Aligned Image Sets under Channel Uncertainty: Settling a Conjecture by Lapidoth, Shamai and Wigger on the Collapse of Degrees of Freedom under Finite Precision CSIT

Understand

A conjecture made by Lapidoth, Shamai and Wigger at Allerton 2005 (also an open problem presented at ITA 2006) states that the DoF of a 2 user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision CSIT.

• In this work we prove that the conjecture is true in all non-degenerate settings (e.g., where the probability density function of unknown channel coefficients exists and is bounded).
• The DoF collapse even when perfect channel knowledge for one user is available to the transmitter.
• This also settles a related recent conjecture by Tandon et al.