Phase disambiguation possible without coherence between receivers?

[jakapoor]

Our recent meeting with Dr. Kan (3/27/18) revealed that ranging with phase difference information requires phase coherence between different antennas at different arrays. My vague understanding of why this is the case is that the phase cycle integer disambiguation process looks for differences in received phase between antennas at precisely the same time of arrival (phase-difference of arrival; requiring phase coherence between antennas) or, when RFID is used, the process looks for a phase difference between the signal on the transmitting antenna and the receiving antenna. In this latter case, because the oscillator responsible for the transmitted signal is coupled with the oscillator for the receiving antenna, the shift in received phase can be estimated from a single receiving antenna. This latter technique is not possible for us since we are using active tags.

The system we have been designing up to now has only considered coherence between antennas in the same array. Krueger and Whiting both have work that allows for coherence between distributed receiver nodes using the hardware we're working with, so if coherent detection on this scale is required, we may still be in the running for using this technique.

Our first line of attack in determining if our system still allows for phase cycle integer disambiguation down the road is to fully understand how disambiguation works.

[jakapoor]

Email communication from Russell Silva (6/7/2018) [edited by Julian Kapoor 6/13/2018]:

This is my understanding of the PDOA approach used in Dr. Kan's system: "The distance from tag to i-th antenna" is computed by the "measured phase of second harmonic backscatter signal" (page 7). This means that the specific phase (along with the disambiguated phase integer) of the tag's signal at each antenna corresponds to a distance from each antenna-receiver much like TDOA (see image1 attachment). More specifically, each tag to antenna distance in an antenna pair, restricts the tag's location to a hyperboloid, which is done for multiple antenna pairs for intersecting hyperboloids (see image2 attachment).

In the PDOA approach used in Dr. Kan's system and various other RFID systems (I am having trouble finding PDOA active radio tag implementations online), we both agree that PDOA requires synchronization among ground-nodes in the receiver network.

Dr. Kan's system and other RFID systems inherently achieve this synchronization by having every antenna in the system connected to a common embedded system device. Even though synchronization is guaranteed in most indoor, local RFID ranging systems, synchronization among receivers in PDOA does not need to be at the nanosecond level. This is because phase differences are being used for ranging purposes which have errors that relate to transmitter velocity (if the transmitter is stationary indefinitely, PDOA accuracy is guaranteed no matter how spread apart measurements are temporally). Nevertheless, receivers must be synchronized to global time at a specified rate to avoid drift because synchronization errors compound over time.

In our case, does this mean we need coherent receiver units for a PDOA system? Phase measurements can be collected at single RTL-SDR units, and distances can be computed in a multi-frequency approach. Also, I believe PDOA would demand a multi-frequency approach for distance ranging in our system (correct me if I'm wrong).

Follow-up email from Russell (same day)

In my last email I made errors confusing TDOA with TOA. TOA estimates locations by determining the points of intersection of circles (2d) or spheres (3d). TDOA and PDOA estimate locations at the intersections of hyperbolas (2d) or hyperboloids (3d).

I am still confused on whether Dr. Kan's system 1. first computes separate tag to antenna distances for each antenna and then applies measured distances to PDOA hyperbolic ranging or 2. compares phase between pairs of antennas as is standard in PDOA hyperbolic ranging.

If the first case is valid, I suggest that we do not need a coherent receivers in our system. If the second case is valid, I suggest that PDOA cannot be implemented for our system, because nanosecond synchronization at faraway receivers would be almost impossible.

