Dzevdan Kapetanovic

Physical layer security for massive MIMO: An overview on passive eavesdropping and active attacks

This article discusses opportunities and challenges of physical layer security integration in MaMIMO systems. Specifically, we first show that MaMIMO itself is robust against passive eavesdropping attacks. We then review a pilot contamination scheme that actively attacks the channel estimation process. This pilot contamination attack not only dramatically reduces the achievable secrecy capacity but is also difficult to detect. We proceed by reviewing some methods from literature that detect active attacks on MaMIMO. The last part of the article surveys the open research problems that we believe are the most important to address in the future and give a few promising directions of research to solve them.

Detection of pilot contamination attack using random training and massive MIMO

Channel estimation attacks can degrade the performance of the legitimate system and facilitate eavesdropping. It is known that pilot contamination can alter the legitimate transmit precoder design and strengthen the quality of the received signal at the eavesdropper, without being detected. In this paper, we devise a technique which employs random pilots chosen from a known set of phase-shift keying (PSK) symbols to detect pilot contamination. The scheme only requires two training periods without any prior channel knowledge. Our analysis demonstrates that using the proposed technique in a massive MIMO system, the detection probability of pilot contamination attacks can be made arbitrarily close to 1. Simulation results reveal that the proposed technique can significantly increase the detection probability and is robust to noise power as well as the eavesdroppers power.

Optimal Two-Dimensional Lattices for Precoding of Linear Channels

Consider the communication system model y = HFx + n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any nonsingular M × 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D4.

Detection of active eavesdroppers in massive MIMO

We consider physical layer security of massive MIMO systems in TDD mode. We show that with massive MIMO a passive eavesdropper is not very dangerous and must therefore be active and attack the training phase. An attack on the training phase is potentially very harmful to the physical layer security, and we therefore investigate three different schemes for detecting the presence of an active eavesdropper. The three schemes differ in the location where the detection is done (base station, intended user, or jointly), and also in the level of system parameters that are assumed known to the base station and/or intended user.

Design of close to optimal Euclidean distance MIMO-precoders

In this work we study the problem of constructing precoders for spatially multiplexed multiple-input multiple output (MIMO) channels with close to optimal minimum Euclidean distance. In order to exploit the full potential of such designs, an ML detector must be used. Our design takes the decoding complexity into account and constrains it to a reasonable level. For our simplest case, the ML detector can be implemented by a Viterbi algorithm operating on a state space of size equal to the size of the modulation alphabet. The design problem will be relaxed by using precoders F such that F*H*HF is a cyclic Toeplitz matrix. Within this class of precoders, the optimal precoder can be found via linear programming. Of uttermost practical importance is the discovery that there only exist very few different effective channels HF even for large MIMO setups; thus, the optimization at the transmitter side reduces into choosing the best precoder from a small list. Receiver tests verify that our method improves upon the currently best precoder designs.

Optimal lattices for MIMO precoding

Consider the communication model ȳ = HF x̄ + n̄, where H; F are real-valued matrices, x̄ is a data vector drawn from some real-valued lattice (e.g. M-PAM), n̄ is additive white Gaussian noise and ȳ is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F x̄ is subject to an average energy constraint. The columns of the matrix HF can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice HF? This particular question remains open within the theory of lattices. This work provides the solution for 2×2 matrices H; F. The answer is an F such that HF is a hexagonal lattice.

Lattice Structures of Precoders Maximizing the Minimum Distance in Linear Channels

This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.

On Precoder Design under Maximum-Likelihood Detection for Quasi-Stationary MIMO Channels

We consider the problem of constructing linear precoders for quasi-stationary multiple-input multiple-output channels. Maximum-likelihood detection is assumed and the objective of the precoding is to maximize the minimum Euclidean distance of the signaling. Since the channel remains constant for some time, the precoding is performed spatially as well as across time. As will be shown, the precoder design is tightly connected to the theory of partial response signaling and precoders can be designed by usage of existing methods. The decoding complexity will be controlled and can be maintained small.

The effect of symbol rate on constrained capacity for linear modulation

We consider the effect of symbol rate on the constrained capacity of linear modulation with a fixed spectral density. We show that constrained capacity grows with the symbol rate for some modulation pulses but shrinks with others. Sufficient conditions on the pulse are derived for the constrained capacity to be monotonically increasing with faster symbol rate. Most standard pulses fulfill these.

The Effect of Signaling Rate on Information Rate for Single Carrier Linear Transmission Systems

We consider the effect of signaling rate (baud rate) on the information rate of single carrier linear transmission systems with Gaussian inputs. Several different communication scenarios are investigated: correlated or uncorrelated symbols, a fixed modulation pulse or a modulation pulse varying with the signaling rate and frequency selective or flat channels. For uncorrelated symbols, we show that the information rate grows monotonically with signaling rate for some cases while it can in fact decrease in other cases. Sufficient conditions on the modulation pulse and the channel impulse response are derived so that the information rate is increasing with increased signaling rate. Especially, these conditions give criterias for when non-orthogonal signaling is beneficial compared to orthogonal signaling in the case of flat fading. For modulation pulses varying with the signaling rate, it is shown that there are pulses for which the information rate is non-decreasing with increasing signaling rate. When correlation between symbols is allowed, we show that one can guarantee increasing information rate with increased signaling rate, no matter the pulse-channel shape (except for some hypothetical special cases), by signaling with an SNR above a certain finite threshold.