On the Degrees of Freedom for Opportunistic Interference Alignment with 1-Bit Feedback: The 3 Cell Case

Opportunistic interference alignment (OIA) exploits channel randomness and multiuser diversity by user selection. For OIA the transmitter needs channel state information (CSI), which is usually measured on the receiver side and sent to the transmitter side via a feedback channel. Lee and Choi show that $d$ degrees of freedom (DoF) per transmitter are achievable in a 3-cell MIMO interference channel assuming perfect real-valued feedback. However, the feedback of a real-valued variable still requires infinite rate. In this paper, we investigate 1-bit quantization for opportunistic interference alignment (OIA) in 3-cell interference channels. We prove that 1-bit feedback is sufficient to achieve the optimal DoF $d$ in 3-cell MIMO interference channels if the number of users per cell is scaled as ${\rm SNR}^{d^2}$. Importantly, the required number of users for OIA with 1-bit feedback remains the same as with real-valued feedback. For a given system configuration, we provide an optimal choice of the 1-bit quantizer, which captures most of the capacity provided by a system with real-valued feedback. Using our new 1-bit feedback scheme for OIA, we compare OIA with IA and show that OIA has a much lower complexity and provides a better rate in the practical operation region of a cellular communication system