In this paper, we investigate a cell-free massive MIMO system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) based on a two-layer decoding structure with maximum ratio (MR) or local minimum mean-square error (MMSE) combining applied in the first layer and optimal large-scale fading decoding method implemented in the second layer, respectively. To maximize the weighted sum SE, an uplink precoding structure based on an Iteratively Weighted sum-MMSE (I-WMMSE) algorithm using only channel statistics is proposed. Furthermore, with MR combining applied in the first layer, we derive novel achievable SE expressions and optimal precoding structures in closed-form. Numerical results validate our proposed results and show that the I-WMMSE precoding can achieve excellent sum SE performance.
Precoding design exploiting deep learning methods has been widely studied for multiuser multiple-input multiple-output (MU-MIMO) systems. However, conventional neural precoding design applies black-box-based neural networks which are less interpretable. In this paper, we propose a deep learning-based precoding method based on an interpretable design of a neural precoding network, namely iPNet. In particular, the iPNet mimics the classic minimum mean-squared error (MMSE) precoding and approximates the matrix inversion in the design of the neural network architecture. Specifically, the proposed …
This study proposes a symbol-level precoding algorithm based on the minimum mean squared error design objective under a strict per antenna power constraint for PSK modulation. The proposed design is then formulated in the standard form of a second-order cone program, allowing for an optimal solution via the interior point method. Numerical results indicate that the proposed design is superior to the existing approaches in terms of bit-error-rate for the low and intermediate SNR regime.
We propose an optimal MMSE precoding technique using quantized signals with constant envelope. Unlike the existing MMSE design that relies on 1-bit resolution, the proposed approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. Moreover, unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conju…
In this work, we propose iterative access point (AP) selection (APS), linear minimum mean-square error (MMSE) precoding and power allocation techniques for Cell-Free Massive multiple-input multiple-output (MIMO) systems. We consider the downlink channel with single-antenna users and multiple-antenna APs. We derive sum-rate expressions for the proposed iterative APS techniques followed by MMSE precoding and optimal, adaptive, and uniform power allocation schemes. Simulations show that the proposed approach outperforms existing conjugate beamforming (CB) and zero-forcing (ZF) schemes and that pe…
In this paper, we propose a symbol-level precoding (SLP) design that aims to minimize the weighted mean square error between the received signal and the constellation point located in the constructive interference region (CIR). Unlike most existing SLP schemes that rely on channel state information (CSI) only, the proposed scheme exploits both CSI and the distribution information of the noise to achieve improved performance. We firstly propose a simple generic description of CIR that facilitates the subsequent SLP design. Such an objective can further be formulated as a nonnegative least squar…
In this paper, we investigate a cell-free massive multiple-input multiple-output system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) for the fully centralized processing scheme and large-scale fading decoding (LSFD) scheme. To further improve the SE performance, we design the uplink precoding schemes based on the weighted sum SE maximization. Since the weighted sum SE maximization problem is not jointly over all optimization variables, two efficient uplink precoding sche…
We consider a hardware-impaired multi-cell Rician faded massive multi-input multi-output (mMIMO) system with two-layer pilot decontamination precoding, also known as large-scale fading precoding (LSFP). Each BS is equipped with a flexible dynamic analog-to-digital converter (ADC)/digital-to-analog converter (DAC) architecture and the user equipments (UEs) have low-resolution ADCs. Further, both BS and UEs have hardwareimpaired radio frequency chains. The dynamic ADC/DAC architecture allows us to vary the resolution of ADC/DAC connected to each BS antenna, and suitably choose them to maximize t…
This article studies a novel distributed precoding design, coined team minimum mean-square error (TMMSE) precoding, which rigorously generalizes classical centralized MMSE precoding to distributed operations based on transmitter-specific channel state information (CSIT). Building on the so-called theory of teams, we derive a set of necessary and sufficient conditions for optimal TMMSE precoding, in the form of an infinite dimensional linear system of equations. These optimality conditions are further specialized to cell-free massive MIMO networks, and explicitly solved for two important exampl…
