Correlated Rayleigh Fading Channels Research Articles

Capacity Optimization for 6G Cell-Free MIMO Systems Over Spatially Correlated Rayleigh Fading Channels

Capacity Optimization for 6G Cell-Free MIMO Systems Over Spatially Correlated Rayleigh Fading Channels

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.

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.

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.

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.

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.

Space-Frequency Coded Quadrature Index Modulation With Linear Maximum Likelihood Detection

This paper focuses on the issue of achieving transmit diversity for the multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system working with quadrature index modulation (QIM). Inspired by the ideas of quadrature spatial modulation (QSM) and quadrature space-frequency index modulation (QSF-IM), parts of the space-frequency resource units in each resource block (RB) of the MIMO-OFDM system are activated twice independently to send the in-phase and quadrature components of a space-frequency code, respectively, to achieve the second order transmit diversity. Thus the proposed scheme is called space-frequency coded QIM (SFC-QIM). The SFC-QIM scheme allows for a linear-complexity maximum likelihood (ML) receiver, which benefits from the orthogonality between the real and imaginary parts of the symbols in the SFC codewords. Owing to obtaining higher diversity order, simulation results of bit error rate (BER) performance demonstrate that the new SFC-QIM scheme outperforms some existing IM schemes in both independent and identically distributed (i.i.d.) and correlated Rayleigh fading channels.

Asymptotic Analysis for Cell-Free Massive MIMO With MMSE Combining and Low-Resolution ADCs

This letter analyses the asymptotic performance of cell-free massive multiple-input and multiple-output (MIMO) with low-resolution analog-to-digital converters (ADCs) over spatially correlated channels. Specifically, we first introduce a quantization-aware technique for channel estimation based on linear minimum mean-square error (LMMSE) theory. On the basis of imperfect channel estimation, we then propose a quantization-aware MMSE combining and derive the asymptotic expression of achievable uplink rate over spatially correlated Rayleigh fading channels. Finally, simulation results validate our theoretical analysis and corroborate that the quantization-aware MMSE combiner can improve performance to a certain extent.

Averting BER Floor with Iterative Source and Channel Decoding for Layered Steered Space-Time Codes.

The widespread development in wireless technologies and the advancements in multimedia communication have brought about a positive impact on the performance of wireless transceivers. We investigate the performance of our three-stage turbo detected system using state-of-the-art high efficiency video coding (HEVC), also known as the H.265 video standard. The system makes use of sphere packing (SP) modulation with the combinational gain technique of layered steered space-time code (LSSTC). The proposed three-stage system is simulated for the correlated Rayleigh fading channel and the bit-error rate (BER) curve obtained after simulation is free of any floor formation. The system employs low complexity source-bit coding (SBC) for protecting the H.265 coded stream. An intermediate recursive unity-rate code (URC) with an infinite impulse response is employed as an inner precoder. More specifically, the URC assists in the prevention of the BER floor by distributing the information across the decoders. There is an observable gain in the BER and peak signal-to-noise ratio (PSNR) performances with the increasing value of minimum Hamming distance () using the three-stage system. Convergence analysis of the proposed system is investigated through an extrinsic information transfer (EXIT) chart. Our proposed system demonstrates better performance of about 22 dB than the benchmarker utilizing LSSTC-SP for iterative source-channel detection, but without exploiting the optimized SBC schemes.

Performance Analysis of Sphere Packed Aided Differential Space-Time Spreading with Iterative Source-Channel Detection.

The introduction of 5G with excessively high speeds and ever-advancing cellular device capabilities has increased the demand for high data rate wireless multimedia communication. Data compression, transmission robustness and error resilience are introduced to meet the increased demands of high data rates of today. An innovative approach is to come up with a unique setup of source bit codes (SBCs) that ensure the convergence and joint source-channel coding (JSCC) correspondingly results in lower bit error ratio (BER). The soft-bit assisted source and channel codes are optimized jointly for optimum convergence. Source bit codes assisted by iterative detection are used with a rate-1 precoder for performance evaluation of the above mentioned scheme of transmitting sata-partitioned (DP) H.264/AVC frames from source through a narrowband correlated Rayleigh fading channel. A novel approach of using sphere packing (SP) modulation aided differential space time spreading (DSTS) in combination with SBC is designed for the video transmission to cope with channel fading. Furthermore, the effects of SBC with different hamming distances but similar coding rates is explored on objective video quality such as peak signal to noise ratio (PSNR) and also the overall bit error ratio (BER). EXtrinsic Information Transfer Charts (EXIT) are used for analysis of the convergence behavior of SBC and its iterative scheme. Specifically, the experiments exhibit that the proposed scheme of error protection of SBC = 6 outperforms the SBCs having same code rate, but with = 3 by 3 dB with PSNR degradation of 1 dB. Furthermore, simulation results show that a gain of 27 dB is achieved with SBC having code rate 1/3 compared to the benchmark Rate-1 SBC codes.

