Correlated Rayleigh Fading Research Articles

On the Performance of the Relay Selection in Multi-hop Cluster-based Wireless Networks with Multiple Eavesdroppers Under Equally Correlated Rayleigh Fading

The performance of multi-hop cluster-based wireless networks under multiple eavesdroppers is investigated in the present work. More precisely, we derive the outage probability (OP) of the considered networks under two relay selection schemes: the channel-gain-based scheme and the random scheme. Although equally correlated Rayleigh fading is taken into consideration, the derived mathematical framework remains tractable. Specifically, we represent the exact expression of the OP under the channel-based scheme in series form, while the OP under the random scheme is computed in a closed-form expression. Additionally, we propose a novel power allocation for each transmitter that strictly satisfies the given intercept probability. Numerical results based on the Monte Carlo method are provided to verify the correctness of the derived framework. These results are also used to identify the influences of various parameters, such as the number of clusters, the number of relays per cluster, and the transmit power.

Estimation of Uplink Channels for Multiple Users Using Tensor Modeling in RIS-Aided MISO Communication

In this paper estimation of uplink channels using tensor modeling is addressed for multiple users in a reconfigurable intelligent surface (RIS)-aided multiple-input single-output (MISO) communication. The coherence interval is divided into structured frames of pilot symbols transmitted by the users and pattern of phase shifts applied by the RIS in order to estimate the base station (BS)-RIS channels and the RIS-user’s channels. Estimation methods that use tensor modeling including Khatri-Rao Factorization (KRF) and bilinear alternating least squares (BALS) are applied to the signal model. Numerical results show that both KRF and BALS are superior to the LS estimator by 10 dB SNR for the correlated Rayleigh fading channel model.

Gain of Spatial Diversity with Conjoint Signals in Arbitrarily Correlated Rayleigh Fading Channels

Coding gains for arbitrarily correlated signals in a spatial diversity system with conjoint signals are presented in this study. The basic form of the proposed signal synthesizer evenly produces phase changes in the output signals. The mixer is an orthogonal transformation matrix, which is energy preserving and blind to the channel correlation matrix. The idea is to synthesize additional conjoint signal copies from the received signals that would be received if there were more antennas. However, these conjoint signals contain a level of correlation with the received signals. With the assumption of flat Rayleigh fading channels, simulation results for symbol error probability (SEP) are presented for different numbers of receive branches and varying correlation conditions. It is shown that under binary phase shift keying (BPSK), the synthesizer achieves decorrelation coding gains of about 1 dB when selection combining (SC) or equal gain combining (EGC) is used. The synthesizer’s performance across M-ary quadrature amplitude modulation (MQAM) signals is also tested. In addition, analytical frameworks are derived for BPSK and MQAM, which are tightly bound by the Monte Carlo simulation results obtained using Matlab. The correlation analysis is performed for different numbers of antennas and varied antenna spacings.

Cooperative RIS and STAR-RIS Assisted mMIMO Communication: Analysis and Optimization

Reconfigurable intelligent surface (RIS) has emerged as a cost-effective and promising solution to extend the wireless signal coverage and improve the performance via passive signal reflection. Different from existing works which do not account for the cooperation between RISs or do not provide full space coverage, we propose the marriage of cooperative double-RIS with simultaneously transmitting and reflecting RIS (STAR-RIS) technologies denoted as RIS/STAR-RIS under correlated Rayleigh fading conditions to assist the communication in a massive multiple-input multiple-output (mMIMO) setup. The proposed architecture is superior since it enjoys the benefits of the individual designs. We introduce a channel estimation approach of the cascaded channels with reduced overhead. Also, we obtain the deterministic equivalent (DE) of the downlink achievable sum spectral efficiency (SE) in closed form based on large-scale statistics. Notably, relied on statistical channel state information (CSI), we optimise both surfaces by means of the projected gradient ascent method (PGAM), and obtain the gradients in closed form. The proposed optimization achieves to maximise the sum SE of such a complex system, and has low complexity and low overhead since it can be performed at every several coherence intervals. Numerical results show the benefit of the proposed architecture and verify the analytical framework. In particular, we show that the RIS/STAR-RIS architecture outperforms the conventional double-RIS or its single-RIS counterparts.

