Multiple-input Multiple-output Rayleigh Fading Channels Research Articles

A Multipath Approach to Self-Interference Cancellation in MIMO Rayleigh Fading Channels

An optically enabled multipath self-interference (MSI) cancellation technique for in-band full duplex (IBFD) multiple input multiple output (MIMO) Radio over Fiber RoF systems under Rayleigh fading channels is proposed. A digitally assisted Rayleigh fading channel model generates the MSI signal. An optically tunable multipath delay lines (OTMDL) module is designed using optical delay lines and an optical attenuator for coarse and fine-tuning of time delays and amplitude matching between the locally generated reference (LR) signal and the MSI signal. The OTMDL module adjusts the LR signal to cancel the effect of MSI on the signal received through the fading channel. The concept is validated using a remote sensor node of a 3 × 3 IBFD MIMO RoF system with a Rayleigh fading channel. The system's performance is evaluated by determining the MSI cancellation depths using the OTMDL section for various cancellation channels and by computing the MSI cancellation for both single band and wideband signals across different cancellation channels. An average value of MSI cancellation depth of 20.38 dB is obtained for a single-tone radio frequency signal in the range 15–25 GHz. Thus, the proposed system for MSI cancellation can be utilized in wireless communication systems in multiple ways.

Ergodic Capacity of MIMO Faster-Than-Nyquist Transmission Over Triply-Selective Rayleigh Fading Channels

Faster-than-Nyquist signaling (FTNS) has already been shown to increase the communication capacity on certain channels such as additive white Gaussian noise and block flat multiple-input multiple-output (MIMO) Rayleigh fading channels. The following issues, however, remain unresolved: 1) whether FTNS enables a capacity increase in generalized MIMO Rayleigh fading channels that are selective in time, frequency, and space; and 2) how channel selectivities affect the capacity and if present, the FTN capacity gain. To address the issues, this paper firstly investigates the ergodic capacity of MIMO-FTN transmission over triply-selective fading channels. We derive a low-complexity approximate capacity formula and also show how it degenerates in other channel models, such as doubly-selective single-input single-output fading channels, which can be considered as the special cases of triply-selective fading channels. The capacity evaluation results obtained under different channel conditions show that: 1) MIMO-FTN outperforms MIMO-Nyquist in terms of capacity; 2) the FTN gains are nearly consistent, while the FTN gains obtained in the frequency-selective fading channels are slightly higher than those obtained in the flat fading channels.

BER Analysis for Downlink MIMO-NOMA Systems over Rayleigh Fading Channels

The Multiple-input multiple-output (MIMO) technique combined with non-orthogonal multiple access (NOMA) has been considered to enhance total system performance. This paper studies the bit error rate of two-user power-domain NOMA systems using successive interference cancellation receivers, with zeroforcing equalization over quasi-static Rayleigh fading channels. Successive interference cancellation technique at NOMA receivers has been the popular research topic due to its simple implementation, despite its vulnerability to error propagation. Closed-form expressions are derived for downlink NOMA in single-input single-output and uncorrelated quasi-static MIMO Rayleigh fading channel. Analytical results are consolidated with Monte Carlo simulation.

Saddle Point Approximation of Mutual Information for Finite-Alphabet Inputs over Doubly Correlated MIMO Rayleigh Fading Channels

Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is studied, and then the mutual information is estimated by the saddle point approximation method with known channel state information. Furthermore, we induce the expectation of mutual information over doubly correlated multiple-input multiple-output (MIMO) Rayleigh fading channels. The validity of the saddle point approximation method is verified by comparing the numerical results of the Monte Carlo method and the saddle point approximation method under different doubly correlated MIMO fading channel scenarios.

Performance Analysis of Space-Time Line Code in Correlated Fading Channels

Recently, the idea of space-time line code (STLC) was developed in [1] as an efficient way to increase the diversity of multiple-input multiple-output (MIMO) communications, with a special code structure that exploits the channel state information (CSI) at the transmitter. In this paper, in order to evaluate the performance of STLC in practical transmission environment, we analyse the bit-error rate (BER) performance of STLC in the context of correlated Rayleigh and Rician fading MIMO channels. Finally, simulation results validate the accuracy of the above theoretical analysis.

Diversity-Multiplexing Tradeoff of Multi-Layer Scattering MIMO Channels

Multi-layer (or multi-cluster) scattering Multiple-Input Multiple-Output (MIMO) channels are considered in the framework of the diversity-multiplexing tradeoff (DMT). This MIMO channel model finds application in indoor networks, typical of 5G architectures, in which the signal propagates from the transmitter to the receiver through the walls and floors of a building (represented by scattering layers). These results extend the seminal work by Zheng and Tse from the independent identically distributed (iid) Rayleigh fading MIMO channel to a channel matrix which is the product of iid Rayleigh fading matrix components. It is worth noting that the resulting product channel matrix elements are not independent. It is shown that the presence of multiple scattering layers eventually degrades the DMT performance of a MIMO channel by an amount depending only on the least three dimensions of the matrices characterizing the product channel matrix.

