# BER Analysis of Dual hop Decode and Forward Relay

I want to perform fair BER analysis between Two-hop Decode and Forward relay communication (S-->R-->D) and Direct Transmission from S-->D. The links have Rayleigh fading. Now for fair analysis 1) Total Transmit Power is kept same 2) Rayleigh Channels with distance are considered for each link.

In the literature,BER vs (Average SNR) is plotted.

How do I calculate Average SNR for dual hop transmission?

and Can I plot BER vs Transmit power?

• Is this a "Do my research project for me" question? – Dilip Sarwate Oct 6 '15 at 16:57
• No, actually I am working on Dual Hop Spatial Modulation and I did some analytical proof. But my analytical and simulation plots for BER vs SNR do not match. Also, I am comparing my approach with direct transmission. So, to have fair analysis I want to make sure I am doing it in correct way. Therefore, if I understand for Dual hop Decode and Forward, I can apply same principle for dual hop Spatial Modulation. – Kunal Oct 7 '15 at 5:01

I am working with a similar kind of network. I don't know if it is correct, but I think the most proper way is to consider the SNR from the first transmitter, not considering what the relay do to the signal. This because you want to analyze the performance of the end-to-end communication. SO you send the signal with some energy, and you want to know the performance of your signal once you have sent it with that energy.

That's the way I am doing, and comparing it to the direct transmission, I am getting a very similar performance: a difference of less than 1dB for the same BER.

I am not amplifying the signal in the relay, so I am just doing the decode and forward (DF). I think it is reasonable to get this "worst" performance in the DF relay compared to the direct transmission because you have two channels, therefore you have two components of noise. You perform the DF in the relay, but it can decode wrong.

Let me know if this answer was useful, and if you have any more questions. I am not an expert in this area, but I am working on it.

• But as distances Source-Relay and Relay-Destination are reduced, which improves SNR. Consider some SNR value for direct transmission. Now if we consider relay exactly in half way, effective SNR between Source-Relay and Relay-Destination can be calculated as using large scale fading as SNR_SR=0.5*SNR*(1/distSR)^2 and SNR_RD=0.5*SNR*(1/distRD)^2. Here, transmission power is considered half for fair comparison with direct transmission. – Kunal Nov 6 '15 at 5:12
• Yes, you are right. I don't think that my answer is correct. But it seems that you figured out the solution. If it is true, could you please write a complete and detailed answer, with resources and etc. So people can understand better the solution. – JohnMarvin Nov 7 '15 at 12:19

Let the channel between node $$X$$ and $$Y$$ is denoted by $$h_{XY}\sim\mathcal{CN}(0,1)$$, then the SNRs between $$S\rightarrow R$$, $$R\rightarrow D$$ and $$S\rightarrow D$$ are given by $$\frac{|h_{SR}|^2P_{SR}}{\sigma_n^2}$$, $$\frac{|h_{RD}|^2P_{RD}}{\sigma_n^2}$$, and $$\frac{|h_{SD}|^2P_{SD}}{\sigma_n^2}$$. Then, the average SNR would be $$\frac{P_{SD}}{\sigma_n^2}$$, where $$\sigma_n^2$$ is the AWGN power. Note that $$P_{SR}=P_{RD}=\frac{P_{SD}}{2}$$ for the two systems to have the same total power budget.

You will need to think about what model you want for the dependence of errors on one hop on the second hop. For instance, the simplest model might be to assume that errors are independent on the two hold. In that case, think about how the BER for the entire link can be determined by the BER in each link.

Hopefully, this gives you enough information to move forward.