Novel Calibration of MIESM and Reduction of CQI Feedback for Improved Fast Link Adaptation

: In mobile communications systems, fast link adaptation (FLA) aims to achieve high system throughput of each user by accurately determining a channel quality indicator (CQI) for feedback, which predicts the next channel based on the current channel state information. In this paper, we propose an improved calibration method of mutual information effective signal-to noise-ratio mapping (MIESM) to determine an accurate CQI feedback value in FLA. Our proposed calibration method derives the optimal calibration factors by considering various channel environments and setting the effective interval of effective signal-to-noise ratio, which is a single value compressing the information of channel characteristics at a time. The simulation is performed in various signal-to-noise ratio (SNR) ranges to account for the actual environments, and the calibration factors are derived from the proposed calibration method. The results show that the CQI feedback value from the derived calibration factors are more accurate than the existing calibration factors. In addition, we discuss a study regarding the time-coherence-based CQI feedback bit reduction scheme. Assuming that each channel is correlated to the previous and subsequent channels, we propose a method to reduce the number of CQI feedback bits adapted to the corresponding SNR regime. Through the simulation, we compare the system throughputs of the proposed adaptive CQI feedback and the conventional CQI feedback scheme. As a result, the proposed CQI feedback has almost the same system throughput as the conventional CQI feedback scheme, but the average number of feedback bits is reduced, thereby improving the efﬁciency of the communication.


Introduction
In mobile communications systems, the channel experienced by each user is apt to having frequency selectivity and time variation. In this situation, the user selects a channel quality indicator (CQI) by estimating an appropriate link quality for the fading channel through fast link adaptation (FLA) and sends the feedback. The base station (BS) selects a modulation and coding scheme (MCS) for transmission based on the CQI feedback from the user [1,2]. If the channel condition is determined to be good enough, the BS increases the modulation order and/or coding rate. In the opposite case, the BS decreases them. This FLA process with resource allocation increases the throughput of the system while maintaining the quality of service (QoS) between the user and the BS [3][4][5][6][7].
Although the FLA can use various metrics to predict link quality [8][9][10], in this paper, we use mutual information effective signal-to-noise-ratio mapping (MIESM) [11,12], which is a tool to obtain an accurate link-quality metric (LQM) to determine the CQI value for the instantaneous channel. The MIESM utilizes the instantaneous signal-to-noise ratios (SNRs) of subcarriers to compute the

Preliminaries
This section describes the MIESM-based FLA mechanism, and introduces the existing calibration method.

MIESM-Based Fast Link Adaptation
A user obtains the channel coefficient information from the orthogonal frequency division multiplexing (OFDM) symbols, determines a CQI suitable for the current channel through the MIESM-based FLA, and reports it to the BS. The goal of the FLA is to increase the throughput of the system while maintaining the target BLER for various channel conditions. The MIESM-based FLA process is described below [20].
Firstly, the effective SNR (SNR eff ), which is a constant representing the channel quality, is calculated from the instantaneous SNRs of the subcarriers based on the estimated values of the channel state information. The equation for this is given in Reference [11] as follows: where P indicates the number of subcarriers, SNR p is the instantaneous SNR of the p-th subcarrier, and β is a calibration factor to minimize the difference between the estimated effective BLER (BLER eff ) and the real BLER for the current channel in the calibration procedure. The function f m (·) is the bit-interleaved coded modulation (BICM) capacity curve which depends on the modulation order m. This capacity is equivalent to the mutual information between channel input and output, which is the reason this process is called MIESM [21]. Secondly, the calculated SNR eff is mapped through the pre-calculated AWGN/BLER look-up table (LUT) to the BLER eff value for each CQI. The AWGN/BLER LUT contains all the BLER information of every CQI under the AWGN channel over various SNR values. Then, we select the largest CQI such that the corresponding BLER eff does not exceed the target BLER, which was set to 0.1 in this paper, and feeds the selected CQI back to the BS.

