32 research outputs found
How user throughput depends on the traffic demand in large cellular networks
Little's law allows to express the mean user throughput in any region of the
network as the ratio of the mean traffic demand to the steady-state mean number
of users in this region. Corresponding statistics are usually collected in
operational networks for each cell. Using ergodic arguments and Palm theoretic
formalism, we show that the global mean user throughput in the network is equal
to the ratio of these two means in the steady state of the "typical cell".
Here, both means account for double averaging: over time and network geometry,
and can be related to the per-surface traffic demand, base-station density and
the spatial distribution of the SINR. This latter accounts for network
irregularities, shadowing and idling cells via cell-load equations. We validate
our approach comparing analytical and simulation results for Poisson network
model to real-network cell-measurements
What frequency bandwidth to run cellular network in a given country? - a downlink dimensioning problem
We propose an analytic approach to the frequency bandwidth dimensioning
problem, faced by cellular network operators who deploy/upgrade their networks
in various geographical regions (countries) with an inhomogeneous urbanization.
We present a model allowing one to capture fundamental relations between users'
quality of service parameters (mean downlink throughput), traffic demand, the
density of base station deployment, and the available frequency bandwidth.
These relations depend on the applied cellular technology (3G or 4G impacting
user peak bit-rate) and on the path-loss characteristics observed in different
(urban, sub-urban and rural) areas. We observe that if the distance between
base stations is kept inversely proportional to the distance coefficient of the
path-loss function, then the performance of the typical cells of these
different areas is similar when serving the same (per-cell) traffic demand. In
this case, the frequency bandwidth dimensioning problem can be solved uniformly
across the country applying the mean cell approach proposed in [Blaszczyszyn et
al. WiOpt2014] http://dx.doi.org/10.1109/WIOPT.2014.6850355 . We validate our
approach by comparing the analytical results to measurements in operational
networks in various geographical zones of different countries
SINR-based k-coverage probability in cellular networks with arbitrary shadowing
We give numerically tractable, explicit integral expressions for the
distribution of the signal-to-interference-and-noise-ratio (SINR) experienced
by a typical user in the down-link channel from the k-th strongest base
stations of a cellular network modelled by Poisson point process on the plane.
Our signal propagation-loss model comprises of a power-law path-loss function
with arbitrarily distributed shadowing, independent across all base stations,
with and without Rayleigh fading. Our results are valid in the whole domain of
SINR, in particular for SINR<1, where one observes multiple coverage. In this
latter aspect our paper complements previous studies reported in [Dhillon et
al. JSAC 2012]
Using Poisson processes to model lattice cellular networks
An almost ubiquitous assumption made in the stochastic-analytic study of the
quality of service in cellular networks is Poisson distribution of base
stations. It is usually justified by various irregularities in the real
placement of base stations, which ideally should form the hexagonal pattern. We
provide a different and rigorous argument justifying the Poisson assumption
under sufficiently strong log-normal shadowing observed in the network, in the
evaluation of a natural class of the typical-user service-characteristics
including its SINR. Namely, we present a Poisson-convergence result for a broad
range of stationary (including lattice) networks subject to log-normal
shadowing of increasing variance. We show also for the Poisson model that the
distribution of all these characteristics does not depend on the particular
form of the additional fading distribution. Our approach involves a mapping of
2D network model to 1D image of it "perceived" by the typical user. For this
image we prove our convergence result and the invariance of the Poisson limit
with respect to the distribution of the additional shadowing or fading.