Spatially Correlated Rayleigh Fading Characteristics of RIS-Aided mmWave MIMO Communications

Spatially Correlated Rayleigh Fading Characteristics of RIS-Aided mmWave MIMO Communications

On the Performance of Training-Based IRS-Assisted Communications Under Correlated Rayleigh Fading

The channel state information (CSI) is crucial in communication systems assisted by intelligent reflecting surfaces (IRSs). This paper is on the phase estimation of individual channels in IRS-assisted communication systems with single-antenna transceivers under the correlated Rayleigh fading. We consider both the fully-active-IRS where all IRS elements are active and the hybrid-IRS where partially IRS elements are active, where an active IRS element is equipped with a sensing device for pilot signal reception. We derive the maximum likelihood (ML) estimator for channel phases of all IRS elements based on the observations on active IRS elements. This estimator is also proved to be the minimum mean square error (MMSE), maximum a posterior (MAP) and minimum mean absolute error (MMAE) estimators. Then we conduct performance analysis in terms of the gain and the capacity of the cascaded transmitter-IRS-receiver channel with perfectly known and estimated individual channel phases. Numerical results are provided to show that the performance of IRS-assisted communication systems with our proposed phase estimator is close to that with perfect CSI and validate our theoretical analysis.

Spatially Correlated Multi-Pair Massive MIMO Relaying With Rician Channel and Phase Shifts

Multi-pair two-way half-duplex massive multiple-input multiple-output (mMIMO) relaying with multiple user-pairs is being actively explored. Most of the existing mMIMO relaying investigations consider either spatially correlated Rayleigh fading or uncorrelated Rician fading channel and also ignore the impact of phase shifts in the line-of-sight (LoS) component due to change in user location and hardware effects. We consider a multi-pair mMIMO amplify-and-forward relay system with spatially correlated Rician channel along with phase shifts. We derive the asymptotic spectral efficiency expressions for different power scaling schemes considering phase aware and phase unaware minimum mean square based channel estimates. Numerical investigations reveal that the impact of LoS component varies with the power scaling schemes.

Impact of Fading Correlation and Finite-Blocklength Regimes on Secrecy

This paper examines secrecy performance of a three-point system|where a main channel and a wiretap channel are present|under outdated channel state information (oCSI), correlated Rayleigh fading and finite-blocklength (FBL) regimes. A main channel and a wiretap channel experience oCSI severity, which impacts the system's average secrecy capacity (ASC) and secrecy outage probability (SOP). Compact expressions for the ASC and SOP will be offered. Hypothetical bounds give fresh insight into secrecy performance. Impact of FBL regimes on secrecy performance is also shown.

Performance Analysis and Power Allocation for Spatial Modulation-Aided MIMO-LDM With Finite Alphabet Inputs

In this paper, we study a spatial modulation (SM) aided multiple-input multiple-output (MIMO) layered division multiplexing (LDM) system for broadcast/multicast service delivery in future broadcast/multicast systems. Comprehensive performance analysis and the injection level (IL) optimization are investigated for the SM-aided MIMO-LDM system over correlated Rayleigh fading channels. First, the symbol detection pairwise error probability (PEP) and the average symbol error rate (SER) union bound under joint maximum-likelihood (ML) detection are derived. Second, the spectral efficiency (SE) of the SM-aided MIMO-LDM system with finite alphabet inputs is analyzed. Since the theoretical SE lacks closed-form expression and involves prohibitive computational complexity, we then derive the closed-form lower bounds and tight approximations for the theoretical SE, in which the computational complexity is relieved by several orders of magnitude compared to direct calculation of the theoretical SE. Third, based on the SE analysis, a weighted sum (WS) SE maximization problem with quality of service (QoS) constraints is formulated to optimize IL for the SM-aided MIMO-LDM system. We first demonstrate that WS SE is a unimodal function of IL, and then develop an efficient golden section search (GSS) based algorithm. Simulation results are provided to validate the theoretical analysis. It is shown that our derived SER union bound well matches the simulated SER in the high SNR region. The tightness of the derived closed-form lower bounds and approximations for theoretical SE and the effectiveness of the developed IL optimization algorithm are also verified by simulation results.

