Forums

Does oversampling bring diversity gain?

Started by Benjamin Jiajia May 11, 2007
On 12 May 2007 18:13:12 -0700, Mark <makolber@yahoo.com> wrote:

>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >> On 11 May 2007 13:01:57 -0700, Mark <makol...@yahoo.com> wrote: >> >> >> Noise is different, since the noise instances in the samples will not >> >> be correlated if the noise is white. >> >> >> So, really, it depends on the channel model. Noise? Sure, >> >> oversampling improves "diversity". Fading? Not gonna help at all. >> >> >If the signal has passed through a bandpass filter near the Nyquist >> >BW, which is the usual case in a receiver, will not the noise during >> >samples taken of any particular symbol, be highly correlated thus >> >reducing any gain of oversampling? >> >> >Mark >> >> Remember that this case is just the usual SNR improvement due to the >> processing gain from oversampling and filtering. Nothing magic going >> on there, it's just that the 'diversity' point of view is another way >> to look at it. >> >> >This usual SNR improvement processing gain applies only to wideband >noise generated after the channel filter and does not apply to narrow >band noise generated before the channel filter.. > >Mark
Certainly the relative bandwidth of the noise matters. The OP didn't specify the architecture, so we can only speculate or generalize. That's why I tried to clarify that diversity really only works if the impairments in the diversity sources are decorrelated. As long as that's true there'll be gain due to diversity. That applies to noise as well, so you're right, if the noise is correlated there won't be an opportunity for gain via diversity combining. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org
>On 12 May :13:, Mark <makolber@yahoo.com> wrote: > >>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >>> On 11 May :01:, Mark <makol...@yahoo.com> wrote: >>> >>> >> Noise is different, since the noise instances in the samples will
not
>>> >> be correlated if the noise is white. >>> >>> >> So, really, it depends on the channel model. Noise? Sure, >>> >> oversampling improves "diversity". Fading? Not gonna help at
all.
>>> >>> >If the signal has passed through a bandpass filter near the Nyquist >>> >BW, which is the usual case in a receiver, will not the noise during >>> >samples taken of any particular symbol, be highly correlated thus >>> >reducing any gain of oversampling? >>> >>> >Mark >>> >>> Remember that this case is just the usual SNR improvement due to the >>> processing gain from oversampling and filtering. Nothing magic
going
>>> on there, it's just that the 'diversity' point of view is another way >>> to look at it. >>> >>> >>This usual SNR improvement processing gain applies only to wideband >>noise generated after the channel filter and does not apply to narrow >>band noise generated before the channel filter.. >> >>Mark > >Certainly the relative bandwidth of the noise matters. The OP didn't >specify the architecture, so we can only speculate or generalize. > >That's why I tried to clarify that diversity really only works if the >impairments in the diversity sources are decorrelated. As long as >that's true there'll be gain due to diversity. That applies to noise >as well, so you're right, if the noise is correlated there won't be an >opportunity for gain via diversity combining. >Eric Jacobsen >Minister of Algorithms >Abineau Communications >http://www.ericjacobsen.org >
The last sentence confused me. Let's consider double spatial diversity. Assume the additive noise at both signal branches are fully correlated. I can still achieve a diversity gain by any combining schemes if both branch signals are not fully correlated, cannot I? LBB _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
On Mon, 14 May 2007 14:38:05 -0500, "lanbaba" <lanbaba@gmx.ch> wrote:

>>On 12 May :13:, Mark <makolber@yahoo.com> wrote: >> >>>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >>>> On 11 May :01:, Mark <makol...@yahoo.com> wrote: >>>> >>>> >> Noise is different, since the noise instances in the samples will >not >>>> >> be correlated if the noise is white. >>>> >>>> >> So, really, it depends on the channel model. Noise? Sure, >>>> >> oversampling improves "diversity". Fading? Not gonna help at >all. >>>> >>>> >If the signal has passed through a bandpass filter near the Nyquist >>>> >BW, which is the usual case in a receiver, will not the noise during >>>> >samples taken of any particular symbol, be highly correlated thus >>>> >reducing any gain of oversampling? >>>> >>>> >Mark >>>> >>>> Remember that this case is just the usual SNR improvement due to the >>>> processing gain from oversampling and filtering. Nothing magic >going >>>> on there, it's just that the 'diversity' point of view is another way >>>> to look at it. >>>> >>>> >>>This usual SNR improvement processing gain applies only to wideband >>>noise generated after the channel filter and does not apply to narrow >>>band noise generated before the channel filter.. >>> >>>Mark >> >>Certainly the relative bandwidth of the noise matters. The OP didn't >>specify the architecture, so we can only speculate or generalize. >> >>That's why I tried to clarify that diversity really only works if the >>impairments in the diversity sources are decorrelated. As long as >>that's true there'll be gain due to diversity. That applies to noise >>as well, so you're right, if the noise is correlated there won't be an >>opportunity for gain via diversity combining. >>Eric Jacobsen >>Minister of Algorithms >>Abineau Communications >>http://www.ericjacobsen.org >> > >The last sentence confused me. Let's consider double spatial diversity. >Assume the additive noise at both signal branches are fully correlated. I >can still achieve a diversity gain by any combining schemes if both branch >signals are not fully correlated, cannot I?
