In article <AGGnc.14351$V97.12110@newsread1.news.pas.earthlink.net>,
Rob Dekker <rob@verific.com> wrote:

  - Planetary TV : 100Mhz-1Ghz. Continuous. Power 10-100kW. Not well
directed.

Only potentially detectable because we currently still use vestigial
sideband AM analogue transmitters, and therefore a large part of
the power is in very narrow band carriers.  Even the 1MW transmitters
used in parts of the USA require more observation time that normally
be allocated to one target, even when doing targetted SETI, and
requires much much more than the transit time for drift scan SETI.

Digital TV spreads the power out much more evenly and is many orders of
magnitude less detectable.  Analogue transmisssion carriers would,
at first sight, look like narrow band beacons.

  - Planetary Radar. 1Mhz-100Ghz. Power 1kW-1000kW pulses. Directed but
infrequent.

Typically 2.2Ghz.  Typical EIRPs are 10s of Terra-watts (1MW feed point
power), so your powers are wildly too low (actually, as noted below,
it is because you are failing to use EIRP).  Typical transmissions are not
pulsed.  About 50% of the time they are sending CW signals, which are
very much detectable.  The same transmitters have been used for 
the very limited active SETI beacons.

The rest of the time they are transmitted with constant power, but
pseudo-randomly phase modulated at about 10k chips per second, degrading
the signal power density by something like 50dB, although that still
makes them more powerful than leaked analogue TV carriers.

Although the CW transmissions are detectable, they are not repeatable,
so would require real time verification.  I don't think the transmit
time for phase modulated signal would be enough to allow detection.

  - Satelite uplink. 1Ghz-20Ghz. Directed. Power 10W-10kW. Continuous. BW
10-100Mhz.

These power figures are confusing as one would normally not use
feedpoint power, but EIRP (Equivalent Isotropic Radiated Power).
Using <http://www.satnews.com/free/linksample.htm> as a reference,
reasonable figures are 75.65dBW (~37MW) in 27MHz.  This example has
no significant carrier component.  In this application having narrow
band components in the signal is likely to overload the transmponders,
so the most detectable condition is undesirable operationally.

Maybe the "WOW" signal was one of them....

It was relatively narrow band (< ~10kHz - limited by receiver resolution),
whereas one would expect an established link to be spread spectrum.  The
best you could hope for is the occasional transmission of a re-acquisition 
pilot signal.

Apart from their power being distributed in broadband (10-100Mhz is
a reasonable guess), they will come to us in bursts of 10-100sec.

To the extent this is true (modern systems) that spreading of the power
is a killer.  With the figures I researched, you are about 90dB below
the signal level that is easily detectable in 10s from the nearest star
as a narrow band beacon.

But noise consistent over time : if we were to listen to a broad band
spectrum
for a considerable time (say 100 sec) and accumulate all noise

You need more than that to detect higher power, narrow band, analogue
TV.

photons over that time before we run the signal through a spectrum

Forget photons.  Microwave SETI is not quantum limited.

analyzer, we will reduce noise influence by a factor of 100 over
a 1Hz bandwidth signal.

Non-coherent integration SNR scales with the square root of the 
observation time, so you will only get a factor of 10 benefit.  However
you don't know the baseline noise level (with narrowband SETI, you 
assume that the adjacent channels provide the baseline, as there aren't
natural narrowband signals.

Effectively, we obtain sensitivity of 1/100 Hz bandwidth if we
listen to any signal (of any bandwidth) for 100 sec.

No.  In fact wide bandwidths are better, given that you are now in
a radio-astronomy configuration, not a technology detection configuration.
A realistic case signal is 90dB below the signal power density detectable
in 10s at 0.1Hz bandwdith,  but has a unit observation time is more like
40ns.  You are proposing an integration time of 100s, giving 2.7E9 
basic observations, so you get an integration gain (improvement in SNR
due to averaging) of 47dB, which leaves you only about 52dB below detection
threshold!  To get back to the detection threshold, your observation 
time has to be increased by a factor of 2.5E10.  Unfortunately, you are
only detecting one such pulse a day, so that is 1E17 days, or some
68 million years!

(Of course, it is probable that the background noise will change by
more than the signal in this period, and more importantly that the
uncertainty would change by more than the signal.  Also the planet
rotation time will change, making it difficult to know when to 
gate the signal for integration.)

I think you will also find that at the power spectral densities assumed
the local star will completely dominate the signal (not true for a 
narrow band beacon).

Note that using wideband receivers and long integration times are
the normal case for general radio astronomy, so signals with such
characteristics would be picked up by such operations.  The problem is
that, even if strong enough, they have natural source characteristics,
so might be treated as such.  The advantage of handling sub-1Hz signals,
as well as the relatively low powers needed, is that there are no known
mechanisms other than engineering for producing them.

In fact, my initial calculations show that we should be
able to detect a 10kW sat-uplink signal transmitted with a 10m dish

Dish size is already accounted for in the EIRP, although is actually
your 10m in my example.

My figures are based on 22 times mean noise, as used in SETI@Home.  
Because they can follow up in real time and maybe don't try so many
combinations of parameters, Phoenix uses 8 times mean noise, which will
reduce your observation time to about 7 million years; however, as
you are going to have to search over many different possible source
planet rotation times, you can't afford a low threshold.  I think my
sensitivity was also based on a slightly optimistic estimate of the
effective aperture of Arecibo.

[ Cross posted into alt.sci.seti, because the original was multiposted
  there.  Please people, if you don't know how to cross-post, please 
  choose just one newsgroup, rather than starting a separate thread in
  each. ]