This paper investigates access point (AP) cooperation cluster formation in user-centric cell-free massive MIMO (CF-mMIMO) communication systems characterized by fronthaul links with capacity restrictions. Specifically, we consider an open radio access network (O-RAN) architecture that, although it favors the deployment of ultra-dense networks, is constrained in the number of APs that can be active simultaneously. In this context, we propose an innovative framework termed pixel-based CF-mMIMO, which enables efficient control of both the AP activation and cooperation cluster formation. Recognizing the parallels with pixel-based reconfigurable antennas, the proposed framework allows dynamic reconfiguration of the network coverage map with reasonably low computational cost. The high scalability and performance of the framework are mainly supported by a learning model based on graph neural networks (GNNs) that effectively exploits the existing graph-like structures in CF-mMIMO systems. Extensive simulation experiments demonstrate that the proposed approach achieves competitive spectral efficiency (SE) in challenging scenarios with dense AP deployments and numerous user equipments (UEs).

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 pseudo-noise term, depending on the number of RIS elements, that is present only for linear precoding techniques. The pseudonoise generally leads to strong limitations for the linear method, especially for random or statistical phase shifts. Moreover, we discuss under which circumstances this pseudo-noise is negligible and in which scenarios DPC and linear precoding lead to the same performance.

We propose decoupling networks for the reconfigurable intelligent surface (RIS) array as a solution to benefit from the mutual coupling between the reflecting elements. In particular, we show that when incorporating these networks, the system model reduces to the same structure as if no mutual coupling is present. Hence, all algorithms and theoretical discussions neglecting mutual coupling can be directly applied when mutual coupling is present by utilizing our proposed decoupling networks. For example, by including decoupling networks, the channel gain maximization in RIS-aided single-input single-output (SISO) systems does not require an iterative algorithm but is given in closed form as opposed to using no decoupling network. In addition, this closed-form solution allows to analytically analyze scenarios under mutual coupling resulting in novel connections to the conventional transmit array gain. In particular, we show that super-quadratic (up to quartic) channel gains w.r.t. the number of RIS elements are possible and, therefore, the system with mutual coupling performs significantly better than the conventional uncoupled system in which only squared gains are possible. We consider diagonal as well as beyond diagonal (BD)-RISs and give various analytical and numerical results, including the inevitable losses at the RIS array. In addition, simulation results validate the superior performance of decoupling networks w.r.t. the channel gain compared to other state-of-the-art methods.

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 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, linear precoding has fundamental limitations when the phases are chosen randomly or based on statistical channel state information (CSI). These limitations do not hold for nonlinear precoding. Moreover, we show that the advantages of THP/DPC are especially pronounced for discrete phase shifts.

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.

Forming effective access point (AP) cooperation clusters is a key challenge in user-centric cell-free massive MIMO (CF-mMIMO). Existing approaches to this task are either computationally prohibitive or overlook the complex interrelationships within communication networks. In this context, we introduce an innovative approach based on graph neural networks (GNNs). By leveraging the inherent graph structure of CF-mMIMO networks, we transform the rate maximization problem into a node classification task, enabling a competitive and robust solution. Simulation results show that the proposed method significantly outperforms conventional baselines in terms of spectral efficiency, computational complexity, and scalability.

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 on the channel statistics through 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.

We consider the problem of sum rate maximization in frequency division duplex (FDD) systems when only imperfect channel state information (CSI) is available. Inspired by the low complexity and generalization ability offered by graph neural networks (GNNs), we propose an end-to-end (E2E) framework for both, precoding and downlink (DL) pilot sequences optimization based on the novel Edge-graph attention network (GAT). The simulation results confirm the potential of the proposed E2E approach to optimize sum rates and its scalability in scenarios with varying numbers of users. Additionally, the superiority of the learned pilot matrix compared to the conventionally employed sub-discrete Fourier transform (DFT) matrix is highlighted.

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.

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.

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.

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.

We propose a versatile feedback scheme for both single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. Particularly, we propose utilizing 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 training samples to approximate the channel distribution of all possible mobile terminals (MTs) within the BS cell. Subsequently, a codebook is constructed, with each element based on one GMM component. Extracting directional information from the codebook or exploiting the GMM’s sample generation ability facilitates joint precoder design for a multi-user MIMO system using state-of-the-art precoding algorithms. After offloading the GMM to the MTs, they can easily determine their feedback by selecting the index of the GMM component with the highest responsibility for their received pilot signal. This strategy exhibits low complexity and supports parallelization. Simulations demonstrate that the proposed approach outperforms conventional methods, which either estimate the channel and utilize a Lloyd codebook or use a deep neural network to determine the feedback in terms of spectral efficiency or sum-rate. The performance gains can be exploited to deploy systems with fewer pilots or feedback bits.

