I'm trying to figure out what -- if any -- improvement in noise figure there is when you have a GPS receiver that uses an I/Q downconversion to baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that uses a downconversion to an IF frequency, followed by a single one-bit ADC. This is assuming that you are sampling all the ADCs at the same rate. Depending on how I approach it, my intuition tells me anywhere between "no difference" and "6dB". So -- anybody know? Got math to back it up? I would _love_ to see an analysis of this, before I spend any more time doing my own. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Intuition vs., well Intuition -- GPS 1-bit ADC Noise Characteristics
Started by ●January 5, 2011
Reply by ●January 5, 20112011-01-05
On 5 Jan., 21:34, Tim Wescott <t...@seemywebsite.com> wrote:> I'm trying to figure out what -- if any -- improvement in noise figure > there is when you have a GPS receiver that uses an I/Q downconversion to > baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that > uses a downconversion to an IF frequency, followed by a single one-bit > ADC. �This is assuming that you are sampling all the ADCs at the same rate. > > Depending on how I approach it, my intuition tells me anywhere between > "no difference" and "6dB". > > So -- anybody know? �Got math to back it up? �I would _love_ to see an > analysis of this, before I spend any more time doing my own. >I'd think twice as many samples, so 3dB better -Lasse
Reply by ●January 5, 20112011-01-05
On 01/05/2011 02:27 PM, langwadt@fonz.dk wrote:> On 5 Jan., 21:34, Tim Wescott<t...@seemywebsite.com> wrote: >> I'm trying to figure out what -- if any -- improvement in noise figure >> there is when you have a GPS receiver that uses an I/Q downconversion to >> baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that >> uses a downconversion to an IF frequency, followed by a single one-bit >> ADC. This is assuming that you are sampling all the ADCs at the same rate. >> >> Depending on how I approach it, my intuition tells me anywhere between >> "no difference" and "6dB". >> >> So -- anybody know? Got math to back it up? I would _love_ to see an >> analysis of this, before I spend any more time doing my own. >> > > I'd think twice as many samples, so 3dB betterWell, your intuition agrees with one of the options that my intuition coughed up. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 5, 20112011-01-05
Tim Wescott wrote:> I'm trying to figure out what -- if any -- improvement in noise figure > there is when you have a GPS receiver that uses an I/Q downconversion to > baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that > uses a downconversion to an IF frequency, followed by a single one-bit > ADC. This is assuming that you are sampling all the ADCs at the same rate. > > Depending on how I approach it, my intuition tells me anywhere between > "no difference" and "6dB". > > So -- anybody know? Got math to back it up? I would _love_ to see an > analysis of this, before I spend any more time doing my own.I/Q 1-bit thing is going to be worse then 1-bit real IF sampling. How much worse: depends on the input SNR. That's because atan2(sign(Q), sign(I)) is not the same thing as atan2(I, Q). I would expect losses at the order of 3dB. Besides, there could be some additional loss due to direct conversion vs superhet tradeoff. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●January 5, 20112011-01-05
On 01/05/2011 03:34 PM, Tim Wescott wrote:> I'm trying to figure out what -- if any -- improvement in noise figure there is when you have a GPS receiver that uses an I/Q > downconversion to baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that uses a downconversion to an IF frequency, > followed by a single one-bit ADC. This is assuming that you are sampling all the ADCs at the same rate. > > Depending on how I approach it, my intuition tells me anywhere between "no difference" and "6dB". > > So -- anybody know? Got math to back it up? I would _love_ to see an analysis of this, before I spend any more time doing my own.Really Tim. This is undergraduate level. cos(a)cos(b) = 0.5 * [cos(a+b) + cos(a-b)] sin(a)cos(b) = 0.5 * [sin(a+b) + sin(a-b)] So, even though you have two ADCs, the input to each 6 dB less (assuming you filter the high terms). Wups - there went your extra bit. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 5, 20112011-01-05
Randy Yates wrote:> On 01/05/2011 03:34 PM, Tim Wescott wrote: > >> I'm trying to figure out what -- if any -- improvement in noise figure >> there is when you have a GPS receiver that uses an I/Q >> downconversion to baseband, followed by a pair of one-bit ADCs, verses >> a GPS receiver that uses a downconversion to an IF frequency, >> followed by a single one-bit ADC. This is assuming that you are >> sampling all the ADCs at the same rate. >> >> Depending on how I approach it, my intuition tells me anywhere between >> "no difference" and "6dB". >> >> So -- anybody know? Got math to back it up? I would _love_ to see an >> analysis of this, before I spend any more time doing my own. > > > Really Tim. This is undergraduate level. > > cos(a)cos(b) = 0.5 * [cos(a+b) + cos(a-b)] > sin(a)cos(b) = 0.5 * [sin(a+b) + sin(a-b)] > > So, even though you have two ADCs, the input to each 6 dB less (assuming > you filter the > high terms). Wups - there went your extra bit.Dear Randy, The bandwidth of I and Q is 1/2 of that of the real signal. High school level, duh. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●January 5, 20112011-01-05