Efficient message exchange protocols exploiting state-of-the-art PHY layer

The paper focuses on the two-way relay channel (TWRC) and the multi-way wireless network with three terminals, where all three want to exchange or share data and have to do that with the help of a relay. This paper shows how it is possible to significantly decrease the number of time slots required to exchange messages between terminals in networks based on time-division multiple access (TDMA), by taking into consideration new techniques at the physical (PHY) layer. The paper considers a PHY layer where physical-layer network coding (PLNC), multiple-input multiple-output (MIMO), and in-band “full-duplex” (IBFD) with loopback interference cancellation are all integrated, so that it is possible to significantly increase the overall throughput of the network. This is entirely attained by transferring the burden from the time domain to the spatial domain, via spatial multiplexing and by simultaneously resorting to non-orthogonal multiple access, which is the consequence of using both PLCN and IBFD. For the TWRC, it is shown that, if a massive MIMO relay is used, a simple lattice-based PLNC can be directly applied and, with typical IBFD interference cancellation amounts, a TWRC can effectively use only one time slot instead of the four needed when adopting the traditional TDMA exchange. In the case of the Y-network (i.e., with three terminals), a technique is presented that allows all the information exchange between terminals to be cut from the six time slots required in TDMA to only one time slot, provided that the information packets are not too short. The error performance of these systems is measured by means of simulation using MIMO Rayleigh fading channels.

Finite-SNR Diversity–Multiplexing Tradeoff With Accurate Performance Analysis for Fully Correlated Rayleigh MIMO Channels

Zheng and Tse were the first to discover the fundamental diversity–multiplexing tradeoff (DMT) that occurs in multiple-input multiple-output (MIMO) systems. Their research was limited to infinite signal-to-noise ratio (SNR) situations. Later, research was also conducted on finite-SNR situations; however, this research had significant problems with coarse approximation. In this paper, we propose more accurate approximations of the finite-SNR DMT and the outage probability for Rayleigh fading MIMO channels to solve these problems. The proposed formulas provide more general solutions that are applicable not only to uncorrelated and semicorrelated channels but also to fully correlated channels, which have not been considered in the literature. Utilizing the proposed finite-SNR DMT, we further investigate the influence of the deviation of the finite-SNR DMT on system performance. We also derived an accurate SNR offset quantity, which provides a link for transformation of finite-SNR DMT to actual outage probability. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

Non-Coherent Open-Loop MIMO Communications Over Temporally-Correlated Channels

This paper investigates the use of non-coherent communication techniques for open-loop transmission over temporally-correlated Rayleigh-fading MIMO channels. These techniques perform data detection without knowing the instantaneous channel coefficients. Three non-coherent Multiple Input Multiple Output (MIMO) schemes, namely, differential unitary space-time modulation, differential space-time block code, and Grassmannian signaling, are compared with several state-of-the-art training-based coherent schemes. This paper shows that the non-coherent schemes are meaningful alternatives to training-based communication, specially as the number of transmit antennas increases. In particular, for more than two transmit antennas, non-coherent communication provides a clear advantage in medium to high mobility scenarios.

The effect of nonlinear distortion on the performance of MIMO systems

Nonlinear amplification in wireless systems results in in-band distortion which degrades system performance. The effect of nonlinear distortion is more severe in multiple-input multiple-output (MIMO) systems because signal encoding at the transmitter (such as transmitter precoding in singular value decomposition (SVD)-based MIMO) results in signals with higher peak-to-average ratio (PAPR) than single-input single-output (SISO) systems. In this paper, the effect of nonlinear amplification on the performance of a MIMO system is analyzed. The performance analysis is based on relating in-band distortion to system BER of a M-QAM modulated signals transmitted over a MIMO Rayleigh fading channel. It is shown that transmitter precoding results in increased in-band distortion and hence, increased system BER over the case when no precoding is used. The results presented in this paper can be used to derive limit of nonlinearity which allow energy efficient MIMO systems.

On the Low SNR Capacity of MIMO Fading Channels With Imperfect Channel State Information

The capacity of multiple-input multiple-output (MIMO) Rayleigh fading channels with full knowledge of channel state information (CSI) at both the transmitter and the receiver (CSI-TR) has been shown recently to scale at low signal-to-noise ratio (SNR) essentially as SNR log(1/SNR), independently of the number of transmit and receive antennas. In this paper, we investigate the ergodic capacity of MIMO Rayleigh fading channel with estimated channel state information at the transmitter (CSI-T) and possibly imperfect channel state information at the receiver (CSI-R). Our framework can be seen as a generalization of previous works as it can capture the perfect CSI-TR as a special case when the estimation error variance goes to zero. In this paper, we mainly focus on the low SNR regime, and we show that the capacity scales as (1 - α) SNR log(1/SNR), where α is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel state information at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can be also extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.