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 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 system (MIMO) operating in frequency-division-duplex (FDD) mode. We propose a statistical precoding design relying on the channels’ second-order information when one-layer RS is implemented. The advantage of the statistical precoding lies in simplifying the precoder design by basing the optimization objective on the slowly-varying channel covariance matrices instead of the fast-changing instantaneous channel estimates. To this end, we use the so- called bilinear precoder, which was shown in Neumann et al. (2018) and Ben Amor et al. (2020) to have limited performance in the high SNR regime due to the imperfect channel state information (CSI) available at the base station (BS). We formulate the DL throughput maximization problem based on a widely used lower bound on the achievable sum rate and propose an iterative approach to solve the underlying optimization problem. Numerical results demonstrate the benefit of implementing one-layer RS. Furthermore, the proposed iterative approach achieves excellent results in terms of spectral efficiency compared to the state-of-the-art techniques.

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.

We consider channel estimation for systems equipped with an intelligent reflecting surface (IRS). We develop least squares (LS) and minimum mean square error (MMSE) estimation for such systems. The appropriate system models are developed and we also discuss the parameters which can be estimated in such a setup because there exists a difficulty due to the ambiguity for the two channels connecting with the IRS. The MMSE estimator is based on a Kronecker product approximation of the channel covariance matrix. The simulations results illustrate the advantage of the optimized pilots and the optimized phase allocations for the channel estimation.

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 achievable sum-rate 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 all channels including all cross-channels, and perform significantly better than decentralized channel estimation schemes which ignore the inter-cell interference.

We propose an innovative machine learning-based technique to address the problem of channel acquisition at the base station in frequency division duplex systems. In this context, the base station reconstructs the full channel state information in the downlink frequency range based on limited downlink channel state information feedback from the mobile terminal. The channel state information recovery is based on a convolutional neural network which is trained exclusively on collected channel state samples acquired in the uplink frequency domain. No acquisition of training samples in the downlink frequency range is required at all. Finally, after a detailed presentation and analysis of the proposed technique and its performance, the “reciprocity of distribution” assumption of the convolutional neural network that is central to the proposed approach is validated with an analysis based on the maximum mean discrepancy metric.

It has been shown that rate splitting multiple access (RSMA) promises high data rates in the multi-user multiple-input single-output broadcast channel (MISO BC) with superior performance under imperfect channel state information (CSI) and the possibility to fulfill various quality of service (QoS) constraints. In this work, we use the 1-layer RS approach for the sum rate maximization under a total power constraint in the multi-user multiple-input multiple-output broadcast channel (MIMO BC). We adapt the iterative weighted minimum mean squared error (WMMSE) approach to the MIMO BC. However, we propose an efficient approach that splits the optimization problem into a "private" part based on the previously proposed linear successive allocation (LISA) method, a "common" part carried out by an iteratively SINR maximizing method, and a power allocation part using the waterfilling algorithm. Numerical simulations show performance gains in the medium and high SNR region when applying the proposed method.

MIMO Radio-over-Copper (MIMO-RoC) is a transport system for indoor coverage that leverages the pre-existing building's copper cabling infrastructure. In MIMO-RoC, the overall channel from the Base Band Units (BBU) to the end-user is the cascade of a MIMO-radio over a MIMO-cable channel and the analog fronthaul together with a wireless channel enables the transport to the mobile users. The entire system poses two main challenges: i) design low-complexity and flexible allocation strategies between wired and wireless resources; ii) design interference cancellation techniques tailored to the mutually coupled wired-wireless interference. While the former has been extensively investigated, the optimal design of precoding algorithms for the MIMO-RoC downlink is still an open issue and is covered here. In particular, in this paper, the Linear Successive Allocation (LISA) algorithm has been revised and adapted to the MIMO amplify-and-forward (AF) structure of MIMO-RoC. Numerical results validate the proposed method considering a realistic radio environment with 100m copper cable remotization.

Interference during the uplink training phase significantly deteriorates the performance of a massive MIMO system. The impact of the interference can be reduced by exploiting the second-order statistics of the channel vectors, e.g., to obtain the minimum mean squared error estimates of the channel. In practice, the channel covariance matrices have to be estimated. The estimation of the covariance matrices is also impeded by the interference during the training phase. However, the coherence interval of the covariance matrices is larger than that of the channel vectors. This allows us to derive methods for accurate covariance matrix estimation by the appropriate assignment of pilot sequences to the users in consecutive channel coherence intervals. To keep the computational complexity in check, we exploit common structure of the covariance matrices.

