By definition, the noise is the unwanted signal that contaminates the original signal causing false decision on the information contained by the original signal at the receiver. There are two types of noise according to their source. The noise is said to be intrinsic if it is generated in the communication devices such as the thermal, the shot and the 1/f noise generated in the resistive elements inside the electronics. This is because of the statistical nature of the electronic conduction in the element of the circuits. The second type of noise is the extrinsic noise which arise from interference of the other signal sources that might be exiting in the same space and time of the original signal. The intrinsic noise is simply called noise and the extrinsic noise is called simply interference signal.
So, at any point of the path between the transmitter and the receiver there is a value for the wanted signal power , say S and there is noise N and interference signal power I.
The mot important point is the point of the decision on the information value of the symbol in the receiver. Ideally at this point theoretically speaking one has to make N=0 and I=0. you can eliminate the interference if it is known. If it is unknown you can measures it and subtract it from the signal. It is the correlation between your signal and interference that can not be eliminated. If the interference and S are not correlated then a correlator can render I =0.
The intrinsic noise can be reduced by using low noise devices and matched filters.
Since the received signal r = s + N + I , and I can be made ZERO if is not correlated to S, then The total noise limit is determined by N. Then N sets the ultimate sensitivity of the receiver.
It is observer that the signal to noise plus interference ratio S/[i+N] at the input of the decision device in the receiver is the performance parameter that defines the bit error ratio.
the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power (from all the other interfering signals) and the power of some background noise.
If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR).
Conversely, zero interference reduces the SINR to the signal-to-noise ratio (SNR)
SINR is commonly used in wireless communication as a way to measure the quality of wireless connections.