Dear Group, I'm a student at the University of Aberdeen. I do a project in the area of Software Defined Radio (SDR). During the system design I came across to topic of using 1-bit ADCs for signal conversion. The following question arose: Is the direct conversion of RF signals possible with 1-bit ADCs? From the signal processing point of view such a conversion method should be no problem, if we want to receive narrow band band-pass signals, i.e. signals having a much higher centre frequency then bandwidth. We can trade precision, i.e. dynamic range against sampling frequency. A single bit ADC should allow for very high sampling frequencies. From what I understand single bit ADC would have the following advantages: -No frequency conversion in the analogue domain. Each analogue signal processing stage will introduce unavoidable noise. This noise can be avoided in the digital domain. -No gain control in the analogue domain. A one bit ADC detects only whether or not the signal has positive voltage and encodes this information into one bit. The ultimate signal levels are not important, i.e. it does not matter whether the signal has +1 or +5 volts. I think this is an important feature of such a converter, because for higher precision ADCs analogue signal conditioning (gain control) is always a topic. -Simple circuits. Due to the fact that a large part of the analogue signal processing is moved into to digital domain there is no analogue circuitry required to perform this processing. The analogue circuits are replaced by digital signal processor chips. I would be graceful for some suggestions for that topic. Oliver Faust
1-bit ADC for RF, is it possible?
Started by ●December 16, 2003
Reply by ●December 16, 20032003-12-16
Oliver Faust wrote:> Dear Group, > > I'm a student at the University of Aberdeen. I do a project in the > area of Software Defined Radio (SDR). During the system design I came > across to topic of using 1-bit ADCs for signal conversion. The > following question arose: > Is the direct conversion of RF signals possible with 1-bit ADCs? > From the signal processing point of view such a conversion method > should be no problem, if we want to receive narrow band band-pass > signals, i.e. signals having a much higher centre frequency then > bandwidth. We can trade precision, i.e. dynamic range against > sampling frequency. A single bit ADC should allow for very high > sampling frequencies. > From what I understand single bit ADC would have the following > advantages: > -No frequency conversion in the analogue domain. > Each analogue signal processing stage will introduce unavoidable > noise. This noise can be avoided in the digital domain. > -No gain control in the analogue domain. > A one bit ADC detects only whether or not the signal has positive > voltage and encodes this information into one bit. The ultimate signal > levels are not important, i.e. it does not matter whether the signal > has +1 or +5 volts. > I think this is an important feature of such a converter, because for > higher precision ADCs analogue signal conditioning (gain control) is > always a topic. > -Simple circuits. > Due to the fact that a large part of the analogue signal processing is > moved into to digital domain there is no analogue circuitry required > to perform this processing. The analogue circuits are replaced by > digital signal processor chips. > I would be graceful for some suggestions for that topic. > > Oliver FaustOliver, I see some wrong impressions that I think you can sort out yourself. Sub-band sampling (sampling a narrow band of RF) can use a rate determined only by the bandwidth, but the sampling jitter and aperture time need to be appropriate to the actual radio frequency. One-bit converters work with as many bits as needed. The DACs that translate 16-bit CD audio are one-bit converters in modern players. They work by oversampling and filtering. At RF, the oversampling rate gets too high to be the best way. (Google for 'software radio' and for 'sigma-delta' and 'delta-sigma'.) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 17, 20032003-12-17
Jerry Avins <jya@ieee.org> wrote in message news:<3fdf1264$0$4747$61fed72c@news.rcn.com>...> > Oliver, > > I see some wrong impressions that I think you can sort out yourself. > > Sub-band sampling (sampling a narrow band of RF) can use a rate > determined only by the bandwidth, but the sampling jitter and aperture > time need to be appropriate to the actual radio frequency. > > One-bit converters work with as many bits as needed. The DACs that > translate 16-bit CD audio are one-bit converters in modern players. They > work by oversampling and filtering. At RF, the oversampling rate gets > too high to be the best way. (Google for 'software radio' and for > 'sigma-delta' and 'delta-sigma'.) > > JerryJerry, Thanks for your answer. But I have some further questions, especially concerning your statement that the over-sampling rate gets to high. My statement is that the necessary