1. Small Aperture, Low SNR Pulsar Detection
Peter East
Small Aperture, Low SNR Pulsar Detection – Peter W East
Scaling measurements using a large dish and an RTL SDR showed that a 3m dish was required to positively detect and identify the strongest pulsars over a reasonable observation time.
Several amateurs have validated this conclusion with 3m and larger parabolic dish antennas and efforts have been made to construct antennas more suitable for a small garden.
The Italian Amateur Permanent Observatory IW5BHY successfully intercepts B daily at 422 MHz with a 2m by 2m 3D corner reflector antenna.
With large aperture antennas, identifying true pulsar signals can be assured with some confidence but the challenge in this paper is to detect the strongest pulsars using a small back-garden antenna, when the integrated pulsar signal still competes with natural noise peaks.
In this talk a pair of 2.5 m long, 17-element Yagi antennas (approximately 1.5 m2 aperture) feeding three parallel RTL SDRs to cover the MHz radio astronomy band is described, together with methods to identify the B pulsar at relatively low signal-to-noise ratios.
Amateur detection of pulsars and proving confirmation with small antennas is not easy and the difficulties and potential noise ambiguities in this quest are explored here.

2. Introduction Background Key System Drivers Low SNR Tests Conclusions
51 years ago Jocelyn Bell detected the first pulsar – she used a 16000m2 aperture antenna array at 80MHz.
At the last EUCARA conference, I presented a paper based on measurements concluding that an amateur radio astronomer could reliably detect the strongest pulsars with a 3m aperture dish using an RTL dongle at 1421MHz.
Since a 3m dish in my small back garden was out of the question, I have spent some time studying what could be achieved with more modest antenna apertures.
I am not alone in this quest and I have been in touch with a colleague in Italy who has demonstrated some superb results, which I have permission to report.
This talk starts with the design basics and how to put it in practice. Finally I show some results and exploit key pulsar properties that eases differentiation between pulsar signals and noise/RFI to enable validation of candidates at low signal to noise ratios.

3. LK Radiometer Equation
The place to start is with the Lorimer and Kramer radiometer equation
Sp is the pulsar mean flux density in janskys
Ae the antenna electrical aperture in m2
Tsys is the RT system temperature
Tint and delta f are the observation time and RF bandwidth respectively
The square root term I will explain later
In the next slide, I have applied this equation for the strongest pulsar in the northern hemisphere, B0329

4. B
These curves show the expected SNR for RTs of various effective apertures.
The antenna is assumed fixed and the source is integrated during transit and takes into account the beamshape sensitivity roll-off.
The green curve shows the predicted SNR of a RT centred on 423MHz and using a single RTL2832U DR dongle with a system temperature of 150deg K
The green dot shows what has been achieved in practice by Andrea Dell’Immagine at his amateur observatory in Barga, Italy.
With 100deg system temperature, he regularly measures the pulsar at SNRs from 10 to 20
With the magenta line and spot, he has recently proved a system using 10MHz bandwidth Airspy SDR and amazingly, a 0.8m2 dual quad antenna.
The blue dot is my modest achievement which I will talk about more later. It is close to the expected level of occasional noise peaks of 3:1
The red curve as another frequency option.
For ease of detection a large SNR is desirable and certainty an SNR greater than 10 is preferable, indicating apertures around 1m2 at for the 300/400MHz RA bands but greater than 2m2 for the 600MHz band.
At 1420MHz, apertures greater than 3m2 and source tracking is required.

5. Mini Pulsar Radio Telescope
GPSDO
I chose a pair of Yagis at 611MHz, for lightness and ease of portability
Other antenna possibilities are, Dish, horn, 3D corner reflector with 3 wavelength gain limitation, dual bi-quad which has a 2 by 1 wavelength gain limitation.
The power combiner is not needed for the other antenna types which offer lower sidelobe and spillover possibilities.
Filtering is required to exclude out of band TV signals at this frequency.
Triple RTL receiver solution needs initial noise switching to synchronise the data. Raspi or Arduino control the switch modulation.
Alternatively a 10MHz bandwidth Airspy is now available
GPSDO useful to simplify searching the right period candidate.

6. System Temperature - TSYS
Receiver noise
power with Antenna..
1. Connected: PAC
2. Feed O/C: POC
3. Feed matched: PML
A low system temperature is essential for success but the value needs to be known to ensure that the receiver has sufficient sensitivity.
Given a system it is quite easy to estimate approximately with the 3 basic measurements shown .
At the SDR output, using software such as SDRsharp,
Measure the noise output with the antenna connected, with the antenna feed open-circuited and with the antenna feed loaded with a matched load.
These two simple ratios provide the Tsys estimate.

