27 research outputs found
Asymptotic Mutual Information Statistics of Separately-Correlated Rician Fading MIMO Channels
Precise characterization of the mutual information of MIMO systems is
required to assess the throughput of wireless communication channels in the
presence of Rician fading and spatial correlation. Here, we present an
asymptotic approach allowing to approximate the distribution of the mutual
information as a Gaussian distribution in order to provide both the average
achievable rate and the outage probability. More precisely, the mean and
variance of the mutual information of the separatelycorrelated Rician fading
MIMO channel are derived when the number of transmit and receive antennas grows
asymptotically large and their ratio approaches a finite constant. The
derivation is based on the replica method, an asymptotic technique widely used
in theoretical physics and, more recently, in the performance analysis of
communication (CDMA and MIMO) systems. The replica method allows to analyze
very difficult system cases in a comparatively simple way though some authors
pointed out that its assumptions are not always rigorous. Being aware of this,
we underline the key assumptions made in this setting, quite similar to the
assumptions made in the technical literature using the replica method in their
asymptotic analyses. As far as concerns the convergence of the mutual
information to the Gaussian distribution, it is shown that it holds under some
mild technical conditions, which are tantamount to assuming that the spatial
correlation structure has no asymptotically dominant eigenmodes. The accuracy
of the asymptotic approach is assessed by providing a sizeable number of
numerical results. It is shown that the approximation is very accurate in a
wide variety of system settings even when the number of transmit and receive
antennas is as small as a few units.Comment: - submitted to the IEEE Transactions on Information Theory on Nov.
19, 2006 - revised and submitted to the IEEE Transactions on Information
Theory on Dec. 19, 200
Finite Random Matrix Theory Analysis of Multiple Antenna Communication Systems
Multiple-antenna systems are capable of providing substantial improvement to wireless communication networks, in terms of
data rate and reliability. Without utilizing extra spectrum or power resources, multiple-antenna technology has already been supported
in several wireless communication standards, such as LTE, WiFi and WiMax. The surging popularity and enormous prospect of
multiple-antenna technology require a better understanding to its fundamental performance over practical environments.
Motivated by this, this thesis provides analytical characterizations of several seminal performance measures in advanced multiple-antenna
systems. The analytical derivations are mainly based on finite dimension random matrix theory and a collection of novel random matrix theory
results are derived.
The closed-form probability density function of the output of multiple-input multiple-output (MIMO) block-fading channels is studied.
In contrast to the existing results, the proposed expressions are very general, applying for arbitrary number of antennas, arbitrary signal-to-noise
ratio and multiple classical fading models. Results are presented assuming two input structures in the system: the independent identical distributed
(i.i.d.) Gaussian input and a product form input. When the channel is fed by the i.i.d. Gaussian input, analysis is focused on the channel matrices
whose Gramian is unitarily invariant. When the channel is fed by a product form input, analysis is conducted with respect to two capacity-achieving
input structures that are dependent upon the relationship between the coherence length and the number of antennas. The mutual information
of the systems can be computed numerically from the pdf expression of the output. The computation is relatively easy to handle, avoiding the
need of the straight Monte-Carlo computation which is not feasible in large-dimensional networks.
The analytical characterization of the output pdf of a single-user MIMO block-fading channels with imperfect channel state information at the receiver
is provided. The analysis is carried out under the assumption of a product structure for the input. The model can be thought of as a perturbation
of the case where the statistics of the channel are perfectly known. Specifically, the average singular values of the channel are given, while the
channel singular vectors are assumed to be isotropically distributed on the unitary groups of dimensions given by the number of transmit and
receive antennas. The channel estimate is affected by a Gaussian distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of
known covariance.
The ergodic capacity of an amplify-and-forward (AF) MIMO relay network over asymmetric channels is investigated. In particular, the source-relay
and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel,
the marginal distribution of an unordered eigenvalue of the cascaded AF channel is presented, thus the analytical expression of the ergodic capacity
of the system is obtained. The results indicate the impact of the signal-to-noise ratio and of the Line-of-Sight component on such asymmetric
relay network
Design and performance analysis of quadratic-form receivers for fading channels
Ph.DDOCTOR OF PHILOSOPH
Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels
We investigate MIMO eigenmode transmission using statistical channel state
information at the transmitter. We consider a general jointly-correlated MIMO
channel model, which does not require separable spatial correlations at the
transmitter and receiver. For this model, we first derive a closed-form tight
upper bound for the ergodic capacity, which reveals a simple and interesting
relationship in terms of the matrix permanent of the eigenmode channel coupling
matrix and embraces many existing results in the literature as special cases.
