Wednesday, December 27, 2023

Remote (POTA) operation from the Conger Mountain BLM Wilderness Area (K-6085)

It is likely that - almost no matter where you were - you were aware that a solar eclipse occurred in the Western U.S. in the middle of October, 2023.  Wanting to go somewhere away from the crowds - but along the middle of the eclipse path - we went to an area in remote west-central Utah in the little-known Conger Mountains.

Clint, KA7OEI operating CW in K-6085 with Conger
mountain and the JPC-7 loaded dipole in the background.
Click on the image for a larger version.

Having lived in Utah most of my life, I hadn't even heard of this mountain range even through I knew of the several (nearly as obscure) ranges surrounding it.  This range - which is pretty low altitude compared to many nearby - peaks out at only about 8069 feet (2460 Meters) ASL and is roughly 20 miles (32km) long.  With no incorporated communities or paved roads anywhere nearby we were, in fact, alone during the eclipse, never seeing any other sign of civilization:  Even at night it was difficult to spot the glow of cities on the horizon.

For the eclipse we set up on BLM (Bureau of Land Management) land which is public:  As long as we didn't make a mess, we were free to be there - in the same place - for up to 14 days, far more than the three days that we planned.  Our location turned out to be very nice for both camping and our other intended purposes:  It was a flat area which lent itself to setting up several antennas for an (Amateur) radio propagation experiment, it was located south and west of the main part of the weather front that threatened clouds, and its excellent dark skies and seeing conditions were amenable to setting up and using my old 8" Celestron "Orange tube" C-8 reflector telescope.

(Discussion of the amateur radio operations during the eclipse are a part of another series of blog entries - the first of which is here:  Multi-band transmitter and monitoring system for Eclipse monitoring (Part 1) - LINK)

Activating K-6085

Just a few miles away, however, was Conger Mountain itself - invisible to us at our camp site owing to a local ridge - surrounded by the Conger Mountain BLM Wilderness Area, which happens to be POTA (Parks On The Air) entity K-6085 - and it had never been activated before.  Owing to the obscurity and relative remoteness of this location, this is not surprising.

Even though the border of the wilderness area was less than a mile away from camp as a crow files, the maze of roads - which generally follow drainages - meant that it was several miles driving distance, down one canyon and up another:  I'd spotted the sign for this area on the first day as we our group had split apart, looking for good camping spots, keeping in touch via radio.

Just a few weeks prior to this event I spent a week in the Needles District of Canyonlands National Park where I could grab a few hours of POTA operation on most days, racking up hundreds of SSB and CW contacts - the majority of being the latter mode (you can read about that activation HERE).  Since I had already "figured it out" I was itching to spend some time activating this "new" entity and operating CW.  Among those others in our group - all of which but one are also amateur radio operators - was Bret, KG7RDR - who was also game for this and his plan was to operate SSB at the same time, on a different band.  As we had satellite Internet at camp (via Starlink) we were able to schedule our operation on the POTA web site an hour or so before we were to begin operation.

In the late afternoon of the day of the eclipse both Bret and I wandered over, placing our stations just beyond the signs designating the wilderness study area (we read the signs - and previously, the BLM web site - to make sure that there weren't restrictions against what we were about to do:  There weren't.) and several hundred feet apart to minimize the probability of QRM.  While Bret set up a vertical, non-resonant end-fed wire fed with a 9:1 balun suspended from a pole anchored to a Juniper, I was content using my JPC-7 loaded dipole antenna on a 10' tall studio light stand/tripod.

Bret, KG7RDR, operating 17 Meter SSB - the mast and
vertical wire antenna visible in the distance.
Click on the image for a larger version.
Initially, I called CQ on 30 meters but I got no takers:  The band seemed to be "open", but the cluster of people sending out just their callsign near the bottom of the band indicated to me that attention was being paid to a rare station, instead.  QSYing up to 20 meters I called CQ a few times before being spotted and reported by the Reverse Beacon Network (RBN) and being pounced upon by a cacophony of stations calling me.

Meanwhile, Bret cast his lot on 17 meters and was having a bit more difficulty getting stations - likely due in part to the less-energetic nature of 17 meter propagation at that instant, but also due to the fact that unlike CW POTA operation where you can be automatically detected and "spotted" on the POTA web site, SSB requires that someone spot your signal for you if you can't do it yourself:  Since we had no phone or Internet coverage at this site, he had to rely on someone else to do this for him.  Despite these challenges, he was able to make several dozen contacts.

