264 research outputs found
Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading
We study zero-forcing detection (ZF) for multiple-input/multiple-output
(MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R
X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix
transformations and multivariate statistics, our exact analysis yields the
signal-to-noise ratio moment generating function (m.g.f.) as an infinite series
of gamma distribution m.g.f.'s and analogous series for ZF performance
measures, e.g., outage probability and ergodic capacity. However, their
numerical convergence is inherently problematic with increasing Rician
K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we
derive differential equations satisfied by the performance measures with a
novel automated approach employing a computer-algebra tool which implements
Groebner basis computation and creative telescoping. These differential
equations are then solved with the holonomic gradient method (HGM) from initial
conditions computed with the infinite series. We demonstrate that HGM yields
more reliable performance evaluation than by infinite series alone and more
expeditious than by simulation, for realistic values of K , and even for N_R
and N_T relevant to large MIMO systems. We envision extending the proposed
approaches for exact analysis and reliable evaluation to more general Rician
fading and other transceiver methods.Comment: Accepted for publication by the IEEE Transactions on Wireless
Communications, on April 7th, 2016; this is the final revision before
publicatio
LOS-based Conjugate Beamforming and Power-Scaling Law in Massive-MIMO Systems
This paper is concerned with massive-MIMO systems over Rician flat fading
channels. In order to reduce the overhead to obtain full channel state
information and to avoid the pilot contamination problem, by treating the
scattered component as interference, we investigate a transmit and receive
conjugate beamforming (BF) transmission scheme only based on the line-of-sight
(LOS) component. Under Rank-1 model, we first consider a single-user system
with N transmit and M receive antennas, and focus on the problem of
power-scaling law when the transmit power is scaled down proportionally to
1/MN. It can be shown that as MN grows large, the scattered interference
vanishes, and the ergodic achievable rate is higher than that of the
corresponding BF scheme based fast fading and minimum mean-square error (MMSE)
channel estimation. Then we further consider uplink and downlink single-cell
scenarios where the base station (BS) has M antennas and each of K users has N
antennas. When the transmit power for each user is scaled down proportionally
to 1/MN, it can be shown for finite users that as M grows without bound, each
user obtains finally the same rate performance as in the single-user case. Even
when N grows without bound, however, there still remains inter-user LOS
interference that can not be cancelled. Regarding infinite users, there exists
such a power scaling law that when K and the b-th power of M go to infinity
with a fixed and finite ratio for a given b in (0, 1), not only inter-user LOS
interference but also fast fading effect can be cancelled, while fast fading
effect can not be cancelled if b=1. Extension to multi-cells and
frequency-selective channels are also discussed shortly. Moreover, numerical
results indicate that spacial antenna correlation does not have serious
influence on the rate performance, and the BS antennas may be allowed to be
placed compactly when M is very large.Comment: 32 pages, 11 figure
Theoretical Performance Limits of Massive MIMO with Uncorrelated Rician Fading Channels
This work considers a multicell Massive MIMO network with cells, each
comprising a BS with antennas and single-antenna user equipments.
Within this setting, we are interested in deriving approximations of the
achievable rates in the uplink and downlink under the assumption that
single-cell linear processing is used at each BS and that each intracell link
forms an uncorrelated MIMO Rician fading channel matrix; that is, with a
deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight
component describing a spatial uncorrelated multipath environment. The analysis
is conducted assuming that and grow large with a given ratio
under the assumption that the data transmission in each cell is affected by
channel estimation errors, pilot contamination, an arbitrary large scale
attenuation and LoS components. Numerical results are used to prove that the
approximations are asymptotically tight, but accurate for systems with finite
dimensions under different operating conditions. The asymptotic results are
also used to evaluate the impact of LoS components. In particular, we exemplify
how the number of antennas for achieving a target rate can be substantially
reduced with LoS links of only a few dBs of strength.Comment: 17 pages, 5 figures. To appear in IEEE Transactions on
Communications. This is a longer version containing all the mathematical
steps for some of the proofs in the Appendice
A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends
Multiple antennas have been exploited for spatial multiplexing and diversity
transmission in a wide range of communication applications. However, most of
the advances in the design of high speed wireless multiple-input multiple
output (MIMO) systems are based on information-theoretic principles that
demonstrate how to efficiently transmit signals conforming to Gaussian
distribution. Although the Gaussian signal is capacity-achieving, signals
conforming to discrete constellations are transmitted in practical
communication systems. As a result, this paper is motivated to provide a
comprehensive overview on MIMO transmission design with discrete input signals.
