I've never heard of P.I.C. before but I can tell you all landline modems use echo cancellation training with test patterns to cancel near and far end echoes.
WiFi on the other hand gets cancellation from any transmitter that echoes off walls with a cancellation effect called Rician Fading or Rice Fading. This can generate a null when an echo is equal amplitude and out of phase and is very common on laptops in apartments near the fringe. Just moving the laptop a few mm can go from -70 to -85 and lose the signal , when there are echoes.
These are mostly half duplex (HDX) modems which need echo cancellation from path echoes in the cable or air. THe same is true for Cable modems and DSL modems.
Now comes a method which PIC which compromises the bit rate with full duplex (FDX) and create multiple frequency echo cancellation using DSP matrix calculations on the digitized transmitted and received signal. The partial cancellation may be a compromise due to the extreme processing power required that achieves a slightly better thruput than a half duplex channel (HDX).
There are many papers on the web that explain the math and the functions.