Back at my station I was kept pretty busy most of the time, rarely needing to call CQ - except, perhaps, to refresh the spotting on the RBN and to do a legal ID every 10 minutes - all the while making good use of the narrow CW filter on my radio.

As it turned out, our choice to wait until the late afternoon to operate meant that our activity spanned two UTC days:  We started operating at the end of October 14 and finished after the beginning of October 15th meaning that with a single sitting, each of us accomplished two activations over the course of about 2.5 hours.  All in all I made 85 CW contacts (66 of which were made on the 14th) while Bret made a total of 33 phone contacts.

We finally called it quits at about the time the sun set behind a local ridge:  It had been very cool during the day and the disappearance of the sun caused it to get cold very quickly.  Anyway, by that time we were getting hungry so we returned to our base camp.

Back at camp - my brother and Bret sitting around
the fake fire in the cold, autumn evening after dinner.
Click on the image for a larger version.

My station

My gear was the same as that used a few weeks prior when I operated from Canyonlands National Park (K-0010):  An old Yaesu FT-100 equipped with a Collins mechanical CW filter feeding a JPC-7 loaded dipole, powered from a 100 amp-hour Lithium-Iron-Phosphate battery.  This power source allowed me to run a fair bit of power (I set it to 70 watts) to give others the best-possible chance of hearing me.

As you would expect, there was absolutely no man-made noise detectable from this location as any noise that we would have heard would have been generated by gear that we brought, ourselves.  I placed the antenna about 25' (8 meters) away from my operating position, using a length of RG-8X as the feedline, placing it far enough away to eliminate any possibility of RFI - not that I've ever had a problem with this antenna/radio combination.

I did have one mishap during this operation.  Soon after setting up the antenna, I needed to re-route the cable which was laying on the ground, among the dirt and rocks, and I instinctively gave it a "flip" to try to get it to move rather than trying to drag it.  The first couple of "flips" worked OK, but every time I did so the cable at the far end was dragged toward me:  Initially, the coax was dropping parallel with the mast, but after a couple flips it was at an angle, pulling with a horizontal vector on the antenna and the final flip caused the tripod and antenna to topple, the entire assembly crashing to the ground before I could run over and catch it.

The result of this was minor carnage in that only the (fragile!) telescoping rods were mangled.  At first I thought that this would put an end to my operation, but I remembered that I also had my JPC-12 vertical with me which uses the same telescoping rods - and I had a spare rod with that antenna as well.  Upon a bit of inspection I realized, however, that I could push an inch or so of the bent telescoping rod back in and make it work OK for the time-being and I did so, knowing that this would be the last time that I could use them.

The rest of the operating was without incident, but this experience caused me to resolve to do several things:

  • Order more telescoping rods.  These cost about $8 each, so I later got plenty of spares to keep with the antenna.
  • Do a better job of ballasting the tripod.  I actually had a "ballast bag" with me for this very purpose, but since our location was completely windless, I wasn't worried about it blowing over.
  • If I need to re-orient the coax cable, I need to walk over to the antenna and carefully do so rather than trying to "flip" it get it to comply with my wishes.

* * *

Epilogue:  I later checked the Reverse Beacon Network to see if I was actually getting out during my initial attempt to operate on 30 meters:  I was, having been copied over much of the Continental U.S. with reasonably good signals.  I guess that everyone there was more interested in the DX!

P.S.  I really need to take more pictures during these operations!

This page stolen from


Wednesday, December 13, 2023

"TDOA" direction finder systems - Part 2 - Determining signal bearing from switching antennas in software.


This is a follow-up to a Part 1 blog post on this topic where we discuss in general how "rotating" (or switched) antennas may be used to determine the apparent bearing of a transmitter.  It is recommended that you read Part 1 FIRST and you can find it at:  "'TDOA' direction finder systems - Part 1 - how they work, and a few examples." - LINK.

In part 1 (linked above) we discussed a simple two-element "TDOA" (Time Difference Of Arrival) system for determining the bearing to a transmitter.  This method takes advantage of the fact that - under normal conditions - one can presume the incoming signal to be a wave "front", which is to say like ripples in water from a very distant source, they "sweep" over the receiver in lines that are at a right-angle to the direction from the transmitter.  Note that in this discussion, most of the emphasis will be placed on how it is done in the analog domain with switching antennas as this can help provide a clearer picture of what is going on.

Why this works

If we are using a two-antenna array, we can divine a difference between the arrival time of the two antennas as this drawing - stolen from part 1 of this article - illustrates:

Figure 1:
A diagram showing how the "TDOA" system works.
Click on the image for a larger version.