[jakapoor]

Correspondence between Edwin Kan and Julian Kapoor (between 3/27/2018 and 4/3/2018)

Julian:

Briefly, I just wanted to make sure I am clear about how our RTL SDR-based system might have to be constructed to be compatible with your multi-frequency phase localization approach. I had previously assumed that the ranging algorithm resolved the wave cycle integer by comparing received phase differences between two antenna elements of the same array (across multiple received frequencies). After today's discussion my impression is that the cycle integer disambiguation occurs only between the received signals of different arrays (i.e. single antenna elements or antenna arrays that are spread across the detection area) and that those arrays must be phase coherent with each other. Is this impression correct? ... Now that I've read a little more about RFID-based ranging (as much as I can understand without the math background) I'd also like to gauge your opinion about whether it's reasonable to expect that a phase-of-arrival based system could be constructed with the active tags (rather than RFID tags) and non-coherent (but beacon-calibrated and synchronized) receivers that my crew is using.

Edwin:

I am not sure about the question on phase-based RF ranging. HMFCW can be applied to active tags using differential distance to dual antennas. We then used the intersection of the hyperbolas to obtain the exact location. The detailed procedure is in our Mobicom 2016 paper.

Julian:

Regarding the phase-based ranging, I think you've basically answered my main question. The crew and I had focused our attention on your other paper that uses beamforming to refine AOA estimates, and we neglected to realize that between-array coherence was necessary. My primary concern at this point is in achieving adequate precision in phase/time synchronization of distributed receiver arrays through beacon-based calibration.

Edwin:

I did not use AoA for localization as the precision is limited. I used only AoA variation to evaluate the weighting of LoS and multi-path. For your outdoor application, this may not be the best choice, but I need it for clustered indoor ambient.

I think beacon-based synchronization can work as long as one receiver is assigned the master and the network can be regarded as a star network (so not an ad hoc network). Another choice will be the GPS signal. As each receiver location needs to be pinned down anyway, if the GPS signal can be retrieved, it will have a very precise reference clock (some drift in short duration due to ionosphere, but stable in the long term).

[jakapoor]

Response to Russell Silva's 6/7/2018 message:

This is my understanding of the PDOA approach used in Dr. Kan's system: "The distance from tag to i-th antenna" is computed by the "measured phase of second harmonic backscatter signal" (page 7). This means that the specific phase (along with the disambiguated phase integer) of the tag's signal at each antenna corresponds to a distance from each antenna-receiver much like TDOA (see image1 attachment). More specifically, each tag to antenna distance in an antenna pair, restricts the tag's location to a hyperboloid, which is done for multiple antenna pairs for intersecting hyperboloids (see image2 attachment).

As you have noted below in your clarification, PDOA sensu Kan provides a differential distance between to receivers and the tag, rather than an absolute difference between a single receiver and a tag. Also, as you indicate lower down, TDOA (as opposed to TOA) does not correspond to a distance, but a differential distance between two distributed receivers. Incidentally, your term "antenna pair" here is ambiguous, but I assume you mean antenna-tag pair.

In the PDOA approach used in Dr. Kan's system and various other RFID systems (I am having trouble finding PDOA active radio tag implementations online), we both agree that PDOA requires synchronization among ground-nodes in the receiver network.

Agreed. I have yet to identify a single paper that references a multi-frequency PDOA approach with active and non-RFID-based transmitters (though I have found active RFID approaches, which we might want to consider). See my communication with Dr. Kan (above) indicating two potential options for adapting his HMFCW ranging approach to active tags: 1) beacons, 2) a GPS signal.

Dr. Kan's system and other RFID systems inherently achieve this synchronization by having every antenna in the system connected to a common embedded system device. Even though synchronization is guaranteed in most indoor, local RFID ranging systems, synchronization among receivers in PDOA does not need to be at the nanosecond level. This is because phase differences are being used for ranging purposes which have errors that relate to transmitter velocity (if the transmitter is stationary indefinitely, PDOA accuracy is guaranteed no matter how spread apart measurements are temporally). Nevertheless, receivers must be synchronized to global time at a specified rate to avoid drift because synchronization errors compound over time.

