Measuring oblique ionograms using KiwiSDRs (1)

Oblique ionogram obtained from a KiwiSDR using GNSS timestamps

How it is done

The receive bandwidth of KiwiSDRs is limited to 12 kHz (20.25 kHz in 3 user channel configuration). In order to synchronously tune to a chirp sounder GNSS-based timestamps are used:

• For the current GNSS timestamp T0 tune the KiwiSDR to the frequency on which the chirp is expected at a time T0+DT.
• Record 10240 IQ samples, corresponding to 20 512-sample long buffers
• Repeat

Timing diagram

In this way, the chirp is always seen at a specific offset. Note that the tuning frequencies are different for each different complete chirp sweep because the KiwiSDR sampling rate is not GNSS-disciplined (the GNSS timestamps are exact).

abs(IQ) vs. frequency

For a chirp rate of 100 kHz/s and sampling rate 12 kHz, the frequency steps are ~85.33 kHz and the group delay resolution is 25 km.

The time offset DT, which depends on the delay between issuing a frequency change command and its effect, is measured at the beginning. It depends on internal KiwiSDR delays and on the network delay. If the KiwiSDR is on a local network this delay is about 2 buffers long, for KiwiSDRs on the internet delays between 8 and 10 buffers were seen.  

KiwiSDR gets CIC compensating filters

In an upcoming update, KiwiSDR's will get proper CIC compensating filters.

How is down-conversion done in the KiwiSDR?

The ADC runs at 66.66666 MHz, and CIC filters are used to down-convert to either 12 or 20.25 kHz. I recommend reading the original paper by Hogenauer which explains how to choose the bit widths of each filter stage in an optimal way.

Down-conversion from 66.66666 MHz to 12kHz (20.25kHz) is done in two steps; for the 12 kHz mode a 1st CIC filter is used to decimate by a factor of 926 to ~72 kHz; this is followed by a 2nd CIC which decimates by a factor of 6 to ~12 kHz.

The problem with CIC filters

CIC filters are optimal in the sense that they do use only addition and subtraction, as opposed to generic FIR filters, and therefore can be efficiently implemented in an FPGA. However, they are not perfect: 

• All signals outside the fundamental domain (+- 6kHz in this case, green dashed lines in the graph below) are mirrored/reflected into it.
• The filter curve of CIC filters is not flat, i.e., there is filter roll-off.

CIC filter response.

Enter CIC compensating filters

Both of these issues are improved by using a CIC compensating filter: instead of using the 2nd CIC filter for down-sampling to 12kHz, it is replaced with another CIC filter which down-samples to 24kHz, followed by a low-pass FIR filter and a final 2:1 down-sampling. The FIR filter makes sure everything out of +-6kHz is suppressed and that the CIC filter roll-off is compensated for. See AN455 for details.

CIC compensating filter with 64 taps for the 12 kHz mode.

CIC compensating filter performance

Using the built-in KiwiSDR signal generator the performance of the CIC+CIC compensating filter can be measured:

• Signal generator is set to sweep from 10 MHz to 10.012 MHz
• IQ mode recording
• Manual AGC
• Any other CIC compensation used previously turned off

Left: waterfall diagram: time vs. frequency; right: blue - signal, red - background.

• The residual CIC filter roll-off from the 1st CIC filter is < 0.2 dB (only the roll-off of the 2nd CIC filter is compensated for)
• Mirror signals are smaller than approximately -50 dB

Some old work

From the IRCA-Reprint-Index, see T-082. This was first published in Medium Wave Cicle News, and is from another time. Unfortunately the graphs are without colors.

HF Over-the-horizon radar processing using GNSS timestamped KiwiSDR IQ samples

OTHR parameters: 

• Chirp repetition time Δt=20 msec
• frequency slope=1 MHz/sec.

Its bandwidth is 20 kHz which fits nicely into the 20.25 kHz bandwidth of KiwiSDRs in 3-ch mode. 