7. Detected Video DC level ≡ Tsys + Tsky Noise ≡ ΔT ~ Tsys /√Bt ~ 3° K
The SDR’s provide IQ data which needs downsampling and square-law detection.
This slide shows a typical result. The DC level corresponds to the system temperature and the noise amplitude reduced by the radiometer equation parameters.
In this case the noise amplitude is equivalent to about 3deg K.
Further integration is required to reduce the noise to below 1/100 of a degree to make the pulsar visible.
Ideally this should look like random noise with little RFI.
B = 2.4MHz, t = 1ms, and, (Tsys + Tsky)/ΔT = 50

8. Folding Algorithm * Pulse adds linearly * Noise adds as square root
* SNR improves as √(Folds = F)
SNR= √ (FPΔf /N) x Tp/Tsys
Optimum bins N = Period/Pwidth
B0329: Tp ~ 0.03°K/m2/pol
The folding algorithm is the popular method of integrating long observations to make the pulsar visible.
The data record is split into blocks equal to the pulsar period P, and these are summed
When the fold period matches the pulsar period exactly, the pulsar pulse always occurs at the same phase and integrates linearly whilst the noise integrates as the power or square root of the voltage.
The expected radiometer integration is reduced by the square root of the number of fold bins and there is an optimum number equal to the pulsar period divided by the pulsar pulse width.
So without further filtering SNR is degraded if large number of bins are needed to investigate pulse detail. P P t t t T

9. Matched Filter - optimises SNR
RAW
DATA FT
OPTIMISED
FOLDED
DATA X
IFT FT
For B0329
To improve visibility with many bins, straightforward low-pass filtering is possible but SNR can be better optimised by matched filtering.
This can be achieved digitally using a target pulse pattern and Fourier transforming and multiplying as shown.
The improvement is remarkable and is assumed in the Lorimer/Kramer radiometer equation on the earlier slide.

10. Finding and Validating
Strong signal - Presto Plot
Weak signal - exploit pulsar characteristics
Correct period –TEMPO + GPS/Rubidium DO
Check pulse width – Matched filter peak
Two-section fold correlation
Two-period fold correlation.
Multi-band correlation.
Period search peak – profile, offset and pulse width
P-dot search peak – profile, offset and pulse width
Dispersion search peak – amplitude and pulse width
We have all the tools now to collect data for analysis.
Now the job is to analyse the data to discover whether the pulsar is present.
With a strong signal, SNR > 10 we can use the professional software PRESTO.
With a weaker SNR more processing is required.
The accepted professional lower SNR limit is around 10:1. The amateurs lower limit is around 6:1.
My system was unlikely to reach these values so I have been investigating characteristics of noise, RFI and pulsars to find methods of differentiating these and find the B0329 pulsar in particular at lower SNR levels.
I have devised these 8 tests to recognise pulsar data at lower SNRs, which I will explain over the next few slides

11. This is a Presto plot of B0329 with a SNR around 10:1.
Plot 1 is the best fold repeated.
Below it the phase-time repeated, where you may just be able to see a hint of the pulse presence.
The second plot is phase against frequency where the pulse presence appears better visible.
The third set of plots display the amplitude effect of changing the period and period rate, pdot.
We expect peaks at zero in both plots
The last bottom-centre plot is the effect of varying the de-dispersion parameter, exhibiting a peak at around DM=27.
The bottom-right plot shows the correlation between p and pdot and a maximum is expected at the centre.
These results appear to confirm pulsar presence.
Note that the Period, P-dot and DM plotted patterns are not responding directly to the pulsar peak in the best profile plot but are measures of the Reduced Chi-square statistic which, for analysis speed reasons, is only seeking deviation of data caused by the pulse presence.

12. Andrea Dell’Immagine - Italy 422MHz + 2
Andrea Dell’Immagine - Italy 422MHz + 2.4MHz RTL+ 3Hrs 2x2x2m 3D corner reflector antenna
Automatic Daily
Observatory
2.5m2 Aperture
SNR = 11.5
The previous result was produced by the first system example and is Andrea Dell’Immagine’s permanent observatory in Barga.
This uses a 3D corner reflector with a gain of 18dB and an effective aperture of 2.5m2.
The receiver is a single RTL2832U dongle clocked at 2.4MHz centred on 422MHz
He achieves excellent results with daily SNRs in the range 10:1 to 20:1.
He has recently built a 422MHz dual bi-quad antenna feeding a 10MHz Airspy SDR and achieved SNR’s in excess of 10:1 with 3hr integration.
The effective collecting area is a record 0.8m2

13. This is a Presto plot of a 4:1 SNR detection – this example was obtained from my system when using an Airspy receiver and software provided by my Italian colleague.
None of the derived sub-plots previously described are convincing.
The reason is that the Presto software uses the chi-squared goodness of fit criterion to identify pulsar presence, which requires a large deviation from Gaussian noise.
This is good for indicating large SNR pulses and also RFI…

