There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.

Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning

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Spotlight Synthetic Aperture Radar Signal Processing Algorithms

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. However, deriving efficient strategies that jointly bring into play the primal and dual problems is a more recent idea that has generated many important new contributions in recent years. These novel developments are grounded in the recent advances in convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with an emphasis on sparsity issues. In this article, we aim to present the principles of primal?dual approaches while providing an overview of the numerical methods that have been proposed in different contexts. Last but not least, primal?dual methods lead to algorithms that are easily parallelizable. Today, such parallel algorithms are becoming increasingly important for efficiently handling high-dimensional problems.

https://hal.archives-ouvertes.fr/hal-01010437/document

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems

This paper reviews recent progress of portable short-range noncontact microwave radar systems for motion detection, positioning, and imaging applications. With the continuous advancements of modern semiconductor technologies and embedded computing, many functionalities that could only be achieved by bulky radar systems in the past are now integrated into portable devices with integrated circuit chips and printed circuits boards. These portable solutions are able to provide high motion detection sensitivity, excellent signal-to-noise ratio, and satisfactory range detection capability. Assisted by on-board signal processing algorithms, they can play important roles in various areas, such as health and elderly care, veterinary monitoring, human-computer interaction, structural monitoring, indoor tracking, and wind engineering. This paper reviews some system architectures and practical implementations for typical wireless sensing applications. It also discusses potential future developments for the next-generation portable smart radar systems.

A Review on Recent Progress of Portable Short-Range Noncontact Microwave Radar Systems

This paper presents a novel nonlinearity correction algorithm for wideband frequency modulated continuous wave (FMCW) radars based on high-order ambiguity functions (HAF) and time resampling. By emphasizing the polynomial-phase nature of the FMCW signal, it is shown that the HAF is an excellent tool for estimating the sweep nonlinearity polynomial coefficients. The estimated coefficients are used to build a correction function which is applied to the beat signal by time resampling. The nonlinearity correction algorithm is tested by simulation and validated on real data sets acquired with an X-band FMCW radar.

/pdf/nonlinearity-correction-algorithm-for-wideband-fmcw-radars-3sktlvsaiw.pdf

Nonlinearity correction algorithm for wideband FMCW radars

This letter proposes a micro-Doppler (m-D) reconstruction method for spaceborne synthetic aperture radar (SAR) images using azimuth time–frequency tracking of the phase history. The algorithm involves an azimuth defocusing of the SAR image in order to gain access to the phase history, followed by a time–frequency tracking algorithm. The tracking in azimuth is based on local polynomial phase modeling using as estimator for the polynomial coefficients the high-order ambiguity function. The approach is presented in the context of vibration estimation for infrastructure monitoring applications, with an emphasis on the estimation of vibration parameters from the reconstructed m-D. The procedure is tested and compared with state-of-the-art methods by various simulation scenarios in keeping with typical high-resolution SAR imaging parameters. Finally, the developed algorithm is applied on real data acquired by the TerraSAR-X satellite over the Puylaurent water dam in France.

Micro-Doppler Reconstruction in Spaceborne SAR Images Using Azimuth Time–Frequency Tracking of the Phase History

Two versions of the RLS algorithm suitable for fixed-point implementation are proposed. A brief analysis concerning the convergence properties and the finite precision effects is performed. The simulation results show superior performances of these algorithms in the context of fixed-point implementation.

On the behavior of RLS adaptive algorithm in fixed-point implementation

Next generation of 5G mobile communications heavily relies on exploiting the spatial degrees of freedom of the radio channels. For this reason, the idea of having base stations (BSs) with a large number of antennas is currently one of the main research topics in the wireless communications field.

Performance analysis of the Singular Value Decomposition with block-diagonalization precoding in Multi-User Massive MIMO systems

In this paper, we present a least-mean-square (LMS) adaptive filter tailored for bilinear forms. The bilinear term is defined with respect to the impulse responses of a spatiotemporal model, which resembles a multiple-input/single-output (MISO) system. A convergence analysis is also provided, outlining the main features of this algorithm. Simulation results support the theoretical findings.

Silviu Ciochina

Papers

Nonlinearity correction algorithm for wideband FMCW radars

Micro-Doppler Reconstruction in Spaceborne SAR Images Using Azimuth Time–Frequency Tracking of the Phase History

On the behavior of RLS adaptive algorithm in fixed-point implementation

Performance analysis of the Singular Value Decomposition with block-diagonalization precoding in Multi-User Massive MIMO systems

Analysis of an LMS algorithm for bilinear forms