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In this work, we propose an approach to robust precoder design based on a minorization maximization technique that optimizes a surrogate function of the achievable spectral efficiency. The presented method accounts for channel estimation errors during the optimization process and is, hence, robust in the case of imperfect channel state information (CSI). Additionally, the design method is adapted such that the need for a line search to satisfy the power constraint is eliminated, that significantly accelerates the precoder computation. Simulation results demonstrate that the proposed robust precoding method is competitive with weighted minimum mean square error (WMMSE) precoding, in particular, under imperfect CSI scenarios.

In this work, we propose a low-cost rate splitting (RS) technique for a multi-user multiple-input single-output (MISO) system operating in frequency division duplex (FDD) mode. The proposed iterative optimisation algorithm only depends on the second-order statistical channel knowledge and the pilot training matrix. Additionally, it offers a closed-form solution in each update step. This reduces the design complexity of the system drastically as we only need to optimise the precoding filters in every coherence interval of the covariance matrices, instead of doing that in every channel state information (CSI) coherence interval. Moreover, since the algorithm is based on closed-form solutions, there is no need for interior point solvers like CVX, which are typically required in most state-of-the-art techniques.

Rate splitting multiple access (RSMA) and reconfigurable intelligent surface (RIS) are two prospective technologies for improving the spectral and energy efficiency in future wireless communication systems. In this work, we investigate a rate splitting (RS) technique for an RIS-aided system in the presence of only statistical channel knowledge. We propose an algorithm with a quasi closed-form solution based only on the second-order channel statistics, which reduces the design complexity of the system as it does not require estimation of the channel state information (CSI) and optimisation of the precoding filters and phase shifts of the RIS in every channel coherence interval., Comment: 5 pages

Deep learning techniques for anatomical landmark localization (ALL) have shown great success, but their reliance on large annotated datasets remains a problem due to the tedious and costly nature of medical data acquisition and annotation. While traditional data augmentation, variational autoencoders (VAEs), and generative adversarial networks (GANs) have already been used to synthetically expand medical datasets, diffusion-based generative models have recently started to gain attention for their ability to generate high-quality synthetic images. In this study, we explore the use of denoising diffusion probabilistic models (DDPMs) for generating medical images and their corresponding heatmaps of landmarks to enhance the training of a supervised deep learning model for ALL. Our novel approach involves a DDPM with a 2-channel input, incorporating both the original medical image and its heatmap of annotated landmarks. We also propose a novel way to assess the quality of the generated images using a Markov Random Field (MRF) model for landmark matching and a Statistical Shape Model (SSM) to check landmark plausibility, before we evaluate the DDPM-augmented dataset in the context of an ALL task involving hand X-Rays., Comment: Accepted for the SASHIMI workshop of MICCAI 2024

We propose to use Tomlinson-Harashima Precoding (THP) for the reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) broadcast channel where we assume a line of sight (LOS) connection between the base station (BS) and the RIS. In this scenario, nonlinear precoding, like THP or dirty paper coding (DPC), has certain advantages compared to linear precoding as it is more robust in case the BS-RIS channel is not orthogonal to the direct channel. Additionally, THP and DPC allow a simple phase shift optimization which is in strong contrast to linear precoding for which the solution is quite intricate. Besides being difficult to optimize, it can be shown that linear precoding has fundamental limitations for statistical and random phase shifts which do not hold for nonlinear precoding. Moreover, we show that the advantages of THP/DPC are especially pronounced for discrete phase shifts.

In this work, we propose a Gaussian mixture model (GMM)-based pilot design scheme for downlink (DL) channel estimation in single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. In an initial offline phase, the GMM captures prior information during training, which is then utilized for pilot design. In the single-user case, the GMM is utilized to construct a codebook of pilot matrices and, once shared with the mobile terminal (MT), can be employed to determine a feedback index at the MT. This index selects a pilot matrix from the constructed codebook, eliminating the need for online pilot optimization. We further establish a sum conditional mutual information (CMI)-based pilot optimization framework for multi-user MIMO (MU-MIMO) systems. Based on the established framework, we utilize the GMM for pilot matrix design in MU-MIMO systems. The analytic representation of the GMM enables the adaptation to any signal-to-noise ratio (SNR) level and pilot configuration without re-training. Additionally, an adaption to any number of MTs is facilitated. Extensive simulations demonstrate the superior performance of the proposed pilot design scheme compared to state-of-the-art approaches. The performance gains can be exploited, e.g., to deploy systems with fewer pilots., Comment: arXiv admin note: substantial text overlap with arXiv:2403.17577

