Abstract--Energy efficiency is becoming increasingly important for small form factor mobile devices, as battery technology has not kept up with the growing requirements stemming from ubiquitous multimedia applications. This paper addresses link adaptive transmission for maximization of energy efficiency rather than throughput. We extend our previous results for flat fading OFDMA to frequency-selective channels. Different from existing water-filling power allocation schemes that maximize throughput subject to overall transmit power constraints, our scheme adapts both overall transmit power and its allocation according to the states of all subchannels and circuit power consumption to maximize energy efficiency. We demonstrate the existence of a unique globally optimal link adaptation solution and provide iterative algorithms to obtain this optimum. Simulation results show at least a 15% improvement in energy utilization when frequency selectivity is exploited.