Interference Alignment With Limited Feedback In Multiuser Interference Networks

Interference alignment (IA) is a scheme to approach the capacity at high signal-noise ratio (SNR) in multiuser networks. To implement the IA scheme in a frequency-division duplexing (FDD) system, channel state information at transmitter (CSIT) is fed back from the receiver with finite bits. However, such CSIT is subject to quan-tization errors, estimation errors, and delays of feedback. In this paper, we analyze the performance of IA system with imperfect CSIT in the single-input single-output (SISO) frequency-selective channel and multiple-input multiple-output (MIMO) chan-nel respectively. To solve the problem of requiring a huge codebook in limited feedback systems, we propose a joint real Grassmannian quantization strategy and a beamforming quantization strategy in this paper.First, basic theories of IA and limited feedback have been introduced. The analysis of Degrees of Freedom (DoF) in several channels and several algorithms of IA are given. Next, limited feedback strategies are introduced, and related theoretical performance analysis is presented.Second, we analyze the performance of SISO IA with limited feedback. We verify that the average performance loss is determined by the average interference leakage. In the further analysis, we derive an upper bound of the average interference leakage. Meanwhile, a noise-limited criterion that the average interference leakage is smaller than thermal noise is proposed to ensure quality of service (QoS) in IA systems. Then, we will compare different quantization strategies under this criterion. Under this cri-terion, the lower bound of the codebook size using the conventional complex Grass-mannian quantization strategy is derived. However, it is observed that a huge codebook size is required at high SNR to implement IA. To reduce the codebook size, we pro-pose a joint real Grassmannian quantization strategy which quantizes the real part and the imaginary part of the channel vector respectively. Theoretical analysis and simula-tions demonstrate that our proposed strategy significantly outperforms the conventional strategy at moderate and high SNR.Finally, we analyze the performance of MIMO IA with imperfect CSIT which consists of quantization errors, estimation errors and delays of feedback. First of all, for the IA scheme with quantization errors, we derive the average interference leakage caused by quantization errors. Under the noise-limited criterion, codebook sizes re-quired by the conventional complex Grassmannian strategy and our proposed joint real Grassmannian quantization strategy are derived. However, for both strategies, code-book sizes are too huge. To reduce the codebook size, we propose a new beamforming quantization strategy which only quantizes and feedbacks precoders instead of channel matrices. Theoretical analysis illustrates that a smaller codebook and fewer feedback bits are required in this new strategy. Next, for the IA scheme with estimation errors, we observe that the average interference leakage depends on the variance of estimation errors. With the MMSE channel estimation, the average interference leakage caused by estimation errors tends to a constant at high SNR and is trivial compared with that caused by quantization errors. Finally, for the IA scheme with delays of feedback, we find that the average interference leakage depends on the channel correlation coefficient between time blocks and increases linearly with SNR. Thus, there is a huge performance degradation at high SNR.