Matrix-Inverse-Free Deep Unfolding of the Weighted MMSE Beamforming Algorithm

Pellaco, Lissy; Bengtsson, Mats; Jaldén, Joakim

doi:10.1109/ojcoms.2021.3139858

Cited by 25 publications

(15 citation statements)

References 54 publications

(80 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our main goal is to replace the complex matrix inverses that appear in the update equations of 1 U (9a), W (9b), and V (9c) with more efficient operations that can leverage parallel implementation. In our previous paper [25], which addresses the MU-MISO scenario, we proposed to circumvent the matrix inverse in V by resorting to projected gradient descent steps. In the MISO case only the update of V involves matrix inverse operations because U and W are scalars.…”

Section: The Matrix-inverse-free Wmmse Algorithmmentioning

confidence: 99%

“…Conversely, in the MU-MIMO scenario, all the three variables (U , W , and V ) are matrices and all the updates involve matrix inverse operations. For V , we can apply the gradient descent (GD) approach as in [25] with the exception that the reformulation proposed by [23] obviates the need for the projection. For U , we can adopt the same approach as for V , but for W we cannot.…”

Section: The Matrix-inverse-free Wmmse Algorithmmentioning

confidence: 99%

“…Next to black-box-based approaches [13]- [21], in which the cumbersome operations of matrix inverse, eigendecomposition, and bisection search are replaced by deep neural networks trained to either approximate the output of the WMMSE algorithm or to directly maximize the WSR, deepunfolding-based approaches have recently emerged [22]- [25]. While black-box approaches can be efficiently executed in parallel, they suffer from poor interpretability, entail the problem of architecture selection, and typically have a large number of parameters which translates to intensive training.…”

Section: Introductionmentioning

confidence: 99%

“…Despite the acceleration in convergence, the proposed approach still heavily relies on matrix inverses, which appear in each algorithm iteration. In [23]- [25], the authors strived to remove matrix inverses within the WMMSE algorithm iterations to make the unfolded algorithm more amenable to real-time implementation. In [23], the authors approximate matrix inversions with a trainable module structured as the first-order Taylor expansion of the matrix inverse operation and introduce the IAIDNN algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…However, the resulting algorithm shows a non-monotic (oscillatory) behaviour in the WSR over the number of algorithm iterations. In [25], we propose a matrix-inverse-free formulation of the WMMSE algorithm by replacing the method of Lagrange multipliers, which leads to a matrix inverse, with a first-order method. However, this strategy is constrained to the multi-user multiple-input single-output (MU-MISO) case and generally cannot be applied to circumvent all the matrix inverses that appear in the WMMSE algorithm in the MU-MIMO scenario.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A matrix-inverse-free implementation of the MU-MIMO WMMSE beamforming algorithm

Pellaco¹,

Jaldén²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for realtime implementation.In our previous work, we considered the MU-MISO case and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case. Our earlier approach does not generalize to this scenario and cannot be applied to replace all the hardto-parallelize operations that appear in the MU-MIMO case. Thus, we propose to leverage a reformulation of the auxiliary WMMSE function given by Hu et al. By applying gradient descent and Schulz iterations, we formulate the first variant of the WMMSE algorithm applicable to the MU-MIMO case that is free from matrix inverses and other serial operations and hence amenable to both real-time implementation and deep unfolding. From a theoretical viewpoint, we establish its convergence to a stationary point of the WSR maximization problem. From a practical viewpoint, we show that in a deep-unfolding-based implementation, the matrix-inverse-free WMMSE algorithm attains, within a fixed number of iterations, a WSR comparable to the original WMMSE algorithm truncated to the same number of iterations, yet with significant implementation advantages in terms of parallelizability and real-time execution.

show abstract

Section: The Matrix-inverse-free Wmmse Algorithmmentioning

confidence: 99%

Section: The Matrix-inverse-free Wmmse Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A matrix-inverse-free implementation of the MU-MIMO WMMSE beamforming algorithm

