Sampling system SNR and SFDR

A couple comments:

First you need more than 48 MSPS to reliably (without aliasing) sample a 24 MHz wide signal. No real filter has a 'brick wall' response.

Second the 72 dB is the ideal SNR, typically ADC datasheets will list actual SNR or ENOB (effective number of bits). For a 12 bit ADC you might have 10-11 ENOB.

One way of looking at the FFT is that you have processing gain equal to the ratio of the noise bandwidth pre-FFT to the noise bandwidth after the FFT. It sounds simple (and sometimes it is) but use some caution here.

Also to calculate the "system" SNR and SFDR you need to take into account what the whole system, not just the digital side. If you have amplifiers, switches, filters etc upstream of the ADC these need to be accounted for (gain, noise figure, IP3, and IP2). This is often done with a spreadsheet, although I generally use Mathcad for the calculations.

This is a deep topic, be prepared to do a lot of reading.

Peter

First, thanks for answering.

Yep, I understand on your statement. Same with the overall system evaluation for SNR and SFDR, but I'm just trying to look at it from the point of intercomparing software defined radio boards. The ADC's have significantly different specs and the boards cost significantly different. One ADC has an ENOB of 9-10, while the other is closer to 12. One data sheet (all from ADI!) lists ENOB/SINAD as a spec, the other has a graph, etc... The max sampling rate for one ADC is 65MSPS while the other is 100 MSPS...

If I look through ADI's papers on sampling, they talk about undersampling and over sampling, mentioning process gain in that circumstance as well as process gain from the FFT afterwards on the actual data. How do I look at the process gain? Should I narrow up my AAF to increase the oversampling/reduce noise in the system? With a higher sampling rate is the system that much more effective?

Q) How do I look at the process gain?
A) Don't'. You said you wanted to compare boards. You can do the same post processing with any of them.

Q)Should I narrow up my AAF to increase the oversampling/reduce noise in the system?
A) You have to know your requirements. The vendor does not tell you what you need to do. What are your requirements? You can not tell which board is best for your specific application unless you know what you want. Ask your systems engineers for requirements.
A suggestion: If you want to compare boards generically (without benefit of your own requirements), then you could form a metric. You could multiply dynamic range by BW and get an idea of what "space" a single board would provide. You could then divide by power consumption, in case power was an important factor.

Q) With a higher sampling rate is the system that much more effective?
A) Only if you need the BW. If you need more BW than sample rate "effectiveness" is linearly increasing with BW. However, you must consider the dynamic range of that BW (see first answer above). If you do not need the BW you could play a little trick and get a smidgen of dynamic range increase (actually just SNR, not an actual increase in DYN RNG) by using the extra samples that are close together as near independent second opinions. You can do this by bandpass or lowpass filtering the oversampled data. Your SNR increase is very slow for a lot of power consumption (IMO).


jsolar

Sorry, the boards have different ADC. Pretend the theoretical number of bits doesn't change with sampling rate.

Process Gain: My thought was it it is proportional to the oversampling the ADC is capable of. ie a 100MSPS adc vs a 20MSPS. If you bandpass sample a 5MHz band, you could do 10x oversampling vs 2x or something like that. 4x oversampling is worth another bit in the ADC?

PG = 10*log10(fs/2*bw)

Over sampling spreads the quantization noise out to the nyqist frequency and then it can be lopped off with a digital filter? I guess that wouldn't be the AAF..

Aren't I saying the same thing as your third answer?

Q) Sorry, the boards have different ADC. Pretend the theoretical number of bits doesn't change with sampling rate.
A) Then just use the lowest cost board with the sample rate that meets your needs. To do a comparison in general you take all of the metrics (like sample rate or better yet sample rate times dynamic range, power consumption, etc) and compare them against the independent variable "cost"; where cost may be money or power or area or weight.


Q) Aren't I saying the same thing as your third answer?

A) Yes, you described the mechanism for undirected noise reduction. Your description assumes frequency domain processing gain. If you signal is code domain or time domain spread then you can despread in either or both domains to get processing gain. i.e. if you have a wide band signal spread by a code, then you compress by the code and you get the processing gain. So, your processing gain can be signal dependent and reviewing the board numbers won't tell you that.


jsolar

Oversampling:
Processing gain in radar usually means using a complex outgoing signal (for example: a chirp, perhaps a Barker Code), and then decoding it during receive (for processing gain). As VisiGoth mentioned, there are many types of coding. There are always trade-offs.

