CDMA with Noise
COMP 5416 Week 9
In the class, we have considered CDMA in an ideal system. However, in reality, we have much more complicated scenario: Users will experience noise.
Consider the scenario with one sender and one receiver. The chipping sequence is (-1 -1 -1 +1 -1 +1 +1 +1). Suppose the sender sends bit ¡°1¡±, then the signal sent will be (-1 -1 -1 +1 -1 +1 +1 +1). In the channel, noise is added to the signal so that the received signal will be (-1+n1 -1+n2 -1+n3 +1+n4 -1+n5 +1+n6 +1+n7 +1+n8), where n1, …, n8 are noise terms. They are independently normally distributed with zero mean and ¦Ò2 variance, in this question, ¦Ò2 = 1. Formally, ni ~ N(0, 1). You should know the normal distribution in a prerequisite course.
After the computing the inner product at the receiver, what ¡°value¡± does the receiver derive? If the value is smaller than 0, it is decoded as -1, otherwise, it is decoded as 1. Use the provided table to find the probability that it is wrongly decoded as -1.
The tail probability (Q function) of a standard normal distribution is given in the attached q_function.pdf.