9,525 research outputs found
A Simple Introduction to Free Probability Theory and its Application to Random Matrices
Free probability theory started in the 1980s has attracted much attention
lately in signal processing and communications areas due to its applications in
large size random matrices. However, it involves with massive mathematical
concepts and notations, and is really hard for a general reader to comprehend.
The main goal of this paper is to briefly describe this theory and its
application in random matrices as simple as possible so that it is easy to
follow. Applying free probability theory, one is able to calculate the
distributions of the eigenvalues/singular-values of large size random matrices
using only the second order statistics of the matrix entries. One of such
applications is the mutual information calculation of a massive MIMO system
Low Complexity Hybrid Precoding and Channel Estimation Based on Hierarchical Multi-Beam Search for Millimeter-Wave MIMO Systems
In millimeter-wave (mmWave) MIMO systems, while a hybrid digital/analog
precoding structure offers the potential to increase the achievable rate, it
also faces the challenge of the need of a low-complexity design. In specific,
the hybrid precoding may require matrix operations with a scale of antenna
size, which is generally large in mmWave communication. Moreover, the channel
estimation is also rather time consuming due to the large number of antennas at
both Tx/Rx sides. In this paper, a low-complexity hybrid precoding and channel
estimation approach is proposed. In the channel estimation phase, a
hierarchical multi-beam search scheme is proposed to fast acquire
(the number of streams) multipath components (MPCs)/clusters with the highest
powers. In the hybrid precoding phase, the analog and digital precodings are
decoupled. The analog precoding is designed to steer along the
acquired MPCs/clusters at both Tx/Rx sides, shaping an equivalent
baseband channel, while the digital precoding
performs operations in the baseband with the reduced-scale channel. Performance
evaluations show that, compared with a state-of-the-art scheme, while achieving
a close or even better performance when the number of radio-frequency (RF)
chains or streams is small, both the computational complexity of the hybrid
precoding and the time complexity of the channel estimation are greatly
reduced.Comment: 11 pages, 9 figures. This paper reports a Low Complexity Hybrid
Precoding and Channel Estimation method for mmWave communication
Full-Duplex Millimeter-Wave Communication
The potential of doubling the spectrum efficiency of full-duplex (FD)
transmission motivates us to investigate FD millimeter-wave (FD-mmWave)
communication. To realize FD transmission in the mmWave band, we first
introduce possible antenna configurations for FD-mmWave transmission. It is
shown that, different from the cases in micro-wave band FD communications, the
configuration with separate Tx/Rx antenna arrays appears more flexible in
self-interference (SI) suppression while it may increase some cost and area
versus that with the same array. We then model the mmWave SI channel with
separate Tx/Rx arrays, where a near-field propagation model is adopted for the
line-of-sight (LOS) path, and it is found that the established LOS-SI channel
with separate Tx/Rx arrays also shows spatial sparsity. Based on the SI
channel, we further explore approaches to mitigate SI by signal processing, and
we focus on a new cancellation approach in FD-mmWave communication, i.e.,
beamforming cancellation. Centered on the constant-amplitude (CA) constraint of
the beamforming vectors, we propose several candidate solutions. Lastly, we
consider an FD-mmWave multi-user scenario, and show that even if there are no
FD users in an FD-mmWave cellular system, the FD benefit can still be exploited
in the FD base station. Candidate solutions are also discussed to mitigate both
SI and multi-user interference (MUI) simultaneously.Comment: This paper explores the combination of full duplex communication and
millimeter wave communication. (To appear in IEEE Wireless Communications
Codebook Design for Millimeter-Wave Channel Estimation with Hybrid Precoding Structure
In this paper, we study hierarchical codebook design for channel estimation
in millimeter-wave (mmWave) communications with a hybrid precoding structure.
Due to the limited saturation power of mmWave power amplifier (PA), we take the
per-antenna power constraint (PAPC) into consideration. We first propose a
metric, i.e., generalized detection probability (GDP), to evaluate the quality
of \emph{an arbitrary codeword}. This metric not only enables an optimization
approach for mmWave codebook design, but also can be used to compare the
performance of two different codewords/codebooks. To the best of our knowledge,
GDP is the first metric particularly for mmWave codebook design for channel
estimation. We then propose an approach to design a hierarchical codebook
exploiting BeaM Widening with Multi-RF-chain Sub-array technique (BMW-MS). To
obtain crucial parameters of BMW-MS, we provide two solutions, namely a
low-complexity search (LCS) solution to optimize the GDP metric and a
closed-form (CF) solution to pursue a flat beam pattern. Performance
comparisons show that BMW-MS/LCS and BMW-MS/CF achieve very close performances,
and they outperform the existing alternatives under the PAPC.Comment: 14 pages, 10 figures. Hierarchical codebook design for mmWave channel
estimation with a hybrid precoding structure. Submitted to TW
Enabling UAV Cellular with Millimeter-Wave Communication: Potentials and Approaches
To support high data rate urgent or ad hoc communications, we consider mmWave
UAV cellular networks and the associated challenges and solutions. To enable
fast beamforming training and tracking, we first investigate a hierarchical
structure of beamforming codebooks and design of hierarchical codebooks with
different beam widths via the sub-array techniques. We next examine the Doppler
effect as a result of UAV movement and find that the Doppler effect may not be
catastrophic when high gain directional transmission is used. We further
explore the use of millimeter wave spatial division multiple access and
demonstrate its clear advantage in improving the cellular network capacity. We
also explore different ways of dealing with signal blockage and point out that
possible adaptive UAV cruising algorithms would be necessary to counteract
signal blockage. Finally, we identify a close relationship between UAV
