I am working on modelling and simulations of synthetic aperture sonar at component/subsystem level. I have started with standard sonar equations for calculating detection ranges for different environmental conditions. One parameter i calculated is Minimum Discernible Signal (MDS) which is difference b/w detection threshold (DT) and array gain/directivity index (AG/DI) (beam forming). According to book definition. MDS is SNR at array's hydrophone face required for detection at some preassigned level of correctness.
After hydrophones, there are of course pre-amplifiers (PA) and ADCs before beam former stage (DI/AG). My confusion is how to interpret this MDS/SNR in terms of PA and ADC specifications?. I have defined and fixed receiving sensitivity of hydrophones, however i need to drive PA and ADCs specifications from calculated MDS especially in terms of noise levels so that same MDS/SNR appearing at array's hydrophones face can appear at beam former input without distortion.
Note: Suppose my MDS/SNR (in terms of acoustic/sound pressure) for certain conditions came out to be -20 dB. Using hydrophone sensitivity, i think same SNR (in terms of voltage) will appear at each hydrophone output (if i am not wrong). Does it mean that even if echo level at input of PA /ADC of each hydrophone in array is 20 dB below PA/ADC noise floor, beam former and post processing will still be able to detect this echo???
It's active sonar at relatively short range (?) so it may be that detection is never noise-limited anyway. Is it? I recall that the intention of signal processing in synthetic aperture applications is to reduce the signal to reverberation ratio by spreading the reverberation spectrum. Then the minimum detectable signal depends on SNR as defined by reverberation levels and not classical "noise" levels.
The minimum detectable signal is always dependent on the type of detection.
You can probably adjust the sonar equation to make up for just about anything. For example, you might not include the directivity index if you relate things to the beamformer output. etc. But synthetic apertures don't rely so much on classical beamformers do they? (Which is not to say that they don't also have beamformers in the classical sense).
One can always design a system so that the A-D converter quantization noise is the limiting factor. Of course, one tries to NOT do that. The point here is that you may or may not be noise-limited and system design / analysis will tell you whether you are or aren't. Same thing for amplifiers. It may be that you are ignoring things in your initial post because you already know these things. But you say "My confusion is how to interpret this MDS/SNR in terms of PA and ADC specifications?." This suggests that you don't know. Good sonar system design practice suggests that it will never be system noise limited. This isn't like those applications where the electronics is limiting. It's the environment and how you use it.... But perhaps I'm missing something.
Also, you ask:
Q: "Does it mean that even if echo level at input of PA /ADC of each hydrophone in array is 20 dB below PA/ADC noise floor, beam former and post processing will still be able to detect this echo???"
A: No. But you've left out an important consideration - bandwidth.
If one assumes that you mean 20dB below amplifier self-noise level across the entire receiver passband but that there is filtering thereafter then maybe.. Without a system block diagram, one can't really comment on questions like this. And, to address such questions requires a system analysis. When you refer to noise levels, it's common to relate them to 1Hz bandwidth ("spectral level") at least for passive sonar. But for active sonar this may not so much be the case except in the system analysis where one may start with noise spectral levels (such as for amplifiers).
Thanks for your time and sorry for late response. You are right that for short ranges, active sonar will be reverberation limited but in designing of active sonar, i think we need to consider both noise limited and reverberation limited conditions.
As for startup, i need to clear my concept by first considering noise limited conditions only. I have attaches a document regarding noise limited active sonar design. If you have time, kindly review it and give your valuable comments if possible.Queries.doc
Thanks & Regards
Too many TLAs! If you can abbreviate it in three letters, you can SPELL IT OUT!
If they're defining the minimum discernible signal as a function of the signal to noise ratio at the hydrophones, then they're (A) assuming that the signal processing chain after the hydrophones isn't adding any appreciable noise, or (B) assuming that any internal noise is reflected back to the hydrophone face in your calculations (it won't be real noise, but rather the noise that would be present if the signal processing were noiseless), and (C), they're not taking the signal strength coming out of the system.
In other words, it's just a measure of any processing gain and/or directional gain (or loss) in the system.
As for analog to digital converter and power amplifier characteristics, you need to take this into account somehow, but that may be part of your calculation outside of the MDS calculation as given.
Dear Tim Wescott
Thanks for reply. I have done some rough sonar calculations for estimations of specifications for ADC and preamplifiers and are attaches as Queries.doc
If you have time, kindly review it and give your valuable comments if possible
Thanks & Regards