SNR_BER

BER and SNR graph

Generate a series of long data sequence e.g. 15k or20k sized vector to simulate randomly occurring binary
series of ±1. Note like in practical situation bothlevels should be equally probable. What is the signal
power?
Now add noise to it; another random sequence of same size i.e. 15k or 20k sized vector with 0 mean and
variable variance. Note for zero mean random variable, noise variance also equates to noise power as
studied in lecture. Hence, by varying its variance you can have noise at specific number of dBs below the
signal to create various SNR ratios. You will keep the fixed signal power of specific value, the wholetime
and vary just the noise, to generate different SNR values. Or you can do just the opposite and fix noise with
particular variance or power and vary your signal power.
Now for a particular value of SNR add this noise tosignal (since noise is additive -AWGN) simulating the
effect of channel noise and noisy signal vector of size 15k or 20k reaching the receiver.
Now implement your own simple receiver decision process based on Maximum Likelihood principle. It is
obvious that from the noisy signal vector received,Rx will map everything to one of legitimate signals
based on whether they are above or below zero. E.g.
-0.2 will be mapped to -1 while +2.1 will be mappedto +1.
Now you can find your practical BER by seeing that out of the 15k or 20k Txed sequence, in how many
occasions Rx made an error i.e. incorrectly took +1for a -1 (due to noise shifting signal more closerto -1)
or viceversa.
Bit Error Rate= instances receiver made error/20 k bits sent.
For various SNR values you should be able to plot graph with SNR on x-axis and BER on y-axis. Plot this
graph. Does the graph differ from the theoretical graphs (you can consult books for this). Why or why not?
Justify your answer in both cases.