Recent results have elucidated the benefits of using improper Gaussian signaling (IGS) as compared to conventional proper Gaussian signaling (PGS) in terms of achievable rate for interference-limited conditions. This paper exploits majorization theory tools to formally quantify the gains of IGS along with widely linear transceivers for MIMO systems in interferencelimited scenarios. The MIMO point-to-point channel with interference (P2P-I) is analyzed, assuming that received interference can be either proper or improper, and we demonstrate that the use of the optimal IGS when received interference is improper strictly outperforms (in terms of achievable rate and mean square error) the use of the optimal PGS when interference is proper. Then, these results are extended to two practical situations. First, the MIMO Z-interference channel (Z-IC) is investigated, where a trade-off arises: with IGS we could increase the achievable rate of the interfered user while gracefully degrading the rate of the non-interfered user. Second, these concepts are applied to a two-tier heterogeneous cellular network (HCN) where macrocells and smallcells coexist and multiple MIMO Z-IC appear.

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