## 4 The Proposed Adaptive Channel Coding Technique  
The objective of the EEACC approach is to design an appropriate link adaptation scheme integrated with a proper selection mechanism of repetition number and MCS for the NB-IoT systemssolely based on the aim of achieving greater energy efficiency, transmission distance, and high throughput while maintaining high transmission reliability.  
The channel coding approach proposed by the present study is a 2-dimensional (2D) link adaptation approach which translates to a dual-objective optimization problem that aims at enhancing the NB-IoT network coverage without compromising on its energy efficiency performance. The proposed adaptive channel coding technique is twofold. It is composed of an inner loop and an outer loop adaptation scheme both aimed at enhancing the energy efficiency as well as the throughput of the network. In particular, the inner loop adaptation scheme is designed based on the channel conditions to guarantee transmission reliability and consequently, enhance the data rate of the network. On the other hand, the outer loop scheme is designed based on the Modulation Coding Scheme (MCS) number and the transmission repetition number.  
Because the channel conditions of NB-IoT systems are known to be quite unstable [51] as their transmission block error ratio (BLER) rapidly changes, the present approach introduces an inner loop link adaptation procedure which focuses on dynamically varying the transmission repetition number based on a periodically sampled and estimated channel condition that is quantified based on the BLER performance. The current BLER performance is used to predict the channel conditions each time on the next transmission based on the Sequential Channel Estimation in the Presence of Random Phase Noise in NB-IoT Systems as proposed by [52]. In this channel estimation model, the main consideration is that although the coherent-time of the fading channel is assumed fairly long due to the assumed low mobility of NB-IoT user-equipments (UEs). Therefore, phase noises are considered before combining the channel estimates over repetition as a mechanism to improve the accuracy of the approach.  
With phase noise \(\phi_{l}[n]\) caused by oscillator fluctuations and a residual FO \(f_{e}\) normalized by the sub-carrier frequency, the time-domain baseband received signal at the \(n\)th sampling time of the \(l\)th orthogonal-frequency-division-multiplexing (OFDM) symbol can be expressed as  
\[s_{l(Estimated)}[n]=e^{i\phi_{l}[n]}(\frac{1}{sqrtN}\sum_{k=-N/2}^{(N/2)-1}S_{ l}[k]e^{i2\pi n(f_{e}+kN)}*h_{l}[n]+w(n) \tag{25}\]  
where \"\(*\)\" denotes the linear convolution, \(S_{l}[k]\) is the transmit symbol on the \(l\)th OFDM symbol and the \(k\)th sub-carrier, \(h[n]\) is discrete fading channel taps, \(w(n)\) is additive-white Gaussian-noise (AWGN), and N is the Fast-Fourier-Transform (FFT) size.  
The purpose of the inner loop link adaptation is to guarantee the transmission BLER to the target. Accordingly, the former is referred to as outer loop link adaptation that is inclusive of MCS level selection and repetition number determination. The proposed link-adaptation method is presented as follows.