Fractional programming (FP) plays an important role in information science because of the Cramer-Rao bound,the Fisher information, and the signal-to-interference-plus-noise ratio (SINR). A state-of-the-art method called the quadratic transform has been extensively used to address the FP problems. This work aims to accelerate the quadratic transform-based iterative optimization via gradient projection and extrapolation. The main contributions of this work are three-fold. First, we relate the quadratic transform to the gradient projection, thereby eliminating the matrix inverse operation from the iterative optimization; our result generalizes the weighted sum-of-rates (WSR) maximization algorithm in [1] to a wide range of FP problems. Second, based on this connection to gradient projection, we incorporate Nesterov's extrapolation strategy [2] into the quadratic transform so as to accelerate the convergence of the iterative optimization. Third, from a minorization-maximization (MM) point of view, we examine the convergence rates of the conventional quadratic transform methods--which include the weighted minimum mean square error (WMMSE) algorithm as a special case--and the proposed accelerated ones. Moreover, we illustrate the practical use of the accelerated quadratic transform in two popular application cases of future wireless networks: (i) integrated sensing and communication (ISAC) and (ii) massive multiple-input multiple-output (MIMO).

翻译：分数规划（FP）在信息科学中扮演重要角色，这得益于克拉美-罗界、费雪信息以及信干噪比（SINR）。一种称为二次变换的先进方法已被广泛用于解决FP问题。本文旨在通过梯度投影和外推法加速基于二次变换的迭代优化。本文的主要贡献有三个方面：首先，我们将二次变换与梯度投影联系起来，从而消除迭代优化中的矩阵求逆运算；我们的结果将[1]中的加权和速率（WSR）最大化算法推广到更广泛的FP问题。其次，基于这种与梯度投影的关联，我们将Nesterov的外推策略[2]引入二次变换，以加速迭代优化的收敛。第三，从极小化-最大化（MM）的角度，我们考察了传统二次变换方法（其中加权最小均方误差（WMMSE）算法是其特例）以及所提出的加速方法的收敛速率。此外，我们还在未来无线网络的两个典型应用场景中展示了加速二次变换的实际应用：（i）集成感知与通信（ISAC）和（ii）大规模多输入多输出（MIMO）。