This study proposes a novel precoding scheme for multiuser multiple-input multiple-output (MIMO) relay systems in the presence of imperfect channel state information (CSI). The base station (BS) and the MIMO relay station (RS) are both equipped with the same codebook of unitary matrices. According to each element of the codebook, we create a latent precoding matrix pair, namely a BS precoding matrix and an RS precoding matrix. The RS precoding matrix is formed by multiplying the appropriate unitary matrix from the codebook by a power scaling factor. Based on the given CSI and a block of transm…
In this letter, we present a widely-linear minimum mean square error (WL-MMSE) precoding scheme employing real-valued transmit symbols for downlink large-scale multi-user multiple-input single-output (MU-MISO) systems. In contrast to the existing WL-MMSE transceivers for single-user multiple-input multiple-output (SU-MIMO) systems, which use both WL precoders and WL detectors, the proposed scheme uses WL precoding only and simple conventional detection at the user terminals (UTs). Moreover, to avoid the computational complexity associated with inversion of large matrices, we modify the WL-MMSE…
The problem of max-min signal-to-interference plus noise ratio (SINR) for uplink transmission of cell-free massive multiple-input multiple-output (MIMO) system is considered. We assume that the system is employed with local minimum mean square error (L-MMSE) combining. The objective is to preserve user fairness by solving max-min SINR optimization problem, by optimizing transmit power of each user equipment (UE) and weighting coefficients at central processing unit (CPU), subject to transmit power constraints of UEs. This problem is not jointly convex. Hence, we decompose original problem into…
Classical antenna selection schemes require instantaneous channel state information (CSI). This leads to high signaling overhead in the system. This work proposes a novel joint receive antenna selection and precoding scheme for multiuser multiple-input multiple-output uplink transmission that relies only on the long-term statistics of the CSI. The proposed scheme designs the switching network and the uplink precoders, such that the expected throughput of the system in the long term is maximized. Invoking results from the random matrix theory, we derive a closed-form expression for the expected…
We consider a scalable user-centric wireless network with dynamic cluster formation as defined by Björnsson and Sanguinetti. After having shown the importance of dominant channel subspace information for uplink (UL) pilot decontamination and having examined different UL combining schemes in our previous work, here we investigate precoding strategies for the downlink (DL). Distributed scalable DL precoding and power allocation methods are evaluated for different antenna distributions, user densities and UL pilot dimensions. We compare distributed power allocation methods to a scheme based on a …
We consider a practical cell-free massive multiple-input-multiple-output (MIMO) system with multi-antenna access points (APs) and spatially correlated Rician fading channels. The significant phase-shift of the line-of-sight component induced by the user equipment movement is modeled randomly. Furthermore, we investigate the uplink spectral efficiency (SE) with maximum ratio (MR)/local minimum mean squared error (L-MMSE) combining and optimal large-scale fading decoding based on the phase-aware MMSE, phase-aware element-wise MMSE and linear MMSE (LMMSE) estimators. Then new closed-form SE expre…
When operating massive multiple-input multiple-output (MIMO) systems with uplink (UL) and downlink (DL) channels at different frequencies (frequency division duplex (FDD) operation), acquisition of channel state information (CSI) for downlink precoding is a major challenge. Since, barring transceiver impairments, both UL and DL CSI are determined by the physical environment surrounding transmitter and receiver, it stands to reason that, for a static environment, a mapping from UL CSI to DL CSI may exist. First, we propose to use various neural network (NN)-based approaches that learn this mapp…
In this paper, we extend the diversity and multiplexing tradeoff (DMT) analysis from point-to-point channels to cellular systems to evaluate the impact of inter-cell interference on the system reliability and efficiency. Fundamental tradeoff among diversity order, multiplexing gain and inter-cell interference intensity is characterized to reveal the capability of multiple antennas in cellular systems. And the detrimental effects of the inter-cell interference on the system performance of diversity and multiplexing is presented and analyzed.
