We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.
We study the Gaussian MISO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, where the transmitter and the helper have an arbitrary number of antennas but the intended receiver and the eavesdropper have only one antenna. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. Assuming Gaussian signaling at the helper, we obtain the optimal beamformers at the transmitter and the helper that achieve the secrecy capacity.
We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with
Mand
Nantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate
RN. The relationship between the average secrecy capacity
CˉNof Gaussian wiretap channel and the average secrecy rate
RˉNachieved by the null-space jamming scheme is investigated, and we prove that
RˉN≤CˉN≤RˉN+1. Based on this inequality and the derived lower and upper bounds on
RN, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when
N>M, the average secrecy capacity increases linearly with the total transmit power; while when
N≤M−1, there exists a performance ceiling on it.
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.
Abstract—This paper addresses secure communications over MIMO wiretap channels with the help of multiple cooperative jammers. The worst-case scenario for Alice, Bob and jammers is considered: Eve has the knowledge of all channel matrices, while neither her channel matrix nor her location is known to the remaining terminals. We propose an artificial noise aided cooperative jamming (AN-CJ) scheme, allowing the total jamming signals to be nulled at Bob. The new scheme is valid for the case where the eavesdropper has more antennas than the transmitter. To evaluate the performance of the AN-CJ scheme, we first derive a closed-form expression for the achievable ergodic secrecy rate with Gaussian input alphabets. Then, we show how Gaussian input alphabets achieve the ergodic secrecy capacity. I.
In a wiretap channel, a transmitter sends confidential messages to an intended legitimate receiver in the presence of an eavesdropper. An external helper can assist secret communication by transmitting independent artificial interference to confuse the eavesdropper. We consider that the legitimate receiver jointly decodes messages from the transmitter and interference from the helper to boost the secrecy rate. In the discrete-memoryless wiretap channel with a helper, we characterize the achievable secrecy rates by comparing the strength of interference at the legitimate receiver and at the eavesdropper. Based on these secrecy rates, we formulate a secrecy rate maximization problem in Gaussian multiple-input multiple-output (MIMO) wiretap channels with a helping interferer, and present an alternating optimization algorithm. Numerical results show that the proposed joint decoding achieves higher secrecy rates than the conventional separate decoding.