On the performance of uplink NOMA‐based satellite‐aerial‐terrestrial integrated networks

In this article, we study the performance for a satellite-aerial-terrestrial integrated network with imperfect successive interference cancellation (SIC), where the combination of uplink non-orthogonal multiple access (NOMA) technology with beamforming (BF) scheme is implemented. First, to maximize the ergodic sum rate of the uplink NOMA-based satellite network, a BF scheme is proposed with statistical channel state information. Then, assuming that the terrestrial-UAV links undergo correlated Rayleigh fading and the UAV-satellite link experiences correlated Shadowed-Rician fading respectively, the derivation processes of the exact expressions are provided for our system sum rate and energy efficiency with imperfect SIC. Eventually, results together with simulation and analysis are given to validate the correctness of our study. In addition, our proposed scheme has superiority in system performance with comparison to the benchmark schemes.

Анализ и оптимизация схем кодирования для каналов с рэлеевскими замираниями

Conventional approach to perform error-correcting decoding in channels with memory is an adoption of interleaving, which increases the receiver complexity and delay. In order to avoid these limitations, approaches for adapting an error-correcting scheme for memory channels may be used. One approach is to use error-correcting codes with modified design and decoding procedure, taking into account the presence of error bursts in the channel. Another approach to adapting the coding scheme for burst error correction is to use product codes with iterative decoding algorithms. Component codes of product codes themselves may not be able to correct error bursts, but a two-dimensional structure of product codes operating as an artificial interleaver and iterative decoding allow for correction of grouping errors. Purpose: The purpose of the study is to analyze the methods of error-correcting code adaptation to burst error correction in channels with memory in order to reduce the probability of error. Results: The study considered methods of error-correcting code scheme adaptation for low-density parity-check codes, polar codes, and product codes for burst error correction in Gilbert-Elliott channel (GE) and correlated Rayleigh fading channel with different correlation coefficients. Degree distribution of low-density parity-check code was optimized for GE channel. The influence of selected parameters of product code component codes on burst error correction in the GE channel was analyzed. The structure of the polar code has been optimized using a genetic algorithm for the correlated Rayleigh channel, which outperforms the 5G polar code design in terms of error probability. Discussion: Existing error-correcting code schemes do not provide theoretically possible limits, so the question remains of developing coding and decoding schemes capable of reaching theoretical limits.

Performance Analysis and Optimization of Multicell Massive MIMO With Variable-Resolution ADCs Over Correlated Rayleigh Fading Channels

This article makes performance analysis and optimization for multicell massive multiple-input and multiple-output (MIMO) systems with variable-resolution analog-to-digital converters (ADCs). In such an architecture, every ADC uses arbitrary quantization resolution to save power and hardware cost. Along this direction, we first introduce a quantization-aware channel estimator based on linear minimum mean-squared error (LMMSE) estimate theory over spatially correlated Rayleigh fading channels. By leveraging on the estimated channel state information (CSI), we derive the theoretical expressions of the achievable uplink spectral efficiency (SE) for maximal ratio combining (MRC), quantization-aware multicell minimum mean-squared error (QA-M-MMSE) combining, and quantization-aware single-cell MMSE (QA-S-MMSE) combining, respectively. We consider the impacts of quantization errors and resort to random matrix theory to derive theoretical results. Afterwards, power and bit allocation problems are investigated under the variable-resolution architecture. Finally, simulation results demonstrate that our theoretical analyses are correct and that the proposed quantization-aware estimator and combiners are more beneficial than their quantization-unaware counterparts. Moreover, simulation results also verify the conclusions of the proposed power and bit allocation schemes.

Noncoherent space-time coding for correlated massive MIMO channel with Riemannian distance

This paper considers a massive multiple-input multiple-output (MIMO) uplink system in correlated Rayleigh fading channels. A transmitter with two antennas needs to send data timely to a base station with a large number of antennas. We assume the channel coefficients keep constant during two consecutive time slots and change independently in the following two successive time slots. We construct a Riemannian-distance (RD) based noncoherent detector for such a system. Also, we propose a novel noncoherent parametric space-time coding method. We first attain the closed-form solutions of the optimal sub-constellation structures for fixed modulation orders with the max-min rule. Then, we determine the optimal modulation order for each sub-constellation. The analytical results show that our proposed scheme can attain a larger RD distance than the existing massive uniquely factorable constellation coding (MUFC) scheme. Further, we illustrate that our proposed coding scheme enables a low-complexity RD decoding algorithm. Simulation results show that our proposed scheme performs better than the current phase shift keying modulation scheme and MUFC scheme.