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 β i,l , l = 1, . . . , 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 [σ 2 1 , . . . , σ 2 N s ]. 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, . . . , N c is the k-th channel instance. N w is the number of noise realizations and w n , n = 1, . . . , N w , is the n-th noise instance. Also, BLER LUT (SNR eff (·, ·, ·)) is the effective BLER obtained by mapping the SNR 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 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 (BLER(H k ,σ 2 j )) over noise is then calculated and accumulated. Then, the average BLER (BLER(σ 2 j )) over a given channel and noise realization is calculated and saved. The BLER LUT is estimated using SNR eff , and this is also averaged over the entire channel.

Algorithm 1 Average calibration method
Input: Calculate noise variance: σ 2 j 5: for k = 1 to N c (for all channel realizations) do 6: Generate channel: H k 7: a = 0 8: for n = 1 to N w (for all noise realizations) do 9: Generate additive noise: w n 10: Calculate real BLER from decoding: bler(H k , w n ) 11: Accumulate: a = a + bler(H k , w n ) 12: end for

13:
Calculate average (over noise) BLER: end for 16: Calculate and save the average (over noise and channel) BLER: 17: end for Calculate and save the effective BLER for the current AWGN SNR: 20: The purpose of the calibration is to predict the BLER LUT as close as possible to the real average 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 where ε(x, y) is an error function that calculates the error by assigning equal weights to x and y.
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].

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 eff for correctness and efficiency of the calibration must be defined before deriving the calibration factor. Since the CQI feedback value is determined on the basis of the target BLER 0.1, the effective interval of SNR eff is defined from the SNR value corresponding to AWGN BLER 0.9, which is denoted by γ i 0.9 , to the SNR value corresponding to AWGN BLER 0.001, which is denoted by γ i 0.001 , 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 eff over a number of channels must be obtained for each given AWGN SNR and each CQI. The distribution of SNR eff for each AWGN SNR almost follows the Gaussian distribution as shown in Figure 1. Let SNR s eff 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(γ i 0.9 ≤ SNR s eff ≤ γ i 0.001 ) ≥ 0.05. Then, let SNR min and SNR max denote the minimum and maximum values of s, respectively. In addition, the probability P(γ i 0.9 ≤ SNR s eff ≤ γ i 0.001 ) from the distribution of each SNR is used as a weight to calculate the total error for the optimal calibration factor. • The effective interval of the SNReff for correctness and efficiency of the calibration must be defined before deriving the calibration factor. Since the CQI feedback value is determined on the basis of the target BLER 0.1, the effective interval of SNReff is defined from the SNR value corresponding to AWGN BLER 0.9, which is denoted by 0.9 , to the SNR value corresponding to AWGN BLER 0.001, which is denoted by 0.001 , 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 SNReff over a number of channels must be obtained for each given AWGN SNR and each CQI. The distribution of SNReff for each AWGN SNR almost follows the Gaussian distribution as shown in Figure 1. Let SNR eff denote the random variable corresponding to the effective SNR for a given AWGN SNR when channel coefficients are considered as random. Then, we set the range of AWGN SNR s for calibration such that ( 0.9 ≤ SNR eff ≤ 0.001 ) ≥ 0.05. Then, let SNRmin and SNRmax denote the minimum and maximum values of , respectively. In addition, the probability ( 0.9 ≤ SNR eff ≤ 0.001 ) 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.

Algorithm 2 Improved calibration method
Input: for j = 1 to N s (for all SNRs from SNR min to SNR max ) do 3: k = 1 4: a = 0 5: Calculate noise variance: σ 2 j 6: while k ≤ N c (for all channel realizations) do 7: Generate channel: H k 8: err cnt = 0 Consider only the channels in the effective interval: 9: if for n = 1 to N w (for all noise realizations) do 11: Generate additive noise: w n Algorithm 2 Cont.

