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To remove the Doppler shift, we can use a bank of matched filter. But, to use this method, we need an interval $[-f_{max};f_{max}]$.

How can we approximate this interval?

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  • $\begingroup$ Is this for detecting a pulsed radar signal, a comms signal, or some other kind? $\endgroup$ – Robert L. Jun 23 '18 at 22:09
  • $\begingroup$ it's for a comms signal $\endgroup$ – bubu Jun 24 '18 at 9:43
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How can we approximate this interval?

you need to model your channel. There's no way around it. If the first thing to observe your signal is only looking in a frequency interval, you need a priori knowledge of what you expect from your channel.

Note that filter banks for doppler compensations are usually the least desirable method of solving such a problem. It's

  • computationally intense
  • scales terribly
  • for comms systems, it contradicts the idea that you've got a time-variant doppler, and will have to interpolate individual filters over time

We typically only do filter banks to deal with unknown frequency errors when there's no other way. Typical examples of that include spread-spectrum signals that simply aren't even detectable without correcting their frequency first.

Most systems you'll meet in the wild go through special lengths to avoid using a general filter bank. Take OFDM with Schmidl&Cox: It's more acceptable to lose maybe ¼ of your channel access time to a cyclic prefix (which OFDM requires) and another two OFDM symbols per Frame to fine and coarse frequency and timing estimation than having a bank of filter banks.

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you sample the interval and build a filter for each frequency shift, unless you don’t need to, like in typical carrier/phase recovery schemes.

You make a bank of filters, particularly if Doppler is of itself, of interest. In SONAR, tones have better Doppler resolution, and the DFT provide a bank of filters.

The ambiguity function function for the waveform will show how much loss you can tradeoff for the frequency sampling you choose.

Each waveform will have different loss for frequency miss-match. The ambiguity function also accounts for delay resolution.

A waveform like hyperbolic FM is robust to Doppler so a single waveform covers a wide range of possible shifts.

Both miss-matches can couple.

In comms, Doppler compensation is usually a matter of compensation of the frequency shift, not full time dilation. Shifting a matched filter is a matter of frequency shifting and can be accommodated in carrier/ phase recovery.

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