Mobile Radio Channels Modeling in MATLAB

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_kostovmail.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 riat the ith time in-stant can be represented as 22)(iiiyxr += , (1) where is the amplitude of the specular component and xi, yiare samples of zero-mean stationary Gaussian random processes each with variance 02. The ratio of specular to defuse energy defines the so-called Rician K-factor, which is given by RADIOENGINEERING, VOL. 12, NO. 4, DECEMBER 2003 13 2022/ =K . (2) The best- and worst-case Rician fading channels associated with K-factors of K = and K = 0 are the Gaussian and Rayleigh channels with strong LOS and no LOS path, res-pectively. So, the Rayleigh fading channel can be conside-red as a special case of a Rician fadi