I want to know what is the formula of received signal by node j separed by distance d from a source i in wsn.
sometimes I find this formula: yij=hij * x+nij
in another yij=sqrt(p * gamma)* hij*x+nij ; where p is the source transmit power and gamma is the pathloss
another formula is yij=sqrt(p) * hij * x+nij ; where p is the source transmit power
They are all valid for analysis purposes. Usually, if you say that x has normalized power, then you include sqrt(p), such that the signal-to-noise ratio (SNR) is P/N, where N is the noise power. Some like to make it more practical by including the pathloss, but I think unless the analysis is about the pathloss, and shadowing effect, it's not necessary to be included. It's just a scaled factor in RF channels.