On the Correlation Characteristics of Random Binary Sequences
DEI PhD Student
DEI - 3B Room
November 16th, 2011
In this seminar I will present a study on the correlation of random binary sequences obtained by clipping input noise sequences.
The problem is to generate a set of binary sequences with a desired cross-correlation by the use of a set of random noise input processes. The binary sequences are obtained by a non-linear operation (thresholding or clipping) applied to the input noise processes. From a general point of view, the operation of clipping a process with a gradual or hard threshold is an operation which has sensible effects on the process spectrum and, consequently on its correlation.
Referring to the theory of noise clipping, the relation between the input process covariance and the output covariance of the clipped sequence is discussed. For the particular case of generating binary sequences from random input processes, the solution to the problem is derived by a series expansion of the joint probability density function of the input process. The series solution allows one to solve the inverse problem of deriving the correct input correlation to obtain a desired covariance after the non-linear transformation.