In this paper, we introduce the LWCoopPG (Learned Weighting Cooperative Projected Gradient Descent) algorithm for fully distributed MIMO signal detection. The proposed algorithm is a fully distributed algorithm, implementing the projected gradient method over a network, and incorporating a trainable step size and trainable weight parameters, which are tuned by deep unfolding. The computations of the proposed algorithm are fully distributed, eliminating the need for a central processor. Numerical experiments affirmed the superiority of the LWCoopPG algorithm over the conventional MMSE algorithm in terms of detection performance.

This paper presents a design method for Mach-Zehnder interferometers (MZIs)-based optical circuits intended for MIMO signal detection that are robust against fabrication errors in MZIs. Typically, faulty MZIs can critically impair the functioning of optical circuits. Our primary objective is to devise a design strategy that ensures the reliability of optical circuits for MIMO linear detection even when faced with faulty MZIs. The cornerstone of our approach is the adjustment of parameters in functional MZIs by minimizing the receiver's mean squared error using a gradient descent method. Numerical experiments underscore that our method enables signal detectors, even with faulty MZIs, to approach the performance of an ideal, faultless MMSE MIMO detector.

Motivated by emerging technologies for energy ef-ficient analog computing and continuous-time processing, this paper proposes continuous-time minimum mean squared error estimation for multiple-input multiple-output (MIMO) systems based on an ordinary differential equation. Mean squared error (MSE) is a principal detection performance measure of estimation methods for MIMO systems. We derive an analytical MSE formula that indicates the MSE at any time. The MSE of the proposed method depends on a regularization parameter which affects the convergence property of the MSE. Furthermore, we extend the proposed method by using a time-dependent regularization parameter to achieve better convergence performance. Numerical experiments indicated excellent agreement with the theoretical values and improvement in the convergence performance owing to the use of the time-dependent parameter.

A continuous-time average consensus system is a linear dynamical system defined over a graph. Each node has its state value, and it evolves according to a simultaneous linear differential equation where a node is allowed to interact with neighboring nodes. An average consensus process eventually converges to the state where all the state values are identical to the average of the initial state values. We first formulate the noisy average consensus system by using stochastic differential equations (SDE). This enables us to use the Euler-Maruyama method, which is a numerical method to solve the SDEs. Error analysis on the Euler-Maruyama method provides the mean squared error (MSE) formula on the noisy average consensus systems. We finally show several bounds on the achievable sum- rate for the MAC realized by noisy average consensus systems.

In this paper, we propose a fully distributed approximate message passing (AMP) algorithm, which reconstructs an unknown vector from its linear measurements obtained at nodes in a network. The proposed algorithm is a distributed implementation of the centralized AMP algorithm, and consists of the local computation at each node and the global computation using communications between nodes. For the global computation, we propose a distributed algorithm named summation propagation to calculate a summation required in the AMP algorithm. The proposed distributed AMP algorithm does not require any central node such as a fusion center, and can be realized only with locally available information at each node. Simulation results show that the proposed algorithm can achieve the same estimation accuracy as that of the centralized AMP algorithm.

Diffusion least-mean-square (LMS) algorithm is a method that estimates an unknown global vector from its linear measurements obtained at multiple nodes in a network in a distributed manner. This paper proposes a novel combination rule in the algorithm used to integrate the local estimates at each node by using the idea of consensus propagation, which is known to be a fast algorithm to achieve the average consensus. Moreover, we optimize constants involved in the proposed combination rule in terms of the steady state mean-square-deviation (MSD) and show an adaptive combination rule, along with an adaptive implementation. Simulation results demonstrate that the proposed combination scheme achieves better MSD performance than conventional combination schemes.