enter image description here

This is a basic figure that explains how Non-Coherent FSK actually works. The incoming signal

$ r (t)=\sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$

where P denotes the signal power in Watts, $T$ denotes the symbol time in seconds, $f$, $i$ $s$ the carrier frequency in Hz, Also, n(t) denotes the AWGN with single-sided power spectral density $No. T.

Now this incoming signal matches to integrator output

$ Zck =\int _ 0^T r(t) \sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$ equation- 1

Similarly, the quadrature integrator output $Zs,k$

$ Zsk =\int _ 0^T r(t) \sqrt{2 P}{Sin}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$ $ equation- 2

Eventually in $fc$ terms are canceled out by low -pass-filters and we are left with other terms.

I tried to solve it by putting r(t) into equation-1 and integrated it. The end result is this enter image description here

Similarly to the quadrature integrator output $Zs,k$ the end result is enter image description here

In the end, I added them and got $1T$ and Noise.

My question is what happens to other integrators where the miss-matching occurs, how we get 0 from it. As this is Non-coherent FSK and spacing is $1/T$ so should we put 1/T instead of fi-fi in equation-1 and 2 to get zero from these orthogonal functions? like the same equations, 1 and 2 now become?

enter image description here



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.