As illustrated in the top portion of the above illustration, the wave front "hits" the two elements at exactly the same time so, in theory, there is no difference between the signal from each of these elements.  In the bottom portion of the illustration, we can see that the wave front will hit the left-most element first and the RF will be out of phase at the second element (e.g. one element will "see" a the positive portion of the wave and the other will see the negative portion of the wave).

If we constrain ourselves with having just ONE receiver to use, you might ask yourself how one might use the signal from two antennas?  The answer is that one switches between the two antennas electronically - typically with diodes.  If the two signals are identical in their time of arrival - and the length of coaxial cable between the antenna and when one switches "perfectly" between the two antennas and there is no disturbance in the received signal, we know that the signal is likely to be broadside of our two-antenna array.

If the signal is NOT broadside to the the array, there will be a "glitch" in the waveform coming out of our receiver when we switch our antenna.  Because we are using an FM receiver - which detects modulation by observing the frequency change caused by audio modulation - we can also detect that "glitch".  To understand how this works, consider the following:

Recall the "Doppler Effect" (Wikipedia article - link) where the pitch of the horn of a car increases from its original when it is moving toward the observer - and it is lower in pitch when it moves away from the observer:  It is only at the instant that the car is closest to the observer that the pitch heard is the actual pitch of the horn.

Now, consider this same thing when we look at the lower diagram of Figure 1.  If we switch from the left-hand antenna to the right-hand antenna, we have effectively moved away from the transmitter and for an instant the frequency of the received signal was lower because - from the point of the receiver on the end of the coax cable - the antenna moved away from the transmitter.  Because changes in frequency going up and down cause the voltage coming out of the receiver to go up and down by the same amount, we will get a brief "glitch" from having changed the frequency for a brief instant when our antenna "moved".

If we then switch back from the right-hand antenna to the left-hand antenna, we have suddenly moved it closer to the transmitter and, again, we shift the frequency - but in the opposite direction, and the glitch we get in the receiver is opposite as well.

We can see the glitching of this signal in the following photo, also stolen from "Part 1" of this article:

Figure 2:
Example of the "glitches" seen on the audio of a receiver connected to a TDOA system that switches antennas.

The photo in Figure 2 is that of an oscilloscope trace of the audio output of the FM receiver connected to it and in it, we can see a positive-going "glitch" when we switch from one antenna to the other, and a negative-going glitch when we switch back again.

If we have a simple circuit that is switching the antennas back-and-forth - and it "knows" when this switch happens, we can determine several things:

  • When the two antennas are broadside to the transmitter.  If we have the situation depicted in the top drawing of Figure 1, both antennas are equidistant and there will be NO glitches detected.
  • When antenna "A" is closer to the transmitter.  If we arbitrarily assign one of the antennas as "A" and the other as "B", we can see - by way of our "thought experiment" above - that if antenna "A" is closer to the transmitter than "B", our frequency will go DOWN for an instant when we switch from "A" to "B" - and vice-versa when it switches back.  Let us say that this produces the pattern of "glitches" that we seen in Figure 2.
  • When antenna "B" is closer to the transmitter.  If we take the above situation and rotate our two-antenna array around 180 degrees, antenna "B" will be closer to the transmitter than "A" and when our switch from "A" to "B" happens, our frequency will go UP for an instant when it does so - and vice-versa.  In that case, our oscilloscope will show the glitches depicted in Figure 2 upside-down.

In other words, by looking at the polarity of the glitches from our receiver, we can tell if the transmitter is to our left or to our right.  We can also infer a little bit about how far to the left or right our transmitter is by looking at the amplitude of the glitches:  If the signal is off the side of the antenna as depicted in the lower part of Figure 1, the glitches will be at the strongest - and the amplitude of the glitches will diminish as we get closer to having the two elements parallel as depicted in the top part of Figure  1.

There is an obvious limitation to this:  Unless we sweep the antenna back and forth, all we can do is tell if the antenna is to our left or right.

Walking about with an antenna like this it is easy to sweep back and forth and with some practice, one can infer whether the the transmitter is to the left or right and in front or behind - but if you have a fixed antenna array (one that is not moving) or if you are in a vehicle where their orientation is fixed with respect to the direction of travel, this becomes inconvenient as you cannot tell if it is in front or behind.

