Hi Marcus,
Thanks for your nice words. GNU Radio is an amazing project and the
email archive is our first resource for finding help. Benefited me numerous
times.
Regarding the necessity of back and forth transmission for ranging, you
already know this stuff but I write the below note for later searchers.
The fundamental question to ask is the following. What are the conditions
under which finding the distance is possible? It turns out that
unsynchronized nodes have a phase offset Theta and a delay Tau between
them. So we have two unknowns.
Now if we implement one way transmission, we get only one equation and
hence it becomes impossible to separate the phase offset from delay.
Time_2 = Time_1 + Theta + Delay
However, there are several ways in which an extra equation can be
provided to this system for range determination (since phase is just
another manifestation of time, so the underlying principles stay the same).
*Method 1*: Synchronize the nodes and hence Theta becomes zero. One
equation and one unknown, i.e., delay.
*Method 2*: Provide an extra independent equation through back and forth
transmission where phase offset Theta appears with a negative sign (because
measurement is at the initiator now).
Time_4 = Time_3 - Theta + Delay
Here, we have two equations that can solve the two unknowns.
*Method 3*: Move one node around that doesn't affect the phase offset Theta
but provides an extra equation for delay Tau. For example, if we take it
twice as far,
Time_4 = Time_3 + Theta + 2*Delay
Again, two equations and two unknowns. The OFDM radar you mentioned is a
generalization of this concept where we do graphs in 2 dimensions and find
the range/velocity through the respective slopes. So basically we provide
the second equation through movement that changes the delay.
As a side remark, I just mention that the large number of subcarriers
doesn't provide independent equations (multiply both sides of the above
equations with 2\piF_k instead of 2\piF_1 to check). However, they help in
solving the range ambiguity problem, e.g., with 2.4 GHz, the maximum range
determination is only 12.5cm. This comes from one wavelength (c/F).
*Method 4*: Place extra anchor nodes around the Tx. Now we have several
extra equations but exactly the same number of extra phase offsets! One
node (even an anchor) then can respond with a reply message where phase
offsets appear with negative signs making the system solvable. This is
usually known as ranging through one-way transmission (because target node
has to transmit only once) or Blink Mode by some.
Cheers,
Qasim
On Sat, Jun 8, 2019 at 11:33 PM Müller, Marcus (CEL) <muel...@kit.edu>
wrote:
> Hi Qasim,
>
> a) it's so nice to see you drop in here from time to time :)
> b) that's true! But reality is even better; the back and forth exchange
> isn't strictly necessary.
> c) I finally find the time to write down what I wanted to write.
>
> ## First, agreeing with you:
>
> One can basically emulate the principle of a correlation-based radar by
> making the other end "reflect" info with a known delay.
>
> All one needs to do is ensure that a reply packet is sent a *fixed*
> amount of time after a packet is received. That interval doesn't have
> to be necessarily short, just known.
>
> From the reply, and its knowledge of the original transmission's time,
> the original transmitter can deduce the double of the one-way
> transmission latency; that can, given enough bandwidth, SNR and
> processing gain, be enough to resolve integer wavelength ambiguities.
> In practice, passband bandwidth will often be the fundamentally
> limiting factor.
>
> With the phase estimate done on the reply, and info on the phase
> estimate done by the replying party, both sides would have relative
> phase CSI, and the original transmitter a distance estimate.
>
> ## Then, disagreeing with you (just a little bit):
>
> Now, while the above works with any transmission that allows phase
> recovery, OFDM frames have the advantage of allowing a two-dimensional
> DFT to be used to estimate range through the time-shift property of the
> DFT. However, that requires knowledge of the transmitted symbols at the
> receiver – which luckily is recoverable in case of successful OFDM
> communication¹.
>
> In fact, that's how OFDM radar works very nicely; it's explained in
> [1].
>
> Imagine a receiver with knowledge of the transmitted signal. While
> lacking a common time base, a receiver can infer distance from the
> development of the phases of entries of a sufficiently large (in both
> number of OFDM symbols and number of subcarriers) OFDM frame.
>
> The idea is simple: assume you know the symbols at the transmitter. The
> speed-of-light induced delay is constant across all subcarriers.
> The resulting phase shift, thus, is proportional to the subcarrier
> frequency, and hence the subcarrier number.
> Therefor, when you observe linear channel phase change over subcarrier,
> you can get a distance estimate. Phase being a linear function of index
> implies we're dealing with a sinusoid – and a DFT in subcarrier
> direction will give us a range plot.
>
> Same idea for Doppler, but with phase on the same subcarrier, but for
> consecutive and hence constant-interval OFDM symbols; do another DFT
> for each subcarrier across OFDM symbols, and get a doppler plot.
>
> Overall: Write down your received OFDM symbols as column vectors of a
> matrix, point-wise divide by the transmitted symbols (normalize
> amplitude if helpful); the result is a matrix full of complex numbers
> with the channel phase for each subcarrier at each symbol time.
> Do an appropriate 2D-DFT, get a range/doppler plane "image". Find the
> peak; use clever interpolation / post-processing to increase resolution
> and/or reduce estimate variance.
>
> Cheers,
> Marcus
>
> ¹ (unless someone inexplicably decided to use differential PSK on the
> subcarriers – looking at DAB, there.)
>
> [1] https://publikationen.bibliothek.kit.edu/1000038892
>
> On Sat, 2019-06-08 at 14:21 +1000, Qasim Chaudhari wrote:
> > Phase information is preserved whether the Rx architecture is zero-IF
> > or not. The OP I guess is already using a back and forth exchange
> > between two USRPs, from which the distance information can be
> > extracted in case of OFDM signals.
> >
> > Cheers,
> > Qasim
>
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