# Question on Signal to noise ratio (SNR)

I am trying to form the SNR expression for the system model but I am getting stucked due to presence of multiple antennas at receiver.

System model: It consists of one single antenna Transmitter, $$L$$ single antenna tags (sensors) and a receiver with $$N$$ antennas. The signal is transmitted by transmitter and received by all tags and receiver. The tags then reflects the signal towards the receiver.

My query is how to form SNR equation at receiver if we assume all the channels to be independent Complex Gaussian random variables.

Any help in this regard will be highly appreciated.

Assuming the path losses are all equal and direct with no subsequent reflections (an unlikely but simplifying assumption), the signals if correlated (phase aligned, which beam-steering would provide) will increase in power by the amount of $$20\log_{10}(N)$$ dB, while the noise contributions if independent will increase by the amount of $$10\log_{10}(N)$$ dB. Thus you will get a processing gain of $$10\log_{10}(N)$$ dB for $$N$$ independent paths.
• Thank you so much sir for detail explanation. I got your point not getting clear thoughts in framing the equation. Suppose we consider the case of single input single output (SISO ) then a received signal equation in is $y = hx +n$ and SNR becomes $\text{SNR} = \frac{|h|^2\cdot P_s}{N_w}$ where $P_s$ variance of transmitted signal and $N_w$ is AWGN variance. My query is how the SNR equation will look like in case of the given system model.