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Although the sufficient condition for a blindly interference-aligned (BIA)2-user 2x1 broadcast channel (BC) in homogeneous fading to achieve its maximal4/3 DoF is well understood, its counterpart for the general K-user 2x1 MISO BCin homogeneous block fading to achieve the corresponding 2k/(2+K-1) (DoF)remains unsolved and is, thus, the focus of this paper. An interference channelis said BIA-feasible if it achieves its maximal DoF only via BIA. In thispaper, we cast this general feasibility problem in the framework of findinginteger solutions for a system of linear Diophantine equations. By assumingindependent user links each of the same coherence time and by studying thesolvability of the Diophantine system, we derive the sufficient and necessaryconditions on the K users' fading block offsets to ensure the BIA feasibilityof the K-user BC. If the K offsets are independent and uniformly distributedover a coherence block, we can further prove that 11 users are enough for oneto find, with certainty of 95%, 3 users among them to form a BIA-feasible3-user 2x1 BC.

Diophantine Approach to Blind Interference Alignment of Homogeneous K-user 2x1 MISO Broadcast Channels