Re: K3: listening to both rcvrs - Reduced receiver noise floor
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Re: K3: listening to both rcvrs - Reduced receiver noise floor
 
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>> So the reduction in SNR (assuming equal noise power) is
>> 3.01 dB, not 6 dB. >That's the best case if the noise power is equal. If the >"other" receiver has higher noise power (wider bandwidth, >more interfering signals, etc.) the S/N reduction is greater. >Even 3 dB reduction in S/N is a big hit if the DX Station >you're trying to hear is at or just below the noise level. >It would be a shame to turn a top performing radio into a >mid-pack device by mixing the audio - because of some old >wife's tail. Let those who want mixing do it externally >so it doesn't impose a S/N penalty otherwise. There seems to be a fundamental mis-understanding on how uncorrelated and correlated noise works. If two receivers are listening to the exact same signal and use the same antenna, then the short answer is that summing the output from these two receivers together will produce the same signal at a level 6 dB higher with no signal to noise change. This assumes the receivers themselves are identical and do not contribute noise (more on this later), so the two receiver outputs will be identical. Band noise from one receiver at any instant in time will look exactly like band noise from the second receiver. The desired stations signal will look the same from both receivers. The point is that magic is not involved, and that neither of these two receivers can tell the difference between band noise and the desired signal and thus will process both the desired station and the band noise the same. Thus, there would be no degradation or improvement in signal to noise ratio as long as we are talking about ideal receivers. However, if the situation is a weak signal situation where the receiver noise floor is at least partially masking the desired signal, we have a different situation. Band noise and stations on the band will both be correlated coming out of both receivers and thus get a 6 dB improvement. On the other hand, the internal noise produced in each receiver is independent and thus uncorrelated. While correlated signals add voltage wise (V + V = 2V or 6 dB gain), uncorrelated noise adds as the square root of the sum of the squares sqrt(V*V + V*V) = 1.4V or 3 dB gain. This means what when adding the output of two identical receivers, the band noise and the desired station signals will increase by 6 dB while the receiver noise contributions will increase by only 3 db. You have in essence created a single composite receiver with a lower noise floor. If you added just enough RF pre-amplification to overcome the signal splitting loss to N receivers, adding more and more receivers in parallel will produce a composite receiver that has a better and better noise floor. This is in essence what the space telescope folks do. They gang many dishes and many receivers together across a very large area to get an enhancement on the signal and space noise and a suppression of the effective receiver noise contribution. Thus, if the noise floor of the receivers are the limit, listening to the same signal with two identical receivers will have the effected of reducing the receiver noise contribution by 3 db. Conversely, that also means that if you are listening on 40m where the band noise is way higher than the receiver sensitivity, reducing the receiver noise contribution will be of no benefit. - Dan Tayloe, N7VE _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
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Tayloe Dan-P26412 wrote:
> However, if the situation is a weak signal situation where > the receiver noise floor is at least partially masking > the desired signal, we have a different situation. Band > noise and stations on the band will both be correlated coming > out of both receivers and thus get a 6 dB improvement. On > the other hand, the internal noise produced in each receiver > is independent and thus uncorrelated. While correlated > signals add voltage wise (V + V = 2V or 6 dB gain), > uncorrelated noise adds as the square root of the sum of the > squares sqrt(V*V + V*V) = 1.4V or 3 dB gain. This implies that if I am listening to a very weak signal close to the rx noise floor (at least at my urban QTH this is rare and would only happen on the higher bands), it would pay to activate the sub-receiver in diversity mode even with the same antenna! -- 73, Vic, K2VCO Fresno CA http://www.qsl.net/k2vco _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
Re: Re: K3: listening to both rcvrs - Reduced receivernoise floor
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>> uncorrelated noise adds as the square root of the sum of the squares
>> sqrt(V*V + V*V) = 1.4V or 3 dB gain. > > This implies that if I am listening to a very weak signal close to the rx > noise floor (at least at my urban QTH this is rare and would only happen > on the higher bands), it would pay to activate the sub-receiver in > diversity mode even with the same antenna! But wouldn't the benefit be purely the result of the psychoacoustical phase difference between the two audio sources rather than amplitude when activating the 2nd Rx? With two correlated signals, it would seem that both noise *and* the desired signal increase by the same amount (i.e., 6 dB). Likewise, with two uncorrelated signals, both the noise and desired signal also increase by the same amount (i.e., 3 dB) So, from a SNR standpoint, what is the benefit? I can see where there may be a psychoacoustical phase benefit, but not of amplitude. Paul, W9AC _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
