Correlated Rayleigh Fading Research Articles

On the Analysis of MIMO-ZF Receiver Over Fully Correlated MIMO Rayleigh Fading with LMMSE Channel Estimation

For multiple-input multiple-output (MIMO) communication systems, the zero-forcing (ZF) receiver has attracted great research interest in recent years. The purpose of this work is to analyze the effect of channel estimation error on the performance of the MIMO-ZF receiver over spatially correlated Rayleigh fading channels. Unlike previous works, where the channel is assumed with transmit correlation but without receiver correlation, we treat the fully correlated channel cases. Furthermore, we assume that the channel estimation error is a Gaussian and correlated matrix. The distribution of the post-processing signal-to-noise ratios is approximated. An approximation of the average bit error rate (BER) is derived and compared to Monte Carlo simulation results. The proposed BER expression takes into consideration that the post-processing noise in not Gaussian. Numerical results show an excellent agreement between the analytical approximation and Monte Carlo simulation curves.

An eigen‐select denoising threshold for channel estimation in OFDM systems

SummaryIn reliable orthogonal frequency division multiplexing systems, channel estimator (CE) plays a crucial role. A pilot‐aided orthogonal frequency division multiplexing CE often employs denoising thresholds to identify significant and noisy channel impulse response taps. When the knowledge of channel statistics (KCS) is completely unavailable, the existing suboptimal thresholds require consistent estimation of one or more KCS parameters. In this paper, the effect of noise variance parameter estimation on CE's mean square error (MSE) performance is characterized analytically by computing threshold's tap‐detection probability. To mitigate MSE degradation due to KCS estimation, an eigen‐select threshold, which does not require any KCS estimation, is proposed. It utilizes eigen values of the auto‐covariance matrix formed by estimated channel impulse response. The proposed threshold is compared with existing state‐of‐art alternatives, for CE's MSE performance and system's BER performance, in correlated Rayleigh fading channel environments. Results reveal that, with the proposed threshold, performance plots converge to optimal solution more closely than the others. Copyright © 2015 John Wiley & Sons, Ltd.

Spectral efficiency analysis of large‐scale distributed antenna system in a composite correlated Rayleigh fading channel

In this study, the downlink spectral efficiency of multi-cell multi-user large-scale distributed antenna systems (DASs) with pilot contamination is studied in a composite correlated Rayleigh fading channel. Firstly, under a physical channel model, the equivalent channel model of large-scale DAS with pilot contamination is given. Secondly, based on the equivalent channel model, the closed-form expression is derived for the downlink achievable rate with maximum ratio transmission, and the ultimate rate is also given when the ratio of the total number of base station antennas to the number of users goes to infinity. Thirdly, the results are validated via numerical simulations. It is shown that the closed-form expression is very accurate, and the downlink achievable rate of the large-scale DAS is much larger than that of the co-located massive multiple-input multiple-output (MIMO) with the same antenna configuration.

Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels

We propose pilot reuse (PR) in single cell for massive multiuser multiple-input multiple-output (MIMO) transmission to reduce the pilot overhead. For spatially correlated Rayleigh fading channels, we establish a relationship between channel spatial correlations and channel power angle spectrum when the base station antenna number tends to infinity. With this channel model, we show that sum mean square error (MSE) of channel estimation can be minimized provided that channel angle of arrival intervals of the user terminals reusing the pilots are non-overlapping, which shows feasibility of PR over spatially correlated massive MIMO channels with constrained channel angular spreads. Regarding that channel estimation performance might degrade due to PR, we also develop the closed-form robust multiuser uplink receiver and downlink precoder that minimize sum MSE of signal detection, and reveal a duality between them. Subsequently, we investigate pilot scheduling, which determines the PR pattern, under two minimum MSE related criteria, and propose a low complexity pilot scheduling algorithm which relies on the channel statistics only. Simulation results show that the proposed PR scheme provides significant performance gains over the conventional orthogonal training scheme in terms of net spectral efficiency.

EXIT-Chart-Based Design Method for Noncoherent LDPC-Coded Modulation in Correlated Rayleigh Fading Channels

In the paper, we investigate LDPC-coded differential amplitude/phase modulation (APM) schemes for correlated Rayleigh fading channels. Through the observation for the mutual information of the extrinsic log-likelihood ratio (LLR) values of the variable nodes in the LDPC decoder, it is found that the code design methods investigated in the previous literature loses their accuracy. Consequently, a modified code design method for the outer LDPC code is proposed in this paper. It is shown that the searched LDPC code effectively improves the error performance, when compared to the convolutional-coded scheme investigated in the previous literature.