positioning and directional millimeter wave user discovery, where update of the
former may directly impact the latter and vice versa.Comment: This paper explores the potentials and approaches to exploit mmWave
communication to establish a UAV cellular. It is to appear in IEEE
Communications Magazin
Minimum Degree-Weighted Distance Decoding for Polynomial Residue Codes with Non-Pairwise Coprime Moduli
This paper presents a new decoding for polynomial residue codes, called the
minimum degree-weighted distance decoding. The newly proposed decoding is based
on the degree-weighted distance and different from the traditional minimum
Hamming distance decoding. It is shown that for the two types of minimum
distance decoders, i.e., the minimum degree-weighted distance decoding and the
minimum Hamming distance decoding, one is not absolutely stronger than the
other, but they can complement each other from different points of view.Comment: 4 page
Error Correction in Polynomial Remainder Codes with Non-Pairwise Coprime Moduli and Robust Chinese Remainder Theorem for Polynomials
This paper investigates polynomial remainder codes with non-pairwise coprime
moduli. We first consider a robust reconstruction problem for polynomials from
erroneous residues when the degrees of all residue errors are assumed small,
namely robust Chinese Remainder Theorem (CRT) for polynomials. It basically
says that a polynomial can be reconstructed from erroneous residues such that
the degree of the reconstruction error is upper bounded by whenever the
degrees of all residue errors are upper bounded by , where a sufficient
condition for and a reconstruction algorithm are obtained. By releasing
the constraint that all residue errors have small degrees, another robust
reconstruction is then presented when there are multiple unrestricted errors
and an arbitrary number of errors with small degrees in the residues. By making
full use of redundancy in moduli, we obtain a stronger residue error correction
capability in the sense that apart from the number of errors that can be
corrected in the previous existing result, some errors with small degrees can
be also corrected in the residues. With this newly obtained result,
improvements in uncorrected error probability and burst error correction
capability in a data transmission are illustrated.Comment: 12 pages, 2 figure
On Full Diversity Space-Time Block Codes with Partial Interference Cancellation Group Decoding
In this paper, we propose a partial interference cancellation (PIC) group
decoding for linear dispersive space-time block codes (STBC) and a design
criterion for the codes to achieve full diversity when the PIC group decoding
is used at the receiver. A PIC group decoding decodes the symbols embedded in
an STBC by dividing them into several groups and decoding each group separately
after a linear PIC operation is implemented. It can be viewed as an
intermediate decoding between the maximum likelihood (ML) receiver that decodes
all the embedded symbols together, i.e., all the embedded symbols are in a
single group, and the zero-forcing (ZF) receiver that decodes all the embedded
symbols separately and independently, i.e., each group has and only has one
embedded symbol, after the ZF operation is implemented. Our proposed design
criterion for the PIC group decoding to achieve full diversity is an
intermediate condition between the loosest ML full rank criterion of codewords
and the strongest ZF linear independence condition of the column vectors in the
equivalent channel matrix. We also propose asymptotically optimal (AO) group
decoding algorithm, which is an intermediate decoding between the MMSE decoding
algorithm and the ML decoding algorithm. The design criterion for the PIC group
decoding applies to the AO group decoding algorithm. It is well-known that the
symbol rate for a full rank linear STBC can be full, i.e., n_t for n_t transmit
antennas. It has been recently shown that its rate is upper bounded by 1 if a
code achieves full diversity with a linear receiver. The intermediate criterion
proposed in this paper provides the possibility for codes of rates between n_t
and 1 that achieve full diversity with a PIC group decoding. This therefore
provides a complexity-performance-rate tradeoff.Comment: 45 pages, 3 figures, partially appeared in the International Symp. on
Information Theory (ISIT), Toronto, Canada, July 6-11, 200
Robust Polynomial Reconstruction via Chinese Remainder Theorem in the Presence of Small Degree Residue Errors
Based on unique decoding of the polynomial residue code with non-pairwise
coprime moduli, a polynomial with degree less than that of the least common
multiple (lcm) of all the moduli can be accurately reconstructed when the
number of residue errors is less than half the minimum distance of the code.
However, once the number of residue errors is beyond half the minimum distance
of the code, the unique decoding may fail and lead to a large reconstruction
error. In this paper, assuming that all the residues are allowed to have errors
with small degrees, we consider how to reconstruct the polynomial as accurately
as possible in the sense that a reconstructed polynomial is obtained with only
the last number of coefficients being possibly erroneous, when the
residues are affected by errors with degrees upper bounded by . In this
regard, we first propose a multi-level robust Chinese remainder theorem (CRT)
for polynomials, namely, a trade-off between the dynamic range of the degree of
the polynomial to be reconstructed and the residue error bound is
formulated. Furthermore, a simple closed-form reconstruction algorithm is also
proposed.Comment: 5 page
Fluorescence Intermittency of A Single Quantum System and Anderson Localization
The nature of fluorescence intermittency for semiconductor quantum dots (QD)
and single molecules (SM) is proposed as a manifestation of Anderson
localization. The power law like distribution for the \emph{on} time is
explained as due to the interaction between QD/SM with a random environment. In
particular, we find that the \emph{on}-time probability distribution behaves
differently in localized and delocalized regimes. They, when properly scaled,
are \emph{universal} for different QD/SM systems. The \emph{on}-time
probability distribution function in the delocalized QD/SM regime can be
approximated by power laws with exponents covering . QD/SM switches
to a dark (\emph{off}) state when a charge of QD/SM hops into the trap states,
which becomes localized after stabilization by the surrounding matrix.Comment: 5 pages, 3 figure
- β¦