MARKOV CHAIN BASED MODELS COMPARISON IN IEEE
802.16E SCENARIO
Floriano De Rango, Andrea Malfitano, Angela Procopio and Salvatore Marano
D.E.I.S. Department, University of Calabria, P.Bucci road, Rende, Italy
Keywords: HAP, IEEE 802.16e, Markov chain, wireless channel, channel modelling.
Abstract: The IEEE 802.16e is a promising technology that allows to provide wireless broadband services to a great
number of mobile users. Considering this interesting scenario enriched by further presence of HAPs (High
Altitude Platform) with the role of Base Stations (BSs), we have proposed a comparison between
performances of a set of Markov Chain based models collected by literature. These following models: MTA
(Markov-based Trace Analysis), Gilbert – Elliot, FSM (Full-State Markov) and HMM (Hidden Markov
Model) are designed using packet error traces (a sequence of “1” and “0”) obtained by a simulator that takes
into account channel impairment effects such as path loss and Doppler effect. To compare the models
performances, by each of them artificial traces are generated and then Entropy Normalized Kullback-Leibler
distance, standard error and other statistical properties of random variable G (free error packets burst length)
and B (corrupted packets burst length) of artificial traces are computed. The purpose of this work is to
identify the model that best describes the channel error behaviour in IEEE 802.16e.
1 INTRODUCTION
In this paper we compare a set of Markov chain
based models collected by literature, these models
are used to describe channel error behaviour of a
particular IEEE 802.16e scenario. This scenario is an
HAP (High Altitude Platform), with the role of base
station (BS), that provides wireless broadband
service to a set of mobile users using IEEE 802.16e
protocol (Amendment 4: IEEE 802.16e-03/07, IEEE
802.16e-2005). HAPs are a new technology of
airships or planes that will operate in the
stratosphere at an altitude of 17-22 km above the
ground (De Rango et al., 2006). The IEEE 802.16e
specifies a system for combined fixed and mobile
BWA supporting subscriber stations moving at
vehicular speeds. It should operates in these bands
supporting bit rates up to 15 Mbit/s to mobile SS
(Subscriber Station) with vehicular mobility up to
approximately 100 km/h. Transmission between BS
and mobile users is affected by impairment effects
as Doppler effect and path loss, that contribute to
impair the transmitted data packets. These effects is
involved in a physical layer simulator realized with
Matlab tool; from simulations a set of packet error
traces is collected. A packet error trace is a sequence
of “flags” and each one of these can take “0” value if
a packet arrives to receiver side in error free manner,
or “1” value if packet is received as corrupted; thus a
trace describes channel error behaviour, or so we can
say that it depicts the MAC – to – MAC (Medium
Access Control) link; in fact in simulator
transmission chain also physical layer error
detection and correction instruments are involved.
Packet error traces obtained by simulations are
used to calculate the parameters for the following
Markov chain based models: Gilbert – Elliot (see
Ebert et al., 1999), MTA (Markov-based Trace
Analysis; see Konrad et al., 2001), FSM (Full State
Markov; see Khayam, 2007) and HMM (Hidden
Markov Model; see Rabiner, 1989). These
introduced models are used to represent channel
error model of IEEE 802.16e scenario, and from
each of these it is possible to generate artificial
packet error traces that can be used in more and
more realistic simulations of network issues. In this
paper we utilize artificial traces, obtained by each
model, to make a performance comparison of
presented models set. The paper focus is to
individuate the model that best approximate the
channel error behaviour; in literature, at the best of
our knowledge, are not preset works that make a
comparison of Markov chain based model
performances applied to IEEE 802.16e. In (Khayam
et al., 2003) is presented a models comparison
applied to Wi-Fi scenario, and in (Konrad et al.,
182
De Rango F., Malfitano A., Procopio A. and Marano S. (2008).
MARKOV CHAIN BASED MODELS COMPARISON IN IEEE 802.16E SCENARIO.
In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 182-185
DOI: 10.5220/0002026501820185
Copyright
c
SciTePress
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1
2001) models comparison is applied to GSM
scenario.
In section 2 scenario with impairments effects
such as path loss and Doppler effect are described;
in section 3 simulation environment is presented. In
section 4 Markov chain based models are
introduced. In section 5 and 6 performance analysis
and conclusions are respectively described.
2 SCENARIO
An HAP serves mobile users. In this architecture,
IEEE 802.16SC is applied. With 802.16SC we refer
the physical layer wirelessMAN-SC of IEEE 802.16
protocol. In IEEE 802.16 protocol, only one MAC
layer but various physical layers are defined. ITU
has licensed frequency bands for the provision of
communication services via HAPs for broadband
services at 28 - 31 GHz and thus this band was
chosen. The wireless channel is a particular kind of
channel affected by phenomena such as path loss
and Doppler effect. The first is typical of each
channel, the second is bound up with relative motion
between the transmitter and receiver. The channel
model of this scenario, used to obtain error traces,
does not take into account multipath fading because
this effect is negligible; see (Mohorcic et al., 2005).