Adding more antennas

Suppose that we want to know both "left and right" and "front and back" at the same time - and in that case, you would be correct if you presumed that you were to be able to do this by adding one more antenna and - and then did some switching between them.  Consider the case in Figure 3, below:

Figure 3:
A 3-antenna vertical array, with elements A, B and C.  A right-angle is formed between antennas "A" and "B" and "A" and "C".   Also see Figure #4.
Click on the image for a larger version.

In Figure 3 and 4 we have three vertical antennas - separated by less than 1/4 wavelength at the frequency of interest 1 and we also have two transmitters located 90 degrees apart from each other.  Note that these antennas are laid out in a "three-sided square" - that is, if you were to draw lines between "A" and "B" and "A" and "C" they would form a precise right angle.

We know already from our example in Figure 1 that if we are receiving Transmitter #1 that we will get our "glitch" if we switch between antenna "A" and "B" - but since antennas "A" and "C" are the same distance from Transmitter #1, we will get NO glitch.

Similarly, if we are listening to Transmitter #2, if we switch between antenna "A" and "C", we will get a glitch as "C" is closer to the transmitter than "A" - but since antennas "A" and "B" are the same distance, we would get not glitch.

From this example we can see that if we have three antennas, we can switch them alternately to resolve our "Left/Right" and "Front/Back" ambiguity at all times.  For example, let us consider what happens in the presence of Transmitter #2:

  • Switch from antenna "A" to antenna "B":  The antennas are equidistant from Transmitter #2, so there is no glitch.
  • Switch from antenna "A" to antenna "C":  We get a glitch in our received audio when we do this because antenna "C" is closer to Transmitter #2 than antenna "A".  Furthermore, we can tell by the polarity of the glitch that antenna "C" is closer to the transmitter.

Let us now presume that our array in Figure 3 and 4 was atop a vehicle and the front of the vehicle was pointed toward the left - toward Transmitter #1:  With just the above information we would know that this transmitter was located precisely to our right - and that if we wanted to drive toward it, we would need to make a right turn.

Figure 4:
A 3-antenna vertical array, with elements A, B and
C as viewed from the top.
Click on the image for a larger version.

Bearings in between the antennas

What if there a third transmitter (Transmitter #3 in Figure 4) located halfway between Transmitter #1 and Transmitter #2 and we were still in our car pointed at Transmitter #1?  You would be correct in presuming that:

  • Switching between Antenna "A" and "B" would indicate that the unknown transmitter would be to the front of the car.
  • Switching between Antenna "A" and "C" would indicate that the unknown transmitter would be to the right of the car.
  • We get "glitches" when switching between either pairs of antennas (A/B and A/C) - but these "glitches" are at lower amplitude than if the transmitter were in the direction of Transmitter #1 or Transmitter #2.

Could it be that if we measured the relative amplitude and polarity of the glitches we get from switching the two pairs of antennas (A/B and A/C) that we could infer something about the bearing of the signal?

The answer is YES.

By using simple trigonometry we can figure out - by comparing the amplitudes of the glitches and noting their relative polarity - the bearing of the transmitter with respect to the antenna array - and the specific thing we need is the inverse function "ArcTangent".

If you set your "Wayback" machine to High School, you will remember that you could plot a point on a piece of X/Y graph paper  and relative to the origin, use the ratio of the X/Y values to determine the angle of a line drawn between that point and the origin.  As it turns out, there is a function in many computer languages that is useful in this case - namely the "atan2()" function in which we put our "x" and "y" values.

Figure 5:
Depiction of the "atan2" function and how to get the angle, θ.
This diagram is modified from the Wikipedia "atan2"
article - link.

Click on the image for a larger version.
Let us consider the drawing in Figure 5.  If you remember much of your high-school math, you'll remember that if straight-up is zero degrees and the right-pointing arrow is 90 degrees that the "mid-point" between the two would naturally be 45 degrees.

What you might also remember is that if you were drop a line between the dot marked as (x,y) in Figure 5 and the "x" axis - and draw another line between it and the "y" axis - those lines would be the same length.

By extension, you can see that if you know the "x" and "y" coordinates of the dot depicted in Figure 5 - and "x" and/or "y" can be either positive or negative - you can represent any angle.

Referring back to Figure 2, recall that you will get a "glitch" when you switch antennas that are at different distances from the transmitter - and further recall that in Figures 3 and 4 that you can use the switching between antennas "A" and "B" to determine if the transmitter is in front or behind the car - and "A" and "C" to determine if it is to the left or right of the car.

If we presume that the "y" axis (up/down) is front/back of the car and the "x" axis is right/left, we can see that if we have an equal amount of "glitching" from the A/B switch ("y" axis) and the A/C switch ("x" axis) - and both of these glitches go positive - we would then know that the transmitter was 45 degrees to the right of straight ahead.

Similarly, if we were to note that our "A/B" ("y" axis) glitch was very slightly negative - indicating that the signal was behind and and that our "A/C" glitch was strongly negative indicating that it was far to our left:  This condition is depicted with the vector terminating in point "A" in Figure 5 to show that the transmitter was, in fact, to the left and just behind us - perhaps at an angle of about 260 degrees.

Using 4 antennas

The use of three antennas isn't common - particularly with an "L" (right-angle) arrangement - but one could do that.  What is more common is to arrange four antennas in a square and "rotate" them using diode switches with one antenna being active at a given instant - and having more antennas and more switching between antennas to create our glitches gives us more data to work with which can only help reduce the uncertainty of the bearing.  Consider the diagram of Figure 6.

Figure 6:
A four antenna arrangement.
Click on the image for a larger version.

In this arrangement we have four antennas arranged in a perfect square - and this time we are going to switch them in the following pattern:


Now let us suppose that we are receiving Transmitter "A" - so we would get the following "glitch" patterns on our receiver:

  • A->B:  Positive glitch (A is closer to TX #1 than B so the the source is seen to move farther away)
  • B->C:  No glitch (B and C are the same distance from TX #1)
  • C->D:  Negative glitch (D is closer to TX #1 than C so the source is seen to move closer)
  • D->A:  No glitch (A and B are the same distance from TX #1)

As expected, going from "A" to "B" results in a glitch that we'll call "positive" as antenna "B" is farther away from the transmitter than "A" - but when we "rotate" to the other side and switch from "C" to "D" - because we are going to an antenna that is closer, the glitch will have the opposite polarity as the one we got when we switched from "A" to "B" - but both glitches will have the same amplitude.

Since antenna pairs B/C and A/D are the same distance from the transmitter we will get no glitch when we switch between those antennas.

As  you can see from the above operation, every time we make one "rotation", we'll get four glitches - but they will be in equal and opposite pairs - which is to say the A->B and the C->D are one pair with opposite polarity and B->C and D->A are the other pair with opposite polarity.  If we take the measured voltage of these pairs of glitches and subtract each set, we will end up with vectors that we can throw into our "atan2" function and get a bearing - and what's more, since we are getting the same information twice (the equal-and-opposite pairs) this serves to increase the effective amplitude of the glitch overall to help make it stand out better from modulation and noise that may be on the received signal.

Similarly, if we were receiving a signal from Transmitter #3 (in Figure 6) we could see that being at a 45 degree angle, each of our four glitches would have the same strength but differing polarities - with the vector pointing in that direction.  What's more, the magnitude of those glitches will be a bit lower than our example with Transmitter #1, above:  Since Transmitter #3 is shifted 45 degrees, this means that the apparent distance between any antenna switch will be about 71% as great as it would have been had it been Transmitter #1 or #2.  If you recognized that 71% - or 0.707 is the sine (or cosine) of 45 degrees, you would be exactly right!

A typical four-antenna ARDF unit will "spin" the antenna at anywhere between 300 and 1000 RPM - the lower frequencies being preferable as it and their harmonics are better-contained within the 3 kHz voice bandwidth of a typical communications-type FM receiver.

Figure 7:
Montreal "Dopplr 3" with compass rose,
digital bearing indication and adjustable switched-
capacitor band-pass filter running "alternate"
firmware (see KA7OEI link below).
Click on the image for a larger version.

Improving performance - filtering

As can be seen in the oscillogram of Figure 2, the switching glitches are of pretty low amplitude - and they are quite narrow meaning that they are easily overwhelmed by incidental audio and - in the case of weaker signals - noise.  One way to deal with this is to use a very narrow audio band-pass filter - typically something on the order of a few Hz to a few 10s of Hz wide.

In the analog world this is typically obtained using a switched-capacitor - the description of which would be worthy of another article - but it has the advantage of its center frequency being set by an external clock signal:  If the same clock signal is used for both the filter and to "spin" the antenna, any frequency drift is automatically canceled out.

It is also possible to use a plain, analog band-pass filter using op amps, resistors and capacitors - but these can be problematic in that these components - particularly the capacitors - are prone to temperature drift which can affect the accuracy of the bearing, often requiring repeated calibration:  This problem is most notable during summer or winter months when the temperature can vary quite a bit - particularly in a vehicle.