We consider the downlink of a cell-free massive multiple-input multiple-output (MIMO) system with \textcolor{red}{single}-antenna access points (APs) and single-antenna users. An iterative robust minimum mean-square error (RMMSE) precoder based on generalized loading is developed to mitigate interference in the presence of imperfect channel state information (CSI). An achievable rate analysis is carried out and optimal and uniform power allocation schemes are developed based on the signal-to-interference-plus-noise ratio. An analysis of the computational costs of the proposed RMMSE and existin…
Millimeter wave (mmWave) communication is expected to play an important role in next generation cellular networks, aiming to cope with the bandwidth shortage affecting conventional wireless carriers. Using side-information has been proposed as a potential approach to accelerate beam selection in mmWave massive MIMO (m-MIMO) communications. However, in practice, such information is not error-free, leading to performance degradation. In the multi-user case, a wrong beam choice might result in irreducible inter-user interference at the base station (BS) side. In this paper, we consider location-a…
The uplink from a very small aperture terminal (VSAT) towards multiple satellites is considered, in this paper. VSATs can be equipped with multiple antennas, allowing parallel transmission to multiple satellites. A low-complexity precoder based on imperfect positional information of the satellites is presented. The probability distribution of the position uncertainty and the statistics of the channel elements are related by the characteristic function of the position uncertainty. This knowledge is included in the precoder design to maximize the mean signal-to-leakage-and-noise ratio (SLNR) at …
User electromagnetic (EM) exposure is continuously being exacerbated by the evolution of multi-antenna portable devices. To mitigate the effects of EM radiation, portable devices must satisfy tight regulations on user exposure level, generally measured by specific absorption rate (SAR). To this end, we investigate the SAR-aware uplink precoder design for the energy efficiency (EE) maximization in multiuser multiple-input multiple-output transmission exploiting statistical channel state information (CSI). As the objective function of the design problem is computationally demanding in the absenc…
We consider the transmission of a Gaussian vector source over a multi-dimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the MMSE performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions …
Minimum mean square error (MMSE) signal detection algorithm is near- optimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity. In this letter, we firstly prove that the MMSE filtering matrix for large- scale MIMO is symmetric positive definite, based on which we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion. The complexity can be reduced from O(K3) to O(K2), where K is the number of users. We also provide the convergence proof o…
In this paper, we study the interference cancellation capabilities of receivers and transmitters in multiple-input-multiple-output (MIMO) systems using theoretical calculations and numerical simulations in Quadriga. We study so-called Reduced Channel Zero-Forcing (RCZF) class of precoding as well as Minimum MSE Interference Rejection Combiner (MMSE-IRC) and QR Maximum Likelihood Detection (QR-MLD) receivers. Based on very simple but extremely useful algebraic manipulations, their asymptotical equivalence is proven analytically and demonstrated via simulations. Our theoretical and experimental …
Satellite communication systems are a fundamental component in support of Europe's ambition to deploy smart and sustainable networks and services for the success of its digital economy. To cope with the 5G and beyond ever increasing demand for larger throughput, aggressive frequency reuse schemes (i.e., full frequency reuse), with the implementation of precoding/beamforming to cope with the massive co-channel interference, are recognised as one of the key technologies. While the best performance can be obtained with the knowledge of the Channel State Information (CSI) at the transmitter, this …
The expected operating scenarios of 5G pose a great challenge to orthogonal frequency division multiplexing (OFDM) which has poor out of band (OoB) spectral properties, stringent synchronization requirements, and large symbol duration. Generalized frequency division multiplexing (GFDM) which is the focus of this work, has been suggested in the literature as one of the possible solutions to meet 5G requirements. In this work, the analytical performance evaluation of MMSE receiver for GFDM is presented. We also proposed precoding techniques to enhance the performance of GFDM. A simplified expres…
