# Non coherent detection BFSK demodulation?

I am simulating BER performance of BFSK under AWGN and Rayleigh fading, BFSK has two symbols one entirely on the real plane while other on the complex plane for representing let's say zero and one, that is how the constellation of BFSK looks like.

s=data + j*(~data); %Baseband BFSK modulation


Now let's say we added AWGN (N) and Rayleigh fading (h) as well.

Rx= h*x + N;


Now when I tried to detect it on the receiving side I will have to divide this entire Rx by an h, well that makes sense.

My entire graphs for the BER curve match non-coherent detection for FSK.

It exactly matched the theory, Eb/N0 vs. BER for BFSK over Rayleigh Channel.

How to do the same for Non-coherent detection?

If I do not divide Rx by h, Rx/h, I get a few very very bad results and that doesn't match anything. Theory tells us that In non-coherent detection, there's no prioir knowledge about the channel impulse response at the receiver.

In coherent systems, the receiver needs phase information of the transmitter (the carrier phase) to recover the transmitted data at the receiver side. I haven't used any such thing but still simulation results for BER matched with that of theory for Coherent FSK.

Can someone here help me with this?

• By not diving by h, will I get better results for Non coherent FSK?
• Whether BPSK or BFSK every time we need to divide h*x + N by an h to get results that match theory.
• I'm confused. You win very little, if anything, by having phase information on the channel in the classical (B)FSK case – your receiver really doesn't care about the phase at all. You cannot compare that to BPSK, where the phase is the actually information-carrying entity. – Marcus Müller May 17 at 11:07
• Your s, however, doesn't look like FSK at all – it's just a BPSK of amplitude $\sqrt2$, rotated by 45° (assuming data just means "a bit of data mapped to $\pm 1$). – Marcus Müller May 17 at 11:10
• For BPSK symbols have 180-degrees phase shift, either both symbols at complex or both symbols at real, this definitely is not BPSK at 45 degrees rotation if one is at zero while other is at 90. "You win very little, if anything, by having phase information" might be true that I win very little but all I am trying to do is achieve BER curves for non-coheret FSK, BFSK over Rayleigh and AWGN so divided s or Rx by h, If I don't it might be but curves tells very sad story that matches absolutely nothing – good_omen92 May 17 at 11:17
• I achieved it for coherent but not for non-cohernt so how to do that? Should I not divide it by h ? – good_omen92 May 17 at 11:20
• seriously, your s is not FSK, it's a PSK or QAM. For data=0, you get s= 1j, and for data=1 you get s=1, and thus you're right, it's not just rotated BPSK, I typed to hastily; it has a simple decision boundary, and it's the diagonal of the upper right quadrant of the complex plane, and that is just the 45° shifted decision boundary of BPSK. – Marcus Müller May 17 at 13:30