Precoding design for STBC‐MIMO system with imperfect feedback in spatially correlated Rayleigh channel

By minimising the pairwise error probability (PEP) bound subject to the fixed power constraint, a suboptimal precoding scheme for space–time block-coded multiple-input–multiple-output (STBC-MIMO) systems with mean and covariance feedback in spatially correlated Rayleigh fading channels is developed, which can include the mean-feedback only and covariance-feedback only as its special cases. This scheme can achieve performances close to the existing optimal scheme while being more computationally efficient. The simulation results show that the proposed scheme can provide better performances than the conventional equal power scheme, and achieve almost the same performances as the existing optimal scheme.

Differential Amplitude/Phase Modulation for Correlated Rayleigh Fading Channels: Performance Analysis and Labeling Design

In this paper, we investigate differential amplitude/ phase modulation (APM) schemes for correlated Rayleigh fading channels. Considering the noncoherent maximum-likelihood receiver, a theoretical pairwise error probability (PEP) formula for differential signal vectors with arbitrary power values is derived. The design criterion for the signal set of differential vectors is then proposed based on the asymptotic analysis of the PEP. For both uncoded and coded APM schemes, the design criteria and optimization procedures for bit labeling rules are investigated. The designed differential APM schemes are shown to provide significant improvement in bit-error-rate performance, particularly in the error-floor regions.

A Simplified Coloring Technique for the Generation of Correlated Rayleigh Fading Envelopes for Multiantenna Systems

In this paper, a simplified technique is proposed for the generation of equal power correlated Rayleigh fading envelopes for multiantenna systems with any desired correlation. The procedure employs consecutive coloring of uncorrelated reference processes using real correlation matrix of envelopes instead of the complex covariance matrix of the Gaussian samples utilized in traditional techniques. Doppler frequency shift, propagation delay spread, and frequency separation between envelopes are also considered for different transmission conditions. The proposed technique can be used for performance evaluation of various multiantenna schemes including single user and multiuser applications. Simulation results of practical examples show that the proposed algorithm provides high accuracy similar to the existing methods with less computational efforts.

Uplink Sum-Rate Analysis of Massive MIMO System with Pilot Contamination and CSI Delay

We consider multi-cell multi-user massive MIMO system under correlated Rayleigh fading channels. Taking pilot contamination and CSI delay into consideration, we derive the equivalent channel model with MMSE channel estimation and one-tap prediction. Employing this equivalent channel model, the lower bound of the uplink sum-rate is derived, and its asymptotical performance is studied when the base station antenna number goes without bound. We find that if we schedule the $$k$$ k -th user of all cells who have the same prediction coefficient, the uplink sum-rate is the same as the one with no CSI delay when the number of BS antennas goes without bound at a much greater rate than the number of users. Simulation results show that the asymptotic approximation has good performance for large $$M$$ M , and suggest that large antenna array can compensate for the decay due to CSI delay. Simulation results also verify our guess that CSI delay does not necessarilly decrease the uplink sum-rate due to the impact of pilot contamination.

A Primer on Energy-Efficient Synchronization of WSN Nodes over Correlated Rayleigh Fading Channels

In this paper we propose a lower bound on the energy required for synchronizing nodes in a Wireless Sensor Network (WSN) by using statistical estimation techniques. The energy required to synchronize a pair of nodes within a network with predefined synchronization accuracy is modelled as function of the transceivers power and the number of transmitted messages. In our analysis, we have considered the dynamic nature of nodes communicating within a correlated Rayleigh fading channel. A unified mathematical model has been defined to analyze the impact of nodes' relative velocity on the pairwise energy and synchronization accuracy trade-off.

On the Performance of the Golden Code in the Presence of Channel Estimation Error in Correlated MIMO Rayleigh Fading Channels

AbstractThe Golden Code (GC) is a full-rate and full-diversity, space-time code for 2 × 2 multiple-input multiple-output (MIMO) systems with non-vanishing minimum determinant. Thanks to its algebraic construction, the GC achieves diversity-multiplexing gain trade-off and preserves the mutual information. The zero-forcing (ZF) detection is one of the simplest detection techniques that has a low computational complexity and provides a suboptimal performance. The purpose of this work is to investigate the effect of channel estimation error on the performance of the MIMO-ZF receiver for golden coded systems in spatio-temporally correlated Rayleigh fading channels. An upper and a lower bounds of the error probability are delivered and compared to the Monte Carlo simulation results. We quantify the capacity reduction due to the channel estimation error and to the spatio-temporally correlation. A tight lower bound of the ergodic capacity is provided. Numerical results show an excellent agreement between analytic bounds and Monte Carlo simulation curves. Moreover, the performances of the GC, in terms of bit error rate (BER) and channel capacity, are compared with those of the Alamouti coding.

