# Novel Calibration of MIESM and Reduction of CQI Feedback for Improved Fast Link Adaptation
## 2 Preliminaries
### Average Method for Calibration of MIESM
## 4 Reduction of CQI Feedback Bits

This section discusses schemes for reducing wideband CQI feedback bits. To date, the conventional differential CQI scheme was applied only to wideband CQI feedback. The proposed scheme also uses the difference of CQIs as the conventional method; however, the difference is not between the average CQI and each CQI, but between adjacent time channels under the assumption of the existence of time correlation in channels. The proposed scheme can be applied no matter which one is considered, i.e., wideband CQI or subband CQI. From this, the number of bits used for CQI feedback is reduced. As in LTE, we assume that CQI takes a value from 0 to 15, and each user sends the 4-bit feedback to BS in the conventional scheme. The detailed description of the proposed scheme is shown below in Algorithm 3. Firstly, we calculate the difference \(\overline{\text{CQI}}_{k}^{\text{diff}}\) between \(\overline{\text{CQI}}_{k}\) which is the CQI temporarily determined in a normal way for the current channel, and \(\text{CQI}_{k-1}\) which is the CQI the BS used for the MCS of the previous channel. The calculated \(\overline{\text{CQI}}_{k}^{\text{diff}}\) is used to determine the integer value of \(\text{CQI}_{k}^{\text{diff}}\) which is sent to the BS after being converted into a binary form \(\text{FB}_{k}\). A detailed description of the above process is shown in Figure 2.

Figure 2: Examples for the process of the 1-bit reduction scheme of channel quality indicator (CQI) feedback. The proposed scheme reduces the number of bits used for CQI feedback by 1 bit and expresses eight CQI indexes with 3 bits in total. Figure 2 shows an example of the CQI feedback range that can be represented by 3 bits according to CQI\({}_{k-1}\). Otherwise, the \(\overline{\text{CQI}}_{k}\) is changed to the CQI closest to the range; then, the bit value of the CQI is fed back. In most cases, the range is specified as \((\text{CQI}_{k-1}-4)\) to \((\text{CQI}_{k-1}+3)\) based on CQI\({}_{k-1}\). The above interval was determined by observing the CQI difference of one million subframes of each SNR. If \(\text{CQI}_{k-1}\) is low or high, it is impossible to use the above definition of interval. Therefore, an adaptive interval setting is necessary, and the relevant examples correspond to Figure 2b,c. The BS uses the \(\text{FB}_{k}\) fed back from the user and performs the recovery algorithm for the actual CQI, as shown in Algorithm 4. Then, it determines resource assignment, MCS, and transport block size (TBS) suitable for the current channel according to the CQI\({}_{k}\) and transmits the data. ```
Input: \(\text{FB}_{k}\to 1\)-bit reduced binary vector received from the user for the \(k\)-th subframe Output: \(\text{CQI}_{k}\to\text{CQI}\) value of the \(k\)-th subframe to be used in BS
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**Algorithm 4** CQI recovery at BS from 1-bit reduced feedback

In a low-SNR environment of fading channels, we observe that the change in CQI values of adjacent channels is not large compared to high-SNR cases. In this situation, CQIs of a small level (i.e., CQI 0, CQI 1, and CQI 2) are frequently generated. We can use this observation to further reduce the bits used for CQI feedback. When the feedback CQI value for the previous channel is CQI\({}_{k-1}=0\), 1, 2, we bound the CQI difference between consecutive channels as \(-2\) to 1, which results in 2-bit feedback for the current channel. The 2-bit CQI feedback representation method for CQIs 0, 1, and 2 is shown in Algorithm 5, and it is noted that the recovery at BS is easily described in the same way with Algorithm 4. ```
Input: \(\text{CQI}_{k-1}\to\text{Integer value of CQI feedback value for the }(k-1)\)-th subframe Output: \(\text{FB}_{k}\to 1\) or 2-bit reduced binary vector to feedback for the \(k\)-th subframe
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**Algorithm 5** The 1- or 2-bit reduction scheme of CQI feedback at each user
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The proposed CQI feedback schemes firstly use the conventional CQI calculation.