Well, I can clarify what I meant: If noise is the only impairment, then diversity combining of two signals will provide gain as long as the noise is not correlated between the diversity sources. With two separate input streams I think it would be pretty tough get the noise correlated, but with one input stream and the "diversity" obtained by taking additional samples, the noise could become correlated if a lot of filtering had been applied. So, in your example, as I understand it, if there are additional fading impairments that are uncorrelated across the two channels, then even if the noise *were* correlated (which would be a pretty cool trick), then there could still be substantial gain due to overcoming the uncorrelated fading. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org
>On Mon, 14 May 2007 14:38:05 -0500, "lanbaba" <lanbaba@gmx.ch> wrote: > >>>On 12 May :13:, Mark <makolber@yahoo.com> wrote: >>> >>>>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >>>>> On 11 May :01:, Mark <makol...@yahoo.com> wrote: >>>>> >>>>> >> Noise is different, since the noise instances in the samples
will
>>not >>>>> >> be correlated if the noise is white. >>>>> >>>>> >> So, really, it depends on the channel model. Noise? Sure, >>>>> >> oversampling improves "diversity". Fading? Not gonna help at >>all. >>>>> >>>>> >If the signal has passed through a bandpass filter near the
Nyquist
>>>>> >BW, which is the usual case in a receiver, will not the noise
during
>>>>> >samples taken of any particular symbol, be highly correlated thus >>>>> >reducing any gain of oversampling? >>>>> >>>>> >Mark >>>>> >>>>> Remember that this case is just the usual SNR improvement due to
the
>>>>> processing gain from oversampling and filtering. Nothing magic >>going >>>>> on there, it's just that the 'diversity' point of view is another
way
>>>>> to look at it. >>>>> >>>>> >>>>This usual SNR improvement processing gain applies only to wideband >>>>noise generated after the channel filter and does not apply to narrow >>>>band noise generated before the channel filter.. >>>> >>>>Mark >>> >>>Certainly the relative bandwidth of the noise matters. The OP didn't >>>specify the architecture, so we can only speculate or generalize. >>> >>>That's why I tried to clarify that diversity really only works if the >>>impairments in the diversity sources are decorrelated. As long as >>>that's true there'll be gain due to diversity. That applies to noise >>>as well, so you're right, if the noise is correlated there won't be an >>>opportunity for gain via diversity combining. >>>Eric Jacobsen >>>Minister of Algorithms >>>Abineau Communications >>>http://www.ericjacobsen.org >>> >> >>The last sentence confused me. Let's consider double spatial diversity. >>Assume the additive noise at both signal branches are fully correlated.
