This paper extends the work presented in [14] by proposing a dynamic optimization framework for link adaptation that can maximize channel efficiency and throughput for LTE/LTE-A; it is also used to design the reward function and transition probability. It is different from [14] through that the previous work does not include the adoption of the modified alpha-Shannon capacity formula in MDP in addition to use the WiMAX rather than LTE/LTE-A environment used in this research. Moreover, parameters such as bandwidth efficiency factor \(\alpha\), target-required SNR factor \(\omega\), and modulation value, that are discussed in the next subsections, are not parts of the previous work. Nonetheless, they played an important role when they are added to this research.
The proposed work enhances the optimal decision of link adaptation for LTE/LTE-A and fits the quality requirements for the LTE/LTE-A. In fact, two link adaptation models are proposed. The first model is called cross-layer link adaptation (CLLA) and is based on the downward cross-layer design approach. The purpose is to consider the disparate of the system at MAC/physical layers. Consequently, at the physical layer, the received frame is measured on the basis of channel condition adaptation and path loss. It is measured by utilizing the mobility distance while adapting the PER at the MAC layer. However, the second model adopts the MDP over the cross-layer design approach (MDP-CLLA). In fact, the MDP-CLLA model uses the measured process of the CLLA model, where the selection of appropriate modulation is optimally chosen for the next frame and is sent as feedback to the sender. Additionally, the evaluation and comparison between the performance of proposed models and the existing LTE system are performed in terms of throughput, packet loss, overhead packet size (optimal packet size), and phase productivity for different modulation schemes with different packet sizes.
CLLA model
The framework of the CLLA model is illustrated in Fig. 1. It is considered a MAC/physical downward cross-layer design. At the receiver side, the SNR is measured at the physical layer by adapting a channel condition and path loss via a mobility distance parameter. Its purpose is to match transmission rates to a time-varying channel at the physical layer. In addition, the PER is measured and used as performance indicator at the MAC layer to improve reliability of the system. At the end, the suitable modulation type is selected, and a feedback is sent to the sender to be used as a trigger for adapting the modulation of the next transmission frame.
The algorithm of the CLLA model constitutes four parts: the main algorithm of the CLLA model; the packetization of data as indicator of MAC layer located at the transmitter side; the de-packetization of data at the receiver side; and the computing part of PER, number of error packets, and throughput. Algorithm 1 represents the algorithm of the CLLA model.
Adopting the MDP over the CLLA model (MDP-CLLA)
As shown in Fig. 2, the MDP-CLLA model uses MDP to the sequence procedure discussed in the CLLA model; hence, the utility/reward function of data transmission based on MAC/physical downward cross-layer technique is formulated systematically.
The MDP-CLLA model consists of modified alpha-Shannon capacity formula and link adaptation and reception scheme.
The modified alpha-Shannon capacity formula addressed in [3] is adopted as part of the reward function to enhance the link adaptation of LTE/LTE-A. The modified alpha-Shannon capacity formula was proposed to predict the LTE/LTE-A throughput accurately because of the implementation issues that face Shannon capacity bound and render it inapplicable to LTE/LTE-A. Such issues are system overhead (system level bandwidth efficiency factor) and implementation margins (SNR efficiency factor) such as channel estimation and CQI. In [26], a simulating model function of LTE/LTE-A evolved RAN is built for handling certain types of traffic in a vehicular network. It modifies the Shannon formula purely on the basis of the LTE/LTE-A bandwidth efficiency factor to fit the Shannon capacity to LTE/LTE-A, which is inaccurate because it overlooks the handling of the SNR efficiency factor. In [27], the alpha-Shannon capacity formula was proposed by modifying the Shannon formula through the addition of the LTE/LTE-A bandwidth efficiency factor and SNR efficiency factor. However, this formula is inaccurate in terms of the maximum capacity/throughput of standard LTE/LTE-A due to the test-bed that was done in [3]. Therefore, the modified alpha-Shannon capacity formula was proposed and discussed in [3] and is considered a part of this research.