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In reply to this post by Tayloe Dan-P26412
On Nov 17, 2008, at 10:06 AM, Tayloe Dan-P26412 wrote: > Band noise from one receiver at > any instant in time will look exactly like band noise from > the second receiver. That is true if the two receivers are tuned to the same passband and you are using an identical antenna for the two receivers. In the case of receiving split, you are not looking at the same noise entering the two receivers. In this case, by combining two different passbands, the desired signal would only come from one receiver but the summed noise would come from both receivers, dropping the SNR by 3 dB. An easy test is to subtract two receiver outputs (assuming the receivers are phase coherent). You should get a "reasonable" null (sky noise and signals are nulled away, leaving just the receiver noise and any gain/phase mismatch in the two passbands) when looking at the same antenna. When you tune one receiver away, the noise level should rise. Come to think of it, it is an easy DSP experiment by looking at the output of two complex mixers using different (numerical) local oscillators. 73 Chen, W7AY _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
RE: Re: K3: listening to both rcvrs - Reduced receiver noise floor
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This is a nice mental thought experiment. Tune two identical
receivers to the same pass band and listen on both. If you sum the outputs together (neglecting the noise generated inside the receivers themselves like we have on a noisy 40m band), the two outputs will be the same. The band noise goes up 2x, the desired signal goes up 2x. Think about what you are proposing: In order for there to be 3 dB SNR degradation, somehow the receiver would have to "know" what "stuff" is "signal" and what stuff is "noise" and treat them differently. A receiver (other than cases like noise blankers) does not do that. The receiver translates both band noise and desired signal to audio. Thus, as long as the signals external to the two receivers swamp the internal noise of the receivers, summing the two outputs of the two receivers driven from the same antenna will not help or hurt the signal to noise ratio. How can it hurt the SNR? How can the audio output **not add** for the desired signal and **add** for the noise? The desired signal adds the same as the undesired band noise add. I was once fooled by this thinking as well. It helped me a lot to understand that to a receiver everything is a signal. The desired station is signal. The undesired band noise is also a signal. Thus adding the output of two receivers together gets 2x "signal" and also 2x "noise". Both will increase by 6 dB, but the ratio of "signal" to "noise" is unchanged. Like I said before, the only potential signal to noise improvement happens when the receiver internal noise starts masking the external desired signals, in which case all external signals double in voltage (both signal and band noise), a 6 dB gain, while the internal noise from the two receivers will not be the same, adding in an uncorrelated manner, seeing only a 3 dB gain. Thus we can see a net signal to noise improvement since the receiver noise component will increase less than the external signal and band noise increases. Receiver noise being a limiting factor happens either under very quite band conditions, or when a very poor antenna is being used. - Dan, N7VE -----Original Message----- From: Kok Chen [mailto:[hidden email]] Sent: Monday, November 17, 2008 12:55 PM To: Elecraft Reflector Cc: Tayloe Dan-P26412 Subject: Re: [Elecraft] Re: K3: listening to both rcvrs - Reduced receiver noise floor On Nov 17, 2008, at 10:06 AM, Tayloe Dan-P26412 wrote: > Band noise from one receiver at > any instant in time will look exactly like band noise from the second > receiver. That is true if the two receivers are tuned to the same passband and you are using an identical antenna for the two receivers. In the case of receiving split, you are not looking at the same noise entering the two receivers. In this case, by combining two different passbands, the desired signal would only come from one receiver but the summed noise would come from both receivers, dropping the SNR by 3 dB. An easy test is to subtract two receiver outputs (assuming the receivers are phase coherent). You should get a "reasonable" null (sky noise and signals are nulled away, leaving just the receiver noise and any gain/phase mismatch in the two passbands) when looking at the same antenna. When you tune one receiver away, the noise level should rise. Come to think of it, it is an easy DSP experiment by looking at the output of two complex mixers using different (numerical) local oscillators. 73 Chen, W7AY _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