I
>>can still achieve a diversity gain by any combining schemes if both
branch
>>signals are not fully correlated, cannot I? > >Well, I can clarify what I meant: If noise is the only impairment, >then diversity combining of two signals will provide gain as long as >the noise is not correlated between the diversity sources. With two >separate input streams I think it would be pretty tough get the noise >correlated, but with one input stream and the "diversity" obtained by >taking additional samples, the noise could become correlated if a lot >of filtering had been applied. > >So, in your example, as I understand it, if there are additional >fading impairments that are uncorrelated across the two channels, then >even if the noise *were* correlated (which would be a pretty cool >trick), then there could still be substantial gain due to overcoming >the uncorrelated fading. > >Eric Jacobsen >Minister of Algorithms >Abineau Communications >http://www.ericjacobsen.org >
What even more confuses me is why you are talking about noise correlation all the time in conjunction with diversity gain. If the RX does not get uncorrelated replica of transmitted signals you can combine as you like and get no diversity gain, and this has nothing to do with the correlation of the additive noise. In the case of "oversampling", I would even not call it a "diversity combining" since there is no diversity conceptually. I would rather call it denoising by averaging if I have to give it a name. LBB _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
On Tue, 15 May 2007 06:48:27 -0500, "lanbaba" <lanbaba@gmx.ch> wrote:

>>On Mon, 14 May 2007 14:38:05 -0500, "lanbaba" <lanbaba@gmx.ch> wrote: >> >>>>On 12 May :13:, Mark <makolber@yahoo.com> wrote: >>>> >>>>>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >>>>>> On 11 May :01:, Mark <makol...@yahoo.com> wrote: >>>>>> >>>>>> >> Noise is different, since the noise instances in the samples >will >>>not >>>>>> >> be correlated if the noise is white. >>>>>> >>>>>> >> So, really, it depends on the channel model. Noise? Sure, >>>>>> >> oversampling improves "diversity". Fading? Not gonna help at >>>all. >>>>>> >>>>>> >If the signal has passed through a bandpass filter near the >Nyquist >>>>>> >BW, which is the usual case in a receiver, will not the noise >during >>>>>> >samples taken of any particular symbol, be highly correlated thus >>>>>> >reducing any gain of oversampling? >>>>>> >>>>>> >Mark >>>>>> >>>>>> Remember that this case is just the usual SNR improvement due to >the >>>>>> processing gain from oversampling and filtering. Nothing magic >>>going >>>>>> on there, it's just that the 'diversity' point of view is another >way >>>>>> to look at it. >>>>>> >>>>>> >>>>>This usual SNR improvement processing gain applies only to wideband >>>>>noise generated after the channel filter and does not apply to narrow >>>>>band noise generated before the channel filter.. >>>>> >>>>>Mark >>>> >>>>Certainly the relative bandwidth of the noise matters. The OP didn't >>>>specify the architecture, so we can only speculate or generalize. >>>> >>>>That's why I tried to clarify that diversity really only works if the >>>>impairments in the diversity sources are decorrelated. As long as >>>>that's true there'll be gain due to diversity. That applies to noise >>>>as well, so you're right, if the noise is correlated there won't be an >>>>opportunity for gain via diversity combining. >>>>Eric Jacobsen >>>>Minister of Algorithms >>>>Abineau Communications >>>>http://www.ericjacobsen.org >>>> >>> >>>The last sentence confused me. Let's consider double spatial diversity. >>>Assume the additive noise at both signal branches are fully correlated. >I >>>can still achieve a diversity gain by any combining schemes if both >branch >>>signals are not fully correlated, cannot I? >> >>Well, I can clarify what I meant: If noise is the only impairment, >>then diversity combining of two signals will provide gain as long as >>the noise is not correlated between the diversity sources. With two >>separate input streams I think it would be pretty tough get the noise >>correlated, but with one input stream and the "diversity" obtained by >>taking additional samples, the noise could become correlated if a lot >>of filtering had been applied. >> >>So, in your example, as I understand it, if there are additional >>fading impairments that are uncorrelated across the two channels, then >>even if the noise *were* correlated (which would be a pretty cool >>trick), then there could still be substantial gain due to overcoming >>the uncorrelated fading. >> >>Eric Jacobsen >>Minister of Algorithms >>Abineau Communications >>http://www.ericjacobsen.org >> > >What even more confuses me is why you are talking about noise correlation >all the time in conjunction with diversity gain. If the RX does not get >uncorrelated replica of transmitted signals you can combine as you like >and get no diversity gain, and this has nothing to do with the correlation >of the additive noise. In the case of "oversampling", I would even not call >it a "diversity combining" since there is no diversity conceptually. I >would rather call it denoising by averaging if I have to give it a name.