We first summarize the existing fundamental results for MIMO systems with
discrete input signals. Then, focusing on the basic point-to-point MIMO
systems, we examine transmission schemes based on three most important criteria
for communication systems: the mutual information driven designs, the mean
square error driven designs, and the diversity driven designs. Particularly, a
unified framework which designs low complexity transmission schemes applicable
to massive MIMO systems in upcoming 5G wireless networks is provided in the
first time. Moreover, adaptive transmission designs which switch among these
criteria based on the channel conditions to formulate the best transmission
strategy are discussed. Then, we provide a survey of the transmission designs
with discrete input signals for multiuser MIMO scenarios, including MIMO uplink
transmission, MIMO downlink transmission, MIMO interference channel, and MIMO
wiretap channel. Additionally, we discuss the transmission designs with
discrete input signals for other systems using MIMO technology. Finally,
technical challenges which remain unresolved at the time of writing are
summarized and the future trends of transmission designs with discrete input
signals are addressed.Comment: 110 pages, 512 references, submit to Proceedings of the IEE
Media-Based Modulation for Future Wireless Systems: A Tutorial
The wireless revolution has already started with the specified vision,
overall objectives, and the first official 3GPP release of 5th generation (5G)
wireless networks. Despite the development of several modern communication
technologies, since the beginning of the modern era of digital communications,
we have been mostly conveying information by altering the amplitude, the phase,
or the frequency of sinusoidal carrier signals, which has inherent drawbacks.
On the other hand, index modulation (IM) provides an alternative dimension to
transmit digital information: the indices of the corresponding communication
systems' building blocks. Media-based modulation (MBM), which is one of the
newest and the most prominent members of the IM family, performs the
transmission of information by altering the far-field radiation pattern of
reconfigurable antennas (RAs) and provides a completely new dimension to convey
information: wireless channel fade realizations themselves through the unique
signature of received signals. The aim of this article is to shed light on this
promising frontier from a broad communication engineering perspective by
discussing the most recent advances as well as possible interesting research
directions in MBM technologies.Comment: 11 pages, 5 figures, 1 table, submitted for possible publicatio
Performance Analysis of Active Large Intelligent Surfaces (LISs): Uplink Spectral Efficiency and Pilot Training
Large intelligent surfaces (LISs) constitute a new and promising wireless
communication paradigm that relies on the integration of a massive number of
antenna elements over the entire surfaces of man-made structures. The LIS
concept provides many advantages, such as the capability to provide reliable
and space-intensive communications by effectively establishing line-of-sight
(LOS) channels. In this paper, the system spectral efficiency (SSE) of an
uplink LIS system is asymptotically analyzed under a practical LIS environment
with a well-defined uplink frame structure. In order to verify the impact on
the SSE of pilot contamination, the SSE of a multi-LIS system is asymptotically
studied and a theoretical bound on its performance is derived. Given this
performance bound, an optimal pilot training length for multi-LIS systems
subjected to pilot contamination is characterized and, subsequently, the
performance-maximizing number of devices that the LIS system must service is
derived. Simulation results show that the derived analyses are in close
agreement with the exact mutual information in presence of a large number of
antennas, and the achievable SSE is limited by the effect of pilot
contamination and intra/inter-LIS interference through the LOS path, even if
the LIS is equipped with an infinite number of antennas. Additionally, the SSE
obtained with the proposed pilot training length and number of scheduled
devices is shown to reach the one obtained via a brute-force search for the
optimal solution
Low-Complexity Channel Estimation in Large-Scale MIMO using Polynomial Expansion
This paper considers pilot-based channel estimation in large-scale
multiple-input multiple-output (MIMO) communication systems, also known as
"massive MIMO". Unlike previous works on this topic, which mainly considered
the impact of inter-cell disturbance due to pilot reuse (so-called pilot
contamination), we are concerned with the computational complexity. The
conventional minimum mean square error (MMSE) and minimum variance unbiased
(MVU) channel estimators rely on inverting covariance matrices, which has cubic
complexity in the multiplication of number of antennas at each side. Since this
is extremely expensive when there are hundreds of antennas, we propose to
approximate the inversion by an L-order matrix polynomial. A set of
low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel
(PEACH) estimators, are introduced. The coefficients of the polynomials are
optimized to yield small mean square error (MSE). We show numerically that
near-optimal performance is achieved with low polynomial orders. In practice,
the order L can be selected to balance between complexity and MSE.
