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The randomized Kaczmarz (RK) algorithm is one of the most computationally and memory-efficient iterative algorithms for solving large-scale linear systems. However, practical applications often involve noisy and potentially inconsistent…

Numerical Analysis · Mathematics 2025-10-10 El Houcine Bergou , Soumia Boucherouite , Aritra Dutta , Xin Li , Anna Ma

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…

Numerical Analysis · Computer Science 2014-02-04 Hemant Kumar Aggarwal , Angshul Majumdar

The Kaczmarz method is a popular iterative scheme for solving large-scale linear systems. The randomized Kaczmarz method (RK) greatly improves the convergence rate of the Kaczmarz method, by using the rows of the coefficient matrix in…

Numerical Analysis · Mathematics 2020-12-01 Yutong Jiang , Gang Wu , Long Jiang

In this letter, we consider the multiple-input multiple-output (MIMO) radar waveform design in the presence of signal-dependent clutters and additive white Gaussian noise. By imposing the constant modulus constraint (CMC) and waveform…

Signal Processing · Electrical Eng. & Systems 2018-05-11 Chenglin Ren , Fan liu , Longfei Zhou , Jianming Zhou , Wu Luo , Shengzhi Yang

Modern wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This technology involves operations with an antenna array at a base station that simultaneously serves multiple mobile devices which also use…

Information Theory · Computer Science 2023-07-26 Evgeny Bobrov , Boris Chinyaev , Viktor Kuznetsov , Hao Lu , Dmitrii Minenkov , Sergey Troshin , Daniil Yudakov , Danila Zaev

We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of…

Numerical Analysis · Mathematics 2014-06-10 Ji Liu , Stephen J. Wright , Srikrishna Sridhar

Large-scale linear systems, $Ax=b$, frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized…

Numerical Analysis · Mathematics 2024-08-26 El Houcine Bergou , Soumia Boucherouite , Aritra Dutta , Xin Li , Anna Ma

Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on…

Numerical Analysis · Mathematics 2026-03-03 James Nguyen , Oleg Presnyakov , Adityakrishnan Radhakhrishnan

When solving linear systems $Ax=b$, $A$ and $b$ are given, but the measurements $b$ often contain corruptions. Inspired by recent work on the quantile-randomized Kaczmarz method, we propose an acceleration of the randomized Kaczmarz method…

Numerical Analysis · Mathematics 2024-10-18 Emeric Battaglia , Anna Ma

A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be…

Information Theory · Computer Science 2013-07-16 Amin Sakzad , J. Harshan , Emanuele Viterbo

Rydberg atomic quantum receivers (RAQRs) are capable of receiving multi-band radio-frequency (RF) signals simultaneously, which are expected to break Chu's limit for classical electronic antennas. However, signals from different users will…

Information Theory · Computer Science 2025-09-10 Jieao Zhu , Linglong Dai

The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz (SSRK) is an variant of RK…

Numerical Analysis · Mathematics 2022-02-04 Yotam Yaniv , Jacob D. Moorman , William Swartworth , Thomas Tu , Daji Landis , Deanna Needell

Much stringent reliability and processing latency requirements in ultra-reliable-low-latency-communication (URLLC) traffic make the design of linear massive multiple-input-multiple-output (M-MIMO) receivers becomes very challenging.…

Information Theory · Computer Science 2021-10-28 Alva Kosasih , Wibowo Hardjawana , Branka Vucetic , Chao-Kai Wen

This paper investigates the linear precoder design for $K$-user interference channels of multiple-input multiple-output (MIMO) transceivers under finite alphabet inputs. We first obtain general explicit expressions of the achievable rate…

Information Theory · Computer Science 2016-11-18 Yongpeng Wu , Chengshan Xiao , Xiqi Gao , John D. Matyjas , Zhi Ding

In this paper, linear transceiver design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (MIMO) relaying systems with Gaussian distributed channel estimation errors is investigated. Commonly used transceiver design…

Information Theory · Computer Science 2016-11-18 Chengwen Xing , Shaodan Ma , Zesong Fei , Yik-Chung Wu , H. Vincent Poor

The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…

Numerical Analysis · Mathematics 2022-10-18 Lionel Tondji , Dirk A Lorenz

We consider the problem of angle-robust joint transmit waveform and receive filter design for colocated Multiple-Input Multiple-Output (MIMO) radar, in the presence of signal-dependent interferences. The design problem is cast as a max-min…

Information Theory · Computer Science 2023-07-19 Wei Zhu , Jun Tang

We analyze scheduling algorithms for multiuser communication systems with users having multiple antennas and linear receivers. When there is no feedback of channel information, we consider a common round robin scheduling algorithm, and…

Information Theory · Computer Science 2016-11-18 Raymond H. Y. Louie , Matthew R. McKay , Iain B. Collings

Extra-large massive multiple-input multiple-output (XL-MIMO) systems is a new concept, where spatial non-stationarities allow activate a high number of user equipments (UEs). This paper focuses on a grant-based random access (RA) approach…

Signal Processing · Electrical Eng. & Systems 2020-09-08 Otávio Seidi Nishimura , José Carlos Marinello Filho , Taufik Abrão

In this work, we propose the joint optimization of the automatic gain control (AGC), which works in the remote radio heads (RHHs), and a low-resolution aware (LRA) linear receive filter based on the minimum mean square error (MMSE), which…

Information Theory · Computer Science 2019-12-16 T. Cunha , R. C. de Lamare , T. N. Ferreira