Ricean Multiple-input Multiple-output Channels Research Articles

Joint Transmit Beamforming and Phase Shift Design for Reconfigurable Intelligent Surface Assisted MIMO Systems

Reconfigurable intelligent surface (RIS) becomes an increasingly important technology in sixth-generation (6G). The key aspect of RIS is smartly configuring the wireless propagation environment and providing supplementary links to enhance the signal transmission between the BS and the UE. In recent years, there has been a surge of interest in RISs in joint active and passive beamforming design to improve the system performance of RIS-assisted systems with the assumption of uncorrelated environments. To date, far too little attention has been paid to the situations that consider the correlations among the antennas and RIS reflecting elements. In this article, we focus on an RIS-assisted multiple-input multiple-output (MIMO) system under spatial fading correlations, with the statistical channel state information (CSI) known at the transmitter and the RIS. We aim to maximize the ergodic spectral efficiency (SE) of this system. At first, we derive a tight upper bound on the ergodic SE. Concise upper bounds are also shown in special cases of independent and identically distributed (i.i.d.) Rician and Rayleigh, correlated Rayleigh as well as extreme Rician MIMO channels. Next, we propose a benchmark algorithm based on the semidefinite relaxation (SDR) technique to jointly optimize the beamforming vector at the transmitter and phase shift matrix of the RIS. Alternative manner is utilised until both arrive at convergence. Furthermore, we apply the dominant eigen direction transmission scheme to do beamforming in order to reduce the complexity of the algorithm, and consider the column control of the RIS to facilitate practical hardware implementation. Numerical results show the tightness of the upper bounds and the effectiveness of our proposed algorithm for improving the ergodic SE as well as the effects of freedom degrees on performances.

Achievable Rate of Rician Large-Scale MIMO Channels With Transceiver Hardware Impairments

Transceiver hardware impairments (e.g., phase noise, in-phase/quadrature-phase imbalance, amplifier nonlinearities, and quantization errors) have obvious degradation effects on the performance of wireless communications. While prior works have improved our knowledge of the influence of hardware impairments of single-user multiple-input multiple-output (MIMO) systems over Rayleigh fading channels, an analysis encompassing the Rician fading channel is not yet available. In this paper, we pursue a detailed analysis of regular and large-scale (LS) MIMO systems over Rician fading channels by deriving new closed-form expressions for the achievable rate to provide several important insights for practical system design. More specifically, for regular MIMO systems with hardware impairments, there is always a finite achievable rate ceiling, which is irrespective of the transmit power and fading conditions. For LS-MIMO systems, it is interesting to find that the achievable rate loss depends on the Rician K- factor, which reveals that the favorable propagation in LS-MIMO systems can remove the influence of hardware impairments. However, we show that the nonideal LS-MIMO system can still achieve high spectral efficiency due to its huge degrees of freedom.

Dual-Polarized Ricean MIMO Channels: Modeling and Performance Assessment

In wireless communication systems, dual-polarized (DP) instead of single-polarized (SP) multiple-input multiple-output (MIMO) transmission is used to improve the spectral efficiency under certain conditions on the channel and the signal-to-noise ratio (SNR). In order to identify these conditions, we first propose a novel channel model for DP mobile Ricean MIMO channels for which statistical channel parameters are readily obtained from a moment-based channel decomposition. Second, we derive an approximation of the mutual information (MI), which can be expressed as a function of those statistical channel parameters. Based on this approximation, we characterize the required SNR for a DP MIMO system to outperform an SP MIMO system in terms of the MI. Finally, we apply our results to channel measurements at 2.53 GHz. We find that, using the proposed channel decomposition and the approximation of the MI, we are able to reproduce the SNR values above which DP MIMO systems outperform SP MIMO systems.

Array Gain in the DMT Framework for MIMO Channels

Following the seminal work by Zheng and Tse on the diversity and multiplexing tradeoff (DMT) of multiple-input multiple-output (MIMO) channels, in this paper, we introduce the array gain to investigate the fundamental relation between transmission rate and reliability in MIMO systems. The array gain gives information on the power offset that results from exploiting channel state information at the transmitter or as a consequence of the channel model. Hence, the diversity, multiplexing, and array gain (DMA) analysis is able to cope with the limitations of the original DMT and provide an operational meaning in the sense that the DMA gains of a particular system can be directly translated into a parameterized characterization of its associated outage probability performance. In this paper, we derive the best DMA gains achievable by any scheme employing isotropic signaling in uncorrelated Rayleigh, semicorrelated Rayleigh, and uncorrelated Rician block-fading MIMO channels. We use these results to analyze the effect of important channel parameters on the outage performance at different points of the DMT curve.