12:
Count block error: err cnt = err cnt + 1 13: end for 14: BLER real (H k , w n ) = err cnt /N w 15: Accumulate difference between BLER real and BLER eff : end while 21: end for 22: end for 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 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 cnt ). The variable err cnt accumulates the number of block errors. It is used to calculate the real BLER (BLER real ) of a physical layer for a given channel and noise. The estimated BLER (BLER eff ) is calculated using the pre-calculated SNR eff , and the error between the BLER real and BLER 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 eff corresponding to each SNR as the weight. The β 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).
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.

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.
Send the feedback FB k to BS Firstly, we calculate the difference CQI diff k between CQI k which is the CQI temporarily determined in a normal way for the current channel, and CQI k−1 which is the CQI the BS used for the MCS of the previous channel. The calculated CQI diff k is used to determine the integer value of CQI diff k which is sent to the BS after being converted into a binary form FB k . A detailed description of the above process is shown in Figure 2. Send the feedback FB to BS Firstly, we calculate the difference CQI ̅̅̅̅̅ diff between CQI ̅̅̅̅̅ which is the CQI temporarily determined in a normal way for the current channel, and CQI −1 which is the CQI the BS used for the MCS of the previous channel. The calculated CQI ̅̅̅̅̅ diff is used to determine the integer value of CQI diff which is sent to the BS after being converted into a binary form FB . A detailed description of the above process is shown in Figure 2. 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 −1 . Otherwise, the CQI ̅̅̅̅̅ 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 (CQI −1 − 4) to ( CQI −1 + 3) based on CQI −1 . The above interval was determined by observing the CQI difference of one million subframes of each SNR. If CQI −1 is low or high, it is impossible to use the 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 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 (CQI k−1 − 4) to (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 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 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.

Algorithm 4 CQI recovery at BS from 1-bit reduced feedback
Input: FB k → 1-bit reduced binary vector received from the user for the k-th subframe Output: CQI k → CQI value of the k-th subframe to be used in BS 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.
Determine CQI diff k and formulate FB k for the other cases such that if 3 ≤ CQI k−1 ≤ 4 and CQI diff k Send the feedback FB k to BS The proposed CQI feedback schemes firstly use the conventional CQI calculation. Then, they perform some comparison operations and simple substitution or subtraction based on the calculated CQI value. The computational complexity of the following operations is negligible compared to the first CQI calculation. Therefore, it can be said that the proposed CQI feedback schemes have almost the same computational complexity as the conventional CQI feedback scheme.

Simulation Results
In this section, we introduce the verification algorithm for evaluating the performance of the newly derived calibration factors. Also, we verify the performance of the proposed method in Sections 3 and 4 through system throughput simulations.

Verification Algorithm for FLA
The simulation was performed at the intermediate SNR of the interval where the SNR eff distribution ratio of each CQI was 5% or more. The information bits were encoded according to the modulation order and coding rate corresponding to 15 CQIs, and were passed through the generated channel and noise. We decoded the received data and calculated BLER real s for all CQIs from the link-level simulation for a given channel and noise. Then, we determined a final CQI (CQI real ) by selecting the largest CQI index such that it satisfied the condition of the target BLER among the BLER real corresponding to each CQI. At the same time, SNR eff corresponding to the current channel was calculated, and the effective CQI (CQI eff ) was determined by calculation. If the CQI real and CQI eff were the same, the link quality was considered correct; then, verification proceeded to the next channel. Otherwise, the number of errors was increased by one before verification proceeded to the next channel.

Performance Evaluation
The following simulations were performed in a single-user (SU) single-input single-output (SISO) environment. It can be noted that all the proposed schemes in this paper can also be applied to MIMO systems, but the superiority of the proposed scheme over conventional ones can be sufficiently shown through just SISO simulations.

