## 2 System Model  
Consider a \(K\) user MIMO IC model, where transmitters and receivers are equipped with \(M\) and \(N\) antennas, respectively. The transmitters and receivers are denoted as \(T_{1}\), \(T_{2}\),..., \(T_{K}\) and \(R_{1}\), \(R_{2}\),..., \(R_{K}\), respectively. A complete IA transmission process consists of the following six steps. 1. Forward link training and estimation: All \(K\) transmitters take turns to broadcast the training symbols. The training matrix for transmitter \(T_{i}\) is denoted by \(\mathbf{\Phi}_{i}\in\mathbb{C}^{M\times\tau}\), where \(\tau\geq M\) is the number of training symbols. Thus, the received signal at receiver \(R_{k}\) can be represented by \[\mathbf{y}_{k}=\sqrt{\frac{P}{M}}\mathbf{H}_{ki}\mathbf{\Phi}_{i}+\mathbf{n} _{k},\] (1) where \(P\) is the transmit power, \(\mathbf{H}_{ki}\in\mathbb{C}^{N\times M}\) denotes the channel matrix between \(T_{i}\) and \(R_{k}\), and \(\mathbf{n}_{k}\) is the Gaussian noise vector. It is assumed that \(\mathbf{H}_{ki}\) represents the uncorrelated Rayleigh small-scale fading channel, i.e., the elements of \(\mathbf{H}_{ki}\) are independently and identically distributed (i.i.d.) according to \(\mathcal{CN}(0,1)\). The simplest training matrix is the identity matrix \(\mathbf{\Phi}_{i}=\mathbf{I}_{M}\). It is assumed that \(R_{k}\) can perfectly estimate \(\mathbf{H}_{ki,1\leq i\leq K}\);
2. Channel quantization: \(R_{k}\) quantizes the estimated channel matrix \(\mathbf{H}_{ki,1\leq i\leq K}\) as \(\mathbf{\hat{H}}_{ki,1\leq i\leq K}\);
3. Quantized channel index feedback: \(R_{k}\) feeds back the quantized information of \(K-1\) interference channels via the reverse channel. All the \(K\) receivers take turns to feed back, and then each transmitter can receive \(K(K-1)\) quantized channel matrices;
4. IA solution computation: It is assumed that each transmitter computes its own IA precoder and decoder. \(T_{k}\) computes precoding matrix \(\mathbf{V}_{k}=[\mathbf{v}_{k}^{1},\mathbf{v}_{k}^{2},...,\mathbf{v}_{k}^{d_{ k}}]\in\mathbb{C}^{M\times d_{k}}\) and decoding matrix \(\mathbf{U}_{k}=[\mathbf{u}_{k}^{1},\mathbf{u}_{k}^{2},...,\mathbf{u}_{k}^{d_{ k}}]\in\mathbb{C}^{N\times d_{k}}\),where \(d_{k}\) is the transmitted data stream number for transceiver pair \(T_{i}\) and \(R_{i}\). For simplicity, the symmetric IC scenario is considered in this paper, and thus \(d_{k}=d\) holds for all transceiver pairs. Except for some special cases, the IA precoding and decoding matrices are determined via iterative methods [30];
5. Quantization and feedback of decoders: To inform \(R_{k}\) of its decoding filter, \(T_{k}\) quantizes \(\mathbf{U}_{k}\) as \(\mathbf{\hat{U}}_{k}\) and broadcasts it;
6. Concurrent data transmission: All transmitters send their desired signals simultaneously. Then, the received signal at \(R_{k}\) can be represented by \[\mathbf{y}_{k}=\sum_{i=1}^{K}\mathbf{H}_{ki}\mathbf{V}_{i}\mathbf{x}_{i}+ \mathbf{n}_{k},\] (2) where \(\mathbf{x}_{i}\in\mathbb{C}^{d}\) is the desired signal from \(T_{i}\) to \(R_{i}\). A typical cellular downlink IA scenario with three user pairs and its transmission process is shown in Figure 1. Via decoding filter \(\mathbf{\hat{U}}_{k}\), the recovered signal for \(R_{k}\) can be written as  
\[\mathbf{\hat{x}}_{k}=\mathbf{\hat{U}}_{k}^{H}\sum_{i=1}^{K}\mathbf{H}_{ki} \mathbf{V}_{i}\mathbf{x}_{i}+\mathbf{\hat{U}}_{k}^{H}\mathbf{n}_{k}. \tag{3}\]  
Therefore, the average achievable rate of IA with LFB can be approximated by [4]  
\[R_{IA}\approx E\left(\sum_{m,k}\log_{2}\left(1+\frac{\frac{P}{d}\big{|} \mathbf{\hat{u}}_{k}^{mH}\mathbf{H}_{kk}\mathbf{v}_{k}^{m}\big{|}^{2}}{\sum \limits_{(k,m)\
eq(i,l)}\frac{P}{d}\big{|}\mathbf{\hat{u}}_{k}^{mH}\mathbf{H}_ {kk}\mathbf{v}_{i}^{m}\big{|}^{2}+\sigma^{2}}\right)\right). \tag{4}\]In (4), \(\frac{p}{d}\Big{|}\mathbf{\hat{u}}_{k}^{mH}\mathbf{H}_{ki}\mathbf{v}_{i}^{l}\Big{|} ^{2}\) is the interference between different users or different streams belonging to the same user.