On the Interference Alignment Designs for Secure Multiuser MIMO Systems

In this paper, we propose two secure multiuser multiple-input multiple-output transmission approaches based on interference alignment (IA) in the presence of an eavesdropper. To deal with the information leakage to the eavesdropper as well as the interference signals from undesired transmitters (Txs) at desired receivers (Rxs), our approaches aim to design the transmit precoding and receive subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals (WSs). The first proposed IA scheme focuses on aligning the WSs into proper subspaces while the second one imposes a new structure on the precoding matrices to force the WSs to zero. When the channel state information is perfectly known at all Txs, in each proposed IA scheme, the precoding matrices at Txs and the receive subspaces at Rxs or the eavesdropper are alternatively selected to minimize the cost function of an convex optimization problem for every iteration. We provide the feasible conditions and the proofs of convergence for both IA approaches. The simulation results indicate that our two IA approaches outperform the conventional IA algorithm in terms of average secrecy sum rate.Comment: Updated version, updated author list, accepted to be appear in IEICE Transaction

Homotopy continuation for spatial interference alignment in arbitrary MIMO X networks

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce.This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, under grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN), MTM2014-57590-P, and FPI grant BES-2014-069786

The spatial state of non-interacting photons

High-dimensional quantum systems are becoming an increasingly important area of study. Due to their ability to encode more information than a two-dimensional system, high-dimensional systems are useful in many applications, from quantum communication to quantum computing. In particular, spatial states of light, such as orbital angular momentum and spatial position, are inherently high-dimensional by nature and lend themselves well to manipulation and measurement. As light is commonly used in communication applications, spatial states could extend the information capacity of quantum communication and make it easier to detect eavesdroppers in the system. This thesis comprises four experiments in which the spatial state of photons is manipulated and measured. The first experiment describes a filter for two dimensional anti-symmetric spatial states. We use a pair of photons entangled in multiple orbital angular momentum states in order to test the filter. We are able to manipulate which two-dimensional subspaces are in symmetric states and which are in anti-symmetric states, and as such we are able to filter out particular subspaces, effectively engineering high-dimensional states via Hong-Ou-Mandel interference. In the second experiment, we use the anti-symmetric state filter in a four-photon system. We begin with two pairs of photons, with entanglement within the pairs but not between the pairs. Combining one photon from each pair in our anti-symmetric state filter, we create entanglement between the other two photons, achieving entanglement swapping. Additionally, due to the two-dimensional nature of the filter, we transcribe entanglement into several two-dimensional subspaces in the process. In the third experiment, we investigate the quantum teleportation that occurs as a side effect of the entanglement swapping. We demonstrate teleportation of several two-dimensional OAM states, and we describe the result of attempted high dimensional teleportation. In the fourth and final experiment, we turn our attention from the OAM of light to the spatial position of light. Using our four-photon system and anti-symmetric state filter, we demonstrate ghost imaging between photons that have never interacted. This is enabled by taking advantage of the correlations produced when entanglement swapping occurs in the filter

Blind Source Separation and Localization Using Microphone Arrays

The blind source separation and localization problem for audio signals is studied using microphone arrays. Pure delay mixtures of source signals typically encountered in outdoor environments are considered. Our proposed approach utilizes the subspace methods, including multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms, to estimate the directions of arrival (DOAs) of the sources from the collected mixtures. Since audio signals are generally considered broadband, the DOA estimates at frequencies with the large sum of squared amplitude values are combined to obtain the final DOA estimates. Using the estimated DOAs, the corresponding mixing and demixing matrices are computed, and the source signals are recovered using the inverse short time Fourier transform. Subspace methods take advantage of the spatial covariance matrix of the collected mixtures to achieve robustness to noise. While the subspace methods have been studied for localizing radio frequency signals, audio signals have their special properties. For instance, they are nonstationary, naturally broadband and analog. All of these make the separation and localization for the audio signals more challenging. Moreover, our algorithm is essentially equivalent to the beamforming technique, which suppresses the signals in unwanted directions and only recovers the signals in the estimated DOAs. Several crucial issues related to our algorithm and their solutions have been discussed, including source number estimation, spatial aliasing, artifact filtering, different ways of mixture generation, and source coordinate estimation using multiple arrays. Additionally, comprehensive simulations and experiments have been conducted to examine various aspects of the algorithm. Unlike the existing blind source separation and localization methods, which are generally time consuming, our algorithm needs signal mixtures of only a short duration and therefore supports real-time implementation.School of Materials Science & Engineerin