For uplink large-scale MIMO systems, linear minimum mean square error (MMSE) signal detection algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose a low-complexity signal detection algorithm based on the successive overrelaxation (SOR) method to avoid the complicated matrix inversion. We first prove a special property that the MMSE filtering matrix is symmetric positive definite for uplink large-scale MIMO systems, which is the premise for the SOR method. Then a low-complexity iterative signal detection algorithm based on the SOR method as wel…
In this paper, we consider the amplify-and-forward relay networks in mmWave systems and propose a hybrid precoder/combiner design approach. The phase-only RF precoding/combining matrices are first designed to support multi-stream transmission, where we compensate the phase for the eigenmodes of the channel. Then, the baseband precoders/combiners are performed to achieve the maximum mutual information. Based on the data processing inequality for the mutual information, we first jointly design the baseband source and relay nodes to maximize the mutual information before the destination baseband …
This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. For precoding at the base stations, channel state information (CSI) is essential at the base stations. A popular technique for obtaining this CSI in time division duplex (TDD) systems is uplink training by utilizing the reciprocity of the wireless medium. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper…
In this paper, we analyze the ergodic capacity of a dual-hop amplify-and-forward relaying system where the relay is equipped with multiple antennas and subject to co-channel interference (CCI) and the additive white Gaussian noise. Specifically, we consider three heuristic precoding schemes, where the relay first applies the 1) maximal-ratio combining (MRC) 2) zero-forcing (ZF) 3) minimum mean-squared error (MMSE) principle to combine the signal from the source, and then steers the transformed signal towards the destination with the maximum ratio transmission (MRT) technique. For the MRC/MRT a…
We investigate Gaussian widely linear precoding known as improper Gaussian signaling for the cellular uplink with inter-cell interference, known as interference multiple access channel (IMAC). This transmission scheme provides extra degrees of freedom by treating the real and imaginary components of the complex Gaussian signal differently. Since current standards mainly utilize linear beamforming for waveform generation, we highlight the benefits of widely linear beamforming over multiple temporal dimensions (symbol extension in time) in the IMAC. This scheme achieves significantly higher info…
In this paper, we derive new closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the two-user multiple access channel (MAC). The derived relations generalize the fundamental relation between the derivative of the mutual information and the minimum mean squared error (MMSE) to multiuser setups. We prove that the derivative of the mutual information with respect to the signal to noise ratio (SNR) is equal to the MMSE plus a covariance induced due to the interference, quantified by a term with respect to the cross correlation of the multiuser…
Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side and is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for multiuser MIMO (MU-MIMO) systems with multiple receive antennas due to the fact that the users are geographically distributed. In this paper, we propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing…
We consider multi-group multicast precoding designs for cell-free massive multiple-input multiple-output (MIMO) systems. To optimize the transmit and receive beamforming strategies, we focus on minimizing the sum of the maximum mean squared errors (MSEs) over the multicast groups, which is then approximated with the sum MSE to simplify the computation and signaling. We adopt an iterative bi-directional training scheme with uplink and downlink precoded pilots to cooperatively design the multi-group multicast precoders at each base station and the combiners at each user equipment in a distribute…
We propose a novel linear minimum-mean-squared-error (MMSE) precoder design for a downlink (DL) massive multiple-input-multiple-output (MIMO) scenario. For economical and computational efficiency reasons low resolution 1-bit digital-to-analog (DAC) and analog-to-digital (ADC) converters are used. This comes at the cost of performance gain that can be recovered by the large number of antennas deployed at the base station (BS) and an appropiate precoder design to mitigate the distortions due to the coarse quantization. The proposed precoder takes the quantization non-linearities into account and…
