Optimal power allocation in block fading Gaussian channels with causal CSI and secrecy constraints

The optimal power allocation that maximizes the secrecy capacity (SC) of block fading Gaussian (BF-Gaussian) networks with causal channel state information (CSI), M-block delay tolerance and a frame based power constraint is examined. In particular, the SC maximization is formulated as a dynamic program. First, the SC maximization without any information on the CSI is studied; in this case the SC is maximized by equidistribution of the power budget, denoted as the 'blind policy'. Next, extending earlier results on the capacity maximization of BF-Gaussian channels without secrecy constraints, transmission policies for the low SNR and the high SNR regimes are proposed. When the available power resources are very low the optimal strategy is a 'threshold policy'. On the other hand when the available power budget is very large a 'constant power policy' maximizes the frame secrecy capacity. Subsequently, a novel universal transmission policy is introduced, denoted in the following as the 'blind horizon approximation' (BHA), by imposing a blind policy in the horizon of unknown events. Through numerical results, the novel BHA policy is shown to outperform both the threshold and constant power policies as long as the mean channel gain of the legitimate user is distinctively greater than the mean channel gain of the eavesdropper. Furthermore, the secrecy rates achieved by the BHA compare well with the secrecy rates of the secure waterfilling policy in the case of acausal CSI feedback to the transmitter.