By narrowing the bandwidth significantly - to just a few Hz - it is far more likely that the energy getting through it will be only from the antenna switching and not incidental audio.

There is another aspect related to narrow-band filtering that can be useful:  Indicating the quality of signal.  In the discussions above, we are presuming that opposite pairs of antennas will yield equal-and-opposite "glitches" (e.g. A->B and C->D are mirror images, and B->C and D->A are also mirror images) - but in the case of multipath distortion - where the receive signal can come from different directions due to reflection and/or refraction - this may not be the case.  If the above "mirroring" effect is not true, this causes changes in the amplitude of the tone from the antenna spin rate (the "switching tone") which can include the following:

  • The switching tone can decrease overall due to a multiplicity of random wave fronts arriving at the antenna array.   If multipath is such that one or more of our antennas gets no signal - or they get a delayed bounce that "looks" like one of the other antennas, you might get a missing glitch or one that has the wrong polarity.  A signal distorted in such a manner probably won't make it through our very narrow band-pass filter very well at all.
  • The switching tone's frequency can double if each antenna's slightly-different position is getting a different portion of a multipath-distorted wave front.  If the multipath is such that every antenna as a different version of the bounced signal it may be that you don't get the "equal and opposite" glitches that you expect.  Again, if our switching tone is doubled, it won't make it through the band-pass filter.
  • The switching tone can be heavily frequency-modulated by the rapidly-changing wave fronts.  Remember that Frequency Modulation is all about the rapid phase changes of the carrier with modulation - but if you are driving through an area with a lot of reflections, this can add random phase shifts to the received signal which can cause the switching tone of our antennas' rotation to be seemingly randomized.  Because the randomization will likely appear as noise, this will likely "dilute" our switching tone and there will be less of it to be able to get through our narrow band-pass filter.
If you have ever operated VHF/UHF from a moving vehicle, you have experienced all three of the above to a degree:  It's likely that you have stopped at a light or a sign, only to find out that the signal to which you were listening faded out and/or got distorted - only to appear again if you moved your vehicle forward or backwards even a few inches/centimeters.  Similarly, you've likely heard noise (e.g. "Picket Fencing") as you have driven through an area with a lot of clutter from buildings and/or terrain:  Imagine this happening to four antennas in slightly different locations on the roof of your vehicle, each getting a signal that is distorted in its own, unique way!

Each of the above cause the switching tone in the receiver to be disrupted and with the worse disruption, less of the signal will get through the narrow filter.  Of course, having a good representation of the antenna's switching tone does not automatically mean that it is going to indicate a true bearing to the transmitter as you could be receive a "clean" reflection - but you at least you can detect - and throw out - obviously "bad" information!

Improving performance - narrow sampling

In addition to - or instead of narrow-band sampling - there's another method that could be used and that is narrow sampling.  Referring to Figure 2 again, you'll note that the peaks of the glitches are very narrow.  While the oscillogram of Figure 2 was taken from the speaker output of the receiver, many radios intended for packet use also include a discriminator output for use with 9600 baud and VARA modes which has a more "pristine" version of this signal.

Because we can know precisely when this glitch arrives (e.g. we know when we switch the antenna - and we can determine by observation when, exactly, it will appear on the radio's output) we can do a grab the amplitude of this pulse with a very  narrow window (e.g. "look" for it precisely when we expect it to arrive) and thus reject much of the audio content and noise that can interfere with our analysis.  

Further discussion of this technique is beyond the scope of this article, but it is discussed in more detail here.

Improving performance - vector averaging

If you have ever used a direction-finding unit with an LED compass rose before, you'll note that in areas of multipath that the bearing seems to go all over the place - but if you look very carefully (and are NOT the one driving) you may notice something interesting:  Even in areas of bad multipath, there is likely to be a statistical weight toward the true bearing rather than a completely random mess.  This is a very general statement and it refers more to those instances where signals are blocked more by local ground clutter rather than a strong reflection from, say, a mountain, which may be more consistent in their "wrongness".

While the trained eye can often spot a tendency from seemingly-random bearings, one can bring math to the rescue once again.  Because we are getting our signal bearings by inputting vectors into the "atan2" function, we could also sum the individual "x" and "y" vectors over time and get an average.  
This works in our favor for at least two reasons:
  1. It is unlikely that even multipath signals are entirely random.  As signals bounce around from urban clutter, it is likely that there will be a significant bias in one particular direction.
  2. Through vector averaging, the relative quality of a signal can be determined.  If you get a "solid" bearing with consistently-good signals, the magnitude of the x/y vectors will be much greater than that from a "noisy" signal with a lot of variation.

In the case of #1, it is often that, while driving through a city among buildings that the bearing to a transmitter will be obfuscated by clutter - but being able to statistically reduce "noise" may help to provide a clue as to a possible bearing.

In the case of #2, being able to determine the quality of the bearing can, through experience, indicate to you whether or note you should pay attention to the information that you are getting:  After all, getting a mix of good and bad information is fine as long as you know which is the bad information!

Typically one would use a sliding average consisting of a recent history of samples.  If one uses the "vector average" method described above it is more likely that poor-quality bearings will have a lesser influence on the result. 

Antenna switching isn't ideal

Up to this point we have been talking about using a single receiver with a multi-antenna array that sequentially switches individual antennas into the mix - but electronic switching of the antennas is not ideal for several reasons:

  • The "modulation" due to the antenna switching imparts sidebands on the received signals.  Because this switching is rather abrupt, this can mean that signals 10s and 100s of kHz away can raise the receive system noise floor and decrease sensitivity.
  • The switching itself is quite noisy in its own right and can significantly reduce the absolute sensitivity of the receive system.  For this reason, only "moderate-to-strong" signals are good candidates for this type of system.
  • In the presence of multipath, the switching itself can result in the signal being more highly disrupted than normal.  This isn't too much of a problem since it is unlikely that one could get a valid bearing in that situation, anyway, but it can still be mitigated with filtering as described above.
If one is actively direction-finding with gear like this, it should not be the only tool in their toolbox:  Having a directional antenna - like a small Yagi - and suitable receiver (one with a useful, wide-ranging signal level meter) is invaluable both for situations where the signal may be too weak to be reliably detected with a TDOA system and when you are so close to it that you may have to get out of the vehicle and walk around.

Doing this digitally

There is something to be said about the relative simplicity of an analog TDOA system:  You slap the antennas on the vehicle, perform a quick calibration using a repeater or someone with a handie-talkie, and off you go.  To be sure, a bit of experience is invaluable in helping you to determine when you should and should not trust the readings that you are getting - but eventually, if the signal persists, you will likely find the source of the signal.

These days there are a number of SDR (Software-Defined Radio) systems - namely the earlier Kerberos and more recent Kraken SDRs.  Both of these units use multiple receivers that are synchronized from the same clock and use in-built references for calibration.

The distinct advantage of having a "receiver per antenna" is that one need not switch the antennas themselves, meaning that the noise and distortion resulting from the electronic "rotation" is eliminated.  Since the antennas are not switched, a different - yet similar - approach is required to determine the bearing of the signal - but if you've made it this far, it's not unfamiliar:  The use of "atan2" again:  One can take the vector difference of the signal between adjacent antennas and get some phasing information - and since we have four antennas, we can, again, get two equal and opposite pairs (assuming no multipath) of bearing data.

If you have two signals from adjacent antennas - let's say "A" and "B" from Figure 6 - we already know that the phasing will be different on the signal if the antenna hits "A" first rather than "B" first and this can be used in conjunction with its opposite pair of antennas ("C" and "D") to divine one of our vectors:  A similar approach can be done with the other opposite pairs - B/C and D/A.

This has the potential to give us better-quality bearings - but the same sorts of averaging and noise filtering must be done on the raw data as it has no real advantage over the analog system in areas where there is severe multipath:  It boils down to how it does its filtering and signal quality assessment and, more importantly, how you, the operator, interpret the data based on experience gained from having used the system enough have become familiar with it.

As far as absolute sensitivity goes between a Kerberos/Kraken SDR and an analog unit - that's a bit of a mixed bag.  Without the switching noise, the absolute sensitivity can be better, but in urban areas - and particularly if there is a strong signal within the passband of the A/D converter (which has only 8 bits) the required AGC may necessarily reduce the gain to where weaker signals disappear.
There are other possibilities when it comes to SDR-based receivers - for example, the SDRPlay RSPduo has a pair of receivers within it that can be synchronous to each other:  Using one of these units with a pair of magnetic loops can be used to effect the digital version of an old-fashioned goniometer!  This has the advantage of relative simplicity and can take advantage of the relatively high performance of the RSP compared to the RTL-SDR. 

