On the Optimality of "Half the Cake" for K-User Rank-Deficient Mk x Mk Interference Channel

By introducing a novel outer bound, we find a sufficient condition for optimality of $\sum_{k=1}^K M_k/2$ degrees of freedom (half the cake per user) for a $K$-user multiple-input- multiple-output (MIMO) interference channel (IC) where the cross-channels have arbitrary rank constraints, and the $k^{th}$ transmitter and receiver are equipped with $M_k$ antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have $M$ antennas; and by Tang et al., of full rank interference channels where the $k^{th}$ user pair has $M_k$ antennas.

I. Introduction

Degrees of freedom (DoF) studies of wireless interference networks have produced a diverse array of new insights into the accessibility of signal dimensions under a variety of channel models. In order to consolidate these insights and to build upon them, it is important to make progress on unifying the underlying channel models. The motivation for this work, summarized in Fig. 1, is to pursue such a generalization of the results from [1], [2], [3]. Specifically, in this work our goal is to consolidate the key insights regarding the optimality of half-the-cake (the “cake” refers to each user's interference-free DoF, cf. [1]) for the K-user MIMO interference channel settings where the number of antennas at each receiver is equal to the number of antennas at the corresponding transmitter, i.e., all the desired channels are square matrices. ¹

Rectangular channels present a significantly different set of challenges, and generally allow more than half-the-cake per user, so they remain outside the scope of this paper.

Fig. 1:

The motivation of this paper.