The uplink achievable rate of massive multiple- input-multiple-output (MIMO) systems, where the low-resolution analog-to-digital converters (ADCs) are assumed to equip at the base station (BS), is investigated in this paper. We assume that only imperfect channel station information is known at the BS. Then a new MMSE receiver is designed by taking not only the Gaussian noise, but also the channel estimation error and quantizer noise into account. By using the Stieltjes transform of random matrix, we further derive a tight asymptotic equivalent for the uplink achievable rate with proposed MMSE …
The objective of this paper is to develop simple techniques to enhance the performance of multi-user RIS aided wireless systems. Specifically, we develop a novel technique called \textit{channel separation} which provides a better understanding of how the RIS phases affect the uplink sum rate and sum rates for ZF and MMSE linear receivers. Leveraging channel separation, we propose a simple iterative algorithm to improve the uplink sum rate and the sum rates of ZF and MMSE linear receivers when discrete RIS phases are considered. For continuous RIS phases, we derive simple closed form solutions…
We propose an optimal low-resolution precoding technique that minimizes the symbol error probability of the users. Unlike existing approaches that rely on QPSK modulation, for the derivation of the minimum symbol error probability objective function the current approach allows for any PSK modulation order. Moreover, the proposed method solves the corresponding discrete optimization problem optimally via a sophisticated branch-and-bound method. Moreover, we propose different approaches based on the greedy search method to compute practical solutions. Numerical simulations confirm the superiorit…
We consider a cell-free massive multiple-input multiple-output (MIMO) system with multi-antenna access points and user equipments (UEs) over Weichselberger Rician fading channels with random phase-shifts. More specifically, we investigate the uplink spectral efficiency (SE) for two pragmatic processing schemes: 1) the fully centralized processing scheme with global minimum mean square error (MMSE) or maximum ratio (MR) combining; 2) the large-scale fading decoding (LSFD) scheme with local MMSE or MR combining. To improve the system SE performance, we propose a practical uplink precoding scheme…
A large majority of cellular networks deployed today make use of Frequency Division Duplexing (FDD) where, in contrast with Time Division Duplexing (TDD), the channel reciprocity does not hold and explicit downlink (DL) probing and uplink (UL) feedback are needed in order to achieve spatial multiplexing gain. To support massive MIMO, the overhead incurred by conventional DL probing and UL feedback schemes scales linearly with the number of BS antennas and, therefore, may be very large. In this paper, we present a new approach to achieve a very competitive trade-off between spatial multiplexing…
In this paper, we generalize the fundamental relation between the mutual information and the minimum mean squared error (MMSE) by Guo, Shamai, and Verdu [1] to K-User Gaussian channels. We prove that the derivative of the multiuser mutual information with respect to the signal to noise ratio (SNR) is equal to the total MMSE plus a covariance term with respect to the cross correlation of the multiuser input estimates, the channels and the precoding matrices. We shed light that such relation is a generalized I-MMSE with one step lookahead and lookback, applied to the Successive Interference Canc…
We consider a practical spatially correlated reconfigurable intelligent surface (RIS)-aided cell-free (CF) massive multiple-input-multiple-output (mMIMO) system with multi-antenna access points (APs) over spatially correlated Rician fading channels. The minimum mean square error (MMSE) channel estimator is adopted to estimate the aggregated RIS channels. Then, we investigate the uplink spectral efficiency (SE) with the maximum ratio (MR) and the local minimum mean squared error (L-MMSE) combining at the APs and obtain the closed-form expression for characterizing the performance of the former.…
The gains afforded by cloud radio access network (C-RAN) in terms of savings in capital and operating expenses, flexibility, interference management and network densification rely on the presence of high-capacity low-latency fronthaul connectivity between remote radio heads (RRHs) and baseband unit (BBU). In light of the non-uniform and limited availability of fiber optics cables, the bandwidth constraints on the fronthaul network call, on the one hand, for the development of advanced baseband compression strategies and, on the other hand, for a closer investigation of the optimal functional s…