Millimeter-wave (mm-wave) communications plays an important role in future cellular networks because of the vast amount of spectrum available in the underutilized mm-wave frequency bands. To overcome the huge free space omnidirectional path loss in those frequency bands, the deployment of a very large number of antenna elements at the base station is crucial. The complexity, power consumption, and costs resulting from the large number of antenna elements can be reduced by limiting the number of RF chains. This leads to hybrid precoding and combining, which, in contrast to the traditional fully digital precoding and combining, moves a part of the signal processing from the digital to the analog domain. This paper proposes new algorithms for the design of hybrid precoders and combiners in a multiuser scenario. The algorithms are based on the previously proposed linear successive allocation method developed for the traditional fully digital version. It successively allocates data streams to users and suppresses the respective interstream interference in two stages, which perfectly matches the hybrid architecture. Furthermore, a low-complexity version is developed by exploiting the typical structure of mm-wave channels. The good performance of the proposed method and its low-complexity version is demonstrated by simulation results.

Pilot contamination is a throughput limiting factor in cellular massive MIMO systems. Previous work has shown that the impact of pilot-contamination can be reduced by exploiting structural information in form of channel covariance matrices. Additionally, significant gains can be obtained through coordinated user assignment. In this paper, we extend these approaches to a realistic scenario with imperfect knowledge of the channel and its distribution at the base station. We formulate an optimization problem for assigning users to the available pilot sequences, which at the same time takes the estimation of the covariance matrices into account and propose a suboptimal greedy algorithm for efficient implementation. Simulation results with established physical channel models demonstrate the significant performance gains of the proposed method in the case of imperfect knowledge of the covariance matrices at the base station.

Recently, ITU finished its standard for G.fast, utilized in so called fiber-to-the-distribution-point (FTTdp) networks, where only the last meters from the fiber link to the customer are bridged by existing copper wires. The target is to increase the data rate over the short copper link up to 1 Gbit/s, which is an increase by the factor of ten compared to VDSL2, by extending the frequency band up to 212 MHz. At higher frequencies, the crosstalk between the lines is amplified, which makes crosstalk management essential to obtain the targeted data rates. Tomlinson-Harashima Precoding (THP) is a non-linear precoding technique, which is considered for the 212 MHz G.fast systems. Up to now, linear zero-forcing (ZF) and weighted minimum mean-square-error (WMMSE) precoding, as well as ZF THP, have been investigated for G.fast. In this paper, we show how WMMSE THP can be utilized in this scenario. We show that WMMSE THP outperforms ZF THP in terms of achievable rate in large systems. However, we see that the rate gain is not significant, although the WMMSE THP solution almost achieves the channel capacity.

Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization.

We evaluate the performance of a set of low complexity successive interference cancellation (SIC) detection algorithms in comparison to optimal maximum a-posteriori probability (MAP) detection and low complexity linear filter detection in a Turbo multiple-input multiple-output (Turbo-MIMO) system. We show that both linear and SIC soft detection algorithms perform similarly poorly for iterative receivers, even if the channel decoder output is available at the detector. We propose a low complexity combined a-priori/a-posteriori information-based error regularization technique, that improves the performance of the Turbo-MIMO design considerably. With this regularization technique, we show that a decoding gain of 2.2 dB can be achieved in an LTE compliant Turbo-MIMO receiver.

We evaluate the capacity bounds and the system performance of a set of detection algorithms for multiple-input multiple-output (MIMO) systems focusing on low complexity interference cancellation methods. Since detection and decoding in a bit-interleaved coded modulation system (BICM) is performed separately, the performance in terms of bit error rate depends on both, the signal constellation and the channel encoder design. In order to find a universal measure for the performance of the detection stage, we evaluate the mutual information of the transmit signal and the a-posteriori bit hypotheses probabilities of the respective decoder. The outcome of our analysis provides bounds for the achievable rates using optimal and suboptimal detection algorithms.

Hybrid copper/fiber networks bridge the gap between the fiber link and the customer by using copper wires over the last meters. This solution combines energy efficiency and low cost of the copper access network with high data rates of a fiber connection. However, the fiber to the distribution point (FTTdp) network must prove its ability to convey data at fiber speed over copper wire bundles under the spectral constraints of the copper access network. This work investigates achievable data rates of the FTTdp network. It provides an analysis of the sources of performance loss in a system implementation due to complexity limitations. Methods to improve achievable rates are shown, that are based on incorporating the limitations in the optimization process. Achievable data rates are analyzed in terms of rate vs. reach curves, based on a statistical channel model and the ITU standard G.fast. The results indicate that optimized linear methods perform well on shorter lines, while nonlinear methods have advantages for long lines.

