becomes

which is known as the DCP algorithm.

MultiObjective Distributed Power Control (MODPC)

This is approximated as 𝜆𝑖,2 (sign ignored)


Convergence

• Important article on power control:

Introduced ”Interference function optimization”. Power updates on the form

• Theorem: will converge to a unique fixed point.


Convergence

• By showing that

fulfills the properties of the previous slide, it follows that:

• (Proposition 1) If the channel gains are static and 𝑷(0) > 0, then the

MODPC converges to a unique fixed point, given by the tradeoff factors 𝜆

• (Proposition 2) For a noiseless feasible system, static channels, 𝑷(0) > 0 and proper values of 𝜆, the algorithm converges to 𝑷∗ , where

𝑷∗ = arg max𝑷≥0

min𝑖

Γ𝑖


MODPC With Quantized SINR

• MODPC assumes Γ𝑖 perfectly known. However, in many systems, only quantized values are available. In the worst case, base station sends only “increase power” or “decrease power” to users.

• Paper combines MODPC with estimation algorithm from

This is called ”MultiObjective Totaly Distributed Distributive Power Control” (MOTDPC), and can be shown to converge when channels are static and 𝑷 0 > 0.


Performance Difference from optimal (centralized) power vector

Static channels Dynamic channels


Performance

Static channels Dynamic channels


multiobjective distributed power control algorithm fro...

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