Return-Path: X-Spam-Checker-Version: SpamAssassin 3.4.0 (2014-02-07) on lipkowski.org X-Spam-Level: X-Spam-Status: No, score=-2.3 required=5.0 tests=HTML_MESSAGE, RCVD_IN_DNSWL_MED,SPF_PASS,T_HEADER_FROM_DIFFERENT_DOMAINS autolearn=unavailable autolearn_force=no version=3.4.0 X-Spam-DCC: : mailn 1480; Body=3 Fuz1=3 Fuz2=3 Received: from post.thorcom.com (post.thorcom.com [195.171.43.25]) by mailn.lipkowski.org (8.14.4/8.14.4/Debian-8+deb8u1) with ESMTP id uATCwV9f002877 for ; Tue, 29 Nov 2016 13:58:33 +0100 Received: from majordom by post.thorcom.com with local (Exim 4.14) id 1cBhuS-0005sR-Bz for rs_out_1@blacksheep.org; Tue, 29 Nov 2016 12:53:20 +0000 Received: from [195.171.43.32] (helo=relay1.thorcom.net) by post.thorcom.com with esmtp (Exim 4.14) id 1cBhuJ-0005sI-Cq for rsgb_lf_group@blacksheep.org; Tue, 29 Nov 2016 12:53:11 +0000 Received: from mout02.posteo.de ([185.67.36.66]) by relay1.thorcom.net with esmtps (TLSv1.2:ECDHE-RSA-AES256-GCM-SHA384:256) (Exim 4.87) (envelope-from ) id 1cBhuG-00064s-NS for rsgb_lf_group@blacksheep.org; Tue, 29 Nov 2016 12:53:10 +0000 Received: from submission (posteo.de [89.146.220.130]) by mout02.posteo.de (Postfix) with ESMTPS id E5B2120470 for ; Tue, 29 Nov 2016 13:53:06 +0100 (CET) Received: from customer (localhost [127.0.0.1]) by submission (posteo.de) with ESMTPSA id 3tSk4243F4zyrG for ; Tue, 29 Nov 2016 13:53:06 +0100 (CET) Message-ID: <583D7A30.7050403@posteo.de> Date: Tue, 29 Nov 2016 13:53:04 +0100 From: DK7FC User-Agent: Mozilla/5.0 (Windows; U; Windows NT 6.1; de; rv:1.9.1.8) Gecko/20100227 Thunderbird/3.0.3 MIME-Version: 1.0 To: rsgb_lf_group@blacksheep.org References: <158aff9cf67-1fc0-11313@webprd-a60.mail.aol.com> In-Reply-To: <158aff9cf67-1fc0-11313@webprd-a60.mail.aol.com> X-Scan-Signature: b42857a5fad6e32377447282c21f62b1 Subject: Re: LF: Optimum weighting in the presence of variable noise Content-Type: multipart/alternative; boundary="------------090801060801010000030700" X-SA-Exim-Scanned: Yes Sender: owner-rsgb_lf_group@blacksheep.org Precedence: bulk Reply-To: rsgb_lf_group@blacksheep.org X-Listname: rsgb_lf_group X-SA-Exim-Rcpt-To: rs_out_1@blacksheep.org X-SA-Exim-Scanned: No; SAEximRunCond expanded to false X-Scanned-By: MIMEDefang 2.75 Status: O X-Status: X-Keywords: X-UID: 9615 This is a multi-part message in MIME format. --------------090801060801010000030700 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Hi Markus, Thanks, i've been waiting for that message. It seems i need a firmware update to decode that message, also my RAM is close to the limit. It's about M copy only :-) 73, Stefan Am 29.11.2016 13:05, schrieb Markus Vester: > When combining a number of measurements with uncorrelated noise, the > in-phase signal contributions add up linearly while the noise adds up > quadratically. If the individual measurements are scaled by weighting > factors w, the combined SNR is > > (S/N)combined = (w1 S1 + w2 S2 + ...) / sqrt(|w1 N1|^2 + |w2 N2|^2 + ...) > > Combined SNR can be maximized if the weight factors are chosen > proportional to the expected signal voltages divided by the noise powers: > > w ~ S*/|N|^2, > > with the asterisk denoting the complex conjugate which is used to > align the expected signal phases. The rule is easy to derive using the > well-known differentiation formula (u/v)' = (vu'-uv')/v^2. > > The optimum weighting rule is rather generic and has been applied in > the frequency domain (Wiener matched filter), spatial domain (maximum > ratio combined array antennas), or time domain (EbNaut day/night > stacking). It could conceptually be decomposed into two steps: > > w ~ (1/|N|) (S*/|N|), > > where we first normalize to constant noise level, and then weight the > measurements according to their individual SNR. > > For example, let's assume that a VLF signal is 6 dB stronger at night, > but the noise increases by 10 dB. Thus the nighttime measurement > should be down-weighted by (+6-20) dB= -14 dB, which is more > redunction than noise normalization. > > The optimum weighting concept could also be applied to spherics > blanking. The classic "noise blanker" basically works by nulling all > samples above a pre-set threshold. This can be viewed as a crude > binary approximation of optimum inverse-noise-power weighting, but > requires an empirical selection of a threshold depending on QRN > statistics (sparse local lightning crashes versus many distant > spherics). An optimum weighting "super-AGC" would continuously monitor > the noise level, and reduce the gain proportional to it's square with > a short time constant ("The Strong will become Weak"). > > One caveat is that a statistically significant measurement of > "instantaneous" noise power requires a large number of samples (e.g. > 100) to be incoherently added. If the noise measurements are taken > only from within the signal channel itself, gain adaptation needs to > be slow compared to the symbol rate. For the purpose of spherics > blanking, one would want to evaluate the noise in a relatively large > bandwidth (preferably several kHz). > > Best 73, > Markus (DF6NM) > --------------090801060801010000030700 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Hi Markus,

