impulse response - How to estimate the number of taps needed for subsequent channel estimation algorithms?

I recently implemented an MMSE channel equalizer, and I have read about many other types of channel estimation/compensation algorithms out there. However, one thing that is never talked about it how to estimate the number of taps in your model of the channel you are trying to estimate. How is this accomplished?

For example, in the MMSE implementation I have, I know the training sequence, and thus, and use the training sequence to minimize my error. However, what if the channel impulse response is longer than the training sequence? I would never see its effects, and thus its effects on the training sequence will not be seen. How does one then estimate the number of taps needed for channel estimation?

Thanks!

Answer

What you're looking for is a way to estimate the channel's delay spread. The delay spread is a measure of the effective duration of the channel's impulse response (often caused by multipath, which is useful for deciding how long your equalizing filter must be.

How you go about doing this will vary depending upon the characteristics of your system. A couple potential approaches are:

• 
  

  If you have the ability to institute a training period to your communication system, you can use a channel sounding technique to estimate the response of your channel. There are a few ways to do this: you can transmit a short, impulse-like waveform through the channel and directly measure the impulse response, or you could send a waveform with known spectral properties (such as pseudorandom white noise) and measure the frequency response at the receiver. You can then inverse-transform the frequency response to get an estimate of the channel's impulse response. Then, estimate the effective length of the response by inspection of the result. These methods of estimating the delay spread somewhat defeat the purpose of using an adaptive equalizer, but if the channel's delay spread isn't expected to change much during system operation, then it can work.

  
  


• 
  

  If your waveform has good autocorrelation properties, like a direct-sequence spread spectrum signal or an OFDM waveform with a cyclic prefix, then you can use a correlator-based approach. During the synchronization process for signals such as these, one will often use a correlator (e.g. a matched filter) to obtain accurate symbol timing by searching for peaks in the correlator's output. If there is multipath present in the channel, the correlator output will contain multiple peaks commensurate with the different paths that the signal can take through the channel. The delay spread can be estimated by measuring the duration in time between the first and last peaks.

  
  
  

Just like for equalizers in general, there is a lot of literature out there on methods of delay spread estimation. If you combine that search with the type of system that you're looking to implement, you are more likely to find results that work for your application.