Regarding the path loss calculation (Spillard et al.,
2005), the Free Space Path Loss (FSPL) model is
considered. Doppler effect impairment is evaluated
as in (Spillard et al., 2005).
3 SIMULATION ENVIRONMENT
To obtain error traces and subsequently the channel
error behaviour, various simulation campaigns are
needed. On the basis of previous impairment
models, a simulator was realized with Matlab tool
(MathWorks Inc., 2004). Table 1 contains
simulation parameters. The different traces were
obtained varying Doppler effect in range 1-4000 Hz
that corresponds to max mobility of 150 km/h.
Table 1: Simulation parameters.
Modulation QPSK
BW(Mhz) 20
Bit rate(Mbps) 32
Path loss (dB) -150
Eb/N0 (dB) 22
Frequency carrier (GHz) 28
Doppler effect range (Hz ) 1 - 4000
4 MARKOV CHAIN BASED
MODELS
A Markov chain is a stochastic process, where if “t”
is the observation instant, the process evolution from
instant “t” depends only from this instant and not by
previous temporal instants, in particular, in case of
DTMC (Discrete Time Markov chain) the condition
can be expressed with the following equation:
(1)
where t
k
is the selected observation instant. A
generic Markov chain can be represented by a
matrix M. This matrix is the transition probability
matrix, and it is defined stochastic matrix because it
must respect the property that the sum of elements of
each row must be equal to one, this condition is
expressed by the following equation:
(2)
This paper is not intended to be a tutorial on
different treated models, the attention is focused on
the evaluation of their performances. To more clarity
see referenced works.
5 PERFORMANCE ANALYSIS
In this section the performances of previous
presented models are discussed. The parameters of
each model is calculated by packet error traces
obtained by simulations, thus each model describes
channel error behaviour and has the capability to
generate an artificial packet error trace. For each
model a number (10 artificial traces) of artificial
traces are obtained and to make performance models
comparison, the artificial traces are statistically
analyzed and compared with the simulation trace. To
evaluate performances a set of statistical property
are considered and applied to two different random
variables elaborated by trace. The variable are B and
G, the first one indicate the error burst length and the
second one indicate the error free burst length. The
statistical property considered to make model
evaluation are the following:
- Entropy Normalized Kullback-Leibler distance:
this value, indicated in the following as ENK value,
is a statistical divergence measure between two
probability distributions. The ENK value is a metric
derived by Kullback-Leibler distance and presented
in (Khayam et al., 2003). The relation (3) allows to
calculate the ENK value:
MARKOV CHAIN BASED MODELS COMPARISON IN IEEE 802.16E SCENARIO
183
||
||
(3)
where H(p(x)) is the entropy value that normalizes
Kullback-Leibler distance D(p(x)||q(x)). The first
one is defined by:
∑
log
(4)
and instead, the second one is:
|
∑
log
⁄
(5)
In relations (3) x is a random variable defined
over an alphabet set S. Instead p(x) and q(x) are two
probability distributions defined for the random
variable x. The ENK value, as defined by equation
(3), can be computed between two distributions. In
our case we consider initially three packet error
traces obtained by simulations, we call this traces as
s
1
, s
2
and s
3
, and then compute ENK values on these
traces in this way:
9 ENK(S
1
||S
3
): S
1
is the probability distribution of
a random variable, elaborated by trace s
1
.
S
3
instead is the probability distribution
elaborated by trace s
3
.
9 ENK(S
2
||S
3
): in analogue way S
2
and S
3
are the
probability distributions evaluated on random
variable elaborated by trace s
2
and s
3
respectively.
These two values are considered as reference
values for ENK values computed over distributions
extracted by artificial traces. Thus for each model
we generate artificial trace and compute
ENK(S1||Xm) and ENK(S2||Xm), where Xm is
probability distribution derived from artificial trace.
This procedure is repeated for each model and then
the ENK values obtained from each model is
compared with the pair of values initially computed.
If the ENK(S1||Xm) and ENK(S2||Xm) are smaller
than reference values then the considered Markov
chain based model is a good model for channel, i.e.
it models channel error behaviour with good
approximation. Obviously the ENK values are
related to particular random variable and also the
goodness of model is related to variable choice, thus
we consider two random variables, and the
procedure is repeated for both B and G.
- standard error: is an error measure that can be
computed between two random variable
distributions. Standard error is used to calculate the
“distance” between artificial trace burst lengths
distribution and simulation trace burst length
distribution related both B and G variables. The
relation (6) allows to calculate this error.
∑
∑
∑
∑
·
(6)
In equation (6) x and y are random variable defined
over an alphabet set S.