Improved Calibration Method
We present CQI feedback error rate and system throughput as measures for performance evaluation of the proposed calibration method. The common simulation parameters for evaluating the performance of the proposed calibration factors in this paper are presented in Table 1. In order to guarantee the reliability of the verification, 5000-10,000 channels were generated until the feedback error count exceeded 100 in each SNR. Noise occurred a maximum of 2000 times until the accumulated number of subframe transmission failures reached 100. Figure 3 shows the CQI feedback error rates for the calibration factors of the existing average calibration method and the calibration factors derived from the improved calibration method. Based on the verification algorithm in Section 5.1, the CQI feedback error rate was calculated by counting the number of times that the CQI real determined by the BLER real from the physical layer simulation was not equal to the CQI eff determined by SNR eff . In the case of SNR = −2 dB, the CQI feedback error rate of the proposed method was larger than that of the conventional method by 10.31%, and for SNR = 8 and 22 dB, the CQI feedback error rates of the proposed method were lower than those of the conventional method by 20.38% and 48.78%, respectively. Based on Figure 3, the calibration factors derived from the proposed method show smaller CQI feedback error rates than the conventional method for all SNR values >2 dB, but they show similar to or slightly larger rates than those of the conventional method for SNR ≤2 dB. This result in low-SNR environments is due to the BLER curve slope of the AWGN channel. In the proposed method, we set the SNR corresponding to BLER 0.9 and 0.001 of each CQI as the effective interval of the effective SNR, and derived the calibration factor using the more valid channel for CQI feedback; however, the calibration factor of the existing method was derived without setting it separately. For small CQI values that occur frequently in the low-SNR range, the BLER curve of the AWGN channel is relatively flat, such that the calibration factor can be calculated by sufficiently including the valid channel near the target BLER with the conventional calibration method. On the other hand, since the BLER curve of the AWGN channel is steep for a large CQI, the conventional method calculates the calibration factor without including the valid channel well. However, the proposed calibration method shows better performance than the conventional method because the effective interval works successfully.

• Comparison of System Throughputs
The system throughput was calculated by applying calibration factors derived from the average calibration method and the improved calibration method to the actual mobile communication environment. The simulation was performed over a wide SNR interval, and the system throughput for each method is shown in Table 2. Table 2. System throughput comparison of the improved calibration method and the average calibration methods (Mbps). SNR-signal-to-noise ratio. In the case of SNR = −2 dB, the CQI feedback error rate of the proposed method was larger than that of the conventional method by 10.31%, and for SNR = 8 and 22 dB, the CQI feedback error rates of the proposed method were lower than those of the conventional method by 20.38% and 48.78%, respectively. Based on Figure 3, the calibration factors derived from the proposed method show smaller CQI feedback error rates than the conventional method for all SNR values >2 dB, but they show similar to or slightly larger rates than those of the conventional method for SNR ≤2 dB. This result in low-SNR environments is due to the BLER curve slope of the AWGN channel. In the proposed method, we set the SNR corresponding to BLER 0.9 and 0.001 of each CQI as the effective interval of the effective SNR, and derived the calibration factor using the more valid channel for CQI feedback; however, the calibration factor of the existing method was derived without setting it separately. For small CQI values that occur frequently in the low-SNR range, the BLER curve of the AWGN channel is relatively flat, such that the calibration factor can be calculated by sufficiently including the valid channel near the target BLER with the conventional calibration method. On the other hand, since the BLER curve of the AWGN channel is steep for a large CQI, the conventional method calculates the calibration factor without including the valid channel well. However, the proposed calibration method shows better performance than the conventional method because the effective interval works successfully.

•
Comparison of System Throughputs The system throughput was calculated by applying calibration factors derived from the average calibration method and the improved calibration method to the actual mobile communication environment. The simulation was performed over a wide SNR interval, and the system throughput for each method is shown in Table 2. The calibration factor obtained using the average method at SNR ≤−7 dB had a maximum system throughput of 0.07 kbps higher than the proposed method. As described above, in an environment in which a low CQI is frequently fed back, the proposed method does not show better performance because the effective interval is not used efficiently. However, in the remaining SNR ranges, the proposed calibration method achieved high system throughput performance of at least 0.18 kbps and up to 9.17 kbps.