Perhaps you missed my first post in the thread where I said: "I think if you really want to stretch the usual use of the term "diversity" you could make that argument, although some people might raise an eyebrow at the idea." I don't disagree with you, but as I mentioned earlier if noise is the only impairment then oversampling a signal, with a noise BW wide enough that the noise is decorrelated between samples, is essentially the same thing as using time diversity to transmit the signal twice and combine them. So from that perspective oversampling to overcome noise is essentially the same thing as time diversity reception. I thought it was important to clarify that because if the impairment is fading then oversampling will be unlikely to provide any diversity gain (since the fading will be correlated), but time diversity *would* still be likely to provide gain as long as the transmissions were separated by more than the channel coherence time. So there's a difference between whether the primary impairment is noise or fading, and to the OPs point noise is the only case that would really work to fit his description. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org
>On Tue, 15 May :48:, "lanbaba" <lanbaba@gmx.ch> wrote: > >>>On Mon, 14 May :38:, "lanbaba" <lanbaba@gmx.ch> wrote: >>> >>>>>On 12 May :13:, Mark <makolber@yahoo.com> wrote: >>>>> >>>>>>On May 11, 7:52 pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >>>>>>> On 11 May :01:, Mark <makol...@yahoo.com> wrote: >>>>>>> >>>>>>> >> Noise is different, since the noise instances in the samples >>will >>>>not >>>>>>> >> be correlated if the noise is white. >>>>>>> >>>>>>> >> So, really, it depends on the channel model. Noise? Sure, >>>>>>> >> oversampling improves "diversity". Fading? Not gonna help
at
>>>>all. >>>>>>> >>>>>>> >If the signal has passed through a bandpass filter near the >>Nyquist >>>>>>> >BW, which is the usual case in a receiver, will not the noise >>during >>>>>>> >samples taken of any particular symbol, be highly correlated
thus
>>>>>>> >reducing any gain of oversampling? >>>>>>> >>>>>>> >Mark >>>>>>> >>>>>>> Remember that this case is just the usual SNR improvement due to >>the >>>>>>> processing gain from oversampling and filtering. Nothing magic >>>>going >>>>>>> on there, it's just that the 'diversity' point of view is another >>way >>>>>>> to look at it. >>>>>>> >>>>>>> >>>>>>This usual SNR improvement processing gain applies only to wideband >>>>>>noise generated after the channel filter and does not apply to
narrow
>>>>>>band noise generated before the channel filter.. >>>>>> >>>>>>Mark >>>>> >>>>>Certainly the relative bandwidth of the noise matters. The OP
didn't
>>>>>specify the architecture, so we can only speculate or generalize. >>>>> >>>>>That's why I tried to clarify that diversity really only works if
the
>>>>>impairments in the diversity sources are decorrelated. As long as >>>>>that's true there'll be gain due to diversity. That applies to
noise
>>>>>as well, so you're right, if the noise is correlated there won't be
an
>>>>>opportunity for gain via diversity combining. >>>>>Eric Jacobsen >>>>>Minister of Algorithms >>>>>Abineau Communications >>>>>http://www.ericjacobsen.org >>>>> >>>> >>>>The last sentence confused me. Let's consider double spatial
diversity.
>>>>Assume the additive noise at both signal branches are fully
correlated.
>>I >>>>can still achieve a diversity gain by any combining schemes if both >>branch >>>>signals are not fully correlated, cannot I? >>> >>>Well, I can clarify what I meant: If noise is the only impairment, >>>then diversity combining of two signals will provide gain as long as >>>the noise is not correlated between the diversity sources. With two >>>separate input streams I think it would be pretty tough get the noise >>>correlated, but with one input stream and the "diversity" obtained by >>>taking additional samples, the noise could become correlated if a lot >>>of filtering had been applied. >>> >>>So, in your example, as I understand it, if there are additional >>>fading impairments that are uncorrelated across the two channels, then >>>even if the noise *were* correlated (which would be a pretty cool >>>trick), then there could still be substantial gain due to overcoming >>>the uncorrelated fading. >>> >>>Eric Jacobsen >>>Minister of Algorithms >>>Abineau Communications >>>http://www.ericjacobsen.org >>> >> >>What even more confuses me is why you are talking about noise
correlation
>>all the time in conjunction with diversity gain. If the RX does not get >>uncorrelated replica of transmitted signals you can combine as you like >>and get no diversity gain, and this has nothing to do with the
correlation
>>of the additive noise. In the case of "oversampling", I would even not
call
>>it a "diversity combining" since there is no diversity conceptually. I >>would rather call it denoising by averaging if I have to give it a
name.
> >Perhaps you missed my first post in the thread where I said: > >"I think if you really want to stretch the usual use of the term >"diversity" you could make that argument, although some people might >raise an eyebrow at the idea." > >I don't disagree with you, but as I mentioned earlier if noise is the >only impairment then oversampling a signal, with a noise BW wide >enough that the noise is decorrelated between samples, is essentially >the same thing as using time diversity to transmit the signal twice >and combine them. So from that perspective oversampling to overcome >noise is essentially the same thing as time diversity reception. > >I thought it was important to clarify that because if the impairment >is fading then oversampling will be unlikely to provide any diversity >gain (since the fading will be correlated), but time diversity *would* >still be likely to provide gain as long as the transmissions were >separated by more than the channel coherence time. > >So there's a difference between whether the primary impairment is >noise or fading, and to the OPs point noise is the only case that >would really work to fit his description. > >Eric Jacobsen >Minister of Algorithms >Abineau Communications >http://www.ericjacobsen.org >
That was a neat summary. LBB _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?