We compare dirty paper coding (DPC) and linear precoding methods in a reconfigurable intelligent surface (RIS)- aided high-signal-to-noise ratio (SNR) scenario, where the channel between the base station (BS) and the RIS is dominated by a line-of-sight (LOS) component. Furthermore, we consider two groups of users where one group can be efficiently served by the BS, whereas the other one has a negligible direct channel and has to be served via the RIS. Within this scenario, we analytically show fundamental differences between DPC and linear methods. In particular, our analysis addresses two essential aspects, i.e., the orthogonality of the BS-RIS channel with the direct channel and a channel mitigation term, depending on the number of RIS elements, that is present only for linear precoding techniques. The mitigation term generally leads to strong limitations for the linear method, especially for random or statistical phase shifts. Moreover, we discuss under which circumstances this mitigation term is negligible and in which scenarios DPC and linear precoding lead to the same performance.

Reconfigurable intelligent surface (RIS) is a promising technology to enhance the spectral and energy efficiency in a wireless communication system. The design of the phase shifts of an RIS in every channel coherence interval demands a huge training overhead, making its deployment practically infeasible. The design complexity can be significantly reduced by exploiting the second-order statistics of the channels. This paper is the extension of our previous work to the design of an RIS for the multi-user setup, where we employ maximisation of the lower bound of the achievable sum-rate of the users. Unlike for the single-user case, obtaining a closed-form expression for the update of the filters and phase shifts is more challenging in the multi-user case. We resort to the fractional programming (FP) approach and the non-convex block coordinate descent (BCD) method to solve the optimisation problem. As the phase shifts of the RIS obtained by the proposed algorithms are based on the statistical channel knowledge, they do not need to be updated in every channel coherence interval.

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.

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.

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.

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets.

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.

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.

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.

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.

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.

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.

Reconfigurable intelligent surface (RIS) is considered a prospective technology for beyond fifth-generation (5G) networks to improve the spectral and energy efficiency at a low cost. Prior works on the RIS mainly rely on perfect channel state information (CSI), which imposes a huge computational complexity. This work considers a single-user RIS-assisted communication system, where the second-order statistical knowledge of the channels is exploited to reduce the training overhead. We present algorithms that do not require estimation of the CSI and reconfiguration of the RIS in every channel coherence interval, which constitutes one of the most critical practical issues in an RIS-aided system., Comment: 6 pages

RISs are an emerging technology for engineering the channels of future wireless communication systems. The vast majority of research publications on RIS are focussing on system-level optimization and are based on very simplistic models ignoring basic physical laws. There are only a few publications with a focus on physical modeling. Nevertheless, the widely employed model is still inconsistent with basic physical laws. We will show that even with a very simple abstract model based on isotropic radiators, ignoring any mismatch, mutual coupling, and losses, each RIS element cannot be modeled to simply reflect the incident signal by manipulating its phase only and letting the amplitude unchanged. We will demonstrate the inconsistencies with the aid of very simple toy examples, even with only one or two RIS elements. Based on impedance parameters, the problems associated with scattering parameters can be identified enabling a correct interpretation of the derived solutions.

In this work, we propose a versatile feedback scheme which can be deployed for both single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. Particularly, we propose to use a Gaussian mixture model (GMM) with a reduced number of parameters for codebook construction, feedback encoding, and precoder design. The GMM is fitted offline at the base station (BS) to uplink (UL) training samples to approximate the channel distribution of all possible mobile terminals (MTs) located inside the BS cell. Afterwards, a codebook is constructed, where each codebook entry is based on one GMM component. By extracting directional information of the constructed codebook, the proposed GMM-based feedback approach allows to jointly design the precoders of a multi-user MIMO (MU-MIMO) system using common precoding algorithms. Alternatively, the GMM's sample generation ability can be utilized to design the precoders using a state-of-the-art stochastic iterative algorithm. After offloading the GMM to the MTs, they determine their feedback simply as the index of the GMM component with the highest responsibility for their received pilot signal. This strategy exhibits low complexity and allows for parallelization. Simulation results show that the proposed approach outperforms conventional methods, especially for a reduced number of pilots., Comment: arXiv admin note: text overlap with arXiv:2205.12002

This work aims to predict channels in wireless communication systems based on noisy observations, utilizing sequence-to-sequence models with attention (Seq2Seq-attn) and transformer models. Both models are adapted from natural language processing to tackle the complex challenge of channel prediction. Additionally, a new technique called reverse positional encoding is introduced in the transformer model to improve the robustness of the model against varying sequence lengths. Similarly, the encoder outputs of the Seq2Seq-attn model are reversed before applying attention. Simulation results demonstrate that the proposed ordering techniques allow the models to better capture the relationships between the channel snapshots within the sequence, irrespective of the sequence length, as opposed to existing methods., Comment: Submitted to IEEE for publication

In this work, we study the asymptotic behavior of the zero-forcing precoder based on the least squares (LS) and the linear minimum mean-square error (LMMSE) channel estimates for the downlink (DL) of a frequency-division-duplex (FDD) massive multiple-input-single-output (MISO) system. We show analytically the rather surprising result that zero-forcing precoding based on the LS estimate leads asymptotically to an interference-free transmission, even if the number of pilots used for DL channel training is less than the number of antennas available at the base station (BS). Although the LMMSE channel estimate exhibits a better quality in terms of the MSE due to the exploitation of the channel statistics, we show that in the case of contaminated channel observations, zero-forcing based on the LMMSE is unable to eliminate the inter-user interference in the asymptotic limit of high DL transmit powers. In order for the results to hold, mild conditions on the channel probing phase are assumed. The validity of our analytical results is demonstrated through numerical simulations for different scenarios.

In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical application, recent pilot observations at the base station (BS) can be utilized for training. This is in sharp contrast to state-of-theart machine learning (ML) techniques where a training dataset consisting of perfect channel state information (CSI) samples is a prerequisite, which is generally unaffordable. In particular, we propose an adapted training procedure for fitting the GMM which is a generative model that represents the distribution of all potential channels associated with a specific BS cell. To this end, the necessary modifications of the underlying expectation-maximization (EM) algorithm are derived. Numerical results show that the proposed estimator performs close to the case where perfect CSI is available for the training and exhibits a higher robustness against imperfections in the training data as compared to state-of-the-art ML techniques.

We consider channel estimation in systems equipped with a reconfigurable intelligent surface (RIS). In order to illuminate the additional cascaded channel as compared to systems without a RIS, commonly an unaffordable amount of pilot sequences has to be transmitted over different phase allocations at the RIS. However, for a given base station (BS) cell, there exist immanent structural characteristics of the environment which can be leveraged to reduce the necessary number of phase allocations. We verify this observation by a study on discrete Fourier transform (DFT)-based phase allocations where we exhaustively search for the best combination of DFT columns. Since this brute-force search is unaffordable in practice, we propose to learn a neural network (NN) for joint phase optimization and channel estimation because of the dependency of the optimal phase allocations on the channel estimator, and vice versa. We verify the effectiveness of the approach by numerical simulations where common choices for the phase allocations and the channel estimator are outperformed. By an ablation study, the learned phase allocations are shown to be beneficial in combination with a different state-of-the-art channel estimator as well.

We analyze the influence of a reconfigurable intelligent surface (RIS) on the Gram channel eigenvalues in a high signal-to-noise ratio (SNR) scenario. This allows to connect specific channel properties with the rank improvement capabilities of the RIS. In particular, fundamental limits due to a possible line of sight (LOS) setup between the base station (BS) and the RIS are derived. Furthermore, dirty paper coding (DPC) based schemes are compared to linear precoding in such a scenario and it is shown that under certain channel conditions, the performance gap between DPC and linear precoding vanishes.

In this work, we propose an efficient method for channel state information (CSI) adaptive quantization and feedback in frequency division duplexing (FDD) systems. Existing works mainly focus on the implementation of autoencoder (AE) neural networks (NNs) for CSI compression, and consider straightforward quantization methods, e.g., uniform quantization, which are generally not optimal. With this strategy, it is hard to achieve a low reconstruction error, especially, when the available number of bits reserved for the latent space quantization is small. To address this issue, we recommend two different methods: one based on a post training quantization and the second one in which the codebook is found during the training of the AE. Both strategies achieve better reconstruction accuracy compared to standard quantization techniques.