TAS/STBC系统在相关Rayleigh信道下的性能分析

针对相关Rayleigh信道，研究了使用发射天线选择(TAS)和正交空时分组码(OSTBC)的多输入多输出(MIMO)系统的平均符号误码率(ASEP)性能。首先采用了非常适合室内信道的Laplacian模型，得到了两个天线之间的相关系数，它是天线间隔，功率方位角谱(PAS)的标准差和平均到达角(AOA)三者的函数。然后引入了相关矩阵，建立了TAS/STBC系统的相关信道模型，基于等效的标量加性高斯白噪声(AWGN)信道的方法，得到了系统在接收端信噪比的表达式。最后对不同条件下的系统的平均符号误码率(ASEP)性能做了仿真，仿真结果表明：TAS/STBC系统的ASEP性能受到空间相关性的影响，尤其是天线间隔，功率方位角谱(PAS)的标准差和平均到达角(AOA)三者的影响。 The average symbol error probability (ASEP) of multiple-input multiple-output (MIMO) systems employing transmit antenna selection (TAS) and orthogonal space-time block code (OSTBC) over correlated Rayleigh fading channels is considered. We first derive the correlation coefficients between two antenna elements as a function of the antenna spacing, the standard deviation of the power azimuth spectrum (PAS) and the mean angle of arrival (AOA) for the truncated Laplacian model, which is appropriate for indoor channels. Then we introduce the correlation matrix, and establish a correlated channel model. Based on the equivalent scalar additive white Gaussian noise (AWGN) channel approach, the exact form expressions of the signal-to-noise ratio (SNR) at the receiving end are derived. The system performance under different conditions was evaluated through numerical simulations. Numerical results show that: the ASEP performance is affected by the spatial correlation, which varies according to the antenna spacing, PAS standard deviation and mean AOA.

Performance Analysis of Turbo Codes In CDMA Under AWGN and Fading

In order to have reliable communications, channel coding is often employed. Turbo code as a powerful coding technique has been widely studied and used in communication systems. Turbo code decoder algorithm is studied in details in this paper. The performance of Turbo code used in IS-2000 Code Division Multiple Access (CDMA) reverse or forward link under Additive White Gaussian Noise (AWGN) and slow fading channels is evaluated. The bit error rates (BER) of Turbo code at low signal-to-noise ratio (SNR) are obtained by simulations. Index terms: IS-2000 CDMA, RSC encode, Interleaver, Output puncturing, Fading, AWGN channel, Rayleigh fading channel, Uncorrelated Rayleigh fading generator, Correlated Rayleigh fading generator

SER performance of enhanced spatial multiplexing codes with ZF/MRC receiver in time-varying Rayleigh fading channels.

We propose enhanced spatial multiplexing codes (E-SMCs) to enable various encoding rates. The symbol error rate (SER) performance of the E-SMC is investigated when zero-forcing (ZF) and maximal-ratio combining (MRC) techniques are used at a receiver. The proposed E-SMC allows a transmitted symbol to be repeated over time to achieve further diversity gain at the cost of the encoding rate. With the spatial correlation between transmit antennas, SER equations for M-ary QAM and PSK constellations are derived by using a moment generating function (MGF) approximation of a signal-to-noise ratio (SNR), based on the assumption of independent zero-forced SNRs. Analytic and simulated results are compared for time-varying and spatially correlated Rayleigh fading channels that are modelled as first-order Markovian channels. Furthermore, we can find an optimal block length for the E-SMC that meets a required SER.

Precoder Design for Multiuser MISO Systems Exploiting Statistical and Outdated CSIT

We propose a multiuser downlink transmission scheme exploiting both statistical and outdated channel state information (CSI) at the transmitter. Based on the outdated CSI-aided transmission scheme introduced in (denoted as MAT), the proposed scheme reduces the original K-user MAT system to a two-user virtual MAT system, through statistical precoding in the first two transmission slots. Thus, the proposed scheme (denoted as V-MAT) reduces efficiently the implementation complexity, while increasing the achievable rate at finite signal-to-noise ratios (SNRs). For the V-MAT scheme, we derive an analytical high SNR rate approximation for correlated Rayleigh fading. Furthermore, for independent and identically distributed Rayleigh fading, we derive an exact rate expression at high SNRs, as well as a tight lower bound which applies for arbitrary SNRs. Then, precoder design is investigated, where an efficient near-optimal solution is proposed for arbitrary number of transmit antennas, and a closed-form optimal solution is derived for the two-antenna case. It is demonstrated that the proposed V-MAT scheme yields higher achievable rate than the original MAT scheme at practical SNRs. Moreover, by combining the V-MAT scheme and the generalized MAT scheme of , where precoding is implemented in the third transmission slot, the achievable rate can be further increased.