Interestingly, pilot contamination is beneficial to the PEACH estimators in the
sense that smaller L can be used to achieve near-optimal MSEs.Comment: Published at IEEE International Symposium on Personal, Indoor and
Mobile Radio Communications (PIMRC 2013), 8-11 September 2013, 6 pages, 4
figures, 1 tabl
Schur Complement Based Analysis of MIMO Zero-Forcing for Rician Fading
For multiple-input/multiple-output (MIMO) spatial multiplexing with
zero-forcing detection (ZF), signal-to-noise ratio (SNR) analysis for Rician
fading involves the cumbersome noncentral-Wishart distribution (NCWD) of the
transmit sample-correlation (Gramian) matrix. An \textsl{approximation} with a
\textsl{virtual} CWD previously yielded for the ZF SNR an approximate (virtual)
Gamma distribution. However, analytical conditions qualifying the accuracy of
the SNR-distribution approximation were unknown. Therefore, we have been
attempting to exactly characterize ZF SNR for Rician fading. Our previous
attempts succeeded only for the sole Rician-fading stream under
Rician--Rayleigh fading, by writing it as scalar Schur complement (SC) in the
Gramian. Herein, we pursue a more general, matrix-SC-based analysis to
characterize SNRs when several streams may undergo Rician fading. On one hand,
for full-Rician fading, the SC distribution is found to be exactly a CWD if and
only if a channel-mean--correlation \textsl{condition} holds. Interestingly,
this CWD then coincides with the \textsl{virtual} CWD ensuing from the
\textsl{approximation}. Thus, under the \textsl{condition}, the actual and
virtual SNR-distributions coincide. On the other hand, for Rician--Rayleigh
fading, the matrix-SC distribution is characterized in terms of determinant of
matrix with elementary-function entries, which also yields a new
characterization of the ZF SNR. Average error probability results validate our
analysis vs.~simulation.Comment: 32 pages, 4 figures, 1 tabl
LMMSE Receivers in Uplink Massive MIMO Systems with Correlated Rician Fading
We carry out a theoretical analysis of the uplink (UL) of a massive MIMO
system with per-user channel correlation and Rician fading, using two
processing approaches. Firstly, we examine the linear minimum-mean-square-error
receiver under training-based imperfect channel estimates. Secondly, we propose
a statistical combining technique that is more suitable in environments with
strong Line-of-Sight (LoS) components. We derive closed-form asymptotic
approximations of the UL spectral efficiency (SE) attained by each combining
scheme in single and multi-cell settings, as a function of the system
parameters. These expressions are insightful in how different factors such as
LoS propagation conditions and pilot contamination impact the overall system
performance. Furthermore, they are exploited to determine the optimal number of
training symbols which is shown to be of significant interest at low Rician
factors. The study and numerical results substantiate that stronger LoS signals
lead to better performances, and under such conditions, the statistical
combining entails higher SE gains than the conventional receiver.Comment: 32 pages, 8 figures, accepted to be published in IEEE Transactions on
Communication
Ergodic Spectral Efficiency of Massive MIMO with Correlated Rician Channel and MRC Detection based on LS and MMSE Channel Estimation
In this paper, we study the spectral efficiency (SE) of a multi-cell massive
multiple-input multiple-output (MIMO) system with a spatially correlated Rician
channel. The correlation between least squares (LS) estimator and its error
complicates SE analysis, since signal and interference components become
cross-correlated, too. Minimum mean square error (MMSE) estimators do not
suffer from this burden. In some previous works, a proper part of the signal is
referred to interference, which makes them cross-uncorrelated, and leads to an
SE lower bound. In our modified approach, we extract and refer the
cross-correlated part of interference to the signal to attain this objective.
Here, we use this approach for calculating the instantaneous SE of maximum
ratio combining (MRC) detector under LS and MMSE estimation methods. We also
derive closed-form approximations of their ergodic SE. This approach is also
applicable to other linear channel estimators or data detectors. Numerical
results show that achievable SE surpasses that of the previous approach. They
also show that our approximation is close enough to Monte Carlo simulation
results, especially at the high number of the base station (BS) antennas.Comment: This paper is submitted to IET Communications. If finally accepted,
the copy of the record will be available at the IET Digital Library. Here is
the submission History: Submitted on 2019 Septemaber 5 Majorly Revised on
2019 December 24 Minorly Revised on 2020 May 1
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