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On Nov 17, 2008, at 1:01 PM, Tayloe Dan-P26412 wrote: > How can it hurt the SNR? Because in split operation, you are adding the noise from two different bandpasses, yet you are only hearing the signal from the original single receiver. Let receiver (1) hear s(t) + n1(t) and receiver (2) hear n2(t) . Remember that s(t) is outside the passband of the second receiver, so there is no s(t) component in receiver 2. Sum the two receivers, and you get s(t) + n1(t) + n2(t). Prob( (s+n1+n2)^2 ) = Prob(s^2 + n1^2 + n2^2 + n1.n2 + s.n1 + s.n2). If s, n1 and n2 are uncorrelated, then Prob(n1.n2) = Prob(s.n1) = Prob(s.n2) = 0. Thus the output power of the summed signal is (s^2) + (n1^2) + (n2^2). The original single receiver SNR is (s^2)/(n1^2). The summed receiver SNR is (s^2)/( (n1^2)+ (n2^2) ) 73 Chen _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
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On Nov 17, 2008, at 3:01 PM, Kok Chen wrote: > Prob( (s+n1+n2)^2 ) = Prob(s^2 + n1^2 + n2^2 + n1.n2 + s.n1 + > s.n2). If s, n1 and n2 are uncorrelated, then Prob(n1.n2) = > Prob(s.n1) = Prob(s.n2) = 0. Whoops, that should be Prob( (s+n1+n2)^2 ) = Prob(s^2 + n1^2 + n2^2 + 2.n1.n2 + 2.s.n1 + 2.s.n2) (I should have counted that there are 9 terms altogether on the right hand side :-). But the average of ( n1.n2 ) = 0 implies that the average of ( 2.n1.n2 ) is also identically zero, etc... 73 Chen, W7AY _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
Re: K3: listening to both rcvrs - Reduced receiver
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In reply to this post by Tayloe Dan-P26412
"That is true if the two receivers are tuned to the same passband and
you are using an identical antenna for the two receivers. In the case of receiving split, you are not looking at the same noise entering the two receivers. In this case, by combining two different passbands, the desired signal would only come from one receiver but the summed noise would come from both receivers, dropping the SNR by 3 dB." Chen is correct. Back in my microwave telecom days, we used to combine two receivers from two different microwave antennas both for multipath improvement, and for S/N improvement. The desired main signals from both receivers are highly correlated, but the noise is still uncorrelated (different antennas, slightly different passbands/filter characteristics). So the main signal improves in strength 6dB (adds on a 20log basis), but the noise improves 3dB (adds on a 10log basis). The result is a 3dB S/N improvement. Phil - AD5X _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
Re: K3: listening to both rcvrs - Reduced receiver noise floor
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In reply to this post by Tayloe Dan-P26412
Tayloe Dan-P26412 wrote:
> single composite receiver with a lower noise floor. If you > added just enough RF pre-amplification to overcome the signal > splitting loss to N receivers, adding more and more receivers Only if the pre-amplifiers are noiseless, or at least contribute equivalent input noise power that is much less than the equivalent power generated by the receiver times their gain. In that case, you could do better by using the pre-amp on one receiver and dumping the excess gain later in the system. That's better in noise, but you may compromise dynamic range more. > in parallel will produce a composite receiver that has a > better and better noise floor. This is in essence what the > space telescope folks do. They gang many dishes and many > receivers together across a very large area to get an > enhancement on the signal and space noise and a suppression of > the effective receiver noise contribution. In this case, there is no splitting loss, and the noise is uncorrelated because it is being received at different locations. -- David Woolley "The Elecraft list is a forum for the discussion of topics related to Elecraft products and more general topics related ham radio" List Guidelines <http://www.elecraft.com/elecraft_list_guidelines.htm> _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
Re: K3: listening to both rcvrs - Reduced receiver noise floor
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On Tue, 18 Nov 2008 08:03:53 +0000, David Woolley (E.L) wrote:
>In this case, there is no splitting loss, and the noise is uncorrelated >because it is being received at different locations. It's a risky to assume that ALL RX noise is uncorrelated after being detected. While there may be differences in RF level due to antenna displacement and transmission line length, the detected audio may be correlated if some specific noise source is heard by both receivers. In other words, noise can be random or correlated. Examples: an impulse noise generated from a power line or hash generated by a swithing power supply. While both are broadband sources, they are NOT random. If both antennas hear a source like them, the detected audio will be correlated between the two receivers! So in that case, there's no advantage from combining the two RX outputs. The 3 dB advantage arises when the noise is truly random, like the noise preamps that are not common to the two receivers. 73, Jim Brown K9YC _______________________________________________ Elecraft mailing list Post to: [hidden email] You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com |
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