For uplink large-scale MIMO systems, minimum mean square error (MMSE) algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss-Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose a approximated method to compute log-likelihood ratio…
Base stations with a large number of transmit antennas have the potential to serve a large number of users at high rates. However, the receiver processing in the uplink relies on channel estimates which are known to suffer from pilot interference. In this work, making use of the similarity of the uplink received signal in CDMA with that of a multi-cell multi-antenna system, we perform a large system analysis when the receiver employs an MMSE filter with a pilot contaminated estimate. We assume a Rayleigh fading channel with different received powers from users. We find the asymptotic Signal to…
Transmitter channel state information (CSIT) is indispensable for the spectral efficiency gains offered by massive multiple-input multiple-output (MIMO) systems. In a frequency-division-duplexing (FDD) massive MIMO system, CSIT is typically acquired through downlink channel estimation and user feedback, but as the number of antennas increases, the overhead for CSI training and feedback per user grows, leading to a decrease in spectral efficiency. In this paper, we show that, using uplink pilots in FDD, the downlink sum spectral efficiency gain with perfect downlink CSIT is achievable when the …
In a recent work, we studied a novel precoding design for cell-free networks called team minimum mean-square error (TMMSE) precoding, which rigorously generalizes centralized MMSE precoding to distributed operations based on transmitter-specific channel state information (CSI). Despite its flexibility in handling different cooperation regimes at the CSI sharing level, TMMSE precoding assumes network-wide sharing of the data bearing signals, and hence it is inherently not scalable. In this work, inspired by recent advances on scalable cell-free architectures based on user-centric network cluste…
In this paper, a new state-of-the-art multi-cell MMSE scheme is proposed for massive MIMO networks, which includes an uplink MMSE detector and a downlink MMSE precoder. The main novelty is that it exploits all available pilots for interference suppression. Specifically, let $K$ and $B$ denote the number of users per cell and the number of orthogonal pilot sequences in the network, respectively, where $β= B/K$ is the pilot reuse factor. Then our multi-cell MMSE scheme utilizes all $B$ channel directions, that can be estimated locally at each base station, to actively suppress both intra-cell an…
In this work we extend the concept of uplink-downlink rate balancing to frequency division duplex (FDD) massive MIMO systems. We consider a base station with large number antennas serving many single antenna users. We first show that any unused capacity in the uplink can be traded off for higher throughput in the downlink in a system that uses either dirty paper (DP) coding or linear zero-forcing (ZF) precoding. We then also study the scaling of the system throughput with the number of antennas in cases of linear Beamforming (BF) Precoding, ZF Precoding, and DP coding. We show that the downlin…
In this paper, we investigate a cell-free massive MIMO system with both access points (APs) and user equipments (UEs) equipped with multiple antennas over jointly-correlated Rayleigh fading channels. We study four uplink implementations, from fully centralized processing to fully distributed processing, and derive their achievable spectral efficiency (SE) expressions with minimum mean-squared error successive interference cancellation (MMSE-SIC) detectors and arbitrary combining schemes. Furthermore, the global and local MMSE combining schemes are derived based on full and local channel state …
Massive MIMO systems can achieve high spectrum and energy efficiency in downlink (DL) based on accurate estimate of channel state information (CSI). Existing works have developed learning-based DL CSI estimation that lowers uplink feedback overhead. One often overlooked problem is the limited number of DL pilots available for CSI estimation. One proposed solution leverages temporal CSI coherence by utilizing past CSI estimates and only sending CSI-reference symbols (CSI-RS) for partial arrays to preserve CSI recovery performance. Exploiting CSI correlations, FDD channel reciprocity is helpful …
This paper considers the uplink (UL) of a multi-cell Massive MIMO (multiple-input multiple-output) system with spatially correlated Rician fading channels. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight (NLoS) component describing a spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE) and least-square (LS) channel estimates for this model. Using these estimates for maximum ratio (MR) combining, rigorous closed-form UL spectral efficiency (SE) expressions are derive…
