Information-theoretic and communication-theoretic optimal power allocation for fading channels

In this paper we study power allocation (PA) policies for fading channels when perfect CSIR and perfect CSIT are available. The transmitter has an average power constraint. Information-theoretic (IT) PA policies that maximize the channel capacity and communication-theoretic (CT) PA policies that minimize the symbol-error rate (SER) of uncoded systems are derived for M-PAM. It is shown that these policies are close. These policies are quite different from common policies like waterfilling (WF) and truncated channel inversion (TCI) [l]. We also show that these policies give significant improvements in BER even for Rayleigh fading channel for uncoded, convolutionally and turbo coded systems (turbo code results not shown here). This is in sharp contrast to the negligible capacity improvement with PA reported in [l]. We consider a single user communication system. The symbols are transmitted over a (stationary ergodic) fading channel with AWGN. Assuming coherent demodulation and appropriate samplin the discrete representation of the channel is yk = Xk Uk k = 0,1,2,..., where Xk is the output of the encoder, ak is the fading gain, .?(ak) is the transmitted power and {nk} is an AWGN process with variance u2 = N0/2. Let PA be the p.d.f. of a and xk E x, an M-PAM signal set. Assume the average power constraint S. The IT optimal PA policy and the corresponding channel capacity C, for M-PARI are given by the solution to the following optimization problem: max,(.) JT C,(U)~A(U)~U subj. toJom s(u)~A(~)~u = S,