Non-orthogonal multiple access (NOMA) has been a key enabling technology for the fifth generation (5G) cellular networks. Based on the NOMA principle, a traditional neural network has been implemented for user clustering (UC) to maximize the NOMA system’s throughput performance by considering that each sample is independent of the prior and the subsequent ones. Consequently, the prediction of UC for the future ones is based on the current clustering information, which is never used again due to the lack of memory of the network. Therefore, to relate the input features of NOMA users and capture the dependency in the clustering information, time-series methods can assist us in gaining a helpful insight into the future. Despite its mathematical complexity, the essence of time series comes down to examining past behavior and extending that information into the future. Hence, in this paper, we propose a novel and effective stacked long short term memory (S-LSTM) to predict the UC formation of NOMA users to enhance the throughput performance of the 5G-based NOMA systems. In the proposed strategy, the S-LSTM is modelled to handle the time-series input data to improve the predicting accuracy of UC of the NOMA users by implementing multiple LSTM layers with hidden cells. The implemented LSTM layers have feedback connections that help to capture the dependency in the clustering information as it propagates between the layers. Specifically, we develop, train, validate and test the proposed model to predict the UC formation for the futures ones by capturing the dependency in the clustering information based on the time-series data. Simulation results demonstrate that the proposed scheme effectively predicts UC and thereby attaining near-optimal throughput performance of 98.94% compared to the exhaustive search method.

Imminent 5G and beyond 5G networks are anticipated to provide high spectral-energy efficiency, deliver super-fast data transmission, ensure ultra-reliability, support massive connectivity and guarantee the lowest possible latency compared to its predecessors [

Generally, NOMA is classified into two types, i.e., power-domain NOMA (PD-NOMA) and code-domain NOMA (CD-NOMA). PD-NOMA is the most widely studied NOMA scheme for 5G networks and beyond. The working principle of the PD-NOMA is to allow the non-orthogonal transmission of multiple users’ signals using superposition coding (SC) at the transmitting end, and the superposed signal is then passed through the successive interference cancellation (SIC) receiver at the receiving end to eliminate interference and implement quadrature demodulation. For a multi-carrier PD-NOMA, the subchannel transmission still adopts the orthogonal frequency division multiplexing (OFDM), where the subchannels are partitioned so that they are orthogonal to each other and do not interfere. Unlike orthogonal frequency division multiple access (OFDMA), the subchannel is no longer exclusively assigned to one user only, but it is shared by various users to increase the spectrum utilization. The users who share the same set of subchannels can transmit their signal using power multiplexing technology such as the SC technique. Hence, the signal power of each user arriving at the receiver is unique and distinguishable. Non-orthogonal transmission between different users on the same subchannel will generate co-channel interference between users, which can be solved using SIC technology at the receiver. The SIC implementation enforces a strict power allocation requirement that associates users of good channel conditions with low-power assignment policy while users of poor channel conditions with high-power allocation policy. These policies allow the SIC to effectively eliminate interference and decode the signals for each user [

Over the last few years, user pairing and user clustering (UC) for NOMA networks have been vigorously studied from different perspectives due to the emergence of SIC technology. In [

In general, the UC for a NOMA network is always intertwined with power allocation. The impact of user pairing on the performance of fixed power allocation for a NOMA system and a cognitive radio assisted NOMA was examined in [

From the state-of-the-art, it is observed that the user pairing and clustering for NOMA systems are pretty inflexible. Recently, a dynamic user clustering (DUC) scheme was proposed in [

Machine learning and artificial intelligence (AI) have recently started to make inroads into 5G and beyond 5G networks. In [

Not surprisingly, machine learning has been widely applied to solve various resource allocation problems in NOMA networks. In terms of UC for the NOMA system, the availability of clustering datasets obtained from the B-FS method in [

Taking into account the discussions mentioned above, it is apparent that all the state-of-the-art UC methods only solve the clustering problem for an instantaneous time without considering the historical clustering results and the variation of channel gains and power levels. Theoretically, the channel variations of wireless 5G networks can be modelled statistically and estimated accurately [

Recently, LSTM has been widely applied for natural language processing (NLP) in [

In this paper, the promising deep learning (DL) approach can be integrated into the traditional neural network and the implementation of proposed stacked LSTM (S-LSTM) to perform the learning mechanism that results in the automatic prediction of UC to enhance the throughput performance of the NOMA system. The proposed S-LSTM is also known as deep LSTM. Hence, the two terms will be used interchangeably throughout the paper. Compared to the conventional S-LSTM applied to solve different problems in other domains, we have adapted the S-LSTM to NOMA environments to tackle UC issue. In summary, the main contributions of this paper are summarized as follows:

The UC problem in the NOMA system is investigated with the help of DL by implementing the deep neural network (DNN) with multiple layers to enhance the flexibility of the model.

The S-LSTM architecture is then constructed and integrated into the DNN model to process the time-series data to capture the dependency in the clustering information. This model aims to avoid shrinking gradient values that usually vanish as the information propagates between multiple hidden layers during backward propagation (BP). The power allocation strategy for each user is then derived that can provide optimal throughput performance.

The performance analysis of the proposed S-LSTM-UC NOMA system under various network parameters is provided. Specifically, the average throughput and mean squared error (MSE) has been examined. In addition, significant simulation findings and comparisons are shown to prove the effectiveness and strength of the proposed schemes.

The remaining sections of this paper are laid out as follows. In Section 2, a NOMA-based 5G system model is developed with the temporal channel model. Besides, the SIC constraints are outlined in this section, while the UC and power allocation problems are also formulated. Subsequently, the working principle of S-LSTM-based UC is described in Section 3. The proposed new UC algorithms for training and testing phases are also outlined in this section. Simulation results with in-depth analytical discussions are shown in Section 4. Last but not least, the paper ends with some insightful concluding remarks and navigates the readers to some possible future research directions related to this work in Section 5.