The fact that every 4x reduction in digital filtering and resampling buys an extra bit of the ADC is true for flash / pipeline ADCs--for sigma delta adcs you get much more. You need a filter with a gain of 2 to exploit the extra bit. Processing gain or spreading gain also builds SNR but after the processing so don't confuse that with the ADC effective bits for your application--they are important taking both into account only for a specific system--remember that all signals in the ADC bandwidth need to be accomodated without saturating the ADC.

The composite maximum signal level needs to be compared with the minimum detectable signal level. This tells how many bits are going to be needed.

An FFT give a processing gain if you are looking for signals that are tones or low BW compared with the FFT bin spacing in frequency. it is really simple the FFT of size N give an SNR increase of 10*log10(N) dB from the signal input to the FFT.

in a system i designed the signal of interest at the lowest symbol rate was less than one LSB of the ADC at the ADC output. But AWGN (to "dither the signal")and the fact that I needed to observe 125 MHz of BW and because the low data rate was about 32 ksym/sec--this buys 6 bits due to filtering out of quantization noise alone! pretty significant processing gain number

In the radar I'm working on there are many places for "process gain" (?). We monitor wind speed and typically don't see over 100hz doppler shift. We pulse at 20Khz, we do a 4096 pt fft for each gate. That is just sampling the weather...

Then there is the receive chain, bandpass sample at 60MHz. If we could get a clean pulse through, we could narrow up the AAF as far as possible, say 10Mhz and sample at 80MHz. That is 8x over sampling correct? Then we can also build a good digital filter to cut down the rest of the noise.

I find that one thing that you have to pay attention too with the ADC is the SINAD goes up with sampling rate, which reduces your effective number of bits and it could happen much faster than the over sampling.

It really excersizes the brain trying to figure out the minimum detectable signal for the system...

johnwiss, I thought you could approach one for for every 2X in sample rate (assuming you have a fixed BW of interest). You said 4X and you could do better.

Also, I think with directed dither you can subtract it out and recover some lost ground from the noise you injected. Unless you can inject the dither noise out of the band of interest and simply filter it.

SmuraiMike, It might be a better design to be limited by the environment and front end and not by the converter. You could run your A/D at 8 or so LSB per RMS noise and do OK. Or do a CFAR. Also, remmeber those angels out in the outfiled, they can have greater doppler affects.


jsolar

My understanding frustrates me... Thanks for your time.

VG-
We try and find signals down around -160 dBm. There is a lot of averaging, time series and spectra. The noise level is set at the LSB so the angels don't kill us as easily and data processing chops the bigger signals. We are doing other things to help reduced aliased signals...

I found CFAR on wikipedia and will read up.

when you say "a/d at 8 or so lsb per rms noise and do okay", you mean 8x over sample the band? You mean the over sampling will saturate the ADC?

We are limited by return signals and the MDS w/o saturation of the Mixer/LNA. There are limiters, etc.

SamuraiMike,
-160 dBm, WOW, you are out of my league!
My hat is off to you. I know of work we did for indoor GPS that approached those numbers, but there were tricks and glitches.

You said
"The noise level is set at the LSB"
I made the comment that it was a good idea to set the LSB to a noise level of 4 or maybe 8 LSB's. If you do not toggle enough LSB's with noise then you can not (Well at least I don't know how) signal process down to dig a signal out of that noise. So, I do not how you get good processing gain if you are only toggling 1 bit. So, I did not mean that it was 8x oversampling, but that the RMS voltage was set equal to 8 LSB's.

If you are getting this extreme capability you must have experts in each of these areas to tap. you don't get -160 dBm in multi MHz systems with large dynamic ranges without getting everything right. Congrats!


jsolar

The return comes off of clear air, the discontinuities in the atmostpheric density. We just have to average a millions times to extract it (if you only have pico volts, but they are repeatable you can average enough). It works, but could use some real tweaking. I think most weather radars only use the first few bits because returns vary from minimal - to saturation levels so easily (I guess missle radars have the same problem). We don't have to react quickly to an incoming missle (maybe a hail ball!). You can average time series a million times or do 64k ffts. We'd rather do long ffts because it makes filtering the data easier. Anything you can do to reduce the averaging is good because it creates a lot of data abnormalities... I guess when you say right, right fortunately has a wide range!