We present a low complexity soft detector for multiple-input multiple-output (MIMO) channels. Our proposed minimum mean square error successive interference cancellation (MMSE-SIC) detector is based on a regularization mechanism which reduces error propagation in the channel iterative decoder. Although our proposed detector is easy to implement and has a complexity order that is cubic in the number of transmit antennas, it can reach the performance of the soft max-log maximum-likelihood detector (MLD) under realistic system assumptions, as demonstrated in our simulations.

The aim of this work is to jointly achieve individual rate requirements and minimum total transmit power in the vector Broadcast Channel (BC). Data streams are transmitted from a multi-antenna base station to several non-cooperative single-antenna receivers having perfect Channel-State-Information (CSI). Partial CSI, e.g., obtained via feedback, is used for the design of linear transmit filters at the transmitter. Employing a duality between Multiple Access Channel (MAC) and BC rate regions and the so-called standard interference functions, we propose an algorithmic joint solution for the transmit filter design and the power allocation in this work.

We focus on a linear beamformer design in the downlink with statistical channel state information (CSI) at the transmitter, where the users' ergodic rates are balanced. Simplifying the fading channels to given vectors with random scalar factors, which is a good approximation for rural mobile or satellite communications (SatCom), the stochastic model mismatch is kept small albeit the ergodic rate structure now allows for adapting the perfect CSI balancing algorithms. Although there is no equivalent signal-to-interference-and-noise-ratio (SINR) reformulation for the ergodic constraints, tight inner approximations with SINR structure are found. Based on this observation, a locally optimal sequential approximation strategy is proposed and a fixed point based implementation is provided that requires only few iterations.

The use of proper, i.e., circularly symmetric, complex Gaussian signals for all users is known to be optimal in broadcast channels with proper complex Gaussian noise from an information theoretic point of view, i.e., they are employed in the capacity-achieving strategy. However, such proper per-user transmit signals are not necessarily optimal for problems with quality-of-service (QoS) constraints if the transmit strategy is restricted to widely linear transceivers without time-sharing. This is shown by deriving the QoS feasibility region of the multiple-input multiple-output broadcast channel with improper Gaussian per-user transmit signals and widely linear transceivers.

We focus on the design of linear beamforming based on quality-of-service (QoS) power minimization and rate balancing in the downlink (DL) of a satellite communication system with mobile and static users. Since only the rank-one covariance matrices of the channels to mobile users are known, we introduce average rate requirements for these users contrary to the perfect channel state information (CSI) rate requirements for the static users. Due to the structure of the ergodic rates, we cannot directly resort to the optimization techniques for the purely complete CSI vector broadcast channel (BC). Therefore, we propose two suitable lower and upper bounds on the ergodic rates. Incorporating these bounds in the optimization problems, instead of the ergodic expressions, the usual power minimization algorithms can be applied. This allows the computation of bounds on the optima of the considered problems. Furthermore, employing an additional power allocation on the obtained solutions, we achieve outcomes that reside close to the expected optima.

The problem of stochastic robust sum mean square error (MSE) minimization transceiver design is addressed for multiple-input multiple-output (MIMO) broadcast channels (BCs). The transmitter has only distribution knowledge of the doubly correlated Gaussian channels and the receivers have complete channel state information (CSI). The design is based on an alternating optimization (AO) of the transmit and receive filters. For the users' minimum MSEs (MMSEs), i.e., the achieved MSEs using MMSE equalizers, and the expectations in the AO procedure, novel closed form expressions are calculated via first and second order derivatives of suitable ergodic mutual information expressions.

In this paper, the rate region of the two user MIMO broadcast channel (BC) under linear filtering at high signal-to-noise ratio (SNR) is investigated when time sharing is not available and the transmitter has more antennas than the sum of the receiving antennas. To reach the rate region's boundary, the sum rate is maximized subject to a given ratio between the users rates. The sum rate is first considered asymptotically when the SNR tends to infinity and taken as an affine function of the logarithm of the SNR, with the multiplicative and the additive parameters called the multiplexing gain (MG) and the rate offset (RO), respectively. The maximal MG and the maximal RO are obtained for every rate ratio constraint. Additionally, the asymptotic optimal stream allocations that achieve those values are also derived. Analytical inner and outer bounds, which offer a rough approximation of the boundary but are extremely easy to evaluate even in fading channels, are then developed. The maximization of the rate subject to a rate ratio constraint is then studied at finite SNR. Algorithmic inner and outer bounds for the rate region boundary are derived and shown to be very close to each other and accurate even at intermediate SNR.