- mean and standard deviation: these statistical
values were calculated, as before, both on simulation
traces random variables distributions and both on
random variables distributions related to artificial
traces generated through Markov chain based
models. Table 2 contains performances evaluations
obtained valuing statistical values previously
described. In the first column the models are
indicated and the second one contains the evaluated
random variables. In first step we consider ENK
calculation, in the rows labelled as simulation trace,
the references values are expressed, thus if a model
has ENK values smaller than reference values, it is
possible summarize that the model represents a good
channel behaviour approximation. Considering
MTA model and B random variable, we can say that
MTA is a good model because MTA ENK values
are smaller than reference values and observing the
ENK columns no one model has the same good
results for this statistical parameter. Gilbert – Elliot
model instead presents ENK values that are not
smaller than reference ones, they are small but not
enough; also FSM values are greater than reference
values, thus FSM is not a good model for B random
variable. HMM, considering B random variable,
presents the best results after MTA model, although
ENK(S
2
||X
m
) is greater than reference one for a lot.
Observing G random variable the previous
considerations on MTA are not valid, in fact ENK
values demonstrate that MTA is not a good model
inherently the G random variable, the ENK values
are excessively greater then reference ones. All the
other models have good ENK(S
1
||X
m
) values but no
one have a good ENK(S
2
||X
m
) value, although we
can see that HMM model has a value that is close to
reference one. The standard error column confirms
the best results of MTA for B random variable, and
where the other models present small errors but
greater than MTA case. Also for G random variable,
the standard error confirms that MTA is not a good
channel behaviour approximation.
The other models, in this case, are approximately on
the same floor. Mean and standard error in the sixth
and last columns respectively, confirm previous
consideration. It is interesting to note the excellent
HMM results, this model presents values that are
close to reference ones. Table results can be thus
summarized: no one model presents perfect results
in all cases, MTA obtains good results about B
WINSYS 2008 - International Conference on Wireless Information Networks and Systems
184
Table 2: Model results comparasion.
variable but deplorable results for G; the other
models obtain acceptable but non excellent results
both to B as in G case; among these models, HMM
is preferred to others for its results, thus if we must
choose a model to represent channel error behaviour
of IEEE 802.16e scenario we consider HMM the
best choice for its balanced results. In (Konrad et al.,
2001) authors demonstrate the good results of MTA
in GSM scenario, instead in (Khayam et al., 2003)
authors present the validity of Gilbert – Elliot model
in Wi-Fi scenario.
6 CONCLUSIONS
In this paper a Markov chain based models
comparison is presented. These models, that in
literature are used to describe the channel behaviour
of a particular scenario, are compared in a new
scenario. The best performances is obtained by
MTA model inherently B random variable, and by
HMM inherently G random variable, but altogether
the best results is reached by HMM. This paper
demonstrates that is not possible to say that a model
is better than the others in absolute way, but must
always relates the model to detailed scenario.
REFERENCES
IEEE 802.16e-03/07. “Amendment 4: mobility
enhancements” Draft amendment to IEEE standard for
local and metropolitan area network.
IEEE 802.16e-2005. IEEE Standard for Local and
metropolitan area networks Part 16: Air Interface for
Fixed and Mobile Broadband Wireless Access
Systems Amendment for Physical and Medium Access
Control Layers for Combined Fixed and Mobile
Operation in Licensed Bands.
F. De Rango, M.Tropea, S.Marano, 2006. “Integrated
Services on High Altitude Platform: Receiver Driven
Smart Selection of HAP-Geo Satellite Wireless Access
Segment and Performance Evaluation,” Int. Journ. Of
Wireless Information Networks.
Jean Pierre Ebert, Andreas Willig, 1999. “A Gilbert-Elliot
Bit Error Model and the Efficient Use in Packet Level
Simulation”. Tec. Report. Technical University
Berlin. Telecommunication Networks Group.
Almudena Konrad, et al., 2001."A Markov-Based Channel
Model Algorithm for Wireless Networks". In Proc. of
the 4th Workshop on Modeling Analysis and
Simulation of Wireless and Mobile Systems (MSWIM
2001), pages 28--36, Rome, Italy, July.
M. Mohorcic, T. Javornik , A. Lavric, I. Jelovcan , E.
Falletti, M. Mondin, A. Boch, L. Feletti, L. Lo Presti,
D. Merino, D. Borio, J. A Delgado Penin, F. Arino, E.
Bertran,2005.“Selection of Broadband communication
standard for high-speed mobile scenario” CAP-D09-
WP21-JSI-PUB-01, Report Capanina, February 2005.
C. Spillard, et al., 2005. “Mobile link propagation aspects,
channel model and impairment mitigation tecniques”.
CAP-D14-WP22-UOY-PUB-01, Report CAPANINA,
29 April 2005.pg 33-52.
Matlab The Language of Technical computing.
MathWorks Inc. 2004.
Syed A. Khayam, Hayder Radha, 2003. “Markov based
modelling of wireless local area networks”.
MSWiM’03, September 19, San Diego, California,
USA
L. R. Rabiner, 1989. “A Tutorial on Hidden Markov
Models and Selected Applications in Speech
Recognition, Proceedings of the IEEE, vol. 77, no. 2,
pp. 257–286.
Syed A. Khayam, Hayder Radha, 2007. “On the impact of
ignoring Markovian Channel Memory on the Analysis
of Wireless System”. IEEE International Conference
on Communications 2007, ICC ’07.
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