This paper considers secrecy communication from a signal processing point of view, and studies the maximal achievable secrecy degrees of freedoms (S.D.o.F.) of a helper-assisted Gaussian wiretap channel, consisting of a source, a legitimate receiver, an eavesdropper and an external helper. Each terminal is equipped with multiple antennas. We first propose a cooperative secrecy transmission scheme, and show that it achieves the maximal secrecy degrees of freedom. We then propose a heuristic method, through which, we solve analytically the optimization problem associated with the proposed cooperative secrecy transmission scheme. By this way, we obtain the maximal achievable S.D.o.F. and also the precoding matrices which achieve the maximal S.D.o.F. in closed-form.
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.
This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eve’s channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.
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 investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with
Na,
Nj and
Ne antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.
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 investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with Na, Njand Neantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if Nea+Nj-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where Nea+Nj-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.