I am confused by the following statement from the paper Beamforming: A Versatile Approach to Spatial Filtering by Barry D. and Kevin M.:

There are two basic adaptive approach: 1) block adaption ..., 2) continuous adaption.... If a nonstationary environment is anticipated, block adaption can be used, provided that the weights are recomputed periodically....Continuous adaption is usually preferred when statistics are time-varying or (for computational reasons) when the number of adaptive weights M is moderate to large (values of M>50 is not uncommon).

This statement gives the conditions when the two kinds of adaption methods should be used. But the condition NONSTATIONARY and TIME-VARYING, in my opinion, are the same. Can you point out in what situations they are different? Illustrative examples would be greatly appreciated.

Thank you.


My understanding :

Non-Stationarity is mentioned in statistical sense where channel coefficients are non-stationary random processes. You can look for Wide-Sense Stationary Processes and Strict-Sense Stationary Processes and their definition and properties.

Time-Varying is with regards to time-domain channel impulse response characteristics. Time-variance indicates that depending upon when any specific input is provided to the channel, the output will change because the channel is varying with time.

A particular channel model can be time-varying but wide-sense stationary. This would mean, depending upon when any specific input is provided to the channel, the output changes but the statistical properties of the output like correlation function, mean etc will follow wide-sense stationarity conditions.


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