Interference Subspace Alignment-Based Precoding Design for Multi-Cell Multi-User Systems

Interference alignment (IA) in the spatial domain has been recognized as an important technique to handle the interference in dense network. However, traditional IA is flawed especially for large scale antenna systems. With challenges brought by hybrid precoding, IA cannot be perfectly achieved with limited radio frequency (RF) chains. In this article, we adopt the thought of interference subspace alignment (ISA) and provide full digital and hybrid precoding schemes for multi-cell multi-user systems under an interfering broadcast channel model. For full digital precoding, we derive the requirement for transmitting antennas to achieve ISA. A closed-form ISA solution space is further developed, where the interference subspace of each user is no longer constrained. Then, a projection-based ISA algorithm is proposed for full digital precoding. The projection from the selfish design to the ISA solution space strengthens the desired signal while achieving ISA. For hybrid precoding, we formulate a vector approximation problem to minimize interference misalignment. A novel generalized gradient projection algorithm is proposed to design each RF chain. To approximately achieve ISA, two algorithms are proposed with different approximation principles. For low SNR, a specific vector in the ISA solution space is approximated to combat additive noise, while for high SNR, the whole ISA solution space is approximated to suppress interference. The proposed schemes are further extended to imperfect CSI cases for more practical scenarios. Simulation results highlight that the proposed full digital and hybrid precoding schemes can effectively handle the inter-cell and intra-cell interference and outperform the existing schemes.