shift theorem for wavelets (with application to OFDM)

Started by porterboy November 3, 2003
In an OFDM signal, if the symbol window (of N samples) is misaligned
at the input to the FFT, the constellation points on each tone are
rotated by a certain amount. To undo this effect we use the Fourier
shift theorem which allows us multiply by a complex exponential on
each tone.

I am using a Wavelet Packet Transform instead of an FFT. My question
is, is there an equivalent time/scale shift theorem for wavelets as
there is time/frequency shift theorem for Fourier sinusoids? If so,
what should I do to my received constellation points to recover them.

Note: the FFT basis is complex valued while the waelet basis is real
valued. So there are complex QAM constellation points on the tones in
OFDM but only real valued PAM constellation points on the wavelet
packet modulated signal.

I know this is a pretty difficult question, but even a pointer would
be appreciated. Much appreciated...

I found a partial answer to my own question in
"Effects of a Carrier Frequency Offset on Wavelet Transceivers"
by Bianchi and Argenti... excellent paper presented at Baiano, Sept. 

However, I am more interested in the effect of symbol misalignment
than in the effect of carrier frequency offset (which doesnt happen in
baseband). All I can see is that my constellations are 'messed up'. Is
there any underlying structure to this...