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However, the telescope by its very nature introduces correlations (or redundancy) into our signals. For example, the light-travel time across our array is ~1 microsecond and across 1 dish is ~0.01 microsecond. Therefore, we will hesitate to believe "discoveries" of signals with redundancy on timescales between 0.01 and 1 microsecond, since there are known array artifacts in this range.

Why do we have to ignore them?  If all the arrays are pointed at the same source, then this is simply a multipath environment.  As long as the signals are resolvable, then these time offsets actually can be used to increase our SNR.

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Then there are the Walsh function frequencies which range from some 100 of Hz to 20 kHz. Converting this frequency range to microseconds, we can expect artifacts over time durations of 50 microseconds to 10,000 microseconds.

What exactly are the Walsh function frequenices you are referring to?  The Walsh function that can create a Hadamard matrix?  If so, how does that relate to the frequncies? 

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Then there is self-generated RFI. In a very broad sense of RFI, we can consider receiver noise to be RFI. Essentially, we are making measurements of the electric field arriving from the sky using instruments that are "hot." Our receivers are white-hot at 1.4 GHz. The pitifully weak signals we receive from the sky are completely overwhelmed by the self-generated noise of our receivers. To a pretty good approximation, receiver noise is GWN.

This is a nit-pick here, but in all my work in the communications field, we refer to noise and interference separately.  Noise is random process due to your environment.  Whereas, interference refers to some with structure that is not your signal of interest.  For example your cell phone signal is interference to my cell phone trying to communicate with the cell phone tower and the channel between my cell phone and tower has noise.  Again, a nit-pick so take it FWIW.

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There is another kind of self-generated RFI, which is in our signal processing room. Here the signals from the antennas are digitized at very high rates and processed with 2-3 GHz CPUs. In order to run this computing equipment we need lots of clocks ticking along with periods anywhere from 1 second (10^6 microseconds) down to 10^-4 microseconds.

Which clocks are you talking about, CPUs, samplers, ... ?  Are you talking clock drift and/or clock jitter?   Why do we need clocks running from 1 Hz to 10 GHz?

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Finally, there is RFI generated by sources other than the ATA. This stuff is all over the place. It looks like sine waves everywhere thanks to the human love of clocks. It looks like dispersed pulsars because radar transmitters often use chirped pulses. It can even look like GWN in constrained frequency ranges. But it isn't noise from the galaxy or cosmic microwave background or even from our antenna receivers. It is satellite signals.The only reason we have hope of overcoming all these sources of noise is that we can either identify them and throw them away, or search in sky-frequency ranges where they don't appear.

I wonder what type of channel estimation is computed?  Seems like there could be some adaptive interference cancellation techniques that could help this issue.

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Other comments:
What is done about fading?  I suppose the location of ATA is such that it is rarely cloudy and minimizes bad effects of our atmosphere.  But the signal does still go through our atmosphere.  There will be some fading happening and the channel will vary ( even if very very slowly ).  Again maybe the ATA is located such that essentially the fading coefficient is the same for each individual receiver. In that case, the fading would essentially lower the effective SNR a little.  I would interested to know what the SETI folks thought about the fading issue and what if any techniques they use for it.