CALIFORNIA STATE UNIVERSITY, NORTHRIDGE FADING CHANNEL CHARACTERIZATION AND MODELING A graduate project submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical Engineering By Chau Vo December 2012 Graduate project of Chau Vo is approved: ________________________________________ _______________________ Prof. James Flynn Date ________________________________________ _______________________ Prof. Xiyi Hang Date ________________________________________ _______________________ Prof. Sharlene Katz, Chair Date California State University, Northridge ii Table of Contents Signature Page .................................................................................................................... ii Abstract .............................................................................................................................. iv 1. Introduction ................................................................................................................. 1 2. Background .................................................................................................................. 2 2.1 Large scale fading ................................................................................................ 3 2.2 Small scale fading ................................................................................................ 4 2.2.1 Time spreading of the signal ......................................................................... 6 2.2.2 Time variance of the channel ........................................................................ 7 2.3 Performance over a slow and flat fading channel ................................................ 9 2.4 Modeling a BFSK and BPSK with Simulink ..................................................... 11 3. Rayleigh fading channel ............................................................................................ 14 3.1 Performance of Rayleigh fading channel ........................................................... 14 3.2 Modeling a Rayleigh fading channel with Simulink .......................................... 16 3.2.1 Block descriptions ....................................................................................... 16 3.2.2 Bit Error Rate Tool in Simulink.................................................................. 17 3.2.3 System design ............................................................................................. 22 4. Rician fading channel ................................................................................................ 27 4.1 Performance of Rician fading channel ............................................................... 27 4.2 Modeling a Rician fading channel with Simulink .............................................. 29 4.2.1 Block descriptions ....................................................................................... 29 4.2.2 Bit Error Rate Tool for Rician fading channel............................................ 30 4.2.3 System design ............................................................................................. 32 5. Summary and Conclusion .......................................................................................... 36 Bibliography ..................................................................................................................... 37 iii ABSTRACT FADING CHANNEL CHARACTERIZATION AND MODELING By Chau Vo Master of Science in Electrical Engineering Multipath fading is one of the significant factors that affect the performance of a wireless communications link. Theoretical results exist for calculating link performance in the presence of a fading channel for some modulation schemes and some types of fading. In other cases, link performance must be evaluated by simulation. Mathworks’ Simulink is one tool used for these simulations. Mathworks provides pre-constructed blocks for both Rician and Rayleigh fading which accept parameters defining these fading models. The proper use of these blocks to include the parameters that define fading channels has been described. These blocks make it easy to model complex fading systems. Simulation results for link performance obtained using these channel-modeling blocks in BPSK and BFSK systems correspond closely to the theoretical results. The work presented here should be of interest to others studying wireless communications. iv 1. Introduction Multipath fading is one of the significant factors that affect the performance of a wireless communications link. Theoretical results exist for calculating link performance in the presence of a fading channel for some modulation schemes and some types of fading. In other cases, link performance must be evaluated by simulation. Mathworks’ Simulink is one tool used for these simulations. Mathworks provides pre-constructed blocks for both Rician and Rayleigh fading which accept parameters defining these fading models. This project studies the use of the various fading channel models available in Simulink. Section 2 of this report provides theoretical background on large and small scale fading. Section 2 also introduces the use of Simulink as a tool for modeling communications links. Section 3 presents the theoretical model of a Rayleigh fading channel and its effect on link performance. These results are compared to those obtained from the Simulink model. Section 4 presents a similar comparison for a Rician fading channel. Section 5 presents the summary and conclusions. 1 2. Background In wireless communications, a signal often undergoes reflection, diffraction and scattering from the buildings, trees, mountains, etc. when propagating from a transmitter to receiver. Therefore, multipath signals will arrive at a receiver with different amplitudes and phases. This phenomenon is referred to as multipath fading. Figure 1 characterizes two types of fading: large scale fading and small scale fading [1]. Large scale fading represents the path loss due to motion over large areas. Small scale fading refers to large changes in the amplitude and phase of a signal caused by a small change in the position of the transmitter or receiver. Small scale fading has two manifestations: time spreading of the signal and time variance of the channel. Fading channel manifestations Large scale fading Small scale fading Mean signal Variations Time spreading Time variance attenuation about the of the signal of the channel vs distance mean Time delay Frequency Time Doppler domain domain domain shift domain Frequency Flat Frequency Flat Fast Slow Fast Slow selective fading selective fading fading fading fading fading fading fading Figure 1: Fading manifestations 2 2.1 Large scale fading Large scale fading represents the path loss of a signal affected by large objects, like hills, forests, buildings, etc. between a transmitter and receiver. It occurs when a mobile transmitter and/or receiver moves over long a distance, resulting in rapid fluctuations in the received signal’s envelope. In mobile communications, large scale fading occurs in urban, outdoor-to-indoor and indoor environments. For both indoor and outdoor channels, the mean path loss ̅̅ ̅( ), as a function of distance, d, between a transmitter and receiver, is directly proportional to the nth power of the ratio of the distance from the transmitter to the receiver and a reference distance d0, as shown in equation 2.1 [1]. This equation was developed based on Okumura’s path-loss measurements. ̅̅̅ ( ) ( ) (equation 2.1) ̅̅̅ or, in decibels: ( ) ( ) ( ) where ( ) = ( ) and n is the path loss exponent described below. The free path loss model assumes that the region between a transmitter and receiver is free of all objects that can absorb or reflect power. In addition, the atmosphere is assumed to be as a non-absorbing medium and its reflection coefficient is negligible. Typically, the value of the reference distance, d0, is 1km for large cellular radio cells, 100m for microcells, and 1m for indoor channels. The path loss exponent, n, depends on the frequency of the propagating signal, antenna height, and propagation environment (in free space n = 2). The value of n can be higher than 2 if there are 3 obstacles between the transmitter and receiver. Table 1 shows the typical large scale path loss over some environments [2]. Environment Path Loss Exponent, n Free space 2 Urban area cellular radio 2.7 to 3.5 Shadowed urban cellular radio 3 to 5 In building line-of-sight 1.6 to 1.8 Obstructed in building 4 to 6 Obstructed in factories 2 to 3 Table 1: Path loss exponents for different environments 2.2 Small scale fading Small scale fading refers to large changes in the amplitude and phase of a signal caused by a small change in the position of the transmitter or receiver (on the order of half a wavelength). This effect is due to constructive and destructive interference of the transmitted signal that occurs at very high carrier frequencies (900 MHz or 1.9 GHz for cellular). Figure2: Multipath fading 4 Both Rayleigh and Rician fading are used to model small scale fading. Figure 2 illustrates multipath fading between a transmitter and receiver. There are line of sight (LOS) or direct paths and non-line of sight (NLOS) paths where the transmitted signal is reflected by obstacles. If there is no line of sight path among the multiple paths between a transmitter and receiver, a Rayleigh fading model is used. Rician fading is used when there is a strong line of sight path between the transmitter and receiver. Small scale