Robust Precoding with Bayesian Error Modeling for Limited Feedback MU-MISO Systems

The final publication is available http://dx.doi.org/10.1109/TSP.2010.2052046[Abstract] We consider the robust precoder design for multiuser multiple-input single-output (MU-MISO) systems where the channel state information (CSI) is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas. We propose to compress the feedback data by projecting the channel estimates onto a vector basis, known at the receivers and the transmitter, and quantizing the resulting coefficients. The channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean-square error (MSE) between the true and the rank-reduced CSI. Expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design. These expressions take into account the following sources of error: channel estimation, truncation for rank reduction, quantization, and feedback channel delay. As an example for the robust problem formulation, vector precoding (VP) is designed based on the expectation of the MSE conditioned on the fed-back CSI. Our results show that robust precoding based on fed-back CSI clearly outperforms conventional precoding designs which do not take into account the errors in the CSI.Galicia, Consellería de Innovación, Industria e Comercio; PGIDT06TIC10501PRMinisterio de Educacion y Ciencia; TEC2007-68020-C04-01Ministerio de Educacion y Ciencia; CSD2008-00010.Ministerio de Educacion y Ciencia; HA2006-0112Alemania. Deutscher Akademischer Austauschdienst; D/06/1280

Design of limited feedback for robust MMSE precoding in multiuser MISO systems

[Resumen] En este trabajo consideramos un sistema multiusuario con múltiples antenas en transmisión y una única antena en cada uno de los usuarios receptores y que se denota por brevedad como MU-MISO, del inglés Multi–User Multiple–Input/Single–Output. Este modelo MU–MISO se ajusta perfectamente al enlace descendente de un sistema de comunicaciones móviles, donde múltiples antenas situadas en la estación base envían información a varios usuarios dentro de su zona de cobertura y cuyos terminales móviles disponen generalmente de una única antena. Este canal descendente se denomina también canal de difusión (BC, del inglés Broadcast Channel). Cuando se considera un canal de difusión, el transmisor centralizado tiene claramente más grados de libertad que cada uno de los receptores descentralizados, por lo que es más apropiado separar las señales aplicando precodificación en transmisión. Para poder realizar el diseño de los parámetros del precodificador, el transmisor necesita conocer la información de canal (CSI, en inglés Channel State Information) correspondiente a los distintos usuarios receptores. En el caso de sistemas FDD (del inglés, Frequency Division Duplex), esta información puede obtenerse (al menos parcialmente) mediante realimentación, siempre tras haber aplicado un proceso de cuantificación de la información enviada con el objetivo de adaptarse a las condiciones de ancho de banda limitado del canal de retorno

Robust Precoding with Limited Feedback Design based on Precoding MSE for MU-MISO Systems

The final publication is available http://dx.doi.org/10.1109/TSP.2012.2186446[Abstract] For the separation of the signals in the vector broadcast channel (BC), some information about the channel state is necessary at the transmitter. In many cases, this channel state information (CSI) must be fed back from the receivers to the transmitter. We jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder-centric criterion, i.e., the minimization of a mean square error (MSE) metric appropriate for the precoder design. This is in contrast to our previous works, where the quantizer design was based on a CSI MSE metric, i.e., based on the minimization of the MSE between the true channel and the channel recovered by the transmitter using a feedback channel. Interestingly, the estimators resulting from this joint formulation are independent of the used codebook. The codebook entries are the employed precoders. Therefore, each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder. Since the quantizers of the different receivers have to work separately, the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output. The proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding.Ministerio de Ciencia e Innovación; TEC2010-19545-C04-01Ministerio de Ciencia e Innovación; CSD2008-00010Galicia. Consellería de Economía e Industria; 09TIC008105P

Robust Symbol-Level Precoding Beyond CSI Models: A Probabilistic-Learning Based Approach

The use of large-scale antenna arrays poses great difficulties in obtaining perfect channel state information (CSI) in multi-antenna communication systems, which is essential for precoding optimization. To tackle this issue, in this paper we propose a probabilistic-learning based approach (PLA), aiming at alleviating the requirement of perfect CSI. The rationale is that the existing precoding algorithms that output a single precoder are often overconfident in their abilities and the obtained CSI. To avoid overconfidence, we incorporate the idea of regularization in machine learning (ML) into precoding models, so as to limit representative abilities of the precoding models. Compared to the state-of-the-art robust precoding designs, an important advantage of PLA is that CSI uncertainty models are not required. As a specific application of PLA, we design an efficient robust symbol-level hybrid precoding algorithm for the millimeter wave system and confirm the effectiveness of PLA via simulations

Alternating Minimization for Wideband Multiuser IRS-Aided MIMO Systems Under Imperfect CSI