Figure 3 thoroughly illustrates the proposed MDP-CLLA optimization model. In this proposed model, the average channel efficiency (throughput) maximization per FER minimization is studied considering the parameters of modulation, received power, mobility distance, channel condition, and path loss. The link adaptation and reception scheme in the MDP-CLLA model consists of AMC selector at the receiver side and AMC controller at the sender side as shown in Figs. 2 and 3. The AMC selector contains the MDP adopted over CLLA to overcome the optimal selection of modulation type. The AMC controller receives the feedback from the receiver and adapts the modulation type on the basis of this feedback. Then, this information is used to send the next frame. In addition, the proposed model is applied for different packet sizes to determine the appropriate packet size for each modulation.
On the basis of MDP algorithm, Fig. 4 presents the process flow of MDP-CLLA link adaptation and reception scheme including the following components of MDP algorithm: states, actions, transmission probability, and reward function.
In addition, the MDP algorithm is solved by the agent component (see Fig. 4) through the use of policy iteration for average cost as a dynamic programming method as shown in Fig. 5.
The algorithm of the MDP-CLLA model consists of the main algorithm of MDP-CLLA model; the packetization of data at the transmitter side; the de-packetization of data at the receiver side; and the computing part of PER, number of error packets, and throughput as shown in Algorithm 2.
The reward function and the dynamic programming method used to obtain the optimal policy through the transition probability are presented below:
Reward function
Several studies on link adaptation have been discussed by using the reward function for throughput maximization. In [28], varying the rate of power transmission for each frame leads to maximize throughput. However, this work is based on changing the distance of user mobility, thereby affecting the calculation of SNR that enhances the throughput. Studying the enhancing throughput leads our concern on the transmission errors’ effects, which are not covered in the literature [29].
To increase the throughput, the range of FER must be adequate. Hence, increasing throughput per decreasing FER is considered the objective function. The proposed objective function is organized as follows:
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1
The received frame comprises NL bits at the receiver side. Here, N is the number of packets in a frame, and L is the number of bits per packet. The current throughput becomes dependent of SNR as long as throughput adaptation is implemented in the downlink channel. Throughput can be calculated using the formula below [3]:
$$\begin{aligned} \alpha *B*\log _{2}\left( 1+\omega *10^{\frac{\mathrm{SINR}_{\mathrm{d}B}}{10}}\right) \end{aligned}$$
(21)
where \(\alpha\) is a bandwidth efficiency factor, B is a bandwidth, and \(\omega\) is a value related to target-required SNR, which is proven mathematically in [3].
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2
The frame is considered the data unit transmitted in point-to-point communication system. Therefore, the frame period time for each transmission is \(\frac{NL}{R}\) sec, where R is the transmission rate. The frame throughput (Th) is given as follows:
$$\begin{aligned} \alpha *B*\log _{2}\left( 1+\omega *10^{\frac{\mathrm{SINR}_{\mathrm{d}B}}{10}}\right) *\frac{NL}{R} \end{aligned}$$
(22)
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3
In addition, the number of bits for each modulation type must be added to the objective function, and it is done by \(\log _{2}(M)\).
$$\begin{aligned} \alpha *B*\log _{2}\left(1+\omega *10^{\frac{\mathrm{SINR}_{\mathrm{d}B}}{10}}\right)*\frac{NL}{R}*\log _{2}(M) \end{aligned}$$
(23)
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4
Now, to calculate the average frame error rate \({\overline{\mathrm{FER}}}\) as in the proposed objective function:
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Let PER imply packet error rate \(1-(1-P_{e})^{L}\). Thus, the FER is given as follows:
$$\begin{aligned} \mathrm{FER}=1-(1-P_{e})^{NL} \end{aligned}$$
(24)
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Since FER should be within an acceptable range, SNR \(\gamma\) is partitioned into K intervals with boundary points denoted as \(0=\Gamma _{0}< \Gamma _{1}<\cdots <\Gamma _{k}\). Hence, mode k is selected when \(\Gamma _{k}< \gamma <\Gamma _{k+1}\).
