151 research outputs found
Randomly Spread CDMA: Asymptotics via Statistical Physics
This paper studies randomly spread code-division multiple access (CDMA) and
multiuser detection in the large-system limit using the replica method
developed in statistical physics. Arbitrary input distributions and flat fading
are considered. A generic multiuser detector in the form of the posterior mean
estimator is applied before single-user decoding. The generic detector can be
particularized to the matched filter, decorrelator, linear MMSE detector, the
jointly or the individually optimal detector, and others. It is found that the
detection output for each user, although in general asymptotically non-Gaussian
conditioned on the transmitted symbol, converges as the number of users go to
infinity to a deterministic function of a "hidden" Gaussian statistic
independent of the interferers. Thus the multiuser channel can be decoupled:
Each user experiences an equivalent single-user Gaussian channel, whose
signal-to-noise ratio suffers a degradation due to the multiple-access
interference. The uncoded error performance (e.g., symbol-error-rate) and the
mutual information can then be fully characterized using the degradation
factor, also known as the multiuser efficiency, which can be obtained by
solving a pair of coupled fixed-point equations identified in this paper. Based
on a general linear vector channel model, the results are also applicable to
MIMO channels such as in multiantenna systems.Comment: To be published in IEEE Transactions on Information Theor
Many-Access Channels: The Gaussian Case with Random User Activities
Classical multiuser information theory studies the fundamental limits of
models with a fixed (often small) number of users as the coding blocklength
goes to infinity. This work proposes a new paradigm, referred to as many-user
information theory, where the number of users is allowed to grow with the
blocklength. This paradigm is motivated by emerging systems with a massive
number of users in an area, such as machine-to-machine communication systems
and sensor networks. The focus of the current paper is the many-access channel
model, which consists of a single receiver and many transmitters, whose number
increases unboundedly with the blocklength. Moreover, an unknown subset of
transmitters may transmit in a given block and need to be identified. A new
notion of capacity is introduced and characterized for the Gaussian many-access
channel with random user activities. The capacity can be achieved by first
detecting the set of active users and then decoding their messages.Comment: 5 pages, 2 figures, to appear in Proceedings of ISIT 201
Tracking Angles of Departure and Arrival in a Mobile Millimeter Wave Channel
Millimeter wave provides a very promising approach for meeting the
ever-growing traffic demand in next generation wireless networks. To utilize
this band, it is crucial to obtain the channel state information in order to
perform beamforming and combining to compensate for severe path loss. In
contrast to lower frequencies, a typical millimeter wave channel consists of a
few dominant paths. Thus it is generally sufficient to estimate the path gains,
angles of departure (AoDs), and angles of arrival (AoAs) of those paths.
Proposed in this paper is a dual timescale model to characterize abrupt channel
changes (e.g., blockage) and slow variations of AoDs and AoAs. This work
focuses on tracking the slow variations and detecting abrupt changes. A Kalman
filter based tracking algorithm and an abrupt change detection method are
proposed. The tracking algorithm is compared with the adaptive algorithm due to
Alkhateeb, Ayach, Leus and Heath (2014) in the case with single radio frequency
chain. Simulation results show that to achieve the same tracking performance,
the proposed algorithm requires much lower signal-to-noise-ratio (SNR) and much
fewer pilots than the other algorithm. Moreover, the change detection method
can always detect abrupt changes with moderate number of pilots and SNR.Comment: 6 pages, 7 figures, submitted to ICC 201
Statistical Physics of Signal Estimation in Gaussian Noise: Theory and Examples of Phase Transitions
We consider the problem of signal estimation (denoising) from a statistical
mechanical perspective, using a relationship between the minimum mean square
error (MMSE), of estimating a signal, and the mutual information between this
signal and its noisy version. The paper consists of essentially two parts. In
the first, we derive several statistical-mechanical relationships between a few
important quantities in this problem area, such as the MMSE, the differential
entropy, the Fisher information, the free energy, and a generalized notion of
temperature. We also draw analogies and differences between certain relations
pertaining to the estimation problem and the parallel relations in
thermodynamics and statistical physics. In the second part of the paper, we
provide several application examples, where we demonstrate how certain analysis
tools that are customary in statistical physics, prove useful in the analysis
of the MMSE. In most of these examples, the corresponding
statistical-mechanical systems turn out to consist of strong interactions that
cause phase transitions, which in turn are reflected as irregularities and
discontinuities (similar to threshold effects) in the behavior of the MMSE.Comment: Submitted to the IEEE Transactions on Information Theor
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