For single-user MIMO channels with partial re ceiver CSI, we study the difference between a lower bound and two alternative upper bounds of the mutual information achieved with Gaussian codebooks. These differences are termed bound gaps Δ and δ, respectively. The latter may serve to derive a capacity bound gap. In contrast to previous studies, we assume that the channel estimation error statistics are not given a priori, but depend on the parameters of a training routine, in which a pilot sequence is transmitted, and where the channel realization is linearly estimated. Under these conditions, we successively determine analytic upper and lower bounds on the mutual information bound gap Δ. We further study the asymptotic behavior of said bound gaps for high SNR and a large number of antennas. This allows us to prove, for example, that for MISO channels and a certain class of semicorrelated MIMO channels, when the training and transmit power levels are equal, the capacity is approached to within min(NT, NR) bits by the capacity bounds, where NTand NRstand for the number of transmit and receive antennas, respectively.

For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution.

Besides the optimal but impractically complex dirty paper coding (DPC), linear precoding and vector precoding (VP) have been proposed for the vector broadcast channel (BC). Linear precoding is simple, as only a linear transform is applied to the data signals, whereas VP necessitates a closest-point search in a lattice to find the perturbation signal which reduces the necessary transmit power. In this paper, we analyze the high signal-to-noise ratio (SNR) performance of VP assuming optimal decoding. As the perturbation process hinders the analytical assessment of the VP performance, lower and upper bounds on the expected data rate of VP systems are reviewed and proposed. Based on these bounds, VP is compared to linear precoding w.r.t. the weighted sum rate, the power resulting from a quality of service (QoS) formulation, and the performance when balancing the rates.

We consider the problem of power minimization under per-user quality of service (QoS) constraints (expressed in terms of rates) in parallel multiple-input single-output (MISO) broadcast channels employing linear zero-forcing precoding. Solving the arising scheduling problem by an exhaustive search is prohibitively complex due to its combinatorial nature so that the use of successive user allocation schemes has been proposed. We show that existing schemes lead to strongly suboptimal solutions in systems with a low number of degrees of freedom and that better performance can be achieved with a new scheduling criterion. By introducing additional correction steps, we end up with an efficient close-to-optimum algorithm.

We investigate the geometry of the feasible Quality of Service (QoS) region in the vector broadcast channel when the available transmit power is unbounded. It turns out that a complete description of the feasible QoS region attains its simplest form in the minimum mean square error (MMSE) domain although most of the literature handles feasibility in the SINR domain. As our main contribution, we show that the closure of the feasible MMSE region is a polytope corresponding to a hyper-cube that maybe is cropped by an additional half-space constraint. Interestingly, this half-space constraint is the only relevant one which separates feasibility from infeasibility and it reflects a lower bound on the sum MMSE. Under the assumption of regular channels, this lower bound does not depend on the channel realization but solely depends on the number of users and antennas deployed at the base station. Testing feasibility of given QoS targets is easily performed by first converting the QoS targets into upper bounds on the MMSEs and afterwards verifying that the sum of target MMSEs is larger than the difference between antennas at the base station and the number of users. The derived results can be used to decide whether a new user with given QoS requirements can be admitted to the system, and if not, how the requirements have to be adapted such that they become feasible.

We investigate the maximization of a quotient of two determinants with different exponents under a Frobenius norm constraint, where each determinant is taken from a matrix-valued Hermitian form. The optimum matrix that constitutes the Hermitian forms is shown to be a scaled partial isometry. For the special case of vector-valued Hermitian forms, the optimality condition turns out to be an implicit eigenproblem and we derive an iterative algorithm where in each step the principal eigenvector of a matrix has to be chosen. In addition, we prove monotonic convergence of the iterative algorithm, which means that the utility increases in every step.

In this paper, the rate region of the two user MIMO broadcast channel (BC) with linear filtering at high signal-to-noise ratio (SNR) is studied when time sharing is not available and the transmitter has fewer antennas than the sum of the receiving antennas. To reach the boundary of the rate region, the sum rate is maximized subject to a rate ratio constraint. Furthermore, the sum rate is approximated as an affine function of the logarithm of the SNR and the two parameters of this approximation, which are the multiplexing gain (MG) and the rate offset (RO), are derived. This leads directly to the asymptotic rate region, particularly interesting because it is obtained in simple analytical form and offers a good approximation at high but finite SNR. We then consider the rate region boundary at finite SNR and derive algorithmic bounds for it, which are accurate even at intermediate SNR.

