On the Secrecy Capacity of the Wiretap Channel With Imperfect Main Channel Estimation

Abstract

Abstract-We study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels, and is the best known upper bound so far. The upper and the lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) are also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.

Achievable Rates of Secure Transmission in Gaussian MISO Channel With Imperfect Main Channel Estimation

“…In [19], the transmitter is provided a noisy version of the main CSI and only the statistics of the eavesdropper's CSI. The authors give a lower bound and an upper bound on the secrecy capacity under this setting.…”

On Secrecy Performance of MISO SWIPT Systems With TAS and Imperfect CSI

“…The figure implies that there exists a unique optimal PS factor, which makes |∆| = 0 and can achieve the tradeoff between information eavesdropping and EH as suggested by Eq. (40). We also find that, when T 1 /T 2 = 2, the optimal PS factor increases while P t /N 0 increasing, it is because in this case more energy can be harvested to deliver the eavesdropped information with a same PS factor, then more power of the received signal can be used to for information decoding.…”

“…11 demonstrates the relationship between |∆| and ρ for various combinations of P t /N 0 and T 1 /T 2 from Eq. (40). The figure implies that there exists a unique optimal PS factor, which makes |∆| = 0 and can achieve the tradeoff between information eavesdropping and EH as suggested by Eq.…”

Rate Adaptation for Secure HARQ Protocols

“…The assumption of the knowledge of the eavesdropper's CSI is an idealization, 2 so [36] studied the case where the channel to the eavesdropper experiences fading not known to the legitimate users. The effect of partial CSI on achievable secure communication rates and on secret-key generation was also investigated in [37], and [38] provided bounds on the ergodic secrecy capacity. The case of transmission without CSI at the encoder was investigated in [39], where the ergodic secrecy capacity for fast fading wiretap channel was characterized; and in [40], which proposed an alternative secrecy outage formulation to measure the probability that message transmission fails to achieve perfect secrecy.…”

“…Let the length of the first transmission blocn ∈ N be larger than (n 1 , n 2 , n 3 , n 4 , n 5 , n 6 , n 7 , n 8 , n 9 ) given by equations (39), (40), (41), (42), (62), (63), (64), (65) and (66). We prove that there exists a HARQ-code c ⋆ ∈ C(n, R, L) with stochastic encoder such that the error probability and the information leakage rate satisfy equation (38), for all channel states…”