1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maximization of the sum of mutual information terms

  1. Aug 3, 2009 #1
    I would like to compute the power distribution that maximizes the sum data rate of a certain communication scheme. The expression follows from the sum of the rate of four messages which interfere with each other. A certain amount of power (here 1 Watt) is assigned to these messages, and there is a further constraint on the sum rate of the first three messages.

    [itex] \begin{equation}
    & \mathrm{maximize} \qquad \underbrace{\log_2\det \left( 1 + \frac{p_{1}}{ p_{2} + \lambda(p_{3}+p_{4}) + \sigma^2} \right)}_{R_{1}} \\
    &\qquad\qquad\qquad + \underbrace{\log_2\det \left( 1 + \frac{p_{3}}{p_{4} + \lambda p_{2}+\sigma^2} \right)}_{R_{3}}\\
    &\qquad\qquad\qquad + \underbrace{\log_2\det \left( 1 + \frac{p_{2}}{\lambda
    p_{4}+\sigma^2} \right)}_{R_{2}}
    + \underbrace{\log_2\det \left( 1 + \frac{p_{4}}{\sigma^2} \right)}_{R_{4}}
    & \mathrm{subject\ to}\qquad p_{1}+p_{2} \leq 1;\ p_{3}+p_{4} \leq 1;\ R_{1}+R_{2}+R_{3} \leq 1
    \end{equation} [/itex]

    The problem is not convex. However, I still would like to find the optimal power assignment [itex] p_1, p_2, p_3, p_4 [/itex]. I have little knowledge of optimization techniques, therefore I would be happy about any advice how to proceed.

    My first idea is, to test if the function is quasi-convex, but I do not know how to proof this property.

    I also would be very happy about concrete advices which technique or solver is suitable to find the solution.

    If the second constraint is a big problem, I would also be happy to find the optimal power assignment for the relaxed problem without this constraint.

    Thank you very much for your attention!

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted