# Novel Calibration of MIESM and Reduction of CQI Feedback for Improved Fast Link Adaptation
## 2 Preliminaries
### Average Method for Calibration of MIESM  
Accurate CQI determination is possible using appropriate calibration factors for effective SNR calculation. The standard calibration procedure was proposed in Reference [12], which requires a vast number of link-level simulations to include a significant number of channel instances. For this reason, in many cases, the optimal calibration factors are practically obtained from the average calibration procedure outlined in Reference [13]. Before describing the calibration procedure, we explain some notations. These notations are also used for the improved calibration method described in Section 3. \(N_{b}\) is the number of candidate calibration factors for every CQI, and \(\beta_{i,l}\), \(l=1,\dots,N_{b}\), is the \(l\)-th calibration factor for CQI \(i\). \(N_{s}\) is the length of AWGN SNR vectors to simulate in search of the optimal calibration factor, where the noise variance corresponding to each SNR is \([\sigma_{1}^{2},\ \dots,\ \sigma_{N_{b}}^{2}]\). The symbol \(N_{c}\) is the number of channel realizations which should be big enough to show the characteristics of the entire channel, and \(H_{k}\), \(k=1,\dots,N_{c}\) is the \(k\)-th channel instance. \(N_{w}\) is the number of noise realizations and \(w_{n}\), \(n=1,\dots,N_{w}\), is the \(n\)-th noise instance. Also, \(\text{BLER}_{\text{LUT}}(\text{SNR}_{\text{eff}}(\cdot,\cdot,\cdot))\) is the effective BLER obtained by mapping the \(\text{SNR}_{\text{eff}}\) using the AWGN/BLER LUT. The calibration steps in Algorithm 1 are further described below. \(N_{c}\) channels and \(N_{w}\) noises are generated for one calibration factor candidate and one AWGN SNR point. The instantaneous \(\text{BLER}(H_{k},\ w_{n})\) is calculated for the generated channel and noise by decoding. This value is 0 if the block is correct, or 1 otherwise. The average BLER (\(\text{BLER}(H_{k}\sigma_{j}^{2})\)) over noise is then calculated and accumulated. Then, the average \(\text{BLER}\) (\(\overline{\text{BLER}}(\sigma_{j}^{2})\)) over a given channel and noise realizationis calculated and saved. The BLER\({}_{\text{LUT}}\) is estimated using SNR\({}_{\text{eff}}\), and this is also averaged over the entire channel. ```
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**Algorithm 1** Average calibration method

The purpose of the calibration is to predict the \(\overline{\text{BLER}}_{\text{LUT}}\) as close as possible to the real average \(\overline{\text{BLER}}\) for all AWGN SNR values and channel conditions. For this, the above calibration procedure is necessary, and the optimal calibration factor is calculated as

\[\beta_{opt}^{av}=\hat{\beta}_{i}\ =\arg\min\limits_{\hat{\beta}_{i,j}\in B_{i}} \sum\limits_{j=1}^{N_{i}}\epsilon(\overline{\text{BLER}}(\sigma_{j}^{2}), \overline{\text{BLER}}_{\text{LUT}}(\sigma_{j}^{2},\beta_{i,j})), \tag{2}\]

where \(\epsilon(x,y)\) is an error function that calculates the error by assigning equal weights to \(x\) and \(y\). \[\epsilon(x,y)=\big{|}\log_{10}\left(x\right)-\log_{10}\left(y\right)\big{|}^{2}. \tag{3}\]

In general, the AWGN SNR range of the average calibration procedure is limited to SNR points of AWGN/BLER 0.95 to BLER 0.01 for each CQI, since all data collected in the link-level simulation are not sufficiently reliable [13]. ## 3 Improved Calibration Method

The existing calibration method has a limitation, whereby only the limited channel quality is considered because the calibration factor is derived by generating noise for the limited range of AWGN SNR corresponding to the BLER 0.95 to BLER 0.01 in order to find the optimum calibration factors. The purpose of the improved calibration method is to derive an optimal calibration factor for accurate CQI determination using various channels from a wide SNR range. The following two steps are required before applying the improved calibration method:

* The effective interval of the SNR\({}_{\text{eff}}\) for correctness and efficiency of the calibration must be defined before deriving the calibration factor.