Based on this closed-form and tractable upper bound expression, we then employ
convex optimization techniques to develop low-complexity power allocation
solutions involving only the channel statistics. Necessary and sufficient
optimality conditions are derived, from which we develop an iterative
water-filling algorithm with guaranteed convergence. Simulations demonstrate
the tightness of the capacity upper bound and the near-optimal performance of
the proposed low-complexity transmitter optimization approach.Comment: 32 pages, 6 figures, to appear in IEEE Transactions on Information
Theor
Approximations for Performance Analysis in Wireless Communications and Applications to Reconfigurable Intelligent Surfaces
In the last few decades, the field of wireless communications has witnessed significant technological advancements to meet the needs of today’s modern world. The rapidly emerging technologies, however, are becoming increasingly sophisticated, and the process of investigating their performance and assessing their applicability in the real world is becoming more challenging. That has aroused a relatively wide range of solutions in the literature to study the performance of the different communication systems or even draw new results that were difficult to obtain. These solutions include field measurements, computer simulations, and theoretical solutions such as alternative representations, approximations, or bounds of classic functions that commonly appear in performance analyses. Field measurements and computer simulations have significantly improved performance evaluation in communication theory. However, more advanced theoretical solutions can be further developed in order to avoid using the ex- pensive and time-consuming wireless communications measurements, replace the numerical simulations, which can sometimes be unreliable and suffer from failures in numerical evaluation, and achieve analytically simpler results with much higher accuracy levels than the existing theoretical ones.
To this end, this thesis firstly focuses on developing new approximations and bounds using unified approaches and algorithms that can efficiently and accurately guide researchers through the design of their adopted wireless systems and facilitate the conducted performance analyses in the various communication systems. Two performance measures are of primary interest in this study, namely the average error probability and the ergodic capacity, due to their valuable role in conducting a better understanding of the systems’ behavior and thus enabling systems engineers to quickly detect and resolve design issues that might arise. In particular, several parametric expressions of different analytical forms are developed to approximate or bound the Gaussian Q-function, which occurs in the error probability analysis. Additionally, any generic function of the Q-function is approximated or bounded using a tractable exponential expression. Moreover, a unified logarithmic expression is proposed to approximate or bound the capacity integrals that occur in the capacity analysis. A novel systematic methodology and a modified version of the classical Remez algorithm are developed to acquire optimal coefficients for the accompanying parametric approximation or bound in the minimax sense. Furthermore, the quasi-Newton algorithm is implemented to acquire optimal coefficients in terms of the total error. The average symbol error probability and ergodic capacity are evaluated for various applications using the developed tools.
Secondly, this thesis analyzes a couple of communication systems assisted with reconfigurable intelligent surfaces (RISs). RIS has been gaining significant attention lately due to its ability to control propagation environments. In particular, two communication systems are considered; one with a single RIS and correlated Rayleigh fading channels, and the other with multiple RISs and non-identical generic fading channels. Both systems are analyzed in terms of outage probability, average symbol error probability, and ergodic capacity, which are derived using the proposed tools. These performance measures reveal that better performance is achieved when assisting the communication system with RISs, increasing the number of reflecting elements equipped on the RISs, or locating the RISs nearer to either communication node.
In conclusion, the developed approximations and bounds, together with the optimized coefficients, provide more efficient tools than those available in the literature, with richer capabilities reflected by the more robust closed-form performance analysis, significant increase in accuracy levels, and considerable reduction in analytical complexity which in turns can offer more understanding into the systems’ behavior and the effect of the different parameters on their performance. Therefore, they are expected to lay the groundwork for the investigation of the latest communication technologies, such as RIS technology, whose performance has been studied for some system models in this thesis using the developed tools
Capacity and performance analysis of advanced multiple antenna communication systems
Multiple-input multiple-output (MIMO) antenna systems have been shown to be able to substantially
increase date rate and improve reliability without extra spectrum and power resources. The increasing
popularity and enormous prospect of MIMO technology calls for a better understanding of the performance
of MIMO systems operating over practical environments. Motivated by this, this thesis provides
an analytical characterization of the capacity and performance of advanced MIMO antenna systems.
First, the ergodic capacity of MIMO Nakagami-m fading channels is investigated. A unified way of
deriving ergodic capacity bounds is developed under the majorization theory framework. The key idea is
to study the ergodic capacity through the distribution of the diagonal elements of the quadratic channel
HHy which is relatively easy to handle, avoiding the need of the eigenvalue distribution of the channel
matrix which is extremely difficult to obtain. The proposed method is first applied on the conventional
point-to-point MIMO systems under Nakagami-m fading, and later extended to the more general distributed
MIMO systems.
Second, the ergodic capacity of MIMO multi-keyhole and MIMO amplify-and-forward (AF) dual-hop
systems is studied. A set of new statistical properties involving product of random complex Gaussian
matrix, i.e., probability density function (p.d.f.) of an unordered eigenvalue, p.d.f. of the maximum
eigenvalue, expected determinant and log-determinant, is derived. Based on these, analytical closedform
expressions for the ergodic capacity of the systems are obtained and the connection between the
product channels and conventional point-to-point MIMO channels is also revealed.
Finally, the effect of co-channel interference is investigated. First, the performance of optimum combining
(OC) systems operating in Rayleigh-product channels is analyzed based on novel closed-form
expression of the cumulative distribution function (c.d.f.) of the maximum eigenvalue of the resultant
channel matrix. Then, for MIMO Rician channels and MIMO Rayleigh-product channels, the ergodic capacity
at low signal-to-noise ratio (SNR) regime is studied, and the impact of various system parameters,
such as transmit and receive antenna number, Rician factor, channel mean matrix and interference-tonoise-
ratio, is examined