On the Application of Character Expansions for MIMO Capacity Analysis

To evaluate the unitary integrals, such as the well-known Harish–Chandra–Itzykson–Zuber integral, character expansions were developed by Balantekin, where the matrix integrand is a group member; i.e., a square matrix with a nonzero determinant. Recently, this method has been exploited to derive the joint eigenvalue distributions of the Wishart matrices; i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\bf H}{\bf H}^{\ast}$</tex></formula> where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\bf H}$</tex></formula> is the complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system. The joint eigenvalue distributions are used to calculate the moment generating function of the mutual information (ergodic capacity) of a MIMO channel. In this paper, we show that the previous integration framework presented in the literature is not correct, and results in incorrect joint eigenvalue distributions for the Ricean and full-correlated Rayleigh MIMO channels. We develop a new framework to apply the character expansions for integrations over the unitary group, involving general rectangular complex matrices in the integrand. We derive the correct distribution functions and use them to obtain the capacity of the Ricean and correlated Rayleigh MIMO systems in a unified and straightforward approach. The integration technique proposed in this paper is general enough to be used for other unitary integrals in engineering, mathematics, and physics.

Regional Diversity-Multiplexing Tradeoff

The concept of regional diversity-multiplexing tradeoff (DMT) is introduced by extending the asymptotic outage probability expression for multiple-input multiple-output (MIMO) channels. It is shown that for both Rayleigh and Rician MIMO channels, the regional diversity gain is a linear function of the regional multiplexing gain and that the original DMT curve can be obtained from the set of regional DMT lines. As a result, vital information for capturing both finite and infinite signal-to-noise ratio characteristics in terms of DMT is provided.

Appropriate Algorithms for Estimating Frequency-Selective Rician Fading MIMO Channels and Channel Rice Factor: Substantial Benefits of Rician Model and Estimator Tradeoffs

The training-based channel estimation (TBCE) scheme in multiple-input multiple-output (MIMO) frequency-selective Rician fading channels is investigated. We propose the new technique of shifted scaled least squares (SSLS) and the minimum mean square error (MMSE) estimator that are suitable to estimate the above-mentioned channel model. Analytical results show that the proposed estimators achieve much better minimum possible Bayesian Cramér-Rao lower bounds (CRLBs) in the frequency-selective Rician MIMO channels compared with those of Rayleigh one. It is seen that the SSLS channel estimator requires less knowledge about the channel and/or has better performance than the conventional least squares (LS) and MMSE estimators. Simulation results confirm the superiority of the proposed channel estimators. Finally, to estimate the channel Rice factor, an algorithm is proposed, and its efficiency is verified using the result in the SSLS and MMSE channel estimators.

On the Capacity Achieving Covariance Matrix for Rician MIMO Channels: An Asymptotic Approach

In this paper, the capacity-achieving input covariance matrices for coherent block-fading correlated multiple input multiple output (MIMO) Rician channels are determined. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In the asymptotic regime where the number of transmit and receive antennas converge to infinity at the same rate, new results related to the accuracy of the approximation of the average mutual information are provided. Based on the accuracy of this approximation, an attractive optimization algorithm is proposed and analyzed. This algorithm is shown to yield an effective way to compute the capacity achieving matrix for the average mutual information and numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.

Cross-layer based transmit antenna selection for decision-feedback detection in correlated Ricean MIMO channels

In this paper, we investigate a cross-layer transmit antenna selection (AS) approach for the decision-feedback detector (DFD) over spatially correlated flat Rician fading multiple-input multiple-output (MIMO) channels. Closed-form expressions for the system throughput with both perfect and imperfect channel estimation are derived. Considering a training-based channel estimation technique, we show that the capacity-based AS is more robust to imperfect channel estimation. However, in all cases, the cross-layer AS delivers higher throughput gains than the capacity-based AS.

