Re: Time to scrap SETI?

From: David Woolley (david_at_djwhome.demon.co.uk)
Date: 12/19/04 

Date: Sun, 19 Dec 2004 09:55:08 +0100

In article <CmSwd.204$5R.135@newssvr21.news.prodigy.com>,
Rob Dekker <rob@verific.com> wrote:

> the data transfer will occur in some (limited) bandwidth, or (in case of
> true spread-spectrum transmission) in limited time (very short pulses).

I assume you mean direct sequence, rather than frequency hopping,
spread spectrum. That is normally sent with no gaps between pulses.
If you know the spreading code and rate, you can still achieve good signal
to noise ratios, but it is not susceptible to S@H type pulse analysis.
(Actually, the theoretical throughput of a channel using a very large
bandwidth and very weak signal is higher than that using a very strong
signal in a small bandwidth, assuming a constant power spectral density
for the noise, and idealised noise - see below.)

> Either way, ANY communication signal, no matter how intelligent the designer
> was, will be distinguishable from natural thermal noise, which is neither

Natural noise isn't just thermal.

> limited in bandwidth, nor in time.

The most fundamental problem here is that more than half the power in
an AM (double side band, full carrier) signal is wasted in the carrier,
even when fully modulated. That carrier can easily be well under 0.1Hz
wide and approach the theoretical limits for spectrum spreading in
interstellar space. That means that most of an AM signal is available
with only the noise contribution from 0.1Hz of bandwidth.

With more efficient methods, the power is spread across the whole channel,
which will be several hundred Hz wide for telephone quality digital
speech, even using the most bandwidth efficient codings normally used,
and much more for typical mobile phone applications. That means that you
have 1,000s to 100,000s of times the noise in the receiver compared with
an AM carrier. That's a penalty of 30 to 300 in the detectable power
(this is for detecting presence, not recovering the signal). Speech is
a relatively poor example, because relatively little power is used for
telephone quality speech. For TV, the power is spread over several MHz,
giving a detection penalty of several 1000 to 1.

These detection scenarios assume that:

1) the channel exists in isolation (in reality there will be many channels
   adjacent to each other, and whilst they may currently have guard bands
   between them, these are reducing as technology gets better).

2) the signal is narrow enough that one can assume the sky noise doesn't
   vary across the channel

> Besides that, there are applications where the data rate is very low.
> Surveillance radar is one example. For surveillance radar, you only need to
> know if there is an object or not. That is only one bit of information.

That represents a misunderstanding about the information theory definition
of a bit. One is actually interested in knowing that the target is:

- at a particular range;
- at a particular time;
- of a particular approximate size;
- has a particular range;
- (in a particular direction and with a particular angular velocity).

That requires quite a lot of bits.

A bit in information theory is not the same as a Boolean in a programming
language; it represents relative probabilities; the existence of an
improbable event conveys many more bits of information than the common case.
It is that definition of bit that determines the required SNR (and that
definition of bit that means that S@H has to have a detection threshold of
22 times mean noise, not of 1 times mean noise).

> Intelligently designed radar systems will use this to be either very limited
> in bandwidth and/or in time, but always within the limit :

> data=SNR*time/bandwidth

The correct formula (Shannon-Hartley theorem) is:

<theoretical max data rate> = <bandwidth> * log2 (1 + <SNR>)

One can't, strictly speaking, simply multiply this by time (the
formula is the asymptotic one for infinite time), although
for a reasonably long time period you will get quite close, but with
a finite error rate:

~ data = log2 (1 + SNR) * time * bandwidth

(Note no divisions.)

Typical applications of surveillance radar require that results be
provided promptly, so channel capacity has to be much higher than
that needed to support the long term average data rate. This is
partially mitigated, in air defence radars by having separate tracking
and acquisition modes, so that an acquired target is not diluted by
observations of empty space.

In practice, relatively low power primary surveillance radars do use
short pulse. These have to be short enough to give good range resolution,
resulting in a large signal bandwidth. For military applications, these
pulses will not be at fixed intervals, because that makes jamming more
difficult and because fixed intervals can result in aliasing of Doppler
rates that may make a target appear not to be moving at an interesting
speed. The lack of fixed intervals will make S@H type pulse detection
unworkable.

Very high power surveillance radars (always, I believe) and planetary
radar in ranging mode transmit pseudo random sequences at constant
power and then despread the result. That allows them to use much lower
peak powers.

Air surveillance radars will get a lot of their noise from ground clutter,
rather than the nice well behaved noise that the channel capacity
formulae assume.

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