Consider a downlink NOMA-based single-cell 5G system with a single BS located at the center of the cell, within which

In the NOMA system, the 5G spectrum is partitioned into

In the conventional OMA system (also known as Orthogonal Frequency Division Multiple Access (OFDMA)), the users perceive different channel gains on different subcarriers and let the channel gain experienced by user

Precisely,

In a power-domain NOMA-based 5G system, users can share a set of exclusive subcarriers in which superposition coding (SC) is used to multiplex users on the same subcarriers. Let

Let’s assume that the cardinality of

At a specific time slot

The SIC condition in

To better model the SIC implementation mathematically, the order of decoding for each user

Based on the Shannon capacity formula, the achievable throughput

Based on

Let the UC indicator vector of a user

To fulfil the SIC conditions, power allocation of the users on the shared subcarriers must be prudently implemented. Let

In this context, the sum throughput of the NOMA system is defined as the objective function, and the joint clustering and power allocation problem for throughput maximization in a downlink NOMA system can be formulated as

This paper presents a novel machine learning approach to solve the UC problem formulated in

Similarly, even though power allocation is one of the maximizing variables in [

This section presents the proposed stacked LSTM based UC (S-LSTM-UC) technique for the NOMA downlink. We first describe the generation and the attributes of the dataset and then explain the holistic working principle of S-LSTM-UC in detail.

To train the proposed S-LSTM-UC, the B-FS based UC (B-FS-UC) [

In S-LSTM-UC, each LTSM layer consists of multiple LSTM cells, and the internal structure of the LSTM cell is shown in

As illustrated in

The forget gate governs what information to be retained and what information to be removed from the previous cell state

The input gate

The output gate

Finally, to predict the best UC formation, a dense layer connects all the neurons in the

The working principle of S-LSTM-UC during the training and testing phases are summarized in Algorithm 1 and Algorithm 2, respectively.

This section verifies the effectiveness of the proposed S-LSTM-UC via extensive MATLAB simulation. More specifically, we have done an extensive hyper-parameter tuning on the proposed S-LSTM-UC model to investigate the influence of hyper-parameters. The learning rate, activation functions, length of training data samples, network depth, number of hidden layer nodes, and number of epochs on the MSE and the average throughput performance of S-LSTM-UC in NOMA downlink systems for different numbers of users will be thoroughly analyzed. The performance of the proposed S-LSTM-UC will also be compared against the existing OMA, DUC, ANN-UC, and B-FS-UC schemes.

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

Number of data samples | 48000 |

Length of training data | 24000, 28800, 33600, 38400 |

Length of validation data | 7200 |

Length of testing data | 7200 |

Number of LSTM layers | 4 |

Learning rate | 0.1, 0.02, 0.01, 0.002, 0.001 |

Number of input layer nodes | 48 |

Number of LSTM layer nodes | 40 |

Number of output layer nodes | 24 |

Batch sizes | 10, 20, 50, 100 |

Activation functions | ReLu, Sigmoid, Sine, Tanh |

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

Cell radius | 100 m |

The bandwidth of the resource, |
180 kHz |

Downlink transmission power for a cluster, |
46 dBm |

Detection threshold at SIC receiver, |
10 dBm |

Noise power | −118 dBm |

Number of NOMA users | 2–24 |

Number of subcarriers | 256 |

Deployment of NOMA users | random and uniform |

Path loss | |

Shadowing effect |

Having studied the influence of the length of the training samples and number of users,

In

Since activation function is one of the essential hyper-parameters in S-LSTM-UC, the effects of 4 well-known activation functions, i.e., ReLu, Sigmoid, Sine and Tanh, on the average throughput performance during the testing phase are investigated in

In

To assess the effectiveness of the proposed S-LSTM-UC scheme, four benchmarked techniques have been identified, i.e., BF-S-UC, ANN-UC, DUC, and OMA.

This work proposes a novel S-LSTM-UC to tackle the UC problem in NOMA 5G systems by capitalizing on the underlying deep temporal dynamics of the time-series inputs captured via long-term memory cells and its deep architecture. The S-LSTM-UC can better characterize the non-linear transformation of diversity in channel gains and powers into cluster formation by including more LSTM layers in the model. Following the cluster formation, a power allocation method is implemented to ensure all users in each cluster achieve the minimum throughput requirement while adhering to the SIC constraint. To optimize the hyper-parameters of the S-LSTM-UC, extensive simulations have been conducted. It is found that the proposed S-LSTM-UC achieves the best performance for all the scenarios considered when it is equipped with four hidden layers and 40 nodes. With these optimal settings, the proposed S-LSTM-UC scheme could significantly outperform the existing schemes and achieve a near-optimal throughput performance, around 98.94% of the throughput attained by the B-FS-UC method. In addition, the robustness of the S-LSTM-UC has also been tested in diverse NOMA deployment scenarios. The results reveal that the proposed method could effectively adapt to different NOMA environments without the need for re-training. In general, S-LSTM-UC is efficient to forecast UC formation based on the time-series data collected over a period of time. To make it more efficient and robust, more stacking LSTM layers can be incorporated, but this will increase the complexity of the model, which will require a longer time to train and test. Furthermore, S-LSTM-UC is sensitive to different random weight initializations. As future work, the proposed S-LSTM can be developed deeper to accurately learn more complex time-series data to make a more precise prediction. To cope with the complexity due to deeper S-LSTM model, some model compression techniques such as pruning can be implemented. Besides, more analysis can be done to maximize the throughput performance and minimize bit error rate and computational complexity.