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FER, when using the \(k_{th}\) mode, is denoted by \(\mathrm{FER}_{k}(\gamma ),\) and it can be estimated as follows:
$$\begin{aligned} \mathrm{FER}_{k}(\gamma )=\begin{Bmatrix} 1&,if 0<\gamma <\gamma _{n}, \\ 1-(1-P_{e})^{NL}&,if \gamma \geqslant \gamma _{n}, \end{Bmatrix} \end{aligned}$$
(25)
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The probability density function (PDF)\(p(\gamma )=\frac{1}{\gamma _{0} }exp(-\frac{\gamma }{\gamma _{0} })\) [30] for the \(\gamma\) frame can be used to determine the equation, which selects the mode k, as follows:
$$\begin{aligned} \zeta _{k}=\int _{\Gamma _{k} }^{\Gamma _{k+1}}p(\gamma ) \mathrm{d}\gamma , k=1,\ldots ,K. \end{aligned}$$
As a result, PDF becomes as follows:
$$\begin{aligned} \zeta _{k}=\left( exp\left( -\frac{\Gamma _{k}}{\gamma _{0} } \right) \right) -\left( exp\left( -\frac{\Gamma _{k+1}}{\gamma _{0} } \right) \right) \end{aligned}$$
(26)
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In Eq. (25), no transmission exists if the channel quality below \(\gamma _{n} ; \gamma _{n}\) could be specified by solving the following:
$$\begin{aligned} \int _{\gamma _{n} }^{\infty }1-(1-P_{e}(\gamma _{n}) )^{NL} p(\gamma )\mathrm{d}\gamma =1 \end{aligned}$$
(27)
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Let \(\overline{\mathrm{FER}_{k}}\), for mode k, present the average FER (i.e., the ratio of the number of incorrectly received packets over transmitted packets) and be mathematically represented as follows:
$$\begin{aligned} \overline{\mathrm{FER}_{k}}=\frac{1}{\zeta _{k}}\int _{\Gamma _{k} }^{\Gamma _{k+1}}1-(1-P_{e}(\gamma ) )^{NL} p(\gamma ) \mathrm{d}\gamma \end{aligned}$$
(28)
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FER is considered a performance indicator of the link layer in the reward function. The utility function per frame is presented as follows:
$$\begin{aligned} \frac{\alpha *B*\log _{2}(1+\omega *10^{\frac{\gamma _{0} }{10}})*\frac{NL}{R}*S(\gamma ,M)*\log _{2}(M)}{{\overline{\mathrm{FER}}}} \end{aligned}$$
(29)
Thus, the reward function is expressed as:
$$\begin{aligned} R(\gamma , M)=\begin{Bmatrix} \frac{\alpha *B*\log _{2}(1+\omega *10^{\frac{\gamma _{0} }{10}})* \frac{NL}{R}*S(\gamma ,M)*\log _{2}(M)}{{\overline{\mathrm{FER}}}}\\ ,if \gamma \geqslant \gamma _{n}, \\ \\ 0 \\ ,otherwise \quad or \quad \gamma < \gamma _{n}, \end{Bmatrix} \end{aligned}$$
(30)
where (\(\gamma\)) is a state, and (M) is the action that can be taken by the control agent.
Optimal dynamic programming solution
Maximizing the objective function through determining the decision policy \(\pi : S\rightarrow A\) is involved in the MDP’s solution. Hence, various typical objective functions are introduced such as discounted and average rewards. As the proposed solution in this paper is based on maximizing throughput per minimizing FER, the MDP policy iteration for average cost method is implemented. This method fits the optimal equation Bellman that requires knowledge of the state transition probability [31] for all \(s \epsilon S\).
$$\begin{aligned} \eta ^{*}+h^{*}(s)=\underset{a\rightarrow A(s)}{max}\left[ R(s,a)+\sum _{{s}'\epsilon 1}^{|S|}P_{s,{s}'}(a)h^{*}({s}') \right] , \end{aligned}$$
(31)
where \(\eta ^{*}\) is the optimal average reward per stage and \(h^{*}(s)\) is called optimal relative state-value function for each state s.