Reduction of CQI Feedback Bits
Through this experiment, the system throughput of the conventional CQI feedback method and the time-coherence-based CQI feedback method were compared. The simulation set-up is listed in Table 3.  Table 4 shows the system throughput according to the existing 4-bit wideband CQI feedback report in various SNR environments, and Table 5 shows the difference in system throughput between the existing method and the proposed method. In addition, all the system throughputs and the difference for each SNR are shown in Figure 4.   In the legend of Figure 4, "Existing" represents the conventional CQI feedback scheme in LTE, "PROP-3bit" represents the 1-bit reduced CQI feedback scheme proposed in Algorithm 3, and "PROP-2,3bit" represents the 1-or 2-bit reduced CQI feedback scheme proposed in Algorithm 5. In some SNR environments, the system throughput of existing CQI feedback schemes was slightly higher than that of the proposed scheme. However, the system throughput of the proposed technique was higher at some SNR points (5,11, and 20 dB). Because of the limited range of CQI variation, the proposed method often provided more stable CQI feedback for the next channel than the conventional method. Though the proposed scheme uses limited CQI index representation for bit reduction, the above simulation results show that the system throughput difference is negligible. Table 6 shows the average number of bits of PROP_2,3bit used for CQI feedback according to the SNR environment. From the results in Figure 4 and Tables 5 and 6, we can observe that, in low-SNR environments, only 2 bits are sufficient for CQI feedback.

Conclusions
In this paper, we proposed an improved calibration factor derivation method for accurate linkquality determination of mobile communications in various channel environments, and we also suggested a CQI feedback bit reduction scheme for reporting downlink channel state information to BS. The improved calibration method sets the effective interval for the effective SNR to derive the In the legend of Figure 4, "Existing" represents the conventional CQI feedback scheme in LTE, "PROP-3bit" represents the 1-bit reduced CQI feedback scheme proposed in Algorithm 3, and "PROP-2,3bit" represents the 1-or 2-bit reduced CQI feedback scheme proposed in Algorithm 5. In some SNR environments, the system throughput of existing CQI feedback schemes was slightly higher than that of the proposed scheme. However, the system throughput of the proposed technique was higher at some SNR points (5,11, and 20 dB). Because of the limited range of CQI variation, the proposed method often provided more stable CQI feedback for the next channel than the conventional method. Though the proposed scheme uses limited CQI index representation for bit reduction, the above simulation results show that the system throughput difference is negligible. Table 6 shows the average number of bits of PROP_2,3bit used for CQI feedback according to the SNR environment. From the results in Figure 4 and Tables 5 and 6, we can observe that, in low-SNR environments, only 2 bits are sufficient for CQI feedback.

Conclusions
In this paper, we proposed an improved calibration factor derivation method for accurate link-quality determination of mobile communications in various channel environments, and we also suggested a CQI feedback bit reduction scheme for reporting downlink channel state information to BS. The improved calibration method sets the effective interval for the effective SNR to derive the optimal calibration factor used by the MIESM using more valid channels in a wide SNR range. The CQI feedback bit reduction scheme applies a differential CQI technique based on the time correlation between adjacent channels, which change over time, and decreases the number of bits used for CQI feedback.
The two proposed methods were evaluated and analyzed through simulation. Firstly, the calibration factor derived from the improved calibration method reduced the CQI feedback error rate by 48.8% over the existing calibration factor in the range of SNR >2 dB. Also, the system throughput of proposed scheme was a maximum of 9.17 dB higher than that of the conventional scheme at SNR ≥−7 dB. This means that, by setting the effective interval in the wide SNR range, the newly derived calibration factor performs better than the existing one. Next, using a reduction of the CQI feedback scheme can be used to transmit uplink scheduling information by a reduced number of bits, though the system throughput is almost the same or a maximum of 1.3 kbps lower than the conventional single 4-bit wideband CQI feedback.

Conflicts of Interest:
The authors declare no conflict of interest.