DESIGN AND PERFORMANCES ANALYSIS OF HIGH SPEED AWGN COMMUNICATION CHANNEL EMULATOR Adel Ghazel (1) , Emmanuel Boutillon (2) , Jean-Luc Danger (3) , Glenn Gulak (4) , Hédi Laamari (1) (1) UTIC - Ecole Supérieure des Communications, Rte de Raoued km 3.5 – 2083 El Ghazala –Tunisia (2) LESTER. University of Bretagne Sud, 56100 Lorient, France (3) ENST PARIS, Ecole Nationale Supérieure des Télécommunications 46 rue Barrault, 75634 PARIS CEDEX 13, France (4) EECG, University of Toronto, 10 King's College Street Toronto, M5S 3G Ontario adel.ghazel@supcom.rnu.tn, emmanuel.boutillon@univ-ubs.fr, danger@enst.fr, gulak@eecg.toronto.edu Abstract A Gaussian noise generator model adapted to hardware implementation is developed for mobile communication channel emulation in FPGA circuit. High accuracy is reached for the random distribution by combining the Box-Muller and Central limit methods. The proposed present model is based on reduced computation operations and memories in order to get a fast and low-cost emulation plat-form. The performance of the designed model is investigated by MATLAB simulation. The complexity and the performance level are given for some configurations and show the interest of the proposed model. 1 Introduction The software estimation of the performances of a communication system is very time consuming. Indeed, with a Monte-Carlo simulation, an accurate (+-3.3%) estimation of a Binary Error Rate around 10 -6 needs 10 9 iterations. Moreover, many variables (sampling frequency, digital format, carrier resolution, rounding and quantification etc.) have to be optimized for satisfying the best trade-off between performances and complexity. In order to speed up the final parameter optimization of a design, we proposed to perform direct hardware simulation (emulation) on a FPGA. Such a simulation needs a hardware emulation of the communication channel. In this paper, the authors (a joined research group with ENST- Paris (France), SUP’COM (Tunisia), LESTER (France) and the University of Toronto (Canada)) focus their attention on the design of a "high quality" White Gaussian Noise Generator (WGNG). The "high quality" WGNG considered in this paper is the generation of a random variable X with the following characteristics: - at least b=6 bits of resolution after the decimal point, - a periodicity of the WGNG greater than 2 48 samples (function rand48 of C ANSI), - a flat spectrum. - a “(4σ, 1%) normal like probability density function (p.d.f.)” i.e. the absolute value of the relative error ξ X (x) defined as: ) )( 1 , 0 ( ) )( 1 , 0 ( ) ( ) ( x N x N x X x X - = ξ (1) between the p.d.f. of X and the normal distribution N(0,1) - mean 0 and standard deviation σ = 1 - is less than 1% for all |x| < 4σ . With the use of this WGNG, the Additive White Gaussian Noise (AWGN) channel can be emulated as well as more complex channels like Rayleigh channel and Ricean channel (using filtering and appropriate mathematical functions [1]). Sections 2 and 3 briefly present the two well-known methods for generating a Gaussian noise, namely, the central limit and the Box-Muller methods, and give some developments for achieving better accuracy. Section 4 presents an efficient combination of the two methods. Performances and hardware complexity are evaluated. 2 Central limit based method The central limit theorem tell us that if X is a real random variable (r.v.) of mean m x and standard deviation σ x , the random variable (r.v). X N defined as: ∑ - = - = 1 0 ) ( 1 N i x i x N m x N X σ (2) where x i , i=0..N-1 are N independent determinations of the variable X, tends toward the normal distribution N(0,1, when N tends toward infinity. The central limit theorem gives a very simple method to generate a white gaussian noise. Indeed, it is well known that a Linear Feedback Shift Register (LFSR) of length l can generate a very good random like binary variable of periodicity 2 l -1. The concatenation of q different LFSRs, gives a q bits vector U q . This vector can be seen as a random variable uniformly distributed over {0, 1, 2, .., 2 q -1 }. Thus, the random variable U q N obtained using (2) with N independent determinations of U q leads, after appropriate scaling, to a good approximation of N(0,1) if N is large enough. Figure 2 shows the ξ X (x) function obtained for X=U q N , with q=8 and N=2, 4, 8, 16, 32.