Partially Coherent Constellation Design and Bit-Mapping with Coding for Correlated Fading Channels

The space-time (ST) constellation design problem and the related bit mapping schemes for multiple-input multipleoutput (MIMO) systems in spatially correlated Rayleigh fading channels with imperfect channel estimation at the receiver are considered. We assume that the channel estimation error covariance matrix, as well as transmit and receive correlation matrices are perfectly known both at the transmitter and at the receiver. We derive the cutoff rate (CR) and an upper bound (UB) on the average bit error probability (ABEP) expression for spatially correlated channels and propose them as the constellation design criteria subject to a given average transmit power constraint. Additionally, to use the resulting constellations together with forward error correction (FEC) codes requires efficient bit mapping schemes. Because these constellations lack geometrical symmetry in general, the Gray mapping is not always possible in the majority of the constellations obtained. Moreover, different mapping schemes may lead to highly different bit error rate (BER) performances. Thus, an efficient bit mapping scheme called the modified binary switching algorithm (MBSA) is proposed. It minimizes an upper bound on the ABEP (UB-ABEP) and is used to find the bit mapping schemes. Numerical examples show that the designed constellation and its optimized bit mapping together with turbo codes outperform the conventional constellations with respect to the frame error rate (FER).

Investigation of Correlated Rayleigh Fading Channel with Alamouti’s STBC-MRC system

The effect of antenna diversity for a double transmit and multiple receive antenna supported wireless communication system is investigated, that employs multi user Alamouti’s space time block coding (STBC) and maximal ratio combining (MRC) scheme on secured text message transmission. The FEC encoded Alamouti’s-MRC transmission system under investigation implements RSA cryptographic algorithm and deploys various multi-level digital modulations (16-PSK and 16-QAM) techniques over an Additive White Gaussian Noise (AWGN) and Correlated Rayleigh Fading Channels. Rayleigh channel correlation parameter ρ is varied from 0 to 0.9. It has been observed from the study that in case of without receive antenna diversity the system shows comparatively worst performance in 16PSK scheme and satisfactory performance in 16-QAM for the correlation parameter ρ=0.9. It can also be seen that the system performance is improved with increase in number of receive antenna. The performance analysis shows that with implemented Alamouti’s-MRC scheme under 16-QAM digital modulation, the system provides excellent performance over a significantly low signal to noise ratio (SNR) values.

Design of efficient full‐rate linear dispersion space‐time block codes over correlated fading channels

In this study, the authors present a method to design efficient full-rate linear dispersion space-time block codes (LD-STBCs) in correlated Rayleigh fading channels with simple detection at the receiver. The authors first derive a formula for the achievable capacity of an LD-STBC coded multi-input multiple-output (MIMO) system as a function of correlation at the transmitter and the receiver. Moreover, the authors compute closed-form bit-error rate equations for multiple phase shift keying (M-PSK) and multiple quadrature amplitude modulation (M-QAM) schemes. Then, the authors present a method to construct LD-STBCs over correlated Rayleigh fading MIMO channels. Finally, the authors design LD-STBCs for two and four transmit antennas. The designed LD-STBCs enjoy full-rate, minimum power fluctuation, simple structure, simple processing at the receiver. Moreover, the designed LD-STBCs for two transmit antennas provide better performance than Alamouti and LYC codes and the designed LD-STBCs for four transmit antennas provide better performance than TV codes at practical signal-to-noise ratios. Simulation results show that when the proposed LD-STBC for two transmit antennas is concatenated with an efficient outer channel encoder, it provides better performance than LYC code over correlated fading channels.

Capacity analysis of Rayleigh fading channels in low signal‐to‐noise ratio regime for maximal ratio combining diversity because of combining errors

In this research work, the authors derive closed-form expressions for capacity per unit bandwidth (spectrum efficiency) of correlated Rayleigh fading channels under maximal ratio combining diversity at low signal-to-noise ratios (SNRs). Spectrum efficiency expressions are derived for M diversity branches under adaptation policies, such as: (i) optimal power and rate adaptation (OPRA) policy, (ii) optimal rate adaptation (ORA) policy and (iii) truncated channel inversion with fixed rate (TIFR) policy. Even at low SNRs, if space diversity is exercised using a single-input multiple-output system, spectrum efficiency achieved is higher compared with that achieved when signals are uncorrelated and have no diversity. This forms the focal point of this study. Analytical results show accurately that OPRA policy provides highest capacity over other adaptation policies. The spectrum efficiency for the three policies and outage probability for the low SNR case are derived, plotted and analysed in detail in this work.

Accurate Closed-Form Approximation of BER for OSTBCs with Estimated CSI on Spatially Correlated Rayleigh Fading MIMO Channels

In this contribution, we present a novel accurate closed-form approximation for the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) employing quadrature amplitude modulation with Gray-mapping on spatially correlated Rayleigh fading MIMO channels, in the presence of channel estimation errors. The presented BER expression allows to accurately examine the impact of spatial correlation and channel estimation errors on the BER for any OSTBC or signal-to-noise ratio, even in case of highly correlated channels.