over-sampling rate is only determined by the signal bandwidth. Say, if we have a signal with a bandwidth of 1MHz and we want to perform a 200 times over-sampling we need to generate a sampling frequency of at least 200MHz. The first Nyquist range for that sampling frequency goes form dc to 100MHz. It does not matter where the 1MHz signal is located within this 100MHz. As long as we know centre frequency of that signal we can bring it down into the base-band. This base-band signal is complex, therefore it is represented by I and Q signals. The next step is to filter these signals with a low pass filter having a cut off frequency of 1MHz. This operation increases the signal to noise ratio. Due to the fact that the quantization noise is equally distributed over the complete frequency range while the signal of interest is centred at DC. The filtering cuts away all the noise above 1MHz and leaves the signal of interest untouched. After these noise reduction filters, it is save to perform a down sampling. The output rate of the down sampler is then just as high as the maximum signal bandwidth in the RF domain. In the case of the 1MHz signal, the output rate is also only 1MHz, but the sample values are complex and therefore they are represented using I and Q signals. This method is different from the sigma-delta converters used in audio applications. These converters assume that the centre frequency of the signal is lower then the signal bandwidth. This is not the case for narrowband band-pass signals, used in wireless communications. I can see two restrictions in that kind of conversion scheme: 1.) The signal in the radio domain must be located within the first Nyquist range of the sampling frequency. 2.) The over sampling rate mast be high enough in order to reduce the signal to noise ratio. Both restrictions are due to a limited sampling frequency. In other words, as the sampling frequency gets higher the better for the type of signal conversion. Oliver Faust
Reply by ●December 17, 20032003-12-17
>Say, if we have a signal with a bandwidth of > 1MHz and we want to perform a 200 times over-sampling we need to > generate a sampling frequency of at least 200MHz. The first Nyquist > range for that sampling frequency goes form dc to 100MHz. It does not > matter where the 1MHz signal is located within this 100MHz. As long as > we know centre frequency of that signal we can bring it down into the > base-band.The centre frequency will be quite high ie perhaps say 50MHz as an example... now any sampling jitter from the ADC clock etc expressed as a percentage of the period of the 50MHz would be: %jitter = jitter*50Mhz Hence as the RF frequency (sic) increases so too does the proportional jitter due to the sampling process. I think this is the issue that Jerry was trying to get across... The jitter of the sampling process will have to be more controlled as the RF frequency increases. Hence the signal to noise ratio of the system will not be frequency independant, instead as the (shifted) frequency increases the signal to noise ratio gets worse.> I can see two restrictions in that kind of conversion scheme: > 1.) The signal in the radio domain must be located within the first > Nyquist range of the sampling frequency. > 2.) The over sampling rate mast be high enough in order to reduce the > signal to noise ratio.I assume that you mean 'increase the signal to noise ratio'. I can't see why you'd want a higher sample rate just to reduce the signal to noise ratio... perhaps the noise to signal ratio :P Certainly the sampling rate must be high enough to give sufficient signal to noise gains to perform any baseband processing of the signal.
Reply by ●December 17, 20032003-12-17
"Oliver Faust" <newsgroup_faust@web.de> wrote in message news:e33b6813.0312162255.65809ae1@posting.google.com... <snip>> Jerry, > Thanks for your answer. But I have some further questions,especially> concerning your statement that the over-sampling rate gets to high.My> statement is that the necessary over-sampling rate is onlydetermined> by the signal bandwidth. Say, if we have a signal with a bandwidthof> 1MHz and we want to perform a 200 times over-sampling we need to > generate a sampling frequency of at least 200MHz. The first Nyquist > range for that sampling frequency goes form dc to 100MHz. It doesnot> matter where the 1MHz signal is located within this 100MHz. As longas> we know centre frequency of that signal we can bring it down intothe> base-band. This base-band signal is complex, therefore it is > represented by I and Q signals. The next step is to filter these > signals with a low pass filter having a cut off frequency of 1MHz. > This operation increases the signal to noise ratio. Due to the fact > that the quantization noise is equally distributed over the complete > frequency range while the signal of interest is centred at DC. The > filtering cuts away all the noise above 1MHz and leaves the signalof> interest untouched.<snip>> Oliver FaustOliver, as well as Jerry's google suggestions try "band pass sigma delta" (and variants). Also, have a look for papers by Richard Schreier, for example. What you say above is correct, but not the whole story. Regards Ian