In this work, we propose variations of a Gaussian mixture model (GMM) based channel estimator that was recently proven to be asymptotically optimal in the minimum mean square error (MMSE) sense. We account for the need of low computational complexity in the online estimation and low cost for training and storage in practical applications. To this end, we discuss modifications of the underlying expectation-maximization (EM) algorithm, which is needed to fit the parameters of the GMM, to allow for structurally constrained covariances. Further, we investigate splitting the 2D time and frequency estimation problem in wideband systems into cascaded 1D estimations with the help of the GMM. The proposed cascaded GMM approach drastically reduces the complexity and memory requirements. We observe that due to the training on realistic channel data, the proposed GMM estimators seem to inherently perform a trade-off between saving complexity/parameters and estimation performance. We compare these low-complexity approaches to a practical and low cost method that relies on the power delay profile (PDP) and the Doppler spectrum (DS). We argue that, with the training on scenario-specific data from the environment, these practical baselines are outperformed by far with equal estimation complexity.

To fully unlock the benefits of multiple-input multiple-output (MIMO) networks, downlink channel state information (CSI) is required at the base station (BS). In frequency division duplex (FDD) systems, the CSI is acquired through a feedback signal from the user equipment (UE). However, this may lead to an important overhead in FDD massive MIMO systems. Focusing on these systems, in this study, we propose a novel strategy to design the CSI feedback. Our strategy allows to optimally design variable length feedback, that is promising compared to fixed feedback since users experience channel matrices differently sparse. Specifically, principal component analysis (PCA) is used to compress the channel into a latent space with adaptive dimensionality. To quantize this compressed channel, the feedback bits are smartly allocated to the latent space dimensions by minimizing the normalized mean squared error (NMSE) distortion. Finally, the quantization codebook is determined with k-means clustering. Numerical simulations show that our strategy improves the zero-forcing beamforming sum rate by 17%, compared to CsiNetPro. The number of model parameters is reduced by 23.4 times, thus causing a significantly smaller offloading overhead. At the same time, PCA is characterized by a lightweight unsupervised training, requiring eight times fewer training samples than CsiNetPro., Comment: Accepted by IEEE for publication

In this work, we present new results for the application of rate splitting multiple access (RSMA) to the downlink (DL) of a massive multiple-input-multiple-output (MaMIMO) system operating in frequency-division-duplex (FDD) mode. Due to the lack of uplink (UL) - DL channel reciprocity in such systems, explicit training in the DL has to be performed in order to gain knowledge about the single-antenna users' channels at the base station (BS). This is ensured through a feedback link from the users to the BS. Dealing with the DL of a massive MIMO system implies that acquiring the DL channel state information (CSI) comes at the cost of a huge training overhead that scales with the number of BS antennas. Therefore, we limit the resources allocated to training by reusing the pilot sequences among the BS antennas that results in a contaminated channel observation. Despite this incomplete channel knowledge at the transmitter side, the proposed RS approach combined with a statistical precoder relying on the channels' second-order information achieves excellent results in terms of spectral efficiency compared to the state-of-art techniques. This is demonstrated via Monte-Carlo simulations of typical communication scenarios.

We present distributed methods for jointly optimizing Intelligent Reflecting Surface (IRS) phase-shifts and beamformers in a cellular network. The proposed schemes require knowledge of only the intra-cell training sequences and corresponding received signals without explicit channel estimation. Instead, an SINR objective is estimated via sample means and maximized directly. This automatically includes and mitigates both intra- and inter-cell interference provided that the uplink training is synchronized across cells. Different schemes are considered that limit the set of known training sequences from interferers. With MIMO links an iterative synchronous bi-directional training scheme jointly optimizes the IRS parameters with the beamformers and combiners. Simulation results show that the proposed distributed methods show a modest performance degradation compared to centralized channel estimation schemes, which estimate and exchange all cross-channels between cells, and perform significantly better than channel estimation schemes which ignore the inter-cell interference., Comment: Submitted for publication in an IEEE conference