## 1 Introduction
Existing performance analysis works of LFB-based IA can be mainly classified into two types: the DoF analysis and the sum-rate analysis. DoF is defined as the ratio of the achievable sum-rate to the logarithm of normalized transmit power \(\rho\), and can act as an effective measure of the sum-rate growth in high signal-to-noise ratio (SNR) regimes. Many DoF analysis works established the relationship between the rate loss lower/upper bounds and the quantization bit number, and have concluded that to guarantee the DoF performance in IA, the number of feedback bits should scale with \(\rho\)[12; 13; 14; 15]. In DoF-based performance analysis, the RVQ and Grassmannian codebooks obtains identical results. [PERSON] and [PERSON] were the first to analyze IA performance with LFB, and they found that in \(K\)-user frequency-selective single-input single-output (SISO) ICs, the feedback bit number from each receiver should be proportional to \(K\log_{2}\rho\)[12]. Their analysis method and conclusions were then extended to multi-antenna IA cases, whereby in frequency-selective MIMO ICs, the feedback bit number should scale with the product of transmit and receiver antenna numbers to maintain the DoF slope [13]. When only multi-antenna-domain IA is considered instead of the time or the frequency domain, [PERSON] et al. analyzed the effective DoF in \(K\)-user \(M\times M\) ICs, where the fed channel quantization bits from each receiver should be \((M^{2}-1)\log_{2}\rho\) to maintain the effective DoF [14]. Most works on the DoF performance analyses of LFB-based IA have only focused on the quantization and feedback of CSI and ignored the influence of precoders' and decoders' feedback. [PERSON] et al. considered a general centralized feedback model in which the feedback procedures for CSI, precoders and decoders are all involved [16]. In this model, a central unit (CU) is deployed to collect the quantized CSI, design the precoders and decoders, and then separately send the quantized precoders and decoders to transmitters and receivers. By analyzing the influence of quantization bits on rate loss, they also derived the scaling laws of three kinds of feedback bits, i.e., to achieve the same DoF as perfect IA, the feedback bits for each precoder, decoder and channel matrix should be at least \((M-1)\log_{2}\rho\), \((N-1)\log_{2}\rho\), and \((MN-1)\log_{2}\rho\), respectively. The results in [16] are backward compatible with the DoF analyses in [14; 15]. Except for the IC case, the IMACs and IBCs are also common IA deployment scenarios in cellular networks, their DoF performance with LFB was investigated in [17; 18; 19; 20], and similar results were also obtained. In addition to the quantitative analysis of DoF performance with quantization bit numbers, some researchers dealt with the imperfect CSI by the Gaussian channel error model to analyze the corresponding rate loss and DoF performance [21; 22; 23]. However, they did not further connect CSI mismatch to quantization bit numbers. Since DoF is less effective in measuring the performance at low-moderate SNR regimes, closed-form sum-rate analyses can provide a more direct and accurate rate expression with a given quantization bit number, which is more convenient for performance evaluation during the whole SNR regime. However, different from the diversity of DoF analysis works, sum-rate analysis is rarely involved in IA performance analysis. [PERSON] and [PERSON] discussed the relationship between the average achievable rate and feedback bit number, derived the closed-form rate formulas, and then also obtained the DoF scaling law, i.e., the DoF performance of LFB-based IA will be identical to perfect CSI cases, as each receiver's quantization bits increase with \((MN-1)\log_{2}\rho\)[15]. Similarly, [PERSON] et al. comprehensively analyzed the average sum-rate, outage probability, and symbol error rate performances of IA with CSI quantization error, and derived the corresponding closed-form expressions [24].