Reply by ●December 17, 20032003-12-17
Oliver Faust wrote:> Jerry Avins <jya@ieee.org> wrote in message news:<3fdf1264$0$4747$61fed72c@news.rcn.com>... > >>Oliver, >> >>I see some wrong impressions that I think you can sort out yourself. >> >>Sub-band sampling (sampling a narrow band of RF) can use a rate >>determined only by the bandwidth, but the sampling jitter and aperture >>time need to be appropriate to the actual radio frequency. >> >>One-bit converters work with as many bits as needed. The DACs that >>translate 16-bit CD audio are one-bit converters in modern players. They >>work by oversampling and filtering. At RF, the oversampling rate gets >>too high to be the best way. (Google for 'software radio' and for >>'sigma-delta' and 'delta-sigma'.) >> >>Jerry > > > Jerry, > Thanks for your answer. But I have some further questions, especially > concerning your statement that the over-sampling rate gets to high. My > statement is that the necessary over-sampling rate is only determined > by the signal bandwidth. Say, if we have a signal with a bandwidth of > 1MHz and we want to perform a 200 times over-sampling we need to > generate a sampling frequency of at least 200MHz. The first Nyquist > range for that sampling frequency goes form dc to 100MHz. It does not > matter where the 1MHz signal is located within this 100MHz. As long as > we know centre frequency of that signal we can bring it down into the > base-band. This base-band signal is complex, therefore it is > represented by I and Q signals. The next step is to filter these > signals with a low pass filter having a cut off frequency of 1MHz. > This operation increases the signal to noise ratio. Due to the fact > that the quantization noise is equally distributed over the complete > frequency range while the signal of interest is centred at DC. The > filtering cuts away all the noise above 1MHz and leaves the signal of > interest untouched. > After these noise reduction filters, it is save to perform a down > sampling. The output rate of the down sampler is then just as high as > the maximum signal bandwidth in the RF domain. In the case of the 1MHz > signal, the output rate is also only 1MHz, but the sample values are > complex and therefore they are represented using I and Q signals. > This method is different from the sigma-delta converters used in audio > applications. These converters assume that the centre frequency of the > signal is lower then the signal bandwidth. This is not the case for > narrowband band-pass signals, used in wireless communications. > I can see two restrictions in that kind of conversion scheme: > 1.) The signal in the radio domain must be located within the first > Nyquist range of the sampling frequency. > 2.) The over sampling rate mast be high enough in order to reduce the > signal to noise ratio. > Both restrictions are due to a limited sampling frequency. In other > words, as the sampling frequency gets higher the better for the type > of signal conversion. > > Oliver FaustOliver, I think there are two kinds of oversampling entwined with each other on your message. http://www.google.com/search?q=delta+sigma+converter will point you to a number of papers that explain how a delta-sigma (a so-called "one-bit") converter works. You will see that for every valid n-bit sample it reports, it actually acquires and processes many one-bit samples. To get a single output of n bits of resolution, the source must be sampled 2^n times*. You don't want to use a delta-sigma converter much above audio. (Besides, it's a red herring. Generally speaking, "over sampling" applies to sampling faster than the Nyquist requirement. There ought to be a different term for the flurry of one-bit samples that are low-pass filtered just to get one n-bit one.) When the signal frequency gets high enough, one thinks of flash converters, not S-D. Jerry ______________________________________ * http://www.microchip.com/download/appnote/devspec/16cxx/00700a.pdf -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 17, 20032003-12-17
Hi Oliver, For RF transmission, I think sigma-delta techniques are a very big deal, because "class D" power amplifiers are very cheap and effiicent, compared to linear power amps that do the same job. It's not too hard to imagine these sorts of circuits working fine, because just about everything can be digital -- you don't really need the analog feedback and comparison if you start with a baseband digital source and precalculate the RF pulse output. Reception, though, requires those analog components, and even the S-D's simple single-bit sampling and feedback can be very difficult at RF speeds. It is probably better just to mix down to baseband or some intermediate frequency and do the Sigma-Delta ADC there, where it's easy.
