The Trans and receive circuitery are sufficiently in isolation when system is used in duplex mode (This is the general case ). Hence The sender effectively does not see the detector and a vice versa.  Both paths have independent SNR.

If it is switched system between trans & receive, then, there will be three cases

1) From sender side 2) From reverse path (Reception side 3) Transition of switching

All three SNR will be different 

Thank you for your answer, can you please provide me some references.

Here I ask the question otherwise,

I am trying to get "SNR" expression at the destination of the system at the pic above; described as follow

- ""No direct link""

- DetF relay (detect & forward)

- half-duplex

- AWGN n1 (Source - relay) & n2 (relay - destination)

- fading channels ; h1 (Source - relay) & h2 (relay - destination)

best regards

• I'm not sure whether the detect & forward means "decode and forword".
• If yes, the end-to-end SNR is the min of SNRs for each hop.
• In your system, this can be expressed as min{P1 * |h1|^2, P2 * |h2|^2}. Here I use P1 and P2 to denote the transmit power of S and R and assume unit noise variance. 
• Hope this can help you. Good luck~

Thank you!

Dear Student,

Please use this formula for finding the SNR.

Output PSD = Input PSD * Trasfer Function ^2

Your case R(f) = S(f) * |H1(f)|^2

and      D(f) = R(f) * |H2(f)|^2 Where H1(f) and H2(f) are the channel impulse responses

Thank you!

Hello,

Power in destination of desired signal is abs(h1)^2*abs(h2)^2*pt

noise power in destination is w1 (in relay)*h2+w2 (in destination)

Total noise power in destination is: Pw1*abs(h2)^2+Pw2

Above expression is valid for independent case of two channels between source-relay and relay-destination.

thank you

As per my understanding of the relaying systems,

The SNR, represented by $\gamma$ of any link (SR (source to relay) or RD (relay to destination)) would be dependent on the channel gain h, corresponding transmitter power P and Noise power N_o or $\sigma^2$, according to the following formula $\gamma=P|h|^2/N_o$. First you need to find the $\gamma_{SR}$ and $\gamm_{RD}$

Then, for Decode and Forward case, end to end SNR calculated at the destination $\gamma_{D}$ is the minimum of both $gamma_{SR}$ and $\gamma_{RD}$.

For AF case you need to use this formula,

$\gamma_{D}=(\gamma_{SR}*\gamma_{RD})/(\gamma_{SR}+\gamma_{RD}+1)$

I hope this is answer to your question.

Correct me if anything is wrong.

Thanks