We present a general rate duality between the multiple access channel (MAC) and the broadcast channel (BC) which is applicable to systems with and without nonlinear interference cancellation. Different to the state-of-the-art rate duality with interference subtraction from Vishwanath et al., the proposed duality is filter-based instead of covariance-based and exploits the arising unitary degree of freedom to decorrelate every point- to-point link. Therefore, it allows for noncooperative stream-wise decoding which reduces complexity and latency. Moreover, the conversion from one domain to the other does not exhibit any dependencies during its computation making it accessible to a parallel implementation instead of a serial one. We additionally derive a rate duality for systems with multi-antenna terminals when linear filtering without interference (pre-)subtraction is applied and the different streams of a single user are not treated as self-interference. Both dualities are based on a framework already applied to a mean-square-error duality between the MAC and the BC. Thanks to this novel rate duality, any rate-based optimization with linear filtering in the BC can now be handled in the dual MAC where the arising expressions lead to more efficient algorithmic solutions than in the BC due to the alignment of the channel and precoder indices.

We prove convexity of the sum-power constrained mean square error (MSE) region in case of two single-antenna users communicating with a multi-antenna base station. Due to the MSE duality this holds both for the vector broadcast channel and the dual multiple access channel. Increasing the number of users to more than two, we show by means of a simple counter-example that the resulting MSE region is not necessarily convex any longer, even under the assumption of single-antenna users. In conjunction with our former observation that the two user MSE region is not necessarily convex for two multi-antenna users, this extends and corrects the hitherto existing notion of the MSE region geometry.

Non-linear precoding for point-to-point (P2P) multiple-input multiple-output (MIMO) systems is considered. First, the minimum mean square error (MMSE) optimal vector precoding (VP) is presented for different receiver structures, viz., weighted identity matrix, diagonal matrix, weighted unitary matrix, and matrix without particular structure. Whereas the former two structures can also be applied to the vector broadcast channel, the latter two are only realizable for cooperative receivers. Second, VP is derived that minimizes the MSE but is restricted to maximize the mutual information of the MIMO channel. Third, the corresponding Tomlinson-Harashima precoding (THP) is found by applying the nearest-plane approximation to the computation of the perturbation signal. The resulting maximum mutual information THP clearly outperforms the state-of-the-art P2P-MIMO THP based on the generalized triangular decomposition (GTD) with respect to MSE and BER.

For the separation of the signals for multiple users in the vector broadcast channel (BC), channel state information (CSI) is necessary at the transmitter. Since the transmitter has no access to this information in many cases, the CSI must be fed back from the receivers to the transmitter. Before the feedback, the receivers estimate the CSI and apply a rank reduction possible due to the channel correlations. We propose a joint optimization of the estimation, the rank reduction, and the codebook used for the feedback. Interestingly, the estimator and the rank reduction resulting from this monolithic formulation are independent of the used codebook which can be computed with the generalized Lloyd algorithm. Applying the proposed feedback design to a system with multi-user precoding based on CSI feedback shows the clear superiority of the optimized codebook compared to previous designs.

In this paper we investigate the design of a robust MMSE linear precoding Multiuser Multiple Input Single Output (MU MISO) system with limited feedback that exploits multiple feedback vectors to improve the quality of the available CSI at transmission. We explain how to appropriately exploit this additional past channel information to design the channel estimator, rank basis reduction and the quantizer parameters.

We consider amulti-usermultiple-inputsingle-output(MU-MISO) scenario, where the decentralized users are served by a centralized transmitter with multiple channel inputs via frequency selective vector channels. For this broadcast setup, we jointly design the transmitter and receivers based on a minimum summeansquareerror(MSE) criterion. Contrary to previous work in this field, we do not restrict the receivers to be scalar weights but employfiniteimpulseresponse(FIR) receive filters. Since the sum MSE minimization has no closed-form solution neither for linear preceding nor forTomlinson-Harashimaprecoding(THP), we propose to use an alternating optimization and prove the convergence of the resulting iterative algorithm. The simulations show that the obtained linear and nonlinear preceding solutions with FIR receivers clearly outperform the state-of-the-art precoders with scalar receivers.

For the single-group multicast scenario, where K users are served with the same data by a base station equipped with N antennas, we present two beamforming algorithms which outperform state-of-the-art multicast filters and feature a drastically reduced complexity at the same time. For the power minimization problem, where QoS constraints need to be satisfied, we introduce a successive beamforming filter computation approach aiming at satisfying at least one additional SNR constraint per orthogonal filter update. As long as the number of users K is smaller than the number N of transmit antennas, this procedure delivers excellent results. Our second approach is an iterative update algorithm for the max-min problem subject to a limitation of the transmit power. Given a low-complexity initialization beamformer, we search within the local vicinity of this filter vector for a filter-update preserving the transmit power and achieving a larger minimum SNR. To this end, we improve the weakest user's SNR during each iteration and keep on applying this procedure as long as the updates increase the smallest SNR. Otherwise, we adapt the step-size and continue investigating the local vicinity. It turns out that this novel approach is superior to existing state-of-the-art multicast beamformers for an arbitrary number of users.