Finally, there exist multi-site TDOA systems where the signals are received and time-stamped with great precision:  By knowing when, exactly, a signal arrives and then comparing this with the arrival time at other, similar, sites it is (theoretically) possible to determine the location of origin - a sort of "reverse GPS" system.  This system has some very definite, practical limits related to dissemination of receiver time-stamping and the nature of the received signal itself and would be a topic of of a blog post by itself!

Equipment recommendations?
My "go to " ARDF unit for in-vehicle use is currently a Montreal "Dopplr 3" running modified firmware (written by me - see the link to the "KA7OEI ARDF page, below) with four rooftop antennas.  Having used this unit for nearly 20 years, I'm very familiar with its operation and have used it successfully many times to find transmitters - both in for fun and for "serious" use (e.g. stuck transmitter, jammer, etc.) 
This unit has the advantage of being "grab 'n' go" in that it takes only a few seconds to "boot up" and it has a very simple, intuitive compass rose display. I believe that its performance is about as good as it can possibly be with a "switched antenna" type of ARDF unit:  For the most part, if a signal is audible, it will produce a bearing.

A disadvantage of this unit to some would be that it's available only in the form or a circuit board (still available from FAR circuits - link ) which means that the would-be builder must get the parts and put it together themselves.

"Pre-assembled" options for this type of unit include the MFJ-5005 which can sometimes be found on the used market and several options from the former Ramsey Electronics - along with the Dick Smith ARDF unit:  Information on these units may be found on the K0OV page linked below.
Comment:  Do NOT try to use ANY ARDF gear with inexpensive Chinese radios like BaoFengs.  The reason for this is that owing to their "receiver on a chip" having its own DSP processor, there are variations on how long the audio is delayed with respect to when the signal arrives at the antenna and this will certainly wreck any attempt at doing anything that requires consistent timing - which is true for all systems that use multiple antennas.  You will be much better off using a "conventional" (non-DSP) receiver:  Radios that are decades old - particularly if they don't have any features - are often ideal as they are typically robust and can be bought inexpensively.

Another possible option is the "Kraken SDR":  I have yet to use one of these units, but I'm considering doing so for evaluation and comparison - which I will report here if I am actually able to do so.

Final words

This (rambling) dissertation about TDOA direction finding hopefully provides a bit of clarity when it comes to understanding how such things work - but there are a few things common to all systems that cannot really be addressed by the method of signal processing - analog or digital:
  • Bearings from a single fixed location should be suspect.  Unless you happen to have an antenna array atop a tall tower or mountain, expect the bearing that you obtain to be incorrect - and even if you do have it located in the clear, bogus readings are still likely.
  • Having multiple sources of bearings is a must.  Having more than one fixed location - or better yet having one or more sources of bearings from moving vehicles is very useful in that this dramatically decreases the uncertainty.
  • The most important information is often just knowing the direction in which you should start driving.  Expecting to be able to located a signal with a TDOA system with any reasonable accuracy is unrealistic.  It is often the case that when a signal appears, the most useful piece of information is simply knowing in which direction - to the nearest 90 degrees - that one should start looking.
  • The experience of the operator is paramount.  No matter which system you are using, its utility is greatly improved with familiarity of its features - and most importantly, its limitations.  In the real world, locating a signal source is often an exercise in frustration as it is often intermittent and variable and complicated by geography.  No-one should reasonably expect to simply purchase/build such a device and have it sit on the shelf until the need arises - and then learn how to use it!

 * * *


  1. On systems like this where one switches between (or uses) multiple antennas - it is necessary that adjacently-compared antennas be less than a quarter wave apart at the highest operational frequency.  While it is possible to get better resolution by increasing the spacing between antennas, the directional response will have multiple lobes meaning that there can be an uncertainty as to which "lobe" is being detected.
Having more than 1/4 wavelength spacing can be useful if you have means of resolving such ambiguities.  Spacing antennas closer than 1/4 wavelength can work, but the phase difference also decreases meaning that differences between antennas reduces making detection of bearing more difficult and increasingly susceptible to incidental signal modulation and the uncertainty that those factors imply.  From a purely practical stand point, the roof of a typical vehicle is only large enough for about 1/4 wavelength spacing on 2 meters, anyway.

Related links:

  • K0OV's Direction Finding page - link - By Joe Moell, this covers a wide variety of topics activities related to ARDF. 
  • WB2HOL's ARDF Projects - link - This page has a number of simple, easy to build antenna/DF projects.
  • KrakenSDR page - link - This is the product description/sales page for the RTL-SDR based VHF/UHF SDR.


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