Exact capacity expressions for dual-branch ricean MIMO channels

In this paper we derive exact expressions for the mutual information (MI) probability density function and the MI cumulative distribution function of dual-branch multipleinput multiple-output (MIMO) systems (either two transmit (Tx) or two receive (Rx) antennas) communicating over a Ricean channel with no constraint on the rank of the line-of-sight (LOS) channel matrix. This is done both for the case where the channel is only known at the Rx, and for the case where the channel is known both at the Tx and the Rx. As an example, to evaluate the expressions, we employ uniform linear arrays and give expressions for the eigenvalues of the LOS channel matrix for the dual-branch case.

On the capacity of orthogonalised correlated MIMO channels under different adaptive transmission techniques

Orthogonal space-time block codes (STBCs) are known to orthogonalise the multiple-input multiple-output (MIMO) wireless channel, thus reducing the space-time vector detection to a simpler scalar detection problem. The capacity of STBCs over correlated Rayleigh and Ricean flat-fading MIMO channels under different adaptive transmitting techniques is studied. Three adaptive schemes known as optimal power and rate allocation, total channel inversion with fixed rate policy and its truncated variant are studied. Taking into account the effect of channel correlation, closed-form expressions are obtained for the capacity of orthogonalised Rayleigh and Ricean MIMO channels under these adaptive transmission techniques in order to avoid Monte-Carlo simulations.

Precoded Orthogonal Space–Time Block Codes Over Correlated Ricean MIMO Channels

A precoder is designed for orthogonal space-time block codes (OSTBCs) for arbitrarily correlated Ricean multiple-input multiple-output (MIMO) channels. Unlike previous literature, our precoder is the first to be designed to minimize the exact symbol error rate (SER) as a function of both a) the joint transmit-receive channel correlation coefficients and b) the MIMO Rice component, which are fed back to the transmitter. It is important to note that the covariance may or may not follow the so-called Kronecker structure. Exact SER expressions are given for multilevel PAM, PSK, and QAM signaling. Several properties of the minimum exact precoder are provided. An iterative numerical optimization algorithm is proposed for finding the exact minimum SER precoder under a power constraint

Exact BER analysis of OSTBCs in spatially correlated MIMO channels

The bit-error rate (BER) performance of orthogonal space-time block codes (STBCs) in correlated multiple-input multiple-output (MIMO) channels is studied. We first derive closed-form exact BER equations for pulse amplitude modulation, quadrature amplitude modulation, and phase-shift keying constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods. Then we consider correlated MIMO channels where the line of sight components exist and they suffer from shadowing, namely, correlated shadowed Rician MIMO channels. For three practical channel scenarios, the BER is analyzed, and closed-form BER equations are presented.

Diversity and outage performance in space-time block coded Ricean MIMO channels

The goal of this paper is to assess the impact of real-world propagation conditions on the maximum achievable diversity performance of communication over Ricean multiple-input multiple-output (MIMO) channels. To this end, we examine a MIMO channel employing orthogonal space-time block codes (OSTBCs) and study the diversity behavior of the resulting effective single-input single-output (SISO) channel. The performance criteria employed are symbol error rate, outage capacity, and wideband spectral efficiency. For general propagation conditions, we establish key quantities that determine performance irrespective of the performance criterion used. Furthermore, we discuss the relation between the notion of diversity order related to the slope of the average error probability versus signal-to-noise ratio (SNR) curve and diversity order related to the slope of the outage probability versus SNR curve. For Ricean fading MIMO channels, we demonstrate the existence of an SNR-dependent critical rate R/sub crit/, below which signaling with zero outage is possible and, hence, the fading channel behaves like an additive white Gaussian noise (AWGN) channel. For SISO channels, R/sub crit/ is always zero. In the MIMO case, R/sub crit/ is a simple function of the angle between the vectorized Ricean component of the channel and the subspace spanned by the vectorized Rayleigh fading component.

General Capacity Bounds for Spatially Correlated Rician MIMO Channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician K-factor, and the geometry of the dominant Rician paths.

Closed-Form Capacity Expressions of Orthogonalized Correlated MIMO Channels

Space-time block codes are known to orthogonalize the multiple-input multiple-output (MIMO) wireless channel, thus reducing the space-time vector detection to a simpler scalar detection problem. The capacity over orthogonalized ergodic correlated Rayleigh and Ricean flat-fading MIMO channels has so far only been given in integral form. This letter derives a closed form capacity expression over such channels, hence avoiding numerical integrations or Monte Carlo simulations.