Probability of Error Analysis Using a Gauss-Chebyshev Quadrature Rule

摘要

One of the most important steps in designing a communication system involves analyzing the error performance of the system to determine if it meets requirements. There are many techniques to accomplish such analysis and the most desirable one is that which can be used quickly and efficiently. This thesis examines one method of error performance analysis that utilizes the two sided Laplace transform of the probability density function (PDF) of a decision statistic. Additionally, a Gauss-Chebyshev quadrature rule is utilized to attain the error probability. This method is used to find the error performance of several communication systems of varying complexity in order to verify the use of the method and investigate its implementation. The models considered are antipodal baseband signaling in additive white Gaussian noise (AWGN), BPSK in AWGN and an imperfect carrier reference in the receiver, and BPSK and NFSK in AWGN with Rayleigh fading. The results are implemented using a computer and are compared to known results. All results are shown to match theoretical results. Additionally, up to a 99% computational time savings was realized using this method to analyze error performance of the BPSK case with an imperfect carrier reference in the receiver.