14. 611MHz + 6MHz (3x2.4MHz) + 2Hrs Twin 2.5m Yagis
Minimal Affordable System
1.5m2 aperture
B Pulsar
period: ms
SNR = 4.5
This is my antenna system and is the reason I have had to look at validating low SNR measurements.
They comprise two 17-element Yagis tuned to the 611MHz band.
They are not good on sidelobes and because of the close proximity of house and trees surrounding the array, my system noise temperature is closer to 200deg K.
The best SNR I have achieved is just between 5 and to 6:1.
This is with both a 6MHz triple bank of RTL SDRs and a 10MHz Airspy.
I now need to explain how I believe this is a valid detections

15. B0329 Tests 1,2. Period/Pulse Width Check
This plot shows the result of folding the data at the predicted correct period.
There are 714 fold bins and the baseline measured in 1ms units
Firstly a strong candidate appears at an SNR just greater than 4:1, which also matches the expected pulse width.
There are several other peaks around SNR 2.5:1 that are also potential candidates – some clearly do not meet the pulse width criterion

16. Test 3. Half File Correlation
The data record is now split into two successive halves and folded separately.
But overlaid in the display.
This shows that noise largely uncorrelated between halves but pulsar presence/position is consistent.
Note reduction in SNR
Note, there are also some correlations with the weaker candidates

17. Test 4. 2-Period Fold - 2 sections overlaid
Now, the fold period is twice that expected for the pulsar so that in fold plot, we expect two pulses to appear spaced one period apart
The display splits the record into two equal parts and overlays the successive periods to show the expected correlation.
This does show that our candidate comprises a pulse train with the correct period.
Note there are instances where the background noise also appears to correlate.
Note reduction in SNR

18. Test 4. cont’d. Falling Raster
Time
Here the data is split into 6 equal time sub-sections and each is folded separately and combined in this falling raster plot.
The data amplitudes are split into 6 levels from the red, the highest, light green, dark green,blue and dark blue
Our central strong candidate is largely visible throughout with some peaks indicating scintillation is present and produces a large pulse on integration.
Some of the other noise candidates can be discounted as are only present in sub-sections.
Note that most of the large noise peaks are constrained to one time subsection but still give rise to peak in the summed record.

19. Test 5. Sub-Band Correlation
In this plot, the 3 RF sub-bands are folded separately and overlaid.
Pulsar signal is present at the expected position in all three bands,
Once again some of the earlier noise candidates can be discounted as not correlating in all 3 sub-bands.
Note reduction in SNR.

20. Test 6. Period Search Properties
P-pP
P-pP T t
t+pP
t+2pP
New Width: pT
New Peak: –pT/2
Example; T=7000s
p = -1ppm, P=700ms
Peak shift = +3.5ms
pT/W = 0,1,2,3
The previous tests whilst promising cannot be considered definitive, since all these tests could have happened by random chance.
Normally, the period search just examines the peak pulse amplitude and checks that a peak occurs at the expected pulsar period.
In fact the amplitude profile can be predicted as well as the peak offset and pulse width.
These more detailed tests exploit the pulsar characteristics in more detail and add a quantitative aspect to validation
When the pulsar fold period matches the pulsar period the pulsar pulses align in each fold window and adds to give a maximum.
2. Decreasing the fold period slightly causes the pulse to increasingly shift to the right along the observation record within the fold range smearing out the pulse.3. The maximum shift occurs within the last fold period and totals ‘F.P' where ‘p.P = ppm x P' is the fold period shift and ‘F' is the total number of folds (T=FP)..
4. If 'T' is the total observation time, then F = T/P and the pulse total spread extent is pT.
5. In summary, the with 'p' ppm search period change the mean pulse width increases to 'pT' and the pulse centre position changes to pT/2
The plot models the pulse centre shift and typical shape change for a Gaussian pulse width W in increments, pT/W.
So what we are looking for when we change the period is for the pulse width to change but also its position to change the calculated amounts.
This will only be correct if the pulsar is acquired continuously over the observation period. Scintillation will affect the pulse shape and for low SNR’s the background noise will have a distortion effect
With pT/W equals 2 the peak value drops to half the matched peak.
Note that most amateurs look for just the amplitude change (black dotted line) to confirm large SNR detections. Whereas we are looking for amplitude, offset and increasing pulse width.
Techniques similar to this have been used before see…
Keith MJ et al, ‘Discovery of 28 pulsars using new techniques for sorting pulsar candidates’ Mon.Not. R. Astron.Soc. 395, pp (2009)
They recognise that human-eye aspects of pulsar searching cannot easily be replicated by machine although they go on to offer algorithms to quantify the parameter change I described
Half height, p=2W/T

