97 research outputs found
Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach
In this work, we study the performance of random isometric precoders over
quasi-static and correlated fading channels. We derive deterministic
approximations of the mutual information and the
signal-to-interference-plus-noise ratio (SINR) at the output of the
minimum-mean-square-error (MMSE) receiver and provide simple provably
converging fixed-point algorithms for their computation. Although these
approximations are only proven exact in the asymptotic regime with infinitely
many antennas at the transmitters and receivers, simulations suggest that they
closely match the performance of small-dimensional systems. We exemplarily
apply our results to the performance analysis of multi-cellular communication
systems, multiple-input multiple-output multiple-access channels (MIMO-MAC),
and MIMO interference channels. The mathematical analysis is based on the
Stieltjes transform method. This enables the derivation of deterministic
equivalents of functionals of large-dimensional random matrices. In contrast to
previous works, our analysis does not rely on arguments from free probability
theory which enables the consideration of random matrix models for which
asymptotic freeness does not hold. Thus, the results of this work are also a
novel contribution to the field of random matrix theory and applicable to a
wide spectrum of practical systems.Comment: to appear in IEEE Transactions on Information Theory, 201
Can Hardware Distortion Correlation be Neglected When Analyzing Uplink SE in Massive MIMO?
This paper analyzes how the distortion created by hardware impairments in a
multiple-antenna base station affects the uplink spectral efficiency (SE), with
focus on Massive MIMO. The distortion is correlated across the antennas, but
has been often approximated as uncorrelated to facilitate (tractable) SE
analysis. To determine when this approximation is accurate, basic properties of
the distortion correlation are first uncovered. Then, we focus on third-order
non-linearities and prove analytically and numerically that the correlation can
be neglected in the SE analysis when there are many users. In i.i.d. Rayleigh
fading with equal signal-to-noise ratios, this occurs when having five users.Comment: 5 pages, 3 figures, IEEE International Workshop on Signal Processing
Advances in Wireless Communications (SPAWC), 201
Iterative Deterministic Equivalents for the Performance Analysis of Communication Systems
In this article, we introduce iterative deterministic equivalents as a novel
technique for the performance analysis of communication systems whose channels
are modeled by complex combinations of independent random matrices. This
technique extends the deterministic equivalent approach for the study of
functionals of large random matrices to a broader class of random matrix models
which naturally arise as channel models in wireless communications. We present
two specific applications: First, we consider a multi-hop amplify-and-forward
(AF) MIMO relay channel with noise at each stage and derive deterministic
approximations of the mutual information after the Kth hop. Second, we study a
MIMO multiple access channel (MAC) where the channel between each transmitter
and the receiver is represented by the double-scattering channel model. We
provide deterministic approximations of the mutual information, the
signal-to-interference-plus-noise ratio (SINR) and sum-rate with
minimum-mean-square-error (MMSE) detection and derive the asymptotically
optimal precoding matrices. In both scenarios, the approximations can be
computed by simple and provably converging fixed-point algorithms and are shown
to be almost surely tight in the limit when the number of antennas at each node
grows infinitely large. Simulations suggest that the approximations are
accurate for realistic system dimensions. The technique of iterative
deterministic equivalents can be easily extended to other channel models of
interest and is, therefore, also a new contribution to the field of random
matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4
figure
Optimal Channel Training in Uplink Network MIMO Systems
We consider a multi-cell frequency-selective fading uplink channel (network
MIMO) from K single-antenna user terminals (UTs) to B cooperative base stations
(BSs) with M antennas each. The BSs, assumed to be oblivious of the applied
codebooks, forward compressed versions of their observations to a central
station (CS) via capacity limited backhaul links. The CS jointly decodes the
messages from all UTs. Since the BSs and the CS are assumed to have no prior
channel state information (CSI), the channel needs to be estimated during its
coherence time. Based on a lower bound of the ergodic mutual information, we
determine the optimal fraction of the coherence time used for channel training,
taking different path losses between the UTs and the BSs into account. We then
study how the optimal training length is impacted by the backhaul capacity.
Although our analytical results are based on a large system limit, we show by
simulations that they provide very accurate approximations for even small
system dimensions.Comment: 15 pages, 7 figures. To appear in the IEEE Transactions on Signal
Processin
Massive MIMO has Unlimited Capacity
The capacity of cellular networks can be improved by the unprecedented array
gain and spatial multiplexing offered by Massive MIMO. Since its inception, the
coherent interference caused by pilot contamination has been believed to create
a finite capacity limit, as the number of antennas goes to infinity. In this
paper, we prove that this is incorrect and an artifact from using simplistic
channel models and suboptimal precoding/combining schemes. We show that with
multicell MMSE precoding/combining and a tiny amount of spatial channel
correlation or large-scale fading variations over the array, the capacity
increases without bound as the number of antennas increases, even under pilot
contamination. More precisely, the result holds when the channel covariance
matrices of the contaminating users are asymptotically linearly independent,
which is generally the case. If also the diagonals of the covariance matrices
are linearly independent, it is sufficient to know these diagonals (and not the
full covariance matrices) to achieve an unlimited asymptotic capacity.Comment: To appear in IEEE Transactions on Wireless Communications, 17 pages,
7 figure
Fundamental Asymptotic Behavior of (Two-User) Distributed Massive MIMO
This paper considers the uplink of a distributed Massive MIMO network where
base stations (BSs), each equipped with antennas, receive data from
users. We study the asymptotic spectral efficiency (as )
with spatial correlated channels, pilot contamination, and different degrees of
channel state information (CSI) and statistical knowledge at the BSs. By
considering a two-user setup, we can simply derive fundamental asymptotic
behaviors and provide novel insights into the structure of the optimal
combining schemes. In line with [1], when global CSI is available at all BSs,
the optimal minimum-mean squared error combining has an unbounded capacity as
, if the global channel covariance matrices of the users are
asymptotically linearly independent. This result is instrumental to derive a
suboptimal combining scheme that provides unbounded capacity as
using only local CSI and global channel statistics. The latter scheme is shown
to outperform a generalized matched filter scheme, which also achieves
asymptotic unbounded capacity by using only local CSI and global channel
statistics, but is derived following [2] on the basis of a more conservative
capacity bound.Comment: 6 pages, 2 figures, to be presented at GLOBECOM 2018, Abu Dhab
Asymptotic Moments for Interference Mitigation in Correlated Fading Channels
We consider a certain class of large random matrices, composed of independent
column vectors with zero mean and different covariance matrices, and derive
asymptotically tight deterministic approximations of their moments. This random
matrix model arises in several wireless communication systems of recent
interest, such as distributed antenna systems or large antenna arrays.
Computing the linear minimum mean square error (LMMSE) detector in such systems
requires the inversion of a large covariance matrix which becomes prohibitively
complex as the number of antennas and users grows. We apply the derived moment
results to the design of a low-complexity polynomial expansion detector which
approximates the matrix inverse by a matrix polynomial and study its asymptotic
performance. Simulation results corroborate the analysis and evaluate the
performance for finite system dimensions.Comment: 7 pages, 2 figures, to be presented at IEEE International Symposium
on Information Theory (ISIT), Saint Petersburg, Russia, July 31 - August 5,
201
- …