User Subgrouping and Power Control for Multicast Massive MIMO Over Spatially Correlated Channels

Massive multiple-input-multiple-output (MIMO) is unquestionably a key enabler of the fifth-generation (5G) technology for mobile systems, enabling to meet the high requirements of upcoming mobile broadband services. Physical-layer multicasting refers to a technique for simultaneously serving multiple users, demanding for the same service and sharing the same radio resources, with a single transmission. Massive MIMO systems with multicast communications have been so far studied under the ideal assumption of uncorrelated Rayleigh fading channels. In this work, we consider a practical multicast massive MIMO system over spatially correlated Rayleigh fading channels, investigating the impact of the spatial channel correlation on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">favorable propagation</i> , hence on the performance. We propose a subgrouping strategy for the multicast users based on their channel correlation matrices’ similarities. The proposed subgrouping approach capitalizes on the spatial correlation to enhance the quality of the channel estimation, and thereby the effectiveness of the precoding. Moreover, we devise a max-min fairness (MMF) power allocation strategy that makes the spectral efficiency (SE) among different multicast subgroups uniform. Lastly, we propose a novel power allocation for uplink (UL) pilot transmission to maximize the SE among the users within the same multicast subgroup. Simulation results show a significant SE gain provided by our user subgrouping and power allocation strategies. Importantly, we show how spatial channel correlation can be exploited to enhance multicast massive MIMO communications.

Joint Spatial Division and Multiplexing for FDD in Intelligent Reflecting Surface-Assisted Massive MIMO Systems

Channel reciprocity, assumed in fifth-generation (5G) systems such as massive multiple-input-multiple-output (mMIMO), appears to be questioned in practice by recent studies on intelligent reflecting surface (IRS). Hence, contrary to previous works, we consider frequency division duplexing (FDD) to study the performance of an IRS-assisted mMIMO system. However, FDD is not suitable for large number of antennas architectures. For this reason we employ the joint spatial division and multiplexing (JSDM) approach exploiting the structure of the correlation of the channel vectors to reduce the channel state information (CSI) uplink feedback, and thus, allowing the use even of a large number of antennas at the base station. Specifically, we derive the sum spectral efficiency (SE) based on statistical CSI in terms of large-scale statistics by using the deterministic equivalent (DE) analysis while accounting for correlated Rayleigh fading. Subsequently, we formulate the optimization problem concerning the sum SE with respect to the reflecting beamforming matrix (RBM)and the total transmit power, which can be performed at every several coherence intervals by taking advantage of the slow time variation of the large-scale statistics. This notable property contributes further to the decrease of the feedback overhead. Numerical results, verified by Monte-Carlo (MC) simulations, enable interesting observations by elucidating how fundamental system parameters such as the rank of the covariance matrix and the number of groups of UEs affect the performance. For example, the selection of a high rank improves the channel conditioning but increases the feedback overhead.

Performance Analysis on Cell-Free Massive MIMO With Capacity-Constrained Fronthauls and Variable-Resolution ADCs

In the recently proposed cell-free massive multiple-input and multiple-output (MIMO) networks, the capacity of fronthaul links connecting all access points (APs) and a central processing unit (CPU) is limited. In this context, taking into consideration the spatial channel correlation at the APs, this article investigates the performance of cell-free massive MIMO systems with variable-resolution quantization, i.e., each analog-to-digital converter at the APs and quantizer at the CPU use arbitrary bits for quantization. Specifically, we first introduce a technique based on linear minimum mean-square to perform channel estimation. On this basis, we then derive the closed-form expressions of achievable rates over spatially correlated Rayleigh fading channels for both uplink and downlink if maximal ratio combining and maximal ratio transmission are used at the CPU. Finally, simulation results validate our theoretical analyses and corroborate that the performance of channel estimation and achievable rates reduces as the spatial correlation strengthens. Moreover, from a statistic perspective, under the constraint of the total number of quantization bits, it is preferable to assign more bits to the AP with larger aggregated large-scale fading coefficient and lower channel correlation.

