Allerton Conference on Communication, Control, and Computing
How many antennas does a cooperative jammer need for achieving the degrees of freedom of multiple antenna Gaussian channels in the presence of an eavesdropper?
In this work, multiple antenna Gaussian wiretap channels with a multiantenna cooperative jammer are considered. In particular, the focus is on identifying the spatial resources needed at the cooperative jammer in order to achieve a secure degrees of freedom (s.d.o.f.) for the channel in question equal to the degrees of freedom (d.o.f.). In order to accomplish this goal, the cooperative jammer sets out to send correlated jamming signals. Simultaneously, the legitimate transmitter chooses a precoder that perfectly aligns its information signals over the jamming ones at the eavesdropper. Both terminals use structured signaling, i.e., discrete constellations. The proposed approach is shown to achieve full d.o.f. for the channel at hand as long as the cooperative jammer has twice the antennas of the eavesdropper. It is also shown that within 1/2 of the d.o.f. is achievable with one less antenna at the cooperative jammer.
In this work, multiple antenna Gaussian wiretap channels with a multiantenna cooperative jammer are considered. In particular, the focus is on identifying the spatial resources needed at the cooperative jammer in order to achieve a secure degrees of freedom (s.d.o.f.) for the channel in question equal to the degrees of freedom (d.o.f.). In order to accomplish this goal, the cooperative jammer sets out to send correlated jamming signals. Simultaneously, the legitimate transmitter chooses a precoder that perfectly aligns its information signals over the jamming ones at the eavesdropper. Both terminals use structured signaling, i.e., discrete constellations. The proposed approach is shown to achieve full d.o.f. for the channel at hand as long as the cooperative jammer has twice the antennas of the eavesdropper. It is also shown that within 1/2 of the d.o.f. is achievable with one less antenna at the cooperative jammer.
A Gaussian wiretap channel with a helper, i.e., a cooperative jammer, is considered and its secure degrees of freedom (s.d.o.f.) is computed. Previous work showed that the s.d.o.f. is upper bounded by 1 over 2 in this model when all parties are equipped with one antenna each. In this paper, the more challenging scenario where the eavesdropper has multiple antennas is tackled. Relying on structured signaling and cooperative jamming, specifically, by real interference alignment, it is shown that s.d.o.f. of 1 over 2 is achievable irrespective of the number of antennas the eavesdropper may have as long as the cooperative jammer has the same number of antennas as the eavesdropper. The design insight revealed is that the price to pay for the increase in the number of antennas at the eavesdropper is an equivalent increase in the number of antennas at the cooperative jammer in order to maintain the same s.d.o.f.
A multiple antenna Gaussian wiretap channel with a multiantenna cooperative jammer (CJ) is considered and the secure degrees of freedom (s.d.o.f.), with N antennas at the sender, receiver, and eavesdropper, is derived for all possible values of the number of antennas at the cooperative jammer, K. In particular, the upper and lower bounds for the s.d.o.f. are provided for different ranges of K and shown to coincide. Gaussian signaling both for transmission and jamming is shown to be sufficient to achieve the s.d.o.f. of the channel, when the s.d.o.f. is integer-valued. By contrast, when the channel has a non-integer s.d.o.f., structured signaling and joint signal space and signal scale alignment are employed to achieve the s.d.o.f.
The secure degrees of freedom (s.d.o.f.) of a multiantenna Gaussian wiretap channel with N antennas at the transmitter and receiver and an arbitrary number of antennas, M, at the wiretapper is characterized when a multiantenna cooperative jammer (CJ) is available as a helper. This generalizes our previous result that assumed the same number of antennas at the eavesdropper as the legitimate parties. In particular, for arbitrary values of N andM, the s.d.o.f. is derived for all possible values of the number of antenna at the CJ, K. The achievability is based on a variety of signalling, beamforming, and alignment techniques which vary according to the value of K, whether M is larger than, smaller than, or equal to N, and whether the s.d.o.f. is integer valued or not an integer. The converse is based on combining an upper bound for the s.d.o.f. which allows for cooperation between the transmitter and CJ and holds for some values of K, with another upper bound which exploits the secrecy and reliability constraints and holds for other values of K.
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 investigate the secure degrees of freedom (SDoF) of the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in the presence of a multi-antenna cooperative jammer. We focus on the practically relevant setting with no channel state information at the transmitters (CSIT). More specifically, the legitimate transmitter and the cooperative jammer only have statistical knowledge of the channel in terms of the effective number of ISI channel taps, i.e., channel impulse response (CIR) lengths, toward the legitimate receiver and the eavesdropper. Our main contribution is to show that in the absence of CSIT, positive SDoF can be achieved by carefully exploiting: 1) the heterogeneity of the CIR lengths toward both receivers and 2) the relative number of antennas at the four terminals. To achieve secrecy, we propose a scheme in which the transmitter strategically sends a mixture of information and artificial noise symbols in a way that exploits the heterogeneity of CIR lengths. Additionally, the cooperative jammer transmits artificial noise symbols in a way that completely masks all the information symbols that are received at the eavesdropping node. Under the proposed scheme, positive SDoF can be achieved, even when the number of antennas at the legitimate receiver is less than the number of antennas at the eavesdropper.
We consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. The exact secure d.o.f. of the Gaussian wiretap channel with M helpers with perfect CSI at the transmitters was found in [1], [2] to be M/M+1. One of the key ingredients of the optimal achievable scheme in [1], [2] is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This required perfect eavesdropper CSI at the transmitters. Motivated by the recent result in [3], we propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same secure d.o.f. of M/M+1 in [1], [2] but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper.