The analysis of method to obtain the original singal from a strong interference

Now if we want to transfer a signal to another place but there exist a strong interference field between two place. so how to obtain the original singal?
firstly ,let us generate a sinusoidal signal using matlab
and the image is like this

Then if we assume that there exist a random noise which is very large and have the pdf of normal distribution,And the composite signal may seemed very complexand terrible


so how to obtain the original signal?
we konw y1 = y + n
for which y is the oringal singal and n is the noise obeying normal distribution, so y1 is also distributed normally with
E(y1) = y
var(y1) = var(n) = 10.
so we can repeat this process to get signal y2,y3…yn,with the same expectation and varance.
if we create a funtion
y=(y1+y2+y3+…yn)/n*
so E(y*) = ( E(y1) + E(y2) +…E(yn) )/n = y;
var(y*) = ( var(y1) + var(y2) +…var(yn) )/n^2 = var(y)/n
if n goes to infinite, var(y*) will close to 0;
which is similar to do the measurment in physics experiment.we need to measure one thing for many times and obtain the mean value, which is close to the ture value because the varance of mean value decrease with the increasement on measurement times.


oh look we can obtain the original signal roughly,and if we do this process for 1 000 000 times?

The image is relatively better than before.so if we repeat this process for more time, we can get the original signal preciesly.
However,this method is considerabley time-costing especially for the situation that the noisy is very large.