Suppose I have time domain LTE signal L and time domain WiFi signal W.
L is generated by taking 2048 point IFFT and W is generated by taking 64 point FFT.
Power of L is higher than W in such a way that after adding them, i.e. , L+W and taking 2048 point FFT, the LTE can still be detected and decoded.
Now here is the situation. I received time domain L+W, took 2048 point FFT on L+W denoted by F(L)+F(W).
Now we decode LTE and after that perform some signal processing on F(L)+F(W) in such way that F(L) is perfectly nulled out from F(L)+F(W). In other words interference nulling of LTE from composite signal. After such nulling the residue is F(W). Now if I take 2048 point IFFT of F(W) to get a time domain, i.e., W and then take 64 point FFT of W, i.e., F(W), will I be able to recover WiFi (assuming that nulling of LTE has worked perfectly) from F(W).
Saying simply if F64/F2048 and IF64/IF2048 are 64/2048 point FFT and IFFT operators
then, will F64( IF2048 ( F2048 ( IF64 (A)))) be equal to A ?
Well I tried in Matlab:
a = randn(1,64);
b = fft(ifft(fft(ifft(a,64),2048),2048),64);
result is that a = real(b) apart from rounding issues
Indeed! I also replicated and this happens without zero-padding.
I was in the impression that taking 2048 point FFT of the LTE+WiFi will introduce some ICI in the WiFi sub carriers which WiFi will not able to recover later.
I think there must be a stage of zero padding:
64 points ifft to 2048 fft requires zero adding in center
2048 fft to 2048 ifft, no zero padding
2048 ifft to 64 fft, no zero padding, decimation needed
May be my case could help.
Using 2048 ifft for 10MHz lte I pad extra 1024 zeros in the middle of input then decimate the ifft output by 2.
For 2048 fft I pad input with 1024 zeros at end then decimate fft output by 2