We propose a receiver for multipoint-to-point systems based on theminimummeansquareerror(MMSE) criterion, where the symbols aredetectedingroupsand already detected symbols are fed back for interference subtraction, as known for decision feedback equalization (DFE). The proposedscaledDFE(SDFE) has two special cases: 1) DFE for a group size of one, i.e., for symbol-by-symbol detection. 2)Maximumlikelihooddetection(MLD), if the group comprises all transmitted symbols. The diversity order of SDFE lies between the poor diversity order of DFE and the full diversity order of MLD. Therefore, SDFE offers a trade-off between complexity due to the group-wise symbol detection and the increased diversity order compared to DFE. We also present an algorithm to compute the SDFE filters with an order of complexity which is the same as that to compute linear equalization filters. Motivated by the promising results of detectors based onlatticereduction(LR), we combine SDFE with LR. The resulting detector exhibits full diversity order and improved performance compared to LR-DFE. The simulations show that SDFE is an interesting generalization of DFE for detectors with zero-forcing constraint, since SDFE even outperforms LR-DFE for realisticsignal-to-noise-ratio(SNR). However, LR-DFE exhibits the best results for an affordable complexity, when dropping the zero-forcing constraint.

We address the problem of jointly optimizing the pre coder and the receivers in a multi-user broadcast system for a linear and nonlinear transmitter under sum mean square error (MSE) minimization. By means of alternating optimization (AO), we find an iterative algorithm which always converges to the global optimum. In addition to an elegant initialization of the receivers' weights, we come up with expressions for the speed of convergence. Our algorithm is applicable to both single-antenna and multi-antenna receivers and can be combined with nonlinear Tomlinson-Harashima precoding (THP). For THP, the precoding order can easily be included in the AO. Moreover, we show that for sum MSE minimization the user-wise channels are not necessarily diagonalized and give some ideas how this fact can be exploited

This paper extends the self-contained theory of linear precoding to the field of covariance based spatio-temporal downlink processing for direct-sequence code-division multiple-access (CDMA) systems and shows the applicability to the release 6 of high-speed downlink packet access (HSDPA). To this end, a unifying theory is developed to formulate the three known linear filters, namely, the transmit matched filter, the transmit zero-forcing filter, and the transmit Wiener filter, as optimization problems even in systems, where only covariance knowledge is available at the transmitter. Second, the solutions of these transmit filters are given for such systems with partial channel state information (CSI). Finally, it is shown how covariance-based linear precoding can be employed in the new generation CDMA system HSDPA, i.e., how channel estimation on the secondary common pilot channel allows for optimum full rank linear precoding employing only partial CSI.

Traditionally, channel estimation and equalization are optimized separately and independently. The channel estimate is simply plugged into the equalizer as if it had no errors. We propose a new method for joint pilot symbol assisted channel estimation and equalization and apply it to the design of the space-time decision feedback equalizer. The explicit solution of this joint approach is obtained with the same order of complexity as a separate design and results in a significant performance improvement. Furthermore, we discuss its relation to robust optimization and regularization techniques for equalizer design.

Nonlinear minimum mean square error Tomlinson-Harashima precoding considered in this paper is an attractive solution for a scenario where a transmitter serves spatially separated receivers and no cooperation among them is possible. Unfortunately, the large performance gain against linear precoding comes along with significantly higher complexity than linear filters in the case of a large number of receivers. We show that superior performance of the nonlinear minimum mean square error Tomlinson-Harashima precoding can be obtained with complexity equivalent to linear precoding. Our proposed algorithm reduces the complexity by a factor of N/sub R/ which is the number of receivers.

We derive the minimum mean square error (MMSE) solution to vector precoding for frequency flat multiuser scenarios with a centralized multi-antenna transmitter. The receivers employ a modulo operation, giving the transmitter the additional degree of freedom to choose a perturbation vector. Similar to existing vector precoding techniques, the optimum perturbation vector is found with a closest point search in a lattice. The proposed MMSE vector precoder does not, however, search for the perturbation vector resulting in the lowest transmit energy, as proposed in all previous contributions on vector precoding, but finds an optimum compromise between noise enhancement and residual interference. We present simulation results showing that the proposed technique outperforms existing vector precoders, as well as the MMSE Tomlinson-Harashima precoder.

