General formula for distribution of the Correlator outcome in DSSS-CDMA

Abstract

The Direct sequence spectrum (DSSS) systems are using a sequence to present a bit. These sequences are orthogonal. Base on the orthogonality of these sequences, multiple users can use a single channel simultaneously. There are different methods to generate these orthogonal sequences. One of the well known methods is using chaotic sequences. A chaotic sequences are generated by using a seed value and a mapping function. The seed acts as a initial value for the mapping function. Then, the map function makes a sequence with an infinite number of elements. In addition, by using different seed, it can make orthogonal sequences. The common sequences have a determined probability density function (pdf). So, in the performance analysis of DSSS system, they are considered as a random variable (r.v) with known pdf. Also, in analyzing DSSS systems’ performance, it is common to find the distribution of the correlator output which represents the decision variable. The decision variable can be expressed as a combination of multiple random variables (r.v.s). In addition, it is very frequent in DSSS studies to find the distribution of r.v.s combination. Therefore , we have been motivated by these characteristics of the decision variable to develop a general formula for calculating the mean and variance of combinations of r.v.s. These two parameters are sufficient to characterize the density function of the correlator output in the case when this function is Gaussia. This case happens when the decision variable is a sum of a large number of random variables.