Reply by ●December 18, 20032003-12-18
Matt Timmermans wrote:> Hi Oliver, > > For RF transmission, I think sigma-delta techniques are a very big deal, > because "class D" power amplifiers are very cheap and effiicent, compared to > linear power amps that do the same job. It's not too hard to imagine these > sorts of circuits working fine, because just about everything can be > digital -- you don't really need the analog feedback and comparison if you > start with a baseband digital source and precalculate the RF pulse output. > > Reception, though, requires those analog components, and even the S-D's > simple single-bit sampling and feedback can be very difficult at RF speeds. > It is probably better just to mix down to baseband or some intermediate > frequency and do the Sigma-Delta ADC there, where it's easy.What am I missing? Sigma-delta converters provide exactly the same outputs as successive-approximation or flash designs except for increased latency that renders them unsuitable for certain applications. They trade in complexity for speed, just as a serial adder is less complex than a parallel adder, but needs to run faster. Just as a sum is a sum, so is a conversion a conversion. That the optimum circuit configuration depends on the specifics of sampling rate and latency need should be no surprise. Engineering is like that. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 18, 20032003-12-18
"Bevan Weiss" <kaizen__@NOSPAMhotmail.com> wrote in message news:<3fe02ef5$1@news.orcon.net.nz>...> >Say, if we have a signal with a bandwidth of > > 1MHz and we want to perform a 200 times over-sampling we need to > > generate a sampling frequency of at least 200MHz. The first Nyquist > > range for that sampling frequency goes form dc to 100MHz. It does not > > matter where the 1MHz signal is located within this 100MHz. As long as > > we know centre frequency of that signal we can bring it down into the > > base-band. > > The centre frequency will be quite high ie perhaps say 50MHz as an > example... > now any sampling jitter from the ADC clock etc expressed as a percentage of > the period of the 50MHz would be: > %jitter = jitter*50Mhz > > Hence as the RF frequency (sic) increases so too does the proportional > jitter due to the sampling process. > I think this is the issue that Jerry was trying to get across... The jitter > of the sampling process will have to be more controlled as the RF frequency > increases. Hence the signal to noise ratio of the system will not be > frequency independant, instead as the (shifted) frequency increases the > signal to noise ratio gets worse. >Bevan, I agree that jitter is a critical property of a communication system. As I understand it in "normal" receiver systems we have similar problems. To transfer the RF signal into an intermediate frequency (IF) signal we use an analogue voltage controlled oscillator (VCO). I guess this frequency generator will introduce similar jitter. (jitter=jitter*f_c (RF)). But for "normal" systems the sampling clock represents a second jitter source. According to your formula this clock will introduce: jitter=jitter*f_IF. The system I propose goes away with the jitter source located in the analogue tuner. There is only the sampling clock left. The down mixing in the digital domain won't introduce any additional jitter. Now the question is: Is the jitter for the sampler in the new system harder to control than in a "normal" receiver? I doubt that, because to tune to a specific frequency in an analogue tuner a voltage controlled oscillator is used. I guess that such a VCO will introduce more jitter then a fixed sampling frequency.> > I can see two restrictions in that kind of conversion scheme: > > 1.) The signal in the radio domain must be located within the first > > Nyquist range of the sampling frequency. > > 2.) The over sampling rate mast be high enough in order to reduce the > > signal to noise ratio. > > I assume that you mean 'increase the signal to noise ratio'.Yes, Your assumption is correct. Error on my side. Oliver
Reply by ●December 18, 20032003-12-18
Oliver Faust wrote: ...> As I understand it in "normal" receiver systems we have similar > problems. To transfer the RF signal into an intermediate frequency > (IF) signal we use an analogue voltage controlled oscillator (VCO). I > guess this frequency generator will introduce similar jitter. > (jitter=jitter*f_c (RF)). But for "normal" systems the sampling clock > represents a second jitter source. According to your formula this > clock will introduce: jitter=jitter*f_IF. > The system I propose goes away with the jitter source located in the > analogue tuner. There is only the sampling clock left. The down mixing > in the digital domain won't introduce any additional jitter. Now the > question is: > Is the jitter for the sampler in the new system harder to control than > in a "normal" receiver? > I doubt that, because to tune to a specific frequency in an analogue > tuner a voltage controlled oscillator is used. I guess that such a VCO > will introduce more jitter then a fixed sampling frequency.Jitter in modulators and demodulators is often referred to phase noise. A-to-D concerters have an uncertainty in the time between a command to sample is given, and when the sample is actually taken. Converters intended for use at higher frequencies have smaller uncertainties. Even though it is capable of the necessary sampling rate, a given converter may not have small enough "aperture" uncertainty to successfully sample a narrow band on a high-frequency carrier. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
