Power Allocation for Discrete-Input Delay-Limited Fading Channels

We consider power allocation algorithms for fixed-rate transmission over Nakagami-m nonergodic block-fading channels with perfect transmitter and receiver channel state information and discrete input signal constellations, under both shortand long-term power constraints. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. We show that the SNR exponent of the optimal short-term scheme is given by m times the Singleton bound. We also illustrate the significant gains available by employing long-term power constraints. In particular, we analyze the optimal long-term solution, showing that zero outage can be achieved provided that the corresponding short-term SNR exponent with the same system parameters is strictly greater than one. Conversely, if the short-term SNR exponent is smaller than one, we show that zero outage cannot be achieved. In this case, we derive the corresponding long-term SNR exponent as a function of the Singleton bound. Due to the nature of the expressions involved, the complexity of optimal schemes may be prohibitive for system implementation. We therefore propose simple sub-optimal power allocation schemes whose outage probability performance is very close to the minimum outage probability obtained by optimal schemes. We also show the applicability of these techniques to practical systems employing orthogonal frequency division multiplexing. K. D. Nguyen and L. K. Rasmussen are with the Institute for Telecommunications Research, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes 5095, South Australia, Australia, e-mail: [email protected], [email protected]. A. Guillén i Fàbregas is with the Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK, e-mail: [email protected]. Parts of this work will be presented in the 2007 IEEE Information Theory Workshop, Lake Tahoe, CA, USA, September 2007. This work has been supported by the Australian Research Council under ARC grants RN0459498 and DP0558861. February 5, 2008 DRAFT ar X iv :0 70 6. 20 33 v1 [ cs .I T ] 1 4 Ju n 20 07