Moreover, we present some new results for Poisson model allowing one to
calculate the distribution function of the SINR in its whole domain. We use
them to study and optimize the mean energy efficiency in cellular networks
Wireless networks appear Poissonian due to strong shadowing
Geographic locations of cellular base stations sometimes can be well fitted
with spatial homogeneous Poisson point processes. In this paper we make a
complementary observation: In the presence of the log-normal shadowing of
sufficiently high variance, the statistics of the propagation loss of a single
user with respect to different network stations are invariant with respect to
their geographic positioning, whether regular or not, for a wide class of
empirically homogeneous networks. Even in perfectly hexagonal case they appear
as though they were realized in a Poisson network model, i.e., form an
inhomogeneous Poisson point process on the positive half-line with a power-law
density characterized by the path-loss exponent. At the same time, the
conditional distances to the corresponding base stations, given their observed
propagation losses, become independent and log-normally distributed, which can
be seen as a decoupling between the real and model geometry. The result applies
also to Suzuki (Rayleigh-log-normal) propagation model. We use
Kolmogorov-Smirnov test to empirically study the quality of the Poisson
approximation and use it to build a linear-regression method for the
statistical estimation of the value of the path-loss exponent
Effect of Opportunistic Scheduling on the Quality of Service Perceived by the Users in OFDMA Cellular Networks
International audienceOur objective is to analyze the impact of fading and opportunistic scheduling on the quality of service perceived by the users in an Orthogonal Frequency Division Multiple Access (OFDMA) cellular network. To this end, assuming Markovian arrivals and departures of customers that transmit some given data volumes, as well as some temporal channel variability (fading), we study the mean throughput that the network offers to users in the long run of the system. Explicit formulas are obtained in the case of allocation policies, which may or may-not take advantage of the fading, called respectively opportunistic and non-opportunistic. The main practical results of the present work are the following. Firstly we evaluate for the non-opportunist allocation the degradation due to fading compared to Additive White Gaussian Noise (AWGN) (that is, a decrease of at least 13% of the throughput). Secondly, we evaluate the gain induced by the opportunistic allocation. In particular, when the traffic demand per cell exceeds some value (about 2 Mbits/s in our numerical example), the gain induced by opportunism compensates the degradation induced by fading compared to AWGN
Account for fading in the dynamic performance evaluation of OFDMA cellular networks
International audienceThe objective of the present paper is to build a model which permits to capture and analyze the principal impacts of fading and multiuser diversity gain on the dynamic performance of an OFDMA cellular network. To this end, assuming Markovian arrivals and departures of customers that transmit some given data-volumes, as well as some temporal channel variability (fading), we study the mean throughput (and delay) that the network offers to users in the long-term evolution of the system. Explicit formulas are obtained in the case of allocation policies, which may or may-not take advantage of the fading, called respectively opportunistic and non-opportunistic. The main practical results of the present work are the following. Firstly we evaluate for the non-opportunistic allocation the degradation due to fading compared to AWGN (that is, a decrease of at least 13% of the throughput). Secondly, we evaluate the gain induced by the opportunistic allocation. In particular, when the traffic demand per cell exceeds some value (about 2.5 Mbps in our example), the gain induced by opportunism compensates the degradation induced by fading compared to AWGN
Linear-Regression Estimation of the Propagation-Loss Parameters Using Mobiles' Measurements in Wireless Cellular Networks
Cellular NetworksInternational audienceWe propose a new linear-regression model for the estimation of the path-loss exponent and the parameters of the shadowing from the propagation-loss data collected by the mobiles with respect to their serving base stations. The difficulty consists in deriving the parameters of the distribution of the propagation loss with respect to an arbitrary base station from these regarding the strongest one. The proposed solution is based on a simple, explicit relation between the two distributions in the case of infinite Poisson network and on the convergence of an arbitrary regular (in particular hexagonal) network to the Poisson one with increasing variance of the shadowing. The new approach complements existing methods, in particular the one based on COSTWalfisch-Ikegami model, which does not allow for the shadowing estimation and is not suited for indoor scenario
Up and Downlink Admission/Congestion Control and Maximal Load in Large Homogeneous CDMA Networks
This paper proposes scalable admission and congestion control schemes that allow each base station to decide independently of the others what set of voice users to serve and/or what bit rates to offer to elastic traffic users competing for bandwidth. These algorithms are primarily meant for large CDMA networks with a random but homogeneous user distribution. They take into account in an exact way the influence of geometry on the combination of inter-cell and intra-cell interferences as well as the existence of maximal power constraints of the base stations and users. We also study the load allowed by these schemes when the size of the network tends to infinity and the mean bit rate offered to elastic traffic users. By load, we mean here the number of voice users that each base station can serve
Impact of the Geometry, Path-Loss Exponent and Random Shadowing on the Mean Interference Factor in Wireless Cellular Networks
International audienceThe interference factor, defined for a given location in the network as the ratio of the sum of the path-gains form interfering base-stations (BS) to the path-gain from the serving BS is an important ingredient in the analysis of wireless cellular networks. It depends on the geometric placement of the BS in the network and the propagation gains between these stations and the given location. In this paper we study the mean interference factor taking into account the impact of these two elements. Regarding the geometry, we consider both the perfect hexagonal grid of BS and completely random Poisson pattern of BS. Regarding the signal propagation model, we consider not only a deterministic, signal-power-loss function that depends only on the distance between a transmitter and a receiver, and is mainly characterized by the so called path-loss exponent, but also random shadowing that characterizes in a statistical manner the way various obstacles on a given path modify this deterministic function. We present a detailed analysis of the impact of the path loss exponent, variance of the shadowing and the size of the network on the mean interference factor in the case of hexagonal and Poisson network architectures. We observe, as commonly expected, that small and moderate shadowing has a negative impact on regular networks as it increases the mean interference factor. However, as pointed out in the seminal paper Viterbi-Viterbi-Zehavi(1994), this impact can be largely reduced if the serving BS is chosen as the one which offers the smallest path-loss. Revisiting the model studied in this latter paper, we obtain a perhaps more surprising result saying that in large irregular (Poisson) networks the shadowing does not impact at all the interference factor, whose mean can be evaluated explicitly in a simple expression depending only on the path-loss exponent. Moreover, in small and moderate size networks, a very strong variability of the shadowing can be even beneficial in both hexagonal and Poisson networks