Degrees of freedom of interference channel with rank-deficient transfer matrix

We consider the interference channel with K transmitters and K receivers all having a single antenna, wherein the K × K transfer matrix representing this channel has rank D (D <; K) . The degrees of freedom (DoF) of such channels are not known as the rank deficiency in the transfer matrix creates algebraic dependencies between the channel coefficients. We present a modified version of the [CJ08] alignment scheme, to handle these dependencies while aligning interference, and state the sufficient conditions for achieving half rate per user using this scheme. The difficulties in proving these sufficient conditions are shown for K = 4 and K = 5. We also show that these sufficient conditions are not satisfied for K ≥ 6.