Gaussian Random Numbers and Filtered GaussianNoise Wireless Channel models:A Hardware Perspective

Sammanfattning: This thesis comprises two distinctive but interrelated parts:1. Gaussian Random Number Generators (GRNGs)Gaussian Distributed Random Numbers (GRNs) are required for simu-lations in a wide variety of applications. This is because, almost invariably,the processes in nature tend to be a summation of underlying discernible ornon-discernible sub-processes and by virtue of central limit theorem, the sumof sufficiently large random variables tend to become Gaussian distributed. Inthis thesis, we will provide a detailed account of published work on differentarchitectures and methods for generating GRNs in hardware. Contributionsin thesis include:• Improvements in the widely used Box Muller (BM) based GRNGs.• A novel GRNG that combines BM and CORDIC algorithm.• A framework that has been developed to generate GRNs using Cen-tral Limit Theorem. Deviation (error) from ideal Gaussian probabilitydensity function that arises when n Uniformly distributed numbers areadded is computed off-line This error is then corrected in real time re-sulting in GRNGs that exhibit very high accuracy at a low hardwarecost. Using the framework we have demonstrated four different hard-ware implementations of five GRNGs using above framework. Theseprovide varying tail accuracies while consuming much less hardware re-sources than any of the previously published designs.• A novel GRNG that combines CLT and CDF-Inversion algorithm.• A novel GRNG that utilizes only multiplexers and elementary logic gatesto produce GRNs with high tail accuracy at low hardware cost.2. FGN wireless channel modelRadio Channel simulation has always been an extremely important partof testing and evaluation of wireless communication systems. Ever-increasingdemand for higher quality of service and the emergence of new radio standardshave further pushed the need for efficient and accurate software/hardwaresolutions to model signal propagation behavior in radio channels. A popularmodel to simulate Rician/Rayleigh channels is the so called Filter GaussianNoise (FGN) model.In this thesis, we will show how the performance of FGN hardware simula-tors can be improved by optimizing various hardware blocks including DopplerFilters, interpolation filters and random number generators. We will verifythe optimized designs, both analytically and through simulations, to showthat the modifications do not cause any degradation in important simulatorperformance parameters. These include first-order statistical properties likethe probability density function (PDF), and second-order statistical proper-ties like the autocorrelation function.