| # Signal to Interference plus Noise Ratio (SINR) in Wireless Communications Consider a cellular wireless network with transmitter/receiver pairs. Transmit powers are denoted as . Transmitter is supposed to transmit to receiver , but due to interference, signal from the other transmitters is also present. In addition, there is (self-) noise power in each receiver. To measure this, we form the Signal to Interference plus Noise Ratio (SINR) at each receiver. This takes the form where is a measure of the (desired) signal power received from transmitter , is the total signal power received from all the other receivers, and is a measure of the receiver noise. The SINR is a (in general, complicated) function of the power used at the transmitters. ## A Linear Model We can express the SINRs at the receivers in terms of the powers more explicitly by assuming that the received powers , are linear functions of the transmit powers . The model (also known as the Rayleigh fading model) states that and where the coefficients , are known as the path gains from transmitter to receiver . ## A posynomial function The SINR functions are not posynomials, but their inverse are.