© 2023 IEEE. This version of the article has been accepted for publication, after peer review. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The Version of Record is available online at: https://doi.org/10.1109/TSP.2023.3336166[Abstract]: This work focuses on wideband intelligent reflecting surface (IRS)-aided multiuser MIMO systems. One of the major challenges of this scenario is the joint design of the frequency-dependent base station (BS) precoder and user filters, and the IRS phase-shift matrix which is frequency flat and common to all the users. In addition, we consider that the channel state information (CSI) is imperfect at both the transmitter and the receivers. A statistical model for the imperfect CSI is developed and exploited for the system design. A minimum mean square error (MMSE) approach is followed to determine the IRS phase-shift matrix, the transmit precoders, and the receiving filters. The broadcast (BC)- multiple access channel (MAC) duality is used to solve the optimization problem following an alternating minimization approach. Numerical results show that the proposed approach leads to substantial performance gains with respect to baseline strategies that neglect the inter-user interference and do not optimize the IRS phase-shift matrix. Further performance gains are obtained when incorporating into the system design the statistical information of the channel estimation errors.This work was supported by Grants PID2019-104958RB-C42 (ADELE), PID2022-137099NB-C42 (MADDIE), and BES-2017-081955 funded by MCIN/AEI/10.13039/501100011033. José P. González-Coma thanks the Defense University Center at the Spanish Naval Academy for all the support provided for this research

A Unified Framework for Precoding and Pilot Design for FDD Symbol-Level Precoding

Large-scale antenna array techniques are key enablers for modern wireless communication systems. Channel state information (CSI) is indispensable for large-scale multi-antenna systems, but is challenging to obtain. To tackle this issue, in this paper we propose a unified precoding and pilot design frame-work, that allows minimal and precoding-sensitive modified CSI (mCSI) to be collected. This results in a significant reduction in the CSI overheads and complexity compared to classical physical CSI (pCSI) estimation. Based on this unified framework, we further propose an intelligent pilot (IP) approach that senses and selects the mCSI to be collected. The IP approach utilizes a compressive sensing formulation to attach sensing and selection of significant mCSI to precoding optimization. We apply the above techniques to the multi-user frequency division duplexing (FDD) downlink as an example. Our study shows that the advantages of the IP approach are three-fold. First, in contrast to the pCSI, precoding-sensitive information is only captured, which reduces the training and feedback overheads. Second, the precoders are optimized directly based on the mCSI, which avoids recovering the pCSI of high-dimension. Third, since the mCSI of reduced dimension is utilized, the scale of the problem to optimize the precoder is also reduced and thus it is much easier to solve

A Spatial Sigma-Delta Approach to Mitigation of Power Amplifier Distortions in Massive MIMO Downlink

In massive multiple-input multiple-output (MIMO) downlink systems, the physical implementation of the base stations (BSs) requires the use of cheap and power-efficient power amplifiers (PAs) to avoid high hardware cost and high power consumption. However, such PAs usually have limited linear amplification ranges. Nonlinear distortions arising from operation beyond the linear amplification ranges can significantly degrade system performance. Existing approaches to handle the nonlinear distortions, such as digital predistortion (DPD), typically require accurate knowledge, or acquisition, of the PA transfer function. In this paper, we present a new concept for mitigation of the PA distortions. Assuming a uniform linear array (ULA) at the BS, the idea is to apply a Sigma-Delta ($\Sigma \Delta$) modulator to spatially shape the PA distortions to the high-angle region. By having the system operating in the low-angle region, the received signals are less affected by the PA distortions. To demonstrate the potential of this spatial $\Sigma \Delta$ approach, we study the application of our approach to the multi-user MIMO-orthogonal frequency division modulation (OFDM) downlink scenario. A symbol-level precoding (SLP) scheme and a zero-forcing (ZF) precoding scheme, with the new design requirement by the spatial $\Sigma \Delta$ approach being taken into account, are developed. Numerical simulations are performed to show the effectiveness of the developed $\Sigma \Delta$ precoding schemes

Robust Joint Precoder and Equalizer Design in MIMO Communication Systems

We address joint design of robust precoder and equalizer in a MIMO communication system using the minimization of weighted sum of mean square errors. In addition to imperfect knowledge of channel state information, we also account for inaccurate awareness of interference plus noise covariance matrix and power shaping matrix. We follow the worst-case model for imperfect knowledge of these matrices. First, we derive the worst-case values of these matrices. Then, we transform the joint precoder and equalizer optimization problem into a convex scalar optimization problem. Further, the solution to this problem will be simplified to a depressed quartic equation, the closed-form expressions for roots of which are known. Finally, we propose an iterative algorithm to obtain the worst-case robust transceivers.Comment: 2 figures, 5 pages, conferenc