On 01/05/2011 06:24 PM, Vladimir Vassilevsky wrote:> > > Randy Yates wrote: > >> On 01/05/2011 03:34 PM, Tim Wescott wrote: >> >>> I'm trying to figure out what -- if any -- improvement in noise figure there is when you have a GPS receiver that uses an I/Q >>> downconversion to baseband, followed by a pair of one-bit ADCs, verses a GPS receiver that uses a downconversion to an IF frequency, >>> followed by a single one-bit ADC. This is assuming that you are sampling all the ADCs at the same rate. >>> >>> Depending on how I approach it, my intuition tells me anywhere between "no difference" and "6dB". >>> >>> So -- anybody know? Got math to back it up? I would _love_ to see an analysis of this, before I spend any more time doing my own. >> >> >> Really Tim. This is undergraduate level. >> >> cos(a)cos(b) = 0.5 * [cos(a+b) + cos(a-b)] >> sin(a)cos(b) = 0.5 * [sin(a+b) + sin(a-b)] >> >> So, even though you have two ADCs, the input to each 6 dB less (assuming you filter the >> high terms). Wups - there went your extra bit. > > Dear Randy, > The bandwidth of I and Q is 1/2 of that of the real signal. High school level, duh.So? -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 5, 20112011-01-05
On 01/05/2011 03:20 PM, Randy Yates wrote:> On 01/05/2011 03:34 PM, Tim Wescott wrote: >> I'm trying to figure out what -- if any -- improvement in noise figure >> there is when you have a GPS receiver that uses an I/Q >> downconversion to baseband, followed by a pair of one-bit ADCs, verses >> a GPS receiver that uses a downconversion to an IF frequency, >> followed by a single one-bit ADC. This is assuming that you are >> sampling all the ADCs at the same rate. >> >> Depending on how I approach it, my intuition tells me anywhere between >> "no difference" and "6dB". >> >> So -- anybody know? Got math to back it up? I would _love_ to see an >> analysis of this, before I spend any more time doing my own. > > Really Tim. This is undergraduate level. > > cos(a)cos(b) = 0.5 * [cos(a+b) + cos(a-b)] > sin(a)cos(b) = 0.5 * [sin(a+b) + sin(a-b)] > > So, even though you have two ADCs, the input to each 6 dB less (assuming > you filter the > high terms). Wups - there went your extra bit.Not when you throw the 1-bit ADC in there. That's a whopping big nonlinearity that's doing _something_, I'm just not sure what. Without the 1-bit ADC(s), and assuming a perfect I/Q conversion (hah!) the SNR is the same at IF and at baseband. It's _with_ the ADC that is making me sweat. And so far, the group is backing up my intuition -- i.e., the answers are all over the map. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 5, 20112011-01-05
On 01/05/2011 06:50 PM, Tim Wescott wrote:> On 01/05/2011 03:20 PM, Randy Yates wrote: >> On 01/05/2011 03:34 PM, Tim Wescott wrote: >>> I'm trying to figure out what -- if any -- improvement in noise figure >>> there is when you have a GPS receiver that uses an I/Q >>> downconversion to baseband, followed by a pair of one-bit ADCs, verses >>> a GPS receiver that uses a downconversion to an IF frequency, >>> followed by a single one-bit ADC. This is assuming that you are >>> sampling all the ADCs at the same rate. >>> >>> Depending on how I approach it, my intuition tells me anywhere between >>> "no difference" and "6dB". >>> >>> So -- anybody know? Got math to back it up? I would _love_ to see an >>> analysis of this, before I spend any more time doing my own. >> >> Really Tim. This is undergraduate level. >> >> cos(a)cos(b) = 0.5 * [cos(a+b) + cos(a-b)] >> sin(a)cos(b) = 0.5 * [sin(a+b) + sin(a-b)] >> >> So, even though you have two ADCs, the input to each 6 dB less (assuming >> you filter the >> high terms). Wups - there went your extra bit.> Not when you throw the 1-bit ADC in there. That's a whopping big > nonlinearity that's doing _something_, I'm just not sure what.It's converting analog to digital. No mystery there.> Without the 1-bit ADC(s), and assuming a perfect I/Q conversion > (hah!) the SNR is the same at IF and at baseband. It's _with_ the > ADC that is making me sweat.One could shoot down my argument very simply as follows. Assume the analog SNR (e.g., from the LNA/preamp) is much better than the ADC SNR. In that case you could simply lower the reference voltage to the ADC by half and thus recoup the 6 dB you "lose" when doing the (analog) quadrature mixing. So in that case my counter is not really a counter... If the analog SNR was NOT better than the ADC SNR, then it doesn't really matter what you do - it'll swamp ADC quantization noise either way. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 5, 20112011-01-05
On 01/05/2011 08:20 PM, Randy Yates wrote:> On 01/05/2011 06:50 PM, Tim Wescott wrote: > [...] >> Not when you throw the 1-bit ADC in there. That's a whopping big >> nonlinearity that's doing _something_, I'm just not sure what. > > It's converting analog to digital. No mystery there.Sorry - I just realized you mean a _1 bit ADC_, NOT a delta sigma. But I think my arguments (both the one for me and against me...) still hold if you just model the ADC as the sum of the original analog signal with [quantization] noise. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
