On the capacity and energy efficiency of non-coherent Rayleigh fading channels with additive Gaussian mixture noise

This paper studies the capacity and energy efficiency of non-coherent Rayleigh fading channels with Gaussian mixture noise where neither the transmitter nor the receiver has the knowledge of channel state information. The channel under consideration is suited for cellular networks having multi-tier heterogeneous architectures in which the channel conditions change rapidly. In the first part of the paper, we characterize the structure of a capacity-achieving input signal. Specifically, we establish an integrable upper bound on the integrand in the output entropy and demonstrate that there exists a unique optimal input. By formulating the Kuhn-Tucker condition and establishing a diverging lower bound on it, we show that the optimal input is discrete having a finite number of mass points. Using this result, we investigate the capacity and energy efficiency of the considered channel in the second part of the paper. In particular, we first develop a numerical method to evaluate the optimal input and compute the capacity. The energy efficiency, which is related to the capacity and optimal input in low-power regimes, is examined by calculating the minimum bit energy and wideband slope of the spectral-efficiency curve. We also analytically show the optimality of an on-off signal in this regime.