# How does subcarrier correlation affect the BER of OFDM?

I am studying the OFDM system and would like to examine it under different subcarrier correlation scenarios. I have calculated BER for the uncorrelated scenario and now I have rewritten it for the correlated channel.

If there is no noise, BER shoud be 0. It works for the uncorrelated scenario. Why does it not work for the correlated scenario?

OFDM subcarriers are packed relatively tightly together. If you look at the original OFDM signal in the frequency domain, you may wonder why adjacent subcarriers are not interfering with each other. The answer is that subcarriers are orthogonal to each other. Even adjacent subcarriers, have 0 influence on each other, and are independent in that sense.

It can be proven that OFDM is the most efficient way to pack these subcarriers together in the sense that it is the smallest inter-subcarrier spacing whereby the subcarriers can all be orthogonal to each other.

So then, in the real world, during transmission, things may happen besides getting white noise added, that cause the subcarriers to lose orthogonality to each other, and become correlated at the receiver. Probably your textbook would explain what may cause the subcarriers to get correlated?

In that case, there would be inter-subcarrier interference (also known as inter-carrier interference), and that would give you some non-zero BER.

• In any textbook, BER /performance/ SER given < 1. I tried the high correlated scenario with carrier frequency 2.4Ghz and delay spread 35 ns, and BER is > 4 with SNR =30. Is it possible? I understand, if BER >0.6, it means that the estimation of symbols is wrong. May 20 '20 at 7:12
• I think you made a mistake in your BER computation? As BER by definition cannot be greater than 1. It is typically small, like 10^-3. For your scenario, worst case would be BER close to 1, if you're not doing equalizing, etc. May 20 '20 at 8:27
• I have check BER computation with uncorrelated channel...It works great. For correlated channel it doesnt work. Ber comptation / equalization is the same for both cases, isnt? May 20 '20 at 9:03
• BER computation means your simulation knows all the right "answers" (the correct bits), and compares with the bits coming out of your receiver/detector. BER 0 means all the bits match. BER 1 means all the bits are different. It is different from equalizing. Equalizing is something that happens in the receiver as part of the process to detect. May 20 '20 at 9:07
• ok, I start with equalization ( pinv(H)) and then compute BER. are these steps different for the correlated channel? I guess, there should be the same. If the algorithm works for uncorrelated, it shoud work for correlated, shouldn't? May 20 '20 at 10:15

The correlation you're speaking of is in the receiver, not between the subcarriers formed at the transmitter!

The "O" in OFDM says that one carrier should have 0 influence on the others. So, if you see a correlation between subcarriers in the receiver that hasn't been there in the data modulated onto the subcarriers, then you're violating the "O" in OFDM.

So, figure out what causes that. Noise isn't everything that disturbs a receiver!