Channel Estimation for Hybrid Massive MIMO Systems With Adaptive-Resolution ADCs

Achieving high channel estimation accuracy and reducing hardware cost as well as power dissipation constitute substantial challenges in the design of massive multiple-input multiple-output (MIMO) systems. To resolve these difficulties, sophisticated pilot designs have been conceived for the family of energy-efficient hybrid analog-digital (HAD) beamforming architecture relying on adaptive-resolution analog-to-digital converters (RADCs). In this paper, we jointly optimize the pilot sequences, the number of RADC quantization bits and the hybrid receiver combiner in the uplink of multiuser massive MIMO systems. We solve the associated mean square error (MSE) minimization problem of channel estimation in the context of correlated Rayleigh fading channels subject to practical constraints. The associated mixed-integer problem is quite challenging due to the nonconvex nature of the objective function and of the constraints. By relying on advanced fractional programming (FP) techniques, we first recast the original problem into a more tractable yet equivalent form, which allows the decoupling of the fractional objective function. We then conceive a pair of novel algorithms for solving the resultant problems for codebook-based and codebook-free pilot schemes, respectively. To reduce the design complexity, we also propose a simplified algorithm for the codebook-based pilot scheme. Our simulation results confirm the superiority of the proposed algorithms over the relevant state-of-the-art benchmark schemes.

Ergodic Capacity of IRS-Assisted MIMO Systems With Correlation and Practical Phase-Shift Modeling

We focus on the maximization of the exact ergodic capacity (EC) of a point-to-point multiple-input multiple-output (MIMO) system assisted by an intelligent reflecting surface (IRS). In addition, we account for the effects of correlated Rayleigh fading and the intertwinement between the amplitude and the phase shift of the reflecting coefficient of each IRS element, which are usually both neglected despite their presence in practice. Random matrix theory tools allow to derive the probability density function (PDF) of the cascaded channel in closed form, and subsequently, the EC, which depend only on the large-scale statistics and the phase shifts. Notably, we optimize the EC with respect to the phase shifts with low overhead, i.e., once per several coherence intervals instead of the burden of frequent necessary optimization required by expressions being dependent on instantaneous channel information. Monte-Carlo (MC) simulations verify the analytical results and demonstrate the insightful interplay among the key parameters and their impact on the EC.

On the ergodic sum rate for multiuser satellite–aerial–terrestrial networks

In this paper, we investigate the ergodic sum rate (ESR) for the downlink of a multi-user satellite–aerial–terrestrial network (SATN) with decode-and-forward (DF) protocol, where a multi-antenna unmanned aerial vehicle (UAV) acts as an aerial relay to assist the signal convey from satellite to multiple terrestrial users, which is also corrupted by co-channel interference. To maximize the ESR of the considered system, a beamforming (BF) scheme based on statistical channel state information is proposed to conduct space division multiple access (SDMA) in the UAV–terrestrial links. Then, by assuming that the satellite–UAV link and the UAV–terrestrial links undergo correlated Shadowed-Rician fading and correlated Rayleigh fading, respectively, we derive the analytical expression of ESR for our considered system with proposed BF scheme. Finally, numerical results are provided to verify the correctness of the theoretical analysis and demonstrate the superiority of our proposed BF scheme.

On channel estimation and spectral efficiency for cell‐free massive MIMO with multi‐antenna access points considering spatially correlated channels

AbstractChannel estimation (CE) and spectral efficiency (SE) are two processes that have a major influence on system performance, especially in a more practical channel scenario with spatially correlated Rayleigh fading. During this work, we address the uplink phase CE process and the SE for spatially correlated Rayleigh fading in a cell‐free (CF) massive multiple‐input multiple‐output (M‐MIMO) network and in the conventional M‐MIMO network operating under the time‐division duplex protocol. Since practical channels are correlated spatially with Rayleigh fading; thereby, this work addresses spatially correlated Rayleigh fading channels in both networks using a combination of the exponential correlation model with large‐scale variation across the array. Moreover, this work addresses the correlated and uncorrelated channels, where the correlated one is investigated using two array arrangements, namely, a uniform linear array (ULA) and a uniform planar array (UPA). For the two networks, the CE and SE are addressed using the minimum mean square error (MMSE) estimator and the MMSE combining vector, respectively. We propose a novel array design for CF M‐MIMO using the Kronecker product of a ULA arrangement, where each access point has a UPA arrangement. In other words, we propose the covariance matrix generated by the UPA arrangement for CF M‐MIMO using the Kronecker product of the covariance matrix generated by the ULA arrangement for CF M‐MIMO. Numerical results are presented to validate our theoretical expressions, where we evaluate the performance of the MMSE estimator and MMSE combining vector, respectively, using the normalized mean square error metric and the quantity of information effectively transmitted per second.