Enormous capacity advantage can be achieved on a flat MIMO channel compared to single antenna systems. V-BLAST was proposed to obtain such capacity advantage with low complexity. V-BLAST, however, requires multiple matrix (pseudo) inversions that are still computationally intensive for a large number of antennas. Much research has been attracted to reducing the complexity. Our contribution is to show that the MMSE block decision-feedback equalizer equivalent to the MMSE V-BLAST can be calculated via Cholesky factorization of the error covariance matrix with symmetric permutation. Forward and backward filters as well as detection order are jointly optimized with significantly reduced complexity. Simulation results show that MMSE V-BLAST performance can be achieved by the proposed scheme.

The multi-stage transmit Wiener filter (MSTxWF) is presented, an approach to reducing the complexity of the transmit Wiener filter (TxWF). The MSTxWF is found by applying the multi-stage decomposition known from the receive multi-stage Wiener filter (MSWF) to the TxWF. Complexity reduction is achieved by truncating the decomposition. We show that the resulting reduced rank MSTxWF can be interpreted as an approximation of the TxWF in a Krylov subspace, allowing for an efficient computation of the MSTxWF with the Lanczos algorithm. The reduced rank MSTxWF shows near-optimum performance for relatively low rank, making it an interesting alternative to eigenspace-based methods for complexity reduction.

Linear transmit filters depend on current channel state information, which is available from the uplink channel estimation in time division duplex systems. For multiple antenna elements at the transmitter, we illustrate the influence of out-dated channel estimates on link level performance for symmetric and asymmetric traffic, comparing the transmit matched, zero-forcing, and Wiener filters. A Wiener predictor is proposed to improve channel knowledge of the transmitter. We observe an inherent robustness of the transmit matched filter and explain the occurrence of a minimum in the bit error ratio at a finite SNR for the transmit Wiener filter.

In this article, we present different space-time receive processing techniques for frequency selective multiple input multiple output (MIMO) channels and evaluate their performance. We present the solutions for linear zero-forcing (ZF) and Wiener filter (WF) equalization with latency time optimization and incorporate the Bell Laboratories Layered Space Time (BLAST) architecture to gain diversity. Furthermore, we present systems based on decision feedback equalization (DFE). We also combine this equalization method with the BLAST principle.

We present space-time transmit filters for FDD DS-CDMA systems based on partial channel state information, i.e. we do not take into account the channel coefficients. Although the FDD transmit zero-forcing filter seems to be the most intuitive approach, we focus on the FDD transmit matched filter and the FDD transmit Wiener filter. Similarly to the respective receive filters and TDD transmit filters, the FDD matched filter maximizes the desired signal portion at the receiver and is optimum for low signal-to-noise-ratio scenarios, whereas the FDD transmit Wiener filter takes into account the noise power at the receiver and is therefore able to find an optimum trade-off between signal maximization and interference suppression. Additionally, we show that the FDD transmit matched filter is a type of eigenbeamforming. The simulation results reveal the excellent performance of the two FDD transmit filters. The FDD transmit Wiener filter even outperforms the TDD transmit matched filter for high signal-to-noise-ratio which is based on the instantaneous channel properties.

The Wiener filter solves the Wiener-Hopf equation and may be approximated by the multi-stage nested Wiener filter (MSNWF) which lies in the Krylov subspace of the covariance matrix of the observation and the cross-correlation vector between the observation and the desired signal. Moreover, since the covariance matrix is Hermitian, the Lanczos algorithm can be used to compute the Krylov subspace basis. The conjugate gradient (CG) method is another approach to solving a system of linear equations. We derive the relationship between the CG method and the Lanczos based MSNWF and finally transform the formulas of the MSNWF into those of the CG algorithm. Consequently, we present a CG based MSNWF where the filter weights and the mean square error (MSE) are updated at each iteration step. The resulting algorithm is used for linear equalization of the received signal in an enhanced data rates for GSM evolution (EDGE) system. Simulation results demonstrate the ability of the MSNWF to reduce receiver complexity while maintaining the same level of system performance.

Many services of third-generation (3G) mobile radio systems will have higher data rates in the downlink than in the uplink. We propose to utilize adaptive antennas at the base stations because spatial interference suppression is able to reduce the near-far effect in the downlink of single-user detection direct-sequence (DS) code division multiple access (CDMA) systems. Besides the channel parameters in terms of directions of arrival, delays, and medium-term average path attenuations which are estimated in the uplink, we also take into account the correlation properties of the spreading and scrambling codes. In DS-CDMA the users are distinguished by different spreading codes, which change over time due to scrambling. In Brunner et al. (see Proc. EPMCC, p.375-80, 1999), the beamforming vectors at the base station were computed slotwise, whereas in this paper, we favor a symbol-rate beamforming at the base station. The new approach optimizes the actual values of the decision variables of the RAKE demodulators at the receivers. The superiority of the symbol rate beamforming algorithm compared to slotwise beamforming is shown by bit error rate (BER) simulations.