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# RE: [linrad] Linrad

```Leif:

Thanks for your reply and your outstanding work.
I am primarily interested in the short duration,
nearly fixed rate pulse trains.  The longer
duration ones the human ear does not like but seems
to tolerate.  As I have spent 37 years contesting
and about 5 years going to rock concerts, I cannot
tolerate this impulsive noise for long before I am
completely fatigued due to the pain in my inner
ear from the wideband spectrum of these pulses.
So I am motivated!

Fortunately one of my areas of expertise is the
automation of procedures such as the one you
have brought to our attention.  What I will be
attempting to do is build on the thing you have
pointed out, and that is you can subtract a
copy of the pulse as it is presented from
the receiver, even though it has been stretched
by the system, since you have found you can
calculate or guess a few parameters and subtract
the pulse sufficiently from the incoming signal.

To me this is a math problem.  I have a known signal,
a short duration pulse, and it is my job to figure
out three things:

1) it happened
2) what the channel has done to the pulse
3) remodulate the pulse with the parameters
determined in 2)
4) subtract it.

Number 1 and 2 are best done with determining
the parameters of a joint probability distribution.
Since these pulses tend to be nearly periodic,
all one needs to know to tell a lot about where we are
right now in the signal is what we have observed
before.  Since these things can wiggle about and
change with time, it is probabilistic in nature
but this "history determines the present" is still
good.  This kind of signal or "stochastic process"
is a Markov process, so named after the Russian
mathematician who described their properties.
The process is a pulse has happened or not.

The observation we get is through a (changing?)
filter plus more gaussian like noise (thermal).  This
means that we are not observing this Markov process
directly but through a mask.  We can pick out
some features (otherwise Linrad would not work!).
This mask makes the system of pulses plus observations
what is called a Hidden Markov Model.

At the place I work, there was an algorithm discovered
in the early 1960's.  It was rediscovered and popularized
by a scientist named Dempster and is known as the
Maximization/ Expectation algorithm.

I believe this algorithm can be made to directly apply
and that as a result, we can completely automate the
determination of the channel and pulses jointly, and
this will lead to less pulse energy getting passed the
current process as the modeling will be dynamic.  This
last piece is a "theorem":  That this algorithm will
make the fewest mistakes in the minimize mean square error
(power leakage passed the subtracter).

I will be writing this software with Frank, AB2KT.
We will write it C and will share it here.  Thanks
a lot Leif for pointing out this to us!  Those few
issues of QEX with Linrad and the SDR have changed
my hamming quite a bit!

Bob

-----Original Message-----
From: owner-linrad@xxxxxxxxxxxxxxxxxxxxxx
[mailto:owner-linrad@xxxxxxxxxxxxxxxxxxxxxx]On Behalf Of Leif Åsbrink
Sent: Thursday, June 26, 2003 15:47
To: linrad@xxxxxxxxxxxxxxxxxxxxxx
Subject: RE: [linrad] Linrad

Hi All,

Bob, N4HY wrote:
> I would like to hear
> experiences of people using the noise blanker
> in Linrad on HF.
-snip-

So would I ;)

I do not have any experience with HF at all myself.
My interest has always been 144MHz and I do not have
any reasonable HF equipment. I did some rx experiments
though. My general impression is that long distance
QRN will not be improved at all, multipath propagation
will smear out each pulse to a relatively long noise
burst that will be different each time. It can not be
subtracted, blanking is the only possibillity. These
pulses may be short enough to allow a blanker time of
only 100 microseconds or so which will require a bandwidth
of at least 20kHz. A conventional blanker will not work
if there is a strong signal present within this passband
but the Linrad selective limiter will solve that problem
and allows a conventional blanker in many situations where
a normal HF transceiver's blanker would fail.

Local QRN from powerlines, railroads, farmers electrical
fences and so on are efficiently removed with the pulse
fitting procedure.

It is (of course) likely that Linrad does not work as
well as it should because of programming errors and
because of fundamental errors in the algorithms I have
implemented. To find out, I need recordings of situations
where Linrad fails to remove QRN. There are tools included
for this, the timf2 oscilloscope (to look at pulses) and
the "S" command to save raw data on the hard disk.

The Linrad pulse removal can do "magic" things at narrow
bandwidth. On a IC706-MKIIG which has a reasonably good
audio dynamic range it works even a little better than
the builtin blanker when there is no strong signal present.
With a strong signal just outside the passband the Linrad
pulse removal is unaffected (of course) while the builtin
blanker fails completely. Linrad can even do pulse removal
with a rather strong signal within the SSB passband. The next
QEX article will give the details.

73

Leif / SM5BSZ

```
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