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.

中文翻译：

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基于干扰子空间对齐的多小区多用户系统预编码设计

空间域中的干扰对齐（IA）已被认为是处理密集网络中干扰的一项重要技术。但是，传统的IA有缺陷，特别是对于大型天线系统。面对混合预编码带来的挑战，有限的射频（RF）链无法完美实现IA。在本文中，我们采用干扰子空间对齐（ISA）的思想，并在干扰广播信道模型下为多小区多用户系统提供了完整的数字和混合预编码方案。对于全数字预编码，我们得出了发送天线以实现ISA的要求。进一步开发了封闭形式的ISA解决方案空间，其中不再限制每个用户的干扰子空间。然后，提出了一种基于投影的ISA算法进行全数字预编码。从自私的设计到ISA解决方案空间的投影在实现ISA的同时增强了所需的信号。对于混合预编码，我们制定了向量逼近问题，以最大程度地减少干扰失准。提出了一种新颖的广义梯度投影算法来设计每个射频链。为了近似实现ISA，提出了两种具有不同近似原理的算法。对于低SNR，在ISA解决方案空间中近似一个特定的向量以对抗加性噪声，而对于高SNR，则在整个ISA解决方案空间中近似以抑制干扰。对于更实际的情况，建议的方案进一步扩展为不完善的CSI情况。