The low power regime has attracted various researchers in the information theory and communication communities to understand the performance limits of wireless systems. Indeed, the energy consumption is becoming one of the major limiting factors in wireless systems. As such, energy-efficient wireless systems are of major importance to the next generation wireless systems designers. The capacity is a metric that measures the performance limit of a wireless system. The study of the ergodic capacity of some fading channels in the low power regime is the main subject of this thesis. In our study, we consider that the receiver has always a full knowledge of the channel state information. However, we assume that the transmitter has possibly imperfect knowledge of the channel state information, i.e. he knows either perfectly the channel or only an estimated version of the channel. Both radio frequency and free space optical communication channel models are considered. The main contribution of this work is the explicit characterization of how the capacity scales as function of the signal-to-noise ratio in the low power regime. This allows us to characterize the gain due to the perfect knowledge compared to no knowledge of the channel state information at the transmitter. In particular, we show that the gain increases logarithmically for radio frequency communication. However, the gain increases as log2(Pavg) or log4(Pavg) for free-space optical communication, where Pavg is the average power constraint imposed to the input. Furthermore, we characterize the capacity of cascaded fading channels and we applied the result to Rayleigh-product fading channel and to a free-space optical link over gamma-gamma atmospheric turbulence in the presence of pointing errors. Finally, we study the capacity of Nakagami-m fading channel under quality of service constraints, namely the effective capacity. We have shown that the effective capacity converges to Shannon capacity in the very low power regime.
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