12 N. KOSTOV, MOBILE RADIO CHANNELS MODELING IN MATLAB
Mobile Radio Channels Modeling in MATLAB
Nikolay KOSTOV
Department of Radio Engineering, Technical University of Varna, Student 1, 9010 Varna, Bulgaria
n_kostov@mail.bg
Abstract. In this paper, a MATLAB based approach for
mobile radio channels modeling is presented. Specifically,
the paper introduces the basic concepts for modeling flat
fading channels in MATLAB by means of user-defined m-
files. Typical small-scale fading channel models are deri-
ved such as uncorrelated Rician fading channel and Ray-
leigh fading channel with Doppler shift. Further, simple
and useful MATLAB constructions for approximation of
cumulative distribution functions (CDFs) and probability
density functions (PDFs) are also given. Finally, a MAT-
LAB based Monte Carlo simulation example is presented,
which comprises performance estimation of phase shift
keying (PSK) signaling over a Rician fading channel.
Keywords
MATLAB, fading channels, distribution, simulation.
1. Introduction
In digital communication theory the most frequently
assumed model for a transmission channel is the additive
white Gaussian noise (AWGN) channel. However, for ma-
ny communication systems the AWGN channel is a poor
model, and one must resort to more precise and complica-
ted channel models. One basic type of non-Gaussian chan-
nel, which frequently occurs in practice, is the fading chan-
nel. A typical example of such a fading channel is the mo-
bile radio channel, where the small antennas of portable
units pick up multipath reflections. Thus, the mobile chan-
nel exhibits a time varying behavior in the received signal
energy, which is called fading.
Using MATLAB for digital communication systems
simulation one has the advantage of exploiting the power-
ful features of its Communications Toolbox along with
a nice programming language. However, the Communica-
tions Toolbox of MATLAB suffers from absence of proper
mobile channel models. The only available channel model
in the current Communications Toolbox 2.1 is the awgn m-
file, which is appropriate for an AWGN channel simula-
tion. So, the users of MATLAB should build appropriate
channels (i.e., m-files) in their own to reach the desired
simulation model.
The paper is organized as follows. In Section 2, a
brief introduction to fading channels is given. The basic
concepts for modeling flat fading channels in MATLAB
are presented in Section 3. In this section, example m-files
are proposed to model different types of flat fading chan-
nels. In Section 4, a MATLAB based Monte Carlo simula-
tion example is presented, which describes the basic con-
cepts of digital modulations performance estimation over
fading channels. Finally, the concluding remarks are given
in Section 5.
2. The Mobile Radio Channel
The mobile radio channel is characterized by two
types of fading effects: large-scale fading and small scale
fading [1], [2]. Large-scale fading is the slow variation of
the mean (distant-dependent) signal power over time. This
depends on the presence of obstacles in the signal path and
on the position of the mobile unit. The large-scale fading is
assumed to be a slow process and is commonly modeled as
having lognormal statistics. Small-scale fading is also cal-
led Rayleigh or Rician fading because if a large number of
reflective paths is encountered the received signal envelope
is described by a Rayleigh or a Rician probability density
function (PDF) [3]. The small-scale fading under conside-
ration is assumed to be a flat fading (i.e., there is no inter-
symbol interference). It is also assumed that the fading le-
vel remains approximately constant for (at least) one sig-
naling interval. With this model of fading channel the main
difference with respect to an AWGN channel resides in the
fact that fading amplitudes are now Rayleigh- or Rician-
distributed random variables, whose values affect the signal
amplitude (and, hence, the power) of the received signal.
The fading amplitudes can be modeled by a Rician or
a Rayleigh distribution, depending on the presence or ab-
sence of specular signal component. Fading is Rayleigh if
the multiple reflective paths are large in number and there
is no dominant line-of-sight (LOS) propagation path. If
there is also a dominant LOS path, then the fading is Ri-
cian-distributed. The fading amplitude r
i
at the ith time in-
stant can be represented as
22
)(
iii
yxr ++=
β
, (1)
where
β
is the amplitude of the specular component and x
i
,
y
i
are samples of zero-mean stationary Gaussian random
processes each with variance
σ
0
2
. The ratio of specular to
defuse energy defines the so-called Rician K-factor, which
is given by