520 research outputs found
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
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
Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users
In downlink multi-antenna systems with many users, the multiplexing gain is
strictly limited by the number of transmit antennas and the use of these
antennas. Assuming that the total number of receive antennas at the
multi-antenna users is much larger than , the maximal multiplexing gain can
be achieved with many different transmission/reception strategies. For example,
the excess number of receive antennas can be utilized to schedule users with
effective channels that are near-orthogonal, for multi-stream multiplexing to
users with well-conditioned channels, and/or to enable interference-aware
receive combining. In this paper, we try to answer the question if the data
streams should be divided among few users (many streams per user) or many users
(few streams per user, enabling receive combining). Analytic results are
derived to show how user selection, spatial correlation, heterogeneous user
conditions, and imperfect channel acquisition (quantization or estimation
errors) affect the performance when sending the maximal number of streams or
one stream per scheduled user---the two extremes in data stream allocation.
While contradicting observations on this topic have been reported in prior
works, we show that selecting many users and allocating one stream per user
(i.e., exploiting receive combining) is the best candidate under realistic
conditions. This is explained by the provably stronger resilience towards
spatial correlation and the larger benefit from multi-user diversity. This
fundamental result has positive implications for the design of downlink systems
as it reduces the hardware requirements at the user devices and simplifies the
throughput optimization.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 11
figures. The results can be reproduced using the following Matlab code:
https://github.com/emilbjornson/one-or-multiple-stream
Linear Precoding Based on Polynomial Expansion: Large-Scale Multi-Cell MIMO Systems
Large-scale MIMO systems can yield a substantial improvement in spectral
efficiency for future communication systems. Due to the finer spatial
resolution achieved by a huge number of antennas at the base stations, these
systems have shown to be robust to inter-user interference and the use of
linear precoding is asymptotically optimal. However, most precoding schemes
exhibit high computational complexity as the system dimensions increase. For
example, the near-optimal RZF requires the inversion of a large matrix. This
motivated our companion paper, where we proposed to solve the issue in
single-cell multi-user systems by approximating the matrix inverse by a
truncated polynomial expansion (TPE), where the polynomial coefficients are
optimized to maximize the system performance. We have shown that the proposed
TPE precoding with a small number of coefficients reaches almost the
performance of RZF but never exceeds it. In a realistic multi-cell scenario
involving large-scale multi-user MIMO systems, the optimization of RZF
precoding has thus far not been feasible. This is mainly attributed to the high
complexity of the scenario and the non-linear impact of the necessary
regularizing parameters. On the other hand, the scalar weights in TPE precoding
give hope for possible throughput optimization. Following the same methodology
as in the companion paper, we exploit random matrix theory to derive a
deterministic expression for the asymptotic SINR for each user. We also provide
an optimization algorithm to approximate the weights that maximize the
network-wide weighted max-min fairness. The optimization weights can be used to
mimic the user throughput distribution of RZF precoding. Using simulations, we
compare the network throughput of the TPE precoding with that of the suboptimal
RZF scheme and show that our scheme can achieve higher throughput using a TPE
order of only 3
Dual-Branch MRC Receivers under Spatial Interference Correlation and Nakagami Fading
Despite being ubiquitous in practice, the performance of maximal-ratio
combining (MRC) in the presence of interference is not well understood. Because
the interference received at each antenna originates from the same set of
interferers, but partially de-correlates over the fading channel, it possesses
a complex correlation structure. This work develops a realistic analytic model
that accurately accounts for the interference correlation using stochastic
geometry. Modeling interference by a Poisson shot noise process with
independent Nakagami fading, we derive the link success probability for
dual-branch interference-aware MRC. Using this result, we show that the common
assumption that all receive antennas experience equal interference power
underestimates the true performance, although this gap rapidly decays with
increasing the Nakagami parameter of the interfering links. In
contrast, ignoring interference correlation leads to a highly optimistic
performance estimate for MRC, especially for large . In the low
outage probability regime, our success probability expression can be
considerably simplified. Observations following from the analysis include: (i)
for small path loss exponents, MRC and minimum mean square error combining
exhibit similar performance, and (ii) the gains of MRC over selection combining
are smaller in the interference-limited case than in the well-studied
noise-limited case.Comment: to appear in IEEE Transactions on Communication
Non-atomic Games for Multi-User Systems
In this contribution, the performance of a multi-user system is analyzed in
the context of frequency selective fading channels. Using game theoretic tools,
a useful framework is provided in order to determine the optimal power
allocation when users know only their own channel (while perfect channel state
information is assumed at the base station). We consider the realistic case of
frequency selective channels for uplink CDMA. This scenario illustrates the
case of decentralized schemes, where limited information on the network is
available at the terminal. Various receivers are considered, namely the Matched
filter, the MMSE filter and the optimum filter. The goal of this paper is to
derive simple expressions for the non-cooperative Nash equilibrium as the
number of mobiles becomes large and the spreading length increases. To that end
two asymptotic methodologies are combined. The first is asymptotic random
matrix theory which allows us to obtain explicit expressions of the impact of
all other mobiles on any given tagged mobile. The second is the theory of
non-atomic games which computes good approximations of the Nash equilibrium as
the number of mobiles grows.Comment: 17 pages, 4 figures, submitted to IEEE JSAC Special Issue on ``Game
Theory in Communication Systems'
Random Beamforming over Correlated Fading Channels
We study a multiple-input multiple-output (MIMO) multiple access channel
(MAC) from several multi-antenna transmitters to a multi-antenna receiver. The
fading channels between the transmitters and the receiver are modeled by random
matrices, composed of independent column vectors with zero mean and different
covariance matrices. Each transmitter is assumed to send multiple data streams
with a random precoding matrix extracted from a Haar-distributed matrix. For
this general channel model, we derive deterministic approximations of the
normalized mutual information, the normalized sum-rate with
minimum-mean-square-error (MMSE) detection and the
signal-to-interference-plus-noise-ratio (SINR) of the MMSE decoder, which
become arbitrarily tight as all system parameters grow infinitely large at the
same speed. In addition, we derive the asymptotically optimal power allocation
under individual or sum-power constraints. Our results allow us to tackle the
problem of optimal stream control in interference channels which would be
intractable in any finite setting. Numerical results corroborate our analysis
and verify its accuracy for realistic system dimensions. Moreover, the
techniques applied in this paper constitute a novel contribution to the field
of large random matrix theory and could be used to study even more involved
channel models.Comment: 35 pages, 5 figure
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