Secure Multiple-Antenna Block-Fading Wiretap Channels with Limited CSI Feedback

In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. The transmitter, on the other hand, is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback link becomes large, i.e. $B \rightarrow \infty$ ; hence, fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high Signal-to-Noise Ratio (SNR), and evaluate the gap between the bounds.