8,076 research outputs found
Applications of Stochastic Ordering to Wireless Communications
Stochastic orders are binary relations defined on probability distributions
which capture intuitive notions like being larger or being more variable. This
paper introduces stochastic ordering of instantaneous SNRs of fading channels
as a tool to compare the performance of communication systems over different
channels. Stochastic orders unify existing performance metrics such as ergodic
capacity, and metrics based on error rate functions for commonly used
modulation schemes through their relation with convex, and completely monotonic
(c.m.) functions. Toward this goal, performance metrics such as instantaneous
error rates of M-QAM and M-PSK modulations are shown to be c.m. functions of
the instantaneous SNR, while metrics such as the instantaneous capacity are
seen to have a completely monotonic derivative (c.m.d.). It is shown that the
commonly used parametric fading distributions for modeling line of sight (LoS),
exhibit a monotonicity in the LoS parameter with respect to the stochastic
Laplace transform order. Using stochastic orders, average performance of
systems involving multiple random variables are compared over different
channels, even when closed form expressions for such averages are not
tractable. These include diversity combining schemes, relay networks, and
signal detection over fading channels with non-Gaussian additive noise, which
are investigated herein. Simulations are also provided to corroborate our
results.Comment: 25 pages, 10 figures, Submitted to the IEEE transactions on wireless
communication
Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks
Stochastic orders on point processes are partial orders which capture notions
like being larger or more variable. Laplace functional ordering of point
processes is a useful stochastic order for comparing spatial deployments of
wireless networks. It is shown that the ordering of point processes is
preserved under independent operations such as marking, thinning, clustering,
superposition, and random translation. Laplace functional ordering can be used
to establish comparisons of several performance metrics such as coverage
probability, achievable rate, and resource allocation even when closed form
expressions of such metrics are unavailable. Applications in several network
scenarios are also provided where tradeoffs between coverage and interference
as well as fairness and peakyness are studied. Monte-Carlo simulations are used
to supplement our analytical results.Comment: 30 pages, 5 figures, Submitted to Hindawi Wireless Communications and
Mobile Computin
Some stochastic inequalities for weighted sums
We compare weighted sums of i.i.d. positive random variables according to the
usual stochastic order. The main inequalities are derived using majorization
techniques under certain log-concavity assumptions. Specifically, let be
i.i.d. random variables on . Assuming that has a
log-concave density, we show that is stochastically smaller than
, if is majorized by . On the other hand, assuming that has a log-concave density for
some , we show that is stochastically larger than , if is majorized by , where
. These unify several stochastic ordering results for specific
distributions. In particular, a conjecture of Hitczenko [Sankhy\={a} A 60
(1998) 171--175] on Weibull variables is proved. Potential applications in
reliability and wireless communications are mentioned.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ302 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications
Directionally convex () ordering is a tool for comparison of dependence
structure of random vectors that also takes into account the variability of the
marginal distributions. When extended to random fields it concerns comparison
of all finite dimensional distributions. Viewing locally finite measures as
non-negative fields of measure-values indexed by the bounded Borel subsets of
the space, in this paper we formulate and study the ordering of random
measures on locally compact spaces. We show that the order is preserved
under some of the natural operations considered on random measures and point
processes, such as deterministic displacement of points, independent
superposition and thinning as well as independent, identically distributed
marking. Further operations such as position dependent marking and displacement
of points though do not preserve the order on all point processes, are
shown to preserve the order on Cox point processes. We also examine the impact
of order on the second moment properties, in particular on clustering and
on Palm distributions. Comparisons of Ripley's functions, pair correlation
functions as well as examples seem to indicate that point processes higher in
order cluster more. As the main result, we show that non-negative
integral shot-noise fields with respect to ordered random measures
inherit this ordering from the measures. Numerous applications of this result
are shown, in particular to comparison of various Cox processes and some
performance measures of wireless networks, in both of which shot-noise fields
appear as key ingredients. We also mention a few pertinent open questions.Comment: Accepted in Advances in Applied Probability. Propn. 3.2 strengthened
and as a consequence Cor 6.1,6.2,6.
Large-Scale MIMO versus Network MIMO for Multicell Interference Mitigation
This paper compares two important downlink multicell interference mitigation
techniques, namely, large-scale (LS) multiple-input multiple-output (MIMO) and
network MIMO. We consider a cooperative wireless cellular system operating in
time-division duplex (TDD) mode, wherein each cooperating cluster includes
base-stations (BSs), each equipped with multiple antennas and scheduling
single-antenna users. In an LS-MIMO system, each BS employs antennas not
only to serve its scheduled users, but also to null out interference caused to
the other users within the cooperating cluster using zero-forcing (ZF)
beamforming. In a network MIMO system, each BS is equipped with only
antennas, but interference cancellation is realized by data and channel state
information exchange over the backhaul links and joint downlink transmission
using ZF beamforming. Both systems are able to completely eliminate
intra-cluster interference and to provide the same number of spatial degrees of
freedom per user. Assuming the uplink-downlink channel reciprocity provided by
TDD, both systems are subject to identical channel acquisition overhead during
the uplink pilot transmission stage. Further, the available sum power at each
cluster is fixed and assumed to be equally distributed across the downlink
beams in both systems. Building upon the channel distribution functions and
using tools from stochastic ordering, this paper shows, however, that from a
performance point of view, users experience better quality of service, averaged
over small-scale fading, under an LS-MIMO system than a network MIMO system.
Numerical simulations for a multicell network reveal that this conclusion also
holds true with regularized ZF beamforming scheme. Hence, given the likely
lower cost of adding excess number of antennas at each BS, LS-MIMO could be the
preferred route toward interference mitigation in cellular networks.Comment: 13 pages, 7 figures; IEEE Journal of Selected Topics in Signal
Processing, Special Issue on Signal Processing for Large-Scale MIMO
Communication
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