Instantaneous frequency vs. mod(gpssec, 20 msec)

In the following we use GNSS-timestamped IQ samples for performing bi-static radar processing:

• Dechirping and framing into 20 msec long GPS-time-aligned frames
• interpolation in each frame (512 samples/frame)
• compute the 1st FFT along rows -> relative range
• compute the 2nd FFT  along columns on the result from the previous steps -> relative Doppler shift

Shown below are maps with relative Doppler frequency vs. relative range for 30 1-minute long periods, i.e., averaged over 1500 chirps each:

• the main signal comes at two different Doppler shifts and two different ranges, corresponding to two different ionospheric propagation paths.
• The pattern for the main signal can be found in several other places as well: this should correspond to reflections off some targets where the reflected signal then propagates with similar paths than the main component.
• It is interesting that besides the main component there are several instances of another pattern present, having two different Doppler shifts and ranges.
• It might also be that the secondary peaks are artifacts created by the signal processing.

Animation showing relative Doppler frequency vs. relative range.

AM modulation index

This is not the most exciting topic, but on the KiwiSDR forum there were repeated questions on how to measure the AM modulation index.

The best reference which I have found for that is an report from the ITU, R-REP-BS.2433-2018-PDF-E, where the "RMS modulation depth", i.e., the RMS ratio of side-bands and the carrier is being used as a proxy for the modulation index.

GNURadio flowgraph for measuring AM RMS modulation depth 

First, synchronous AM demodulation is performed using a PLL which locks onto the carrier. Then the RMS power in the carrier and in the side-bands is computed and their ratio is formed. Smoothed versions of this variable are shown a number and as a histogram. Note that the "RMS AM modulation depth" block consists of just a few lines of python.

The grayed out, i.e., disabled portions of this flowgraph were used to verify that the normalization is correct.

For the BBC transmitter on 198 kHz, the RMS modulation depth was found to be about 12% at the time of measurement which is consistent with the value quoted in the ITU report mentioned above. However, this number can vary by a factor of 1.5 or more (9-18%) depending on whether the program consists of speech or of music at the time of measurement. Furthermore,  the measured modulation depth indicates that dynamic carrier suppression is being used, see again the ITU report for details.

AM RMS modulation depth for BBC on 198 kHz

HF TDoA multilateration (2)

This is an update to the last blog post where propagation delays from VOACAP are used in addition to great-circle-derived propagation delays.

As VOACAP provides a number of propagation modes (MODE=25) the mode which is most close to the measured time difference is used.

Note that the findings in the plots below might accidentally: when there are enough closely-spaced delays available it is quite likely to match the data.

Nevertheless it can be seen that large deviation from the hypothesis of ground-wave propagation along great-circle paths are due to different reflection heights, i.e.,  1E-1F2, 2F1-1F2, etc: at a given time, a number of different propagation paths are available, and for different combinations of receivers, different propagation modes are in fact observed.

Comparison of measured time delay differences with differences based on ground-wave propagation along great-circle paths and differences based on VOACAP predictions.

Comparison of measured time delay differences with differences based on ground-wave propagation along great-circle paths and differences based on VOACAP predictions.

HF TDoA multilateration (1)

This blog post contains an analysis of TDoA multilateration applied to signal on 13413.4 kHz using a number of KiwiSDRs located in Europe.

For now the assumption used for making the KiwiSDR TDoA maps is that signals propagate with speed of light along the ground. Here we compare the measured delay differences with the ones obtained from this assumption.

All plots shown in this blog post are generated using octave/matlab .mat files available when using the updated KiwiSDR TDoA algorithm.

The cross-correlations for all combinations of used KiwiSDRs, normalized to have their maximum at unity, are shown below.

cross-correlations

Differences between the measured values and the ones obtained from great-circle-derived time delay differences are due to ionospheric propagation. As expected, the ionospheric effects tend to cancel for pairs of KiwiSDRs which are at about the same distance to the transmitter:

Comparison of  measured with great-circle time differences

The following scatter plot shows the effect of ionospheric propagation w.r.t. great-circle propagation. It will be very interesting to re-do this analysis using propagation delays e.g. from VOACAP instead of assuming propagation along great-circles at ground level.

Scatter plot for time differences

Slightly earlier the plots looked like this:

cross-correlations

Comparison of  measured with great-circle time differences

Scatter plot for time differences