Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel

Abstract

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks.At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semiblind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime.Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs 3 times as many antennas as the sender and intended receiver have jointly, and that the optimimum division of antennas between sender and intended receiver is in the ratio of 2 : 1.Index Terms-MIMO wiretap channel, secrecy capacity, cryptography, multiple antennas, broadcast channel.

Secure degrees of freedom for the MIMO wiretap channel with a multiantenna cooperative jammer

“…The covariance matrices K t and K c are chosen so that they are positive definite, i.e., K t , K c ≻ 0, and hence non-singular, in order to guarantee the finiteness of h(Z t ) and h(Z c ) in (26). In…”

Secure Diversity-Multiplexing Tradeoff of Zero-Forcing Transmit Scheme at Finite-SNR

“…Furthermore, the secrecy capacity is given by: C s ≔ sup R∈R s R, where R s is the set of achievable secrecy rates. The secrecy capacity of the MIMO wiretap channel in nats per channel use (npcu) is given by [8]- [10]:…”

Secrecy performance analysis for transmit antenna selection with outdated CSI

“…Motivated by emerging wireless applications with multiple antenna terminals, physical layer security in multiple-input multiple-output (MIMO) wiretap channels has recently been addressed from an information theoretic perspective [1,2]. Taking the statistics of wireless fading into consideration, the secrecy outage probability for different transmission schemes was examined for various fading environments.…”