Pellaco¹,

Jaldén²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

WiThRay: A Versatile Ray-Tracing Simulator for Smart Wireless Environments

Choi

Chung

et al. 2023

IEEE Access

View full text Add to dashboard Cite

Channel simulators capitalizing on the ray-tracing (RT) principle are widely used in wireless communications for generating realistic channel data. By combining the RT algorithm for the signal propagation trajectories with electromagnetic (EM) equations, generalized channel impulse responses (CIRs) are obtained. This paper presents a novel three-dimensional (3D) RT simulator for emerging smart wireless environments, termed as WiThRay, which can be deployed for the performance assessment of various wireless communication techniques, such as channel estimation/tracking, beamforming, and localization, under realistic EM wave propagation conditions. Firstly, a comprehensive comparison of existing RT-based channel simulators is provided, highlighting their wearknesses and limitations for utilization with the latest technologies for the sixth-generation (6G) of wireless systems. The proposed WiThRay simulator modifies the RT algorithm to follow the Fermat's principle, thus, reducing computational complexity, and implements scattering ray calibration providing a precise solution for the analysis of EM propagation. In addition, differently from most of the available RT-based simulators, WiThRay incorporates reconfigurable intelligent surfaces (RISs), which are lately considered as the key technology for RIS-enabled smart wireless communications. We thoroughly show that channel data obtained from WiThRay match sufficiently well with the fundamental EM propagation theory of wireless channels. Furthermore, the proposed simulator was deployed to study the performance of uplink channel estimation in orthogonal frequency-division multiplexing systems, downlink multi-user beamforming, and RIS-enabled coverage extension. The WiThRay versatile simulator is available in open-source mode, facilitating its easy deployment from the wireless research community for developing and testing communications and signal processing techniques in 6G smart wireless environments.INDEX TERMS Channel simulator, channel impulse response, geometric stochastic channel model, MIMO, reconfigurable intelligent surfaces, ray tracing, wireless communications.

show abstract

Bi-Level Deep Unfolding Based Robust Beamforming Design for IRS-Assisted ISAC System

Liu,

Xu,

et al. 2024

IEEE Access

View full text Add to dashboard Cite

In this paper, an intelligent reflecting surface (IRS)-assisted integrated sensing and communication (ISAC) system is considered, where the ISAC base station (BS) serves the communication user equipments (UEs) and tracks sensing targets simultaneously. Unfortunately, it is challenging to obtain the perfect channel state information (CSI) of user equipments (UEs)-related links and target directions in practice. To address the imperfection, we investigate the robust beamforming design under the statistical CSI and bounded target direction uncertainty models. With these considerations, we formulate a Cramér-Rao bound (CRB) of sensing targets minimization problem, subject to the signal-to-interference-plus-noise ratio (SINR) outage probability constraint, the maximum transmit power limits and the unit-modulus constraint of each IRS element. In order to solve this non-convex problem, we formulate the robust beamforming design as a bi-level optimization (BLO) problem and then apply the double-loop deep unfolding (DU) approach to solve this problem. Specifically, we formulate the problem into a primal-dual problem by integrating the SINR outage probability constraint into the objective function which is further approximated by using the worst-case SINR. The projection method and Riemannian manifold optimization method are used to deal with the maximum transmit power constraint and the unit-modulus constraint, respectively. Therefore, the problem can be reformulated as the bi-level optimization (BLO) problem. The lower level (LL) problems aim to find the worst-case CSI and angle of sensing targets. The upper level (UL) problem is the primaldual problem solved by beamforming design and the Lagrange multipliers optimization with the certain CSI and angle. Then, we apply double-loop DU neural network which unfolds the iterative gradient descent into multi-layer structure, and each layer consists of UL loop and LL loop. In addition, the trainable step sizes and offset parameters are introduced as the network parameters, and the network ultimately outputs optimal optimization variables. Simulation results demonstrate the effectiveness of the proposed robust beamforming design algorithm.INDEX TERMS Integrated sensing and communication system, intelligent reflecting surface, robust beamforming, bi-level optimization, deep unfolding, worst-case CRB, SINR outage probability.

show abstract

Matrix-Inverse-Free Deep Unfolding of the Weighted MMSE Beamforming Algorithm

Cited by 25 publications

References 54 publications

A matrix-inverse-free implementation of the MU-MIMO WMMSE beamforming algorithm

A matrix-inverse-free implementation of the MU-MIMO WMMSE beamforming algorithm

WiThRay: A Versatile Ray-Tracing Simulator for Smart Wireless Environments

Bi-Level Deep Unfolding Based Robust Beamforming Design for IRS-Assisted ISAC System

Contact Info

Product

Resources

About