My understanding is that this is incorrect. First, synchronization is not guaranteed in indoor environments; coherence is required between receivers to achieve synchronization regardless of spatial separation because the receivers cannot accurately measure "true" phase without coherence. Nanosecond synchronization (effectively, coherent detection) is not used in ranging applications to compensate for transmitter velocity. Coherence is required to identify phase differences in a signal received at two distributed receivers. The movement of the tag is negligible compared to the speed of light. Coherence is needed to ensure that the two received signals from a single transmission are being compared in a way that guarantees that the two measured phases (phase at receiver one and phase at receiver two) are comparable to each other. This requires that the two receivers "know" their initial phase offsets with respect to each other. This initial phase offset can then be subtracted from the measured offset to calculate the true (+/- measurement error) difference in phase between the signal received at the two receivers. The signal itself consists of a series of heuristically chosen n frequencies and ranging is conducted with the n phase differences. Although the transmitter may have moved slightly (i.e. << 1 wavelength) in the ~ 1 millisecond it will take to cycle through the different frequencies for the HMFCW transmission, this ought to be negligible.

In our case, does this mean we need coherent receiver units for a PDOA system? Phase measurements can be collected at single RTL-SDR units, and distances can be computed in a multi-frequency approach.

Yes. One can obtain a measure of "phase" from a single RTL-SDR, but since the signal is demodulated using a local oscillator, and the initial phase of that local oscillator is 1) unknown, and 2) entirely determines the measured phase of the signal, the phase information from a single receiver is completely useless. PDOA requires that we know a phase-difference, not just phase, and in order to obtain that difference the initial phase offsets of the two (or more) local oscillators must be known, or a single LO must be used.

Also, I believe PDOA would demand a multi-frequency approach for distance ranging in our system (correct me if I'm wrong).

PDOA can be used in a ranging application in one of three ways, each relating to a specific domain: 1) time-domain, 2) frequency-domain, and 3) spatial-domain. See "Multifrequency Phase Difference of Arrival Range Measurement: Principle, Implementation, and Evaluation" by Qiu. The second approach (frequency-domain) requires a multi-frequency signal, but the others (I am assuming) do not necessarily.

Follow-up email from Russell (same day)

In my last email I made errors confusing TDOA with TOA. TOA estimates locations by determining the points of intersection of circles (2d) or spheres (3d). TDOA and PDOA estimate locations at the intersections of hyperbolas (2d) or hyperboloids (3d).

Correct. See above regarding the additional errors in the estimation of distance versus differential distance WRT TOA/POA verses TDOA/PDOA.

I am still confused on whether Dr. Kan's system 1. first computes separate tag to antenna distances for each antenna and then applies measured distances to PDOA hyperbolic ranging or 2. compares phase between pairs of antennas as is standard in PDOA hyperbolic ranging.

Dr. Kan's system uses the latter approach (differential distances between pairs of coherent antennas). Our task is to find a way to synchronize not only the clocks of the distributed receivers (i.e. ground nodes) but also their phases. Whiting has written a paper about this, entitled "Time and Frequency Corrections in a Distributed Network Using GNURadio;" but he doesn't go into great detail on phase offset corrections.

If the first case is valid, I suggest that we do not need a coherent receivers in our system. If the second case is valid, I suggest that PDOA cannot be implemented for our system, because nanosecond synchronization at faraway receivers would be almost impossible.

I disagree. The second case is indeed how Dr. Kan's system works, but "nanosecond synchronization" (i.e. coherent detection) is not only not impossible, but has been accomplished by both Krueger and (I believe) Whiting using the same hardware we are using. Whiting's (above) paper deals with achieving that synchronization, and Krueger's TDOA-based system also achieves synchronization with RTL-SDRs using timing beacons if memory serves me right.

[jakapoor]

Update

I am closing this issue, since we have a good sense now that the answer to the original question: "Is phase disambiguation possible without coherence between receivers?" has been answered. The answer is essentially that coherence is required, but it can be achieved in several different ways. Now the issue is "How do we achieve coherence between distributed ground nodes?"