International Journal of Computers and Applications, Vol. 31, No. 4, 2009 A COMPARATIVE STUDY OF DIFFERENT RAYLEIGH FADING CHANNEL SIMULATORS R. Gupta * and A. Trivedi ** Abstract In this paper, we have presented a comparative study of four different Rayleigh fading channel simulation methods with respect to computational complexity and accuracy. Fidelity of the various simulators is examined in terms of confidence interval also. The sum-of-sinusoids (SOS)-based simulation method can accurately generate a very long sequence without any impact on computer memory usage. The inverse discrete Fourier transform (IDFT)- based simulator is relatively fast and able to generate a sequence corresponding to a given autocorrelation function (ACF). However, its applicability is limited due to large memory space requirement. For small sequences, algorithm based on covariance matrix is most efficient but its time complexity grows many folds as the sequence length is increased. Autoregressive modelling (AR) of fading process is needed when time evolution of fading process is exploited for channel tracking. The accuracy of the generated sequence ACF using the above four methods is also compared through an example. Key Words Channel models, Rayleigh fading, sum of sinusoids, AR process, autocorrelation function 1. Introduction Modelling of a physical fading radio channel plays a sig- nificant role in the simulation studies of wireless mobile communication systems. Amplitude of the received en- velope of a fading signal is Rayleigh distributed in most of the cases. The second order statistics of the fading process, i.e., correlation function, generally depends on the propagation geometry, the velocity of the mobile, and the antenna characteristics. The sum-of-sinusoids (SOS)-based model [1] is com- monly used when correlation statistics of the fading pro- * Department of Electronics Engineering, Madhav Insti- tute of Technology and Science, Gwalior, India; e-mail: rekha652003@yahoo.com ** Department of Information Technology, ABV Indian Institute of Information Technology and Management, Gwalior, India; e-mail: atrivedi@iiitm.ac.in Recommended by Dr. Lonnie Welch (paper no. 202-2359) cess is required to be generated in accordance with the Clarke’s wide-sense stationary (WSS) isotropic scattering model [2]. Smith [3] introduced an easy way to simulate Clarke’s model using inverse discrete Fourier transform (IDFT) operations. In contrast to SOS method, this sim- ulation technique can be extended to the fading process with any arbitrary autocorrelation function (ACF). A new improved method was proposed by Young and Beaulieu [4] using the concept of Smith. This method considerably re- duces the simulation time, but it was found that the ACF of the generated sequence does not completely match with the desired one. In this paper, we apply the IDFT algo- rithm in a different manner, which is simpler and performs better with respect to the accuracy of ACF. A different simulation approach which is known as covariance matrix method is proposed in [5]. In this method, fading sequence is generated by decomposing a covariance matrix which is constructed according to the desired ACF. The implementation of channel estimation using Ka- man filtering motivated the development of the channel simulator based on autoregressive (AR) modelling [6]. In this approach, a white Gaussian random process is passed through the AR process generator [7], which is designed according to the desired ACF. This paper presents the comparative study of various simulators with respect to computational complexity and accuracy of the generated sequence ACF. The correlation properties of a simulator converge to the desired ones when a large number of random observations are used for ensemble average. It has been found that for a given number of independent observations, the ACF of the SOS- based and covariance matrix-based methods lie well within the desired confidence limits for all possible values of lag. Impact of simulators’ correlation statistics in application simulation systems is demonstrated by undertaking the problem of channel estimation in orthogonal frequency division multiplexing (OFDM) system. The paper is organized as follows: Section 2 briefly re- views the various simulation models. Simulation details and the performance comparison are presented in Sections 3 and 4, respectively. Section 5 describes the task of channel estimation in OFDM. Conclusions are drawn in Section 6. 222