Thanks, i've been waiting for that message.
It seems i need a firmware update to decode that message, also my RAM is close to the limit. It's about M copy only :-)

73, Stefan

Am 29.11.2016 13:05, schrieb Markus Vester:
When combining a number of measurements with uncorrelated noise, the in-phase signal contributions add up linearly while the noise adds up quadratically. If the individual measurements are scaled by weighting factors w, the combined SNR is

 (S/N)combined = (w1 S1 + w2 S2 + ...) / sqrt(|w1 N1|^2 + |w2 N2|^2 + ...)

Combined SNR can be maximized if the weight factors are chosen proportional to the expected signal voltages divided by the noise powers:

 w ~ S*/|N|^2,

with the asterisk denoting the complex conjugate which is used to align the expected signal phases. The rule is easy to derive using the well-known differentiation formula (u/v)' = (vu'-uv')/v^2.

The optimum weighting rule is rather generic and has been applied in the frequency domain (Wiener matched filter), spatial domain (maximum ratio combined array antennas), or time domain (EbNaut day/night stacking). It could conceptually be decomposed into two steps:

 w ~ (1/|N|) (S*/|N|),

where we first normalize to constant noise level, and then weight the measurements according to their individual SNR.

For example, let's assume that a VLF signal is 6 dB stronger at night, but the noise increases by 10 dB. Thus the nighttime measurement should be down-weighted by (+6-20) dB= -14 dB, which is more redunction than noise normalization.

The optimum weighting concept could also be applied to spherics blanking. The classic "noise blanker" basically works by nulling all samples above a pre-set threshold. This can be viewed as a crude binary approximation of optimum inverse-noise-power weighting, but requires an empirical  selection of a threshold depending on QRN statistics (sparse local lightning crashes versus many distant spherics). An optimum weighting "super-AGC" would continuously monitor the noise level, and reduce the gain proportional to it's square with a short time constant ("The Strong will become Weak").

One caveat is that a statistically significant measurement of "instantaneous" noise power requires a large number of samples (e.g. 100) to be incoherently added. If the noise measurements are taken only from within the signal channel itself, gain adaptation needs to be slow compared to the symbol rate. For the purpose of spherics blanking, one would want to evaluate the noise in a relatively large bandwidth (preferably several kHz).

Best 73,
Markus (DF6NM)

--------------090801060801010000030700--