# Enhanced NOMA System Using Adaptive Coding and Modulation Based on LSTM Neural Network Channel Estimation

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## Abstract

**:**

## 1. Introduction

## 2. NOMA System Model

#### 2.1. Superposition Coding (SC)

Algorithm 1 SNR comparison and Power Re-Allocation for UEs |

Inputs: Channel Matrices (${H}_{1},{H}_{2},\dots {H}_{N}$) for each UE from the stage of channel estimation (CE) |

1: Loop I = 1: N2:$\text{}SN{R}_{i}={\left|{H}_{i}\right|}^{2}$ (3) |

3: End loop |

4: Sort SNR values in ascending order |

5: Assign the power coefficients according to the SNR values subject to ${{\displaystyle \sum}}_{i=1}^{N}{p}_{i}=1$ given by Equation (2). |

6: Sort the power coefficients, $p$, in descending order. |

7: Update and retransmit the super-positioned sequences with the new power coefficients. |

Outputs: Power coefficients $\left({p}_{1},{p}_{2},\dots ,{p}_{N}\right)$ re-assigned for each user’s transmitted message |

#### 2.2. Data Transmission

#### 2.3. Successive Interference Cancellation (SIC)

## 3. Proposed System Model

#### 3.1. Adaptive BCH Codes

#### 3.2. Modulation, Constellation Rotation, and Cyclic-Q Delay

#### 3.3. LSTM Channel Estimation

Algorithm 2 LSTM Channel Estimation scheme |

Inputs: Transmitted pilot data, x_{i}, for users, target channel matrices, H_{i}. |

1: Randomly initialize the weights (W’s) and bias (b’s) values |

2: The forget gate: ${f}_{t}=sigmoid\left({{\displaystyle \sum}}_{t=1}^{2000}{W}_{f}{H}_{t-1}+{W}_{f}{x}_{t}+{b}_{f}\right)$ |

3: The input gate: ${i}_{t}=sigmoid\left({{\displaystyle \sum}}_{t=1}^{2000}{W}_{i}{H}_{t-1}+{W}_{i}{x}_{t}+{b}_{i}\right)$ |

4: The candidate value: $\tilde{{C}_{t}}=tanh\left({{\displaystyle \sum}}_{t=1}^{2000}{W}_{c}{H}_{t-1}+{W}_{c}{x}_{t}+{b}_{c}\right)$ |

5: Update the old cell state, ${C}_{t-1}$, into the new cell state, ${C}_{t}$, by |

${C}_{t}=({C}_{t-1}\times $${f}_{t})+\left({i}_{t}\times \tilde{{C}_{t}}\right)$ |

6: Update the output of the LSTM by: |

The output gate: ${o}_{t}=sigmoid\left({{\displaystyle \sum}}_{t=1}^{2000}{W}_{o}{H}_{t-1}+{W}_{o}{x}_{t}+{b}_{o}\right)$ |

The estimated channel matrix: ${H}_{t}=\text{}{o}_{t}\times \mathrm{tan}\mathrm{h}\left({C}_{t}\right)$ |

Outputs: Estimated channel matrices, H_{t}, and the equivalent SNR values. |

#### 3.4. Assignment of Power Coefficients

Algorithm 3 Power Coefficient Allocation |

Inputs: Required number of users, N. |

1: loop i = 1: N |

2: $\mathrm{p}\left(\mathrm{i}\right)=\frac{\mathrm{N}!}{i!\left(\mathrm{N}-i\right)!}$ |

3: end loop |

4: Sum = ${{\displaystyle \sum}}_{i=1}^{N}p\left(i\right)$ |

5: loop I = 1: N |

6: p$\left(\mathrm{i}\right)=\frac{a\left(i\right)}{Sum}$ 7: end loop |

8: loop I = 1: N/2 |

9: p(i) = p(i) × (4/5) |

10: end loop |

11: loop I = (N/2) + 1: N |

12: p(i) = p(i) × (1/5) |

13: end loop |

Outputs: Power coefficient, p_{i,} for each user. |

## 4. Proposed System Evaluation

#### 4.1. Outage Probability Calculation

#### 4.2. Sum Rate Calculation

## 5. Simulations and Discussion

#### 5.1. Simulation Settings

^{−06}and an average loss of 1.37 × 10

^{−11}.

#### 5.2. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Spectrum sharing and power allocation in (

**a**) orthogonal frequency division multiple access (OFDMA) and (

**b**) non-orthogonal multiple access (NOMA).

**Figure 3.**Successive interference cancellation (SIC) algorithm [6].

**Figure 7.**Root-mean-square error (RMSE) performance of the proposed LSTM network during the training phase.

**Figure 9.**Bit error rate (BER) against the signal-to-noise ratio (SNR) for the proposed system versus the conventional NOMA and LSTM NOMA.

**Figure 11.**User rates for the proposed NOMA system versus the conventional NOMA system for two items of user equipment (UE).

Parameter | Value |
---|---|

Carrier frequency | 2 GHz |

Base station (BS) power | 46 dBm |

System bandwidth (BW) | 5–10 MHz |

Number of users per cell (N) | 10–20 |

Bandwidth per user | 5.4 MHz |

Number of data subcarriers | 1200 |

Number of pilot subcarriers (${x}_{i}$) | 4 |

Number of guard-band subcarriers | 76 |

Channel matrices (${H}_{i}$) | Rayleigh or Rician fading |

Subcarrier spacing | 15 kHz |

Bose–Chaudhuri–Hocquenghem (BCH) code length | [7,4] up to [31,26] |

Symbol length | Data: 66.67 msec + cyclic prefix: 4.69 msec |

Modulation | QPSK and 64QAM |

Constellation rotation angles | 0.506 rad for QPSK 0.150 rad for 64QAM |

AWGN (w) | −10 to 30 dBm |

Power allocation coefficients (p) | 2/3 and 1/3 3/4 and 1/4 4/5 and 1/5 |

Parameter | Value |
---|---|

Number of layers | 4 |

Number of neurons/layer (Input layer) | 1000 |

Number of neurons/layer (LSTM) | 200 |

Number of neurons/layer (fully connected layer) | 6 |

Learning rates | 0.005, 0.0001 |

Length of training data | 1333 × 1 |

Length of testing data | 666 × 1 |

Size of data | 2000 × 1 |

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## Share and Cite

**MDPI and ACS Style**

AbdelMoniem, M.; Gasser, S.M.; El-Mahallawy, M.S.; Fakhr, M.W.; Soliman, A.
Enhanced NOMA System Using Adaptive Coding and Modulation Based on LSTM Neural Network Channel Estimation. *Appl. Sci.* **2019**, *9*, 3022.
https://doi.org/10.3390/app9153022

**AMA Style**

AbdelMoniem M, Gasser SM, El-Mahallawy MS, Fakhr MW, Soliman A.
Enhanced NOMA System Using Adaptive Coding and Modulation Based on LSTM Neural Network Channel Estimation. *Applied Sciences*. 2019; 9(15):3022.
https://doi.org/10.3390/app9153022

**Chicago/Turabian Style**

AbdelMoniem, Mai, Safa M. Gasser, Mohamed S. El-Mahallawy, Mohamed Waleed Fakhr, and Abdelhamid Soliman.
2019. "Enhanced NOMA System Using Adaptive Coding and Modulation Based on LSTM Neural Network Channel Estimation" *Applied Sciences* 9, no. 15: 3022.
https://doi.org/10.3390/app9153022