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.

Performance Analysis of a Hybrid Codebook for Downlink Relay Systems

In this paper, we propose a novel codebook for multiple-input multiple-output (MIMO) Rician fading channels. While the most conventional codebooks are designed in Rayleigh fading channels, we design a hybrid codebook which combines discrete Fourier transform matrix-based codebook for MIMO Rayleigh fading channels and array matrix-based codebook for MIMO line-of- sight channels. Especially, a backhaul link between base station and relay station can be a good target MIMO channels for the proposed codebook. Link-level simulations performed in a MIMO-OFDM system show that the proposed hybrid codebook outperforms the conventional codebooks when the K factor of Rician distribution is between 0:28 and 0:99. Moreover, the proposed codebook shows almost optimal link-level performances for MIMO Rayleigh fading channels.

Performance and Complexity Analysis of Infinity-Norm Sphere-Decoding

Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l 2 -norm. It was, however, recently observed that using the l ?-norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l ?-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that l ?-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l 2-norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l ?-norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l ?-norm SD and show that it behaves fundamentally different from that of l 2-norm SD.

Fast Interior Point Method for MIMO Transmit Power Optimization with Per-Antenna Power Constraints

For multiple-input multiple-output (MIMO) precoded transmission that has individual constraints on the maximum power of each transmit antenna or a subset of transmit antennas, the transmit power optimization problem is a non-linear convex optimization problem with a high level of computational complexity. In this paper, assuming the use of the interior point method (IPM) to solve this problem, we propose two efficient techniques that reduce the computational complexity of the IPM by appropriately setting its parameters. Based on computer simulation, the achieved reductions in the level of the computational complexity are evaluated using the proposed techniques for both the fairness and the sum-rate maximization criteria assuming i.i.d Rayleigh fading MIMO channels and block diagonalization zero-forcing as a multi-user MIMO (MU-MIMO) precoder.

A novel shifted type of SLS estimator for estimation of Rician flat fading MIMO channels

This paper deals with the training-based channel estimation scheme in Rician distributed flat fading multiple-input multiple-output (MIMO) channels. We propose a new biased shifted scaled least squares (SSLS) technique that is generalized form of the scaled least squares (SLS) approach. This technique is suitable for estimation of both Rayleigh and Rician fading MIMO channels. The performance of the conventional least squares (LS) and SSLS channel estimators is investigated. Moreover, the optimal choice of training sequences is probed using mean square error (MSE) criteria. Analytical and numerical results show that the proposed SSLS estimator significantly outperforms the LS and SLS techniques. It is demonstrated that increasing the Rice factor leads to decreasing the MSE of offered technique, while the performance of LS and SLS estimators is independent of this factor.

Capacity Bounds for MIMO Nakagami-$m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami-m fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter m on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-m and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.

Effect of joint spatial correlation on the diversity performance of space-time block codes

We characterize the effect of joint spatial correlation on the diversity performance of multiple-input multiple-output (MIMO) systems. The joint spatial correlation is structured by the coupling matrix whose elements determine the average power coupling between the transmit and receive eigenmodes. We first derive the closed-form expression for the exact symbol error probability (SEP) of orthogonal space-time block codes over jointly correlated MIMO Rayleigh-fading channels. We then show that the achievable diversity order is equal to the number of nonzero elements of the power coupling matrix and establish the Schur monotonicity theorems on the SEP and the effective fading figure as a functional of elements of the power coupling matrix.

Power allocation for two different traffics in layered MIMO systems

In multiple input multiple output (MIMO) relay networks, an MIMO node can relay different traffics from multiple MIMO source nodes. Thus, an MIMO relay node has to allocate the power across multiple channels to relay different traffics. In this paper, we consider the power allocation across multiple layers of MIMO channel when two different traffics, real-time and best-effort traffics, are presented. Generally, realtime traffics have stringent delay constraints and their data streams could not be multiplexed with the data streams from best-effort traffics due to different quality of service (QoS). Since MIMO channels can provide multiple parallel channels, we are able to transmit both different traffics separately (and simultaneously). For efficient power use, we investigate the power allocation across multiple parallel channels in presence of two different traffics with different performance index for each traffic. Performance analysis is carried out for uncorrelated Rayleigh-fading MIMO channels.

Blind estimation and detection of space-time trellis coded transmissions over the Rayleigh fading MIMO channel

We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).