realization theory 5.5 Notes 116 6. ISOMETRIC AND INNER OPERATORS 6.1 Realization of inner operators 6.2 External factorization 6.3 State-space properties of isometric systems 6.4 Beurling-Lax like theorem 6.5 Example 7. INNER-OUTER FACTORIZATION AND OPERATOR INVERSION 7.1 Introduction 7.2 Inner-outer factorizations 7.3 Operator inversion 7.4 Examples 7.5 Zero structure and its limiting behavior 7.6 Notes Part II INTERPOLATION AND APPROXIMATION 8. J-UNITARY OPERATORS 8.1 Scattering operators 8.2 Geometry of diagonal J-inner product spaces 8.3 State space properties of J-unitary operators 8.4 Past and future scattering operators 210 8.5 J-unitary external factorization 215 8.6 J-Iossless and J-inner chain scattering operators 218 8.7 The mixed causality case 223 9. ALGEBRAIC INTERPOLATION 233 9.1 Diagonal evaluations or the W-transform 235 9.2 The algebraic Nevanlinna-Pick problem 237 9.3 The tangential Nevanlinna-Pick problem 242 9.4 The Hermite-Fejer interpolation problem 242 9.5 Conjugation of a left interpolation problem 245 9.6 Two sided interpolation 250 9.7 The four block problem 260

Radio astronomy is known for its very large telescope dishes, but is currently making a transition towards the use of large numbers of small elements. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations, each consisting of at least 96 low band antennas and 768 high band antennas. For the Square Kilometre Array, planned for 2024, the numbers will be even larger. These instruments pose interesting array signal processing challenges. To present some aspects, we start by describing how the measured correlation data is traditionally converted into an image, and translate this into an array signal processing framework. This paves the way for a number of alternative image reconstruction techniques, such as a Weighted Least Squares approach. Self-calibration of the instrument is required to handle instrumental effects such as the unknown, possibly direction dependent, response of the receiving elements, as well a unknown propagation conditions through the Earth's troposphere and ionosphere. Array signal processing techniques seem well suited to handle these challenges. The fact that the noise power at each antenna element may be different motivates the use of Factor Analysis, as a more appropriate alternative to the eigenvalue decomposition that is commonly used in array processing. Factor Analysis also proves to be very useful for interference mitigation. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.

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The multi-input single-output multi-eavesdropper (MISOME) wiretap channel is one of the generic wiretap channels in physical layer security. In Khisti and Wornell's classical work [1], the optimal secure beamformer for MISOME has been derived under the total power constraint. In this work, we revisit the MISOME wiretap channel and focus on the large-scale transmit antenna regime and the constant modulus beamformer design. The former is motivated by the significant spectral efficiency gains provided by massive antennas, and the latter is due to the consideration of cheap hardware implementation of constant modulus beamforming. However, from an optimization point of view, the secrecy beamforming with constant modulus constraints is challenging, more specifically, NP-hard. In light of this, we propose two methods to tackle it, namely the semidefinite relaxation (SDR) method and the ADMM-Dinkelbach method. Simulation results demonstrate that the ADMM-Dinkelbach method outperforms the SDR method, and can attain nearly optimal secrecy performance for the large-scale antenna scenario.

A fully-asynchronous network with one target sensor and a few anchors (nodes with known locations) is considered. Localization and synchronization are traditionally treated as two separate problems. In this paper, localization and synchronization is studied under a unified framework. We present a new model in which time-stamps obtained either via twoway communication between the nodes or with a broadcast based protocol can be used in a simple estimator based on least-squares (LS) to jointly estimate the position of the target node as well as all the unknown clock-skews and clockoffsets. The Cramér-Rao lower bound (CRLB) is derived for the considered problem and is used as a benchmark to analyze the performance of the proposed estimator.