Pilot Assignment for Joint Uplink-Downlink Spectral Efficiency Enhancement in Massive MIMO Systems With Spatial Correlation

This paper proposes a flexible pilot assignment method to jointly optimize the uplink and downlink data transmission in multi-cell Massive multiple input multiple output (MIMO) systems with correlated Rayleigh fading channels. By utilizing a closed-form expression of the ergodic spectral efficiency (SE) achieved with maximum ratio processing, we formulate an optimization problem for maximizing the minimum weighted sum of the uplink and downlink SEs subject to the transmit powers and pilot assignment sets. This combinatiorial optimization problem is solved by two sequential algorithms: a heuristic pilot assignment is first proposed to obtain a good pilot reuse set and the data power control is then implemented. Numerical results manifest that the proposed algorithm converges fast to a better minimum sum SE per user than the algorithms in previous works.

BER analysis of truncated SVD‐based MU‐MIMO ZF detection scheme under correlated Rayleigh fading channel

SummaryIn multi‐user multiple input multiple output (MU‐MIMO) uplink, the bit error rate (BER) of linear detection schemes, namely, zero forcing (ZF) and minimum mean square error (MMSE) under correlated Rayleigh fading channel deteriorates with increase in spatial correlation and load factor due to the increase in the condition number of the channel matrix. Moreover, the performance gap between ZF and MMSE increases with increase in the antenna number for large load factors. To address this issue, in this paper, truncated singular value decomposition (TSVD), which is a popular method for solving ill‐posed problem, is used in the ZF detection process through proper selection of hard threshold. However, the pseudo‐inverse computed using TSVD is an approximate inverse, which results in interference at the output of the detection process. Therefore, a mathematical expression for the post‐processing signal‐to‐interference‐plus‐noise ratio (SINR) of the substream is derived and subsequently BER is evaluated. Further, the analytical BER is analyzed with respect to the parameters namely, average signal‐to‐noise ratio (SNR) ( ), correlation coefficient ( ), load factor ( ), and number of singular values considered to compute the hard threshold ( ) and also validated by Monte Carlo trails. From the simulation results, it is observed that for higher order MU‐MIMO systems and at lower values of , the performance of TSVD‐based scheme is comparable with that of MMSE by decreasing the truncation parameter ( ). Moreover, as the complexity of TSVD‐based ZF using randomized schemes is ), therefore, the complexity of detection significantly decreases with decrease in .

Uplink Performance Analysis of MU-MIMO ZF Receiver Over Correlated Rayleigh Fading Channel with Imperfect CSI

Uplink Performance Analysis of MU-MIMO ZF Receiver Over Correlated Rayleigh Fading Channel with Imperfect CSI

Performance Analysis of Massive MIMO Relay Systems With Variable-Resolution ADCs/DACs Over Spatially Correlated Channels

The use of low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) is recognized as a practical technique to reduce power consumption and hardware cost for massive multiple-input and multiple-output (MIMO) systems. In this context, by leveraging on the additive quantization noise model (AQNM), this paper investigates the performance of massive MIMO relay systems with a variable-resolution ADC/DAC-based architecture, where each ADC and DAC use arbitrary bits for quantization. To be specific, we first derive the closed-form expression of achievable rate over spatially correlated Rayleigh fading channels by using perfect channel state information (CSI), maximal ratio combining (MRC), and maximal ratio transmission (MRT). Afterwards, we extend the work to the case of imperfect CSI. The analytical expressions reveal some insights of key parameters, i.e., spatial channel correlation, large-scale fading coefficients, estimate errors, and the resolution of ADCs/DACs. Finally, simulation results validate our theoretical analyses and confirm that the achievable rate reduces as the spatial correlation rises. Besides, we provide the condition under which coarse DACs (ADCs) and receive spatial correlation (transmit spatial correlation) dominate the loss of achievable rate. Moreover, provided that the total number of quantization bits is constant, we find that the achievable rate is optimal over spatially correlated channels when all ADC and DAC adopt the same quantization bits from the perspective of statistic.

Fluid Antenna Systems

Over the past decades, multiple antenna technologies have appeared in many different forms, most notably as multiple-input multiple-output (MIMO), that have transformed wireless communications for extraordinary diversity and multiplexing gains. The various MIMO technologies have been based on placing a number of antennas at some fixed locations which dictate the fundamental limit on the achievable performance. By contrast, this paper envisages the scenario in which the physical position of an antenna can be switched freely to one of the $N$ positions over a fixed-length line space to pick up the strongest signal in the manner of traditional selection diversity. We refer to this system as a fluid antenna system (FAS) for tremendous flexibility in its possible shape and position. The aim of this paper is to study the achievable performance of a single-antenna FAS system with a fixed length and $N$ in arbitrarily correlated Rayleigh fading channels. Our contributions include exact and approximate closed-form expressions for the outage probability of FAS. We also derive an upper bound for the outage probability, from which it is discovered that a single-antenna FAS given any arbitrarily small space can outperform an $L$ -antenna maximum ratio combining (MRC) system if $N$ is large enough. Our analysis also reveals the minimum required size of the FAS, and how large $N$ is considered enough for the FAS to surpass MRC.