16 research outputs found
On Convergence Conditions of Gaussian Belief Propagation
In order to compute the marginal probability density function (PDF) with Gaussian belief propagation (BP), it is impor- tant to know whether it will converge in advance. By describing the message-passing process of Gaussian BP on the pairwise factor graph as a set of updating functions, the necessary and sufficient convergence condition of beliefs in synchronous Gaussian BP is first derived under a newly proposed initialization set. The pro- posed initialization set is proved to be largest among all currently known sets. Then, the necessary and sufficient convergence con- dition of beliefs in damped Gaussian BP is developed, with the allowable range of damping factor explicitly established. The re- sults theoretically confirm the extensively reported conjecture that damping is helpful to improve the convergence of Gaussian BP. Under totally asynchronous scheduling, a sufficient convergence condition of beliefs is also derived for the same proposed initializa- tion set. Relationships between the proposed convergence condi- tions and existing ones are established analytically. At last, numer- ical examples are presented to corroborate the established theories.published_or_final_versio
Convergence analysis of the information matrix in Gaussian belief propagation
Gaussian belief propagation (BP) has been widely used for distributed
estimation in large-scale networks such as the smart grid, communication
networks, and social networks, where local measurements/observations are
scattered over a wide geographical area. However, the convergence of Gaus- sian
BP is still an open issue. In this paper, we consider the convergence of
Gaussian BP, focusing in particular on the convergence of the information
matrix. We show analytically that the exchanged message information matrix
converges for arbitrary positive semidefinite initial value, and its dis- tance
to the unique positive definite limit matrix decreases exponentially fast.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0201
Gaussian Message Passing for Overloaded Massive MIMO-NOMA
This paper considers a low-complexity Gaussian Message Passing (GMP) scheme
for a coded massive Multiple-Input Multiple-Output (MIMO) systems with
Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station
with antennas serves sources simultaneously in the same frequency.
Both and are large numbers, and we consider the overloaded cases
with . The GMP for MIMO-NOMA is a message passing algorithm operating
on a fully-connected loopy factor graph, which is well understood to fail to
converge due to the correlation problem. In this paper, we utilize the
large-scale property of the system to simplify the convergence analysis of the
GMP under the overloaded condition. First, we prove that the \emph{variances}
of the GMP definitely converge to the mean square error (MSE) of Linear Minimum
Mean Square Error (LMMSE) multi-user detection. Secondly, the \emph{means} of
the traditional GMP will fail to converge when . Therefore, we propose and derive a new
convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the
LMMSE multi-user detection performance for any , and show that it
has a faster convergence speed than the traditional GMP with the same
complexity. Finally, numerical results are provided to verify the validity and
accuracy of the theoretical results presented.Comment: Accepted by IEEE TWC, 16 pages, 11 figure
An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation
In this work we design a receiver that iteratively passes soft information
between the channel estimation and data decoding stages. The receiver
incorporates sparsity-based parametric channel estimation. State-of-the-art
sparsity-based iterative receivers simplify the channel estimation problem by
restricting the multipath delays to a grid. Our receiver does not impose such a
restriction. As a result it does not suffer from the leakage effect, which
destroys sparsity. Communication at near capacity rates in high SNR requires a
large modulation order. Due to the close proximity of modulation symbols in
such systems, the grid-based approximation is of insufficient accuracy. We show
numerically that a state-of-the-art iterative receiver with grid-based sparse
channel estimation exhibits a bit-error-rate floor in the high SNR regime. On
the contrary, our receiver performs very close to the perfect channel state
information bound for all SNR values. We also demonstrate both theoretically
and numerically that parametric channel estimation works well in dense
channels, i.e., when the number of multipath components is large and each
individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin