# Novel Calibration of MIESM and Reduction of CQI Feedback for Improved Fast Link Adaptation
## 2 Preliminaries
### Average Method for Calibration of MIESM
Since the CQI feedback value is determined on the basis of the target BLER 0.1, the effective interval of SNR\({}_{\text{eff}}\) is defined from the SNR value corresponding to AWGN BLER 0.9, which is denoted by \(\gamma_{0.9}^{i}\), to the SNR value corresponding to AWGN BLER 0.001, which is denoted by \(\gamma_{0.001}^{i}\), for each CQI. The effective interval efficiently includes valid channels for the calibration around the SNR corresponding to AWGN BLER 0.1. * The probability distribution of SNR\({}_{\text{eff}}\) over a number of channels must be obtained for each given AWGN SNR and each CQI. The distribution of SNR\({}_{\text{eff}}\) for each AWGN SNR almost follows the Gaussian distribution as shown in Figure 1. Let SNR\({}_{\text{eff}}^{s}\) denote the random variable corresponding to the effective SNR for a given AWGN SNR \(s\) when channel coefficients are considered as random. Then, we set the range of AWGN SNR \(s\) for calibration such that \(P(\gamma_{0.9}^{i}\leq\text{SNR}_{\text{eff}}^{s}\leq\gamma_{0.001}^{i})\geq 0.05\). Then, let SNR\({}_{\text{min}}\) and SNR\({}_{\text{max}}\) denote the minimum and maximum values of \(s\), respectively. In addition, the probability \(P(\gamma_{0.9}^{i}\leq\text{SNR}_{\text{eff}}^{s}\leq\gamma_{0.001}^{i})\) from the distribution of each SNR is used as a weight to calculate the total error for the optimal calibration factor. The process for deriving the optimal calibration factor is shown below in Algorithm 2. ```
Input: CQI index \(i\) (\(i=1,2,\ldots,15\)) \(B_{i}=\{\beta_{i,1},\,\beta_{i,2},\,\ldots,\,\beta_{i,N_{i}}\}\) Output: \(\hat{\beta}_{i}\)
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**Algorithm 2** Improved calibration method

Figure 1: Selecting the additive white Gaussian noise (AWGN) signal-to-noise ratio (SNR) range from the probability density function (p.d.f) for the improved calibration procedure. To derive the calibration factor corresponding to each CQI, \(N_{b}\) candidates are specified for the calibration factor. In order to derive a calibration factor suitable for a wide range of AWGN SNR, the SNR vector of the proposed method takes the range corresponding to effective SNR (SNR\({}_{\text{eff}}\)) of 5% or more obtained from the preliminary simulation, where \(N_{s}\) is the total number of SNR values to simulate. The \(N_{c}\) channels are generated according to the channel model. Then, noise is generated if the effective SNR is included in the effective interval for the generated channel, and the errors are counted (err\({}_{\text{cnt}}\)). The variable err\({}_{\text{cnt}}\) accumulates the number of block errors. It is used to calculate the real BLER (BLER\({}_{\text{real}}\)) of a physical layer for a given channel and noise. The estimated BLER (BLER\({}_{\text{eff}}\)) is calculated using the pre-calculated SNR\({}_{\text{eff}}\), and the error between the BLER\({}_{\text{real}}\) and BLER\({}_{\text{eff}}\) is accumulated for all the channels. The error function of Equation (3) is again used for the error calculation. The accumulated errors are multiplied by the distribution of SNR\({}_{\text{eff}}\) corresponding to each SNR as the weight. The \(\beta_{l}\) with the smallest sum of these is determined as the optimum value of the calibration factor. The related expression is shown in Equation (4). \[\hat{\rho}_{opt}^{improv}=\hat{\beta}_{i}=\arg\min_{\beta_{ij}\in\mathbb{B}_{ i}}\sum_{j=1}^{N_{s}}\{P(\gamma_{0.9}^{i}\leq\text{SNR}_{\text{eff}}^{s_{j}} \leq\gamma_{0.001}^{i})\times\sum_{k=1}^{N_{c}}\varepsilon(\text{BLER}_{\text{ real}},\text{BLER}_{\text{eff}})\}. \tag{4}\]

The complexity of a calibration method mostly depends on the number of decoding trials at the physical layer. The proposed calibration method has the exact same number of decoding trials as the average method when parameters are identically set. Specifically, the number of decoding trials for both calibration methods is \(N_{b}N_{s}N_{c}N_{w}\). Therefore, it can be said that the improved calibration method does not require more computational complexity than the average method.