[Difx-users] Reg. Fringe Rotation in general..

[Adam Deller]

HI Manikantan,

Answers to your questions:
1.The delay in the fringeRotationVal should be T, not T'.

Also, fractional sample correction is normally done differently in a
baseline based correlator, but the scheme you describe of going into the
frequency domain, correcting, and then back should work (albeit somewhat
computationally expensively).  However, you have either a typo or an error
in your equation: the phasor exponent should be -i*2*PI*channelfreq*Tfc,
not -i*2*PI*Vlo*Tf.  Channelfreq is the frequency of the channel, which
would range from 0 to 4 MHz (for upper sideband data), -4 to 0 MHz (for
lower sideband data), or -2 to 2 MHz (if this complex subband really has
been mixed down to be centred on 0 Hz - see next point).  So the frequency
you are multiplying by is not fixed (otherwise what would be the point of
going to the frequency domain?), it is a ramp across the band.  If this is
really an error and not a typo, then this is certainly destroying your
fringes!

Finally, Vlo (the local oscillator frequency) should be the signed sum of
the effective LO, which is likely at the edge of the 4 MHz band, not in the
middle.  If you have this wrong, you'll then have a residual fringe rate of
half your bandwidth, or 2 MHz in this case.

Don't worry about the interpolators in DiFX: they are just down-sampling
the 5th order polynomial which is valid for 120 seconds to a 1st or 2nd
order polynomial which is valid for of order a few microseconds, for
computational efficiency.

Note that autocorrelations are never really a great test, since they are
insensitive to the phase, which is where almost every mistake is made :)

2.  The fractional bandwidth is irrelevant for fringe rotation: you can
think of the chunk of spectrum as having been shifted in frequency by Vlo
in the downconversion process.  That holds true for every frequency within
the downconverted subband: assuming upper sideband data, then the lowest
band edge has been shifted down from Vlo Hz to 0 Hz, and the upper band
edge has been shifted down from Vlo + B Hz to B Hz.  Hence they've all been
shifted by Vlo, and that single correction is good for all of the
frequencies within the subband.

Cheers,
Adam

On 20 February 2018 at 05:26, Manikantan Ramadas <mramadas at gmail.com> wrote:

> Hi all,
>
> I have a few questions on Fringe Rotation in general for the VLBI
> correlation experts..
>
> A brief paragraph background since it is relevant to some of the design
> choices made:
> I am working on a VLBI correlator in the context of Interplanetary
> Spacecraft Navigation - Delta Differential One-Way Ranging. It is
> essentailly a navigation scheme built upon Delta-VLBI where a session
> comprises looking at the S/C, an angularly nearby Quasar, back to the same
> or another nearby Quasar, etc. from two geographically separated antennas.
> The Quasar scan is essentially to subtract away common error sources such
> as clock offsets, station-specific effects, media effects etc., from the
> S/C signal (near-field source’s) delay measurements.
>
> I have implemented the Quasar (VLBI) correlator based on the XF
> baseline-based model since it seemed most straight-forward and probably
> sufficient for this context. Thanks to the email that I sent in this group
> and the helpful pointers I got earlier, I have a good delay-model based on
> DiFXCalc-11 - where I have the 5th order polynomial coefficients every 2
> mins. I have also implemented the necessary algorithm to convert geocentric
> theoretical delay to base-line theoretical delay with one of the stations
> (Stn-A) as reference. I have model delays in the 10-20ns range of accuracy.
>
> Our data-recording format is based on the CCSDS RDEF format - 2-bit
> complex samples at 4 MHz sampling rate - and we have 5 such channels for
> bandwidth synthesis in S-band.
>
> In the correlator I do the following:
> 1. Take Station-A’s complex sample at time t: A_t
> 2. Get the model delay at time t:
>     (a) The accurate double value obtained from DiFXCalc-11 for delay at
> time t: T.
>     (b) Rounded off to the nearest sample as per sampling time unit Ts of
> 1/4 micro-sec for 4 MHz sampling: T’
>     (c) Fractional error at time t: T’-T = Tf
> 3. The correlator supports a configurable number of lags L:
>     -L/2, …, 0, L/2-1.
>     For each lag in -L/2, …, 0, …, L/2-1:
>         (a) delay=T’+lag*(Ts);
>         (b) fringeRotnVal=cexp(-i*2*PI*Vlo*delay)
> where Vlo is the central local oscillator frequency of the channel used in
> downconversion.
>         (c) Station-B’s complex sample at time t+delay=B_td
>         (d) Correlation value = A_t * fringeRotnVal * conjugate(B_td)
>
> I keep doing this basic loop and accumulate the Correlation values
> lag-wise. Every 64 samples, I do fractional bit-shift correction of the
> averaged lag-wise correlation values by taking the L samples to frequency
> domain, multiply by phasor cexp(-i*2*PI*Vlo*Tfc) where Tfc is the
> fractional error for the central value of the 64 samples. Then I come back
> to time-domain to have the 64 fractional error corrected samples. I also do
> fractional bit shift correction even if 64 samples are not reached -
> whenever a bit shift happens.
> Our typical delay rates are in the 2 micro-sec per sec order, and since we
> are dealing with a 2.3 GHz S-band sky frequency, the natural fringe-rate is
> on the order of 4.6 KHz. Since fringe-rate changes at 2*PI*4600 radians per
> sec., for 1 radian it would take aroundd 35 micro-second which at 1/4
> micro-sec sampling is 140 samples. I could have chosen 128 samples for
> fractional bit-shift correction / first-level averaging, but chose 64 to be
> one-step more conservative to be within 1 radian.
>
> The problem is that I am not seeing any correlation peaks in the lag  vs
> time (accumulation-period) vs amplitude plane. I have done accumulation for
> 64 lags (clock-offsets are known to be within the 64/4 = 16 = +/- 8
> micro-sec range), and further accumulated the first-level 1sec accumulation
> period values, further upto 30 sec.
> I have also implemented the FFT conversion from time-to-delay_rate so that
> I have single-band Fringe-Search grids in the lag vs delay_rate vs
> amplitude 3-D planes. Even here I am not able to see any peaks.
>
> I know from our peer agency that the data is good and successfully
> correlated. I have tested my correlator code for auto-correlation by
> feeding it the same station files and by-passing the delay/fringe-rotation
> steps alone; there are no blatant bugs, correlation peaks are visible in
> this auto-correlation scenario.
>
> My questions / confusions in this context are:
> 1. Am I doing Fringe-Rotation right? Are there any noticeable blunders
> here or gotcha-s that I might have missed?
> I have seen DiFX code in the mode.cpp file where fringe-rotation is done;
> there are interpolators used - linear / quadratic / post-FFT modes. But I
> thought that they may not be required for me since I am getting the
> model-delay calculated for every sampling period from 5th order polynomials
> directly without any further delay-modeling..
> 2. The 4 MHz bandwidth is only a small fraction of the sky-frequency at
> 2.3 GHz. I would not lose correlation amplitude right? Or should I consider
> getting sub-channel-wise Fourier time-series and do Fringe-rotation
> sub-channel-wise?
>
> I have spent quite some time on this, but obviously I must be missing
> something. I would be grateful for any suggestions that you may have. I
> realise that this is not directly related to DiFX per se., but I don’t know
> of any other active VLBI correlator community that I could discuss with. I
> hope that it may still be of general interest for members of the mailing
> list..If you have any helpful pointers / documents - kindly share it with
> me. But I have already searched much of what Google could show me.. Thanks!
>
> Thanks and Regards,
> Manikantan
>
> --
> "By being pleasant always and smiling, it takes you nearer to God, nearer
> than any prayer." - Sri Ramakrishna Paramahamsa
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Dr. Adam Deller
ARC Future Fellow, Senior Lecturer
Centre for Astrophysics & Supercomputing
Swinburne University of Technology
John St, Hawthorn VIC 3122 Australia
phone: +61 3 9214 5307
fax: +61 3 9214 8797

office days (usually): Mon-Thu
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