Channel-Adaptive Pilot Design for FDD-MIMO Systems Utilizing Gaussian Mixture Models

In this work, we propose to utilize Gaussian mixture models (GMMs) to design pilots for downlink (DL) channel estimation in frequency division duplex (FDD) systems. The GMM captures prior information during training that is leveraged to design a codebook of pilot matrices in an initial offline phase. Once shared with the mobile terminal (MT), the GMM is utilized to determine a feedback index at the MT in the online phase. This index selects a pilot matrix from a codebook, eliminating the need for online pilot optimization. The GMM is further used for DL channel estimation at the MT via observation-dependent linear minimum mean square error (LMMSE) filters, parametrized by the GMM. The analytic representation of the GMM allows adaptation to any signal-to-noise ratio (SNR) level and pilot configuration without re-training. With extensive simulations, we demonstrate the superior performance of the proposed GMM-based pilot scheme compared to state-of-the-art approaches.

An Efficient Rate Splitting Precoding Approach in Multi-User MISO FDD Systems

In this work, we develop an efficient precoding strategy for a multi-user multiple-input-single output (MU MISO) system operating in frequency-division-duplex (FDD) mode, where rate splitting multiple access (RSMA) is implemented. To this end, we consider one-layer RS and show its significant impact on the system performance, specifically in the case where the channel state information (CSI) is incomplete at the transmitter. Based on a lower bound on the achievable rate that takes into account the CSI errors, we establish an augmented weighted average mean squared error (AWAMSE) algorithm for the RS setup denoted by AWAMSE-RS, where even the updates for the common and the private precoders are computed via analytical expressions, hence circumventing the need for interior-point methods. Simulation results validate the efficiency of our approach in terms of computational time and its competitiveness in terms of the achievable system throughput compared to state-of-the-art methods and non-RS setups.

Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation

This work proposes a novel channel estimator based on diffusion models (DMs), one of the currently top-rated generative models. Contrary to related works utilizing generative priors, a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information is designed by learning the channel distribution in the sparse angular domain. Combined with an estimation strategy that avoids stochastic resampling and truncates reverse diffusion steps that account for lower SNR than the given pilot observation, the resulting DM estimator has both low complexity and memory overhead. Numerical results exhibit better performance than state-of-the-art channel estimators utilizing generative priors.

On the Asymptotic Mean Square Error Optimality of Diffusion Probabilistic Models

Diffusion probabilistic models (DPMs) have recently shown great potential for denoising tasks. Despite their practical utility, there is a notable gap in their theoretical understanding. This paper contributes novel theoretical insights by rigorously proving the asymptotic convergence of a specific DPM denoising strategy to the mean square error (MSE)-optimal conditional mean estimator (CME) over a large number of diffusion steps. The studied DPM-based denoiser shares the training procedure of DPMs but distinguishes itself by forwarding only the conditional mean during the reverse inference process after training. We highlight the unique perspective that DPMs are composed of an asymptotically optimal denoiser while simultaneously inheriting a powerful generator by switching re-sampling in the reverse process on and off. The theoretical findings are validated by numerical results.

Performance Analysis of Systems with Coupled and Decoupled RISs

We analyze and compare different methods for handling the mutual coupling in RIS-aided communication systems. A new mutual coupling aware algorithm is derived where the reactance of each element is updated successively with a closed-form solution. In comparison to existing element-wise methods, this approach leads to a considerably reduced computational complexity. Furthermore, we introduce decoupling networks for the RIS array as a potential solution for handling mutual coupling. With these networks, the system model reduces to the same structure as when no mutual coupling were present. Including decoupling networks, we can optimize the channel gain of a RIS-aided SISO system in closed-form which allows to analyze the scenario under mutual coupling analytically and to draw connections to the conventional transmit array gain. In particular, a super-quadratic channel gain can be achieved which scales as N^4 where N is the number of RIS elements.

Wireless Channel Prediction via Gaussian Mixture Models

In this work, we utilize a Gaussian mixture model (GMM) to capture the underlying probability density function (PDF) of the channel trajectories of moving mobile terminals (MTs) within the coverage area of a base station (BS) in an offline phase. We propose to leverage the same GMM for channel prediction in the online phase. Our proposed approach does not require signal-to-noise ratio (SNR)-specific training and allows for parallelization. Numerical simulations for both synthetic and measured channel data demonstrate the effectiveness of our proposed GMM-based channel predictor compared to state-ofthe-art channel prediction methods.

Alternating Minimization for Wideband Multiuser IRS-aided MIMO Systems under Imperfect CSI

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.

Limited Feedback on Measurements: Sharing a Codebook or a Generative Model?

Discrete Fourier transform (DFT) codebook-based solutions are well-established for limited feedback schemes in frequency division duplex (FDD) systems. In recent years, data-aided solutions have been shown to achieve higher performance, enabled by the adaptivity of the feedback scheme to the propagation environment of the base station (BS) cell. In particular, a versatile limited feedback scheme utilizing Gaussian mixture models (GMMs) was recently introduced. The scheme supports multi-user communications, exhibits low complexity, supports parallelization, and offers significant flexibility concerning various system parameters. Conceptually, a GMM captures environment knowledge and is subsequently transferred to the mobile terminals (MTs) for online inference of feedback information. Afterward, the BS designs precoders using either directional information or a generative modeling-based approach. A major shortcoming of recent works is that the assessed system performance is only evaluated through synthetic simulation data that is generally unable to fully characterize the features of real-world environments. It raises the question of how the GMM-based feedback scheme performs on real-world measurement data, especially compared to the well-established DFT-based solution. Our experiments reveal that the GMM-based feedback scheme tremendously improves the system performance measured in terms of sum-rate, allowing to deploy systems with fewer pilots or feedback bits.

Highly Accelerated Weighted MMSE Algorithms for Designing Precoders in FDD Systems with Incomplete CSI

In this work, we derive a lower bound on the training-based achievable downlink (DL) sum rate (SR) of a multi-user multiple-input-single-output (MISO) system operating in frequency-division-duplex (FDD) mode. Assuming linear minimum mean square error (LMMSE) channel estimation is used, we establish a connection of the derived lower bound on the signal-to-interference-noise-ratio (SINR) to an average MSE that allows to reformulate the SR maximization problem as the minimization of the augmented weighted average MSE (AWAMSE). We propose an iterative precoder design with three alternating steps, all given in closed form, drastically reducing the computation time. We show numerically the effectiveness of the proposed approach in challenging scenarios with limited channel knowledge, i.e., we consider scenarios with a very limited number of pilots. We additionally propose a more efficient version of the well-known stochastic iterative WMMSE (SIWMMSE) approach, where the precoder update is given in closed form.

A Zero-Forcing Approach for the RIS-Aided MIMO Broadcast Channel

We present efficient algorithms for the sum-spectral efficiency (SE) maximization of the multi-user reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) broadcast channel based on a zero-forcing approach. These methods conduct a user allocation for which the computation is independent of the number of elements at the RIS, that is usually large. Specifically, two algorithms are given that exploit the line-of-sight (LOS) structure between the base station (BS) and the RIS. Simulations show superior SE performance compared to other linear precoding algorithms but with lower complexity.