Related papers: Quadratic Transform for Fractional Programming in …
This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic…
Fractional programming (FP) plays a crucial role in wireless network design because many relevant problems involve maximizing or minimizing ratio terms. Notice that the maximization case and the minimization case of FP cannot be converted…
Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in the field are fractionally structured, e.g., the Cram\'{e}r-Rao bound, the Fisher information, and the…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether the proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has…
Multiplicative Programming (MP) pertains to a spectrum of optimization problems that involve product term(s). As computational paradigms of communication systems continue to evolve, particularly concerning the offloading strategies of…
In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the cells are partitioned into spatial regions with different frequency reuse factors. To date, FFR techniques…