bv_cvxbook_extra_exercises

# 129 optimal jamming power allocation a set of n

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Unformatted text preview: The total interference-plusnoise power at receiver i is given by Ii = Aijk pjk + σ j =i, k=1,...,n where σ &gt; 0 is the known, given (self) noise power of the receivers. Note that the powers of the interference and noise signals add to give the total interference-plus-noise power. The receivers use coherent detection and combining of the desired message signals, which means the eﬀective received signal power at receiver i is given by Si = k=1,...,n 2 (Aiik pik )1/2 . (Thus, the amplitudes of the desired signals add to give the eﬀective signal amplitude.) The total signal to interference-plus-noise ratio (SINR) for receiver i is given by γi = Si /Ii . The problem is to choose transmitter powers pjk that maximize the minimum SINR mini γi , subject to the power limits. Explain in detail how to solve this problem using convex or quasiconvex optimization. If you transform the problem by using a diﬀerent set of variables, explain completely. Identify the objective function, and all constraint functions, indicating if they are convex or quasiconvex, et...
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