I have found some clues in the manual
AN-1508 DP83849 Cable Diagnostics (Rev. A) - Texas Instruments.
The device itself probably is not relevant to your setup, but the information
in the documents seems useful.

The DP83849 provides a method of computing cable length based on
electrical characteristics of the 100Mb Link. This essentially
provides an
**equivalent cable length rather than a measurement of the physical cable length**.

100MB cable length is a linear function of the Analog (AEQ) and
Digital (DEQ) equalization coefficient values in the linked state.

```
if (AEQ == 0) Length = (A1 × DEQ) + B1
if (AEQ == 1) Length = (A2 × DEQ) + B2
and so on ...
```

The algorithm for computing the electrical cable length is depicted
above. The constants {A1, A2, ... } & {B1, B2, ... } are determined by
statistical study of various typical case cables. The computation is
completely handled in hardware.

Another section of the manual throws more light on the measurement method:

**TDR Cable Diagnostics**

The PHYTER Dual implements a Time Domain Reflectometry (TDR) method of
cable length measurement and evaluation which can be used to evaluate
a connected twisted pair cable. The TDR implementation involves
sending a pulse out on either the Transmit or Receive conductor pair
and observing the results on either pair.

The TDR cable diagnostics works best in certain conditions. For
example, an unterminated or open cable provides a good reflection for
measuring cable length, while a cable with an ideal termination at an
unpowered partner may provide no reflection at all. The TDR cable
diagnostics only works for twisted pair (copper) connections and is
not supported over Fiber connections.

The final conclusion is that a pulse is sent on the Transmit or Receive
conductor pair and the results are observed. They are then searched in a table
derived using empirical tests and further improved by the firmware.
The result is not physically accurate, being only a statistical derivation.

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