21. Test 6 cont’d. Period Search Data
This is the result with the real data of the earlier slides.
For this result, it means that the pulse signal identified exists continuously over the observation period
The baseline scale is in ms and the fold includes 714 bins
Note that the peak amplitude and pulse widths follow the pattern in the previous slide, with some distortion due to the underlying noise
Noise peak shifts appear variable and although a short section is shown no other data peak has the same characteristics showing that significant noise peaks are rarely consistent over the observation period.
p = 0, -1,-2,-3ppm

22. Test 7. p-dot (δP/P) Search Properties
P-pdP
P-2pdP t t
t+pdP
t+pdP+2pdP
pd T2/2WP = 0,1,2,3
For small pd
New Width: pdT2/2P
Example; T=7000s
pd = , P=700ms
Median shift = +3.5ms
The p-dot search is designed to detect if there is any spin-down or apparent rotation rate change during the observation period.
The fold period is gradually increased or decreased at a constant rate during the observation.
The effects are somewhat similar to those of period search, but the apparent peak shift and shape are different.
1. Again, when the fold period matches the pulsar period the pulsar pulses align in each fold period and add to improve pulse visibility.
2. Decreasing the fold period rate slightly causes the pulse to increasingly shift within the fold range to the right smearing out the pulse.
3. The maximum shift occurs within the last fold period and totals 'Σfpd P' where 'pd' is the fold period pd =dP/P and ‘f' is the fold number.
4. If 'T' is the total observation time, then the number of folds = F = T/P and the pulse total spread extent is pdT2/2P.
The plot models the pulse centre shift and typical shape change for a Gaussian pulse width W in increments, pd T2 /2WP .
With pd T2 /2WP equals 2 the peak value drops to half the matched peak.

23. Test 7 cont’d. p-dot Search Data
This is the result with real data with a matched fold SNR of just over 4:1
This again means that the pulse signal identified exists continuously over the observation period
The baseline scale is in ms and the fold includes 714 bins
Note that the peak amplitude and pulse widths follow the pattern in the previous slide although more and more corrupted by noise.
Noise peak shifts appear variable and although a short section is shown no other data peak has the same characteristics showing that significant noise peaks are rarely consistent over the observation period.
For small values of p-dot there is a strong similarity with straight period search and positive v negative shifts can be balanced out.
It is possible to examine scintillation along the record by combining a period offset with a small positive or negative p-dot.
pd = 0,-1,-2,-3x10-10

24. Test 8. Dispersion Search Properties
t±D/PW/2
D/PW = 0,1,2,3
Dispersion
Zero at Band Centre
The final, probably the most powerful test is dispersion search which exploits the dispersion property of a pulsar
In that the lower frequencies are delayed by interaction with free electrons in the propagation path.
This causes the pulse width to spread which is normally corrected by de-dispersion
Here, we start with the properly dispersed state – red curve.
Low frequencies are delayed at 611MHz, and DM=27, the dispersion correction is close to 1ms/MHz
For DM search, the data is dispersed about the band centre, giving rise to symmetrical pulse stretching in the noise free case.
Dispersion is linear and expressed in increments of ms/pulse width and can be applied in both positive and negative directions.
The model shows that in the ideal case, the pulse height drops to one half when D/W = 2.

25. Test 8 cont’d. Dispersion Search Data
The real data shows similar amplitude and pulse width as the theory except as expected at this low SNR, noise has a greater distorting effect.
Natural noise peaks do not show theoretical amplitude reduction and pulse broadening..
Positive and negative excursions are averaged here to reduce the effect of underlying noise.
D/W = 0,±1,2,3 - dispersion zero at band centre

26. Low SNR Validation Summary
Pulsar SNR’s below 10:1 require careful validation
Interference and peaks of natural noise cause confusion
The key to identifying these is to exploit the pulsar properties
The 8-point test plan discussed works well down to 4:1 SNRs
In areas of low RFI some candidates are recognised down to 3:1

27. Conclusions
1. Pulsar B0329 can be detected in the 300/400/600Mhz RA RF bands using home-made, small aperture (<2m2 ) antennas.
2. The main antenna design requirement is for low sidelobes.
3. Exploiting pulsar pulse properties* is key to identifying low SNR pulsars in RFI and noise.
4. for more detail…..
*Keith MJ et al, ‘Discovery of 28 pulsars using new techniques for sorting pulsar candidates’ Mon.Not. R. Astron.Soc. 395, pp (2009)
Finally, small aperture pulsar detection in the 300, 400 and 600MHz bands is achievable.
And pulsar validation certainly down to 4:1 SNR and lower is possible with care.