## Sangmi Moon , Hyunsung Kim and Intae Hwang## |

Parameter | Values |
---|---|

Carrier frequency | 60 GHz |

System bandwidth | 500 MHz |

Active BS | 5, 6, 7, 8 |

Active users | From row R1100 to R2000 |

Number of BS antennas | &[TeX:] $$M_{x}=1, M_{y}=8, M_{z}=4$$ |

Number of user antennas | [TeX:] $$M_{x}=1, M_{y}=1, M_{z}=1$$ |

Antenna spacing (in wavelength) | 0.5 |

Number of paths | 5 |

In this subsection, we analyze the computational complexity of the proposed deep learning-based channel estimation and tracking approach in the testing stage. For the proposed approach, the computational complexity originates from the DNN processing for channel estimation and the LSTM processing for channel tracking. Since the fully connected layer for channel estimation is implemented as a matrix-matrix multiplication and addition, the computational complexity of the DNN for channel estimation, ignoring the biases, is [TeX:] $$C_{\mathrm{DNN}} \sim \mathrm{O}\left(\sum_{l=1}^{\mathcal{L}-1} n_{l-1} n_{l}\right)$$. The total number of parameters N in the of LSTM for channel tracking with one cell, ignoring the biases, can be calculated as follows:

where nc is the number of memory cell, ni is the number of input units, and no is the number of output units. The learning time for a network with a relatively small number of inputs is dominated by the the nc × (nc + no) factor [29]. Therefore, the complexity of the deep learning-based algorithm can be expressed as

In this section, we describe the simulation setup in detail (including the channel models and dataset generation) and present the simulation results.

The simulation setup was based on the publicly-available generic DeepMIMO [30] dataset with the parameters described in Table 1. These parameters are constructed using the 3D raytracing software Wireless Insite [31], which captures the channel dependence on the frequency. The development of the system model and channel model is described in Section II. The channel vector was constructed by using parameters such as AoA, AoD, and path loss. More specifically, we set the frequency of the mmWave at 60 GHz. In addition, the four BSs were distributed on top of a building with a height of 50 m. Each BS was equipped with a UPA antenna with [TeX:] $$M=8 \times 4$$ antennas. The user was equipped with one antenna. To predict the channel vector of vehicular mobile users, we constructed a few random routes with moving rates ranging from 10 ms to 30 ms.

Table 2.

Parameter | Values |
---|---|

Optimizer | Adam |

Learning rate | 0.001 |

Dropout | 0.9 |

Regularization | [TeX:] $$l_{2}$$ |

Max. number of epochs | 100 |

Data size | 50,000 |

Dataset split | 80:20 |

The specific simulation environment is illustrated in Fig. 6. The figure shows that the four BSs were placed on different buildings. They covered all the user’s movements. The location of the vehicular UE is selected randomly from a uniform x–y grid of candidate locations. For the channel tracking, the dots represent the movement of the vehicular UE. Two tracks are apparent in the figure. Each BS received an omni-directional signal, as described in Section III, which was sent to the same cloud as the dataset for the deep learning model. In the cloud, the omni-directional signals of all the BSs were combined, and the final input was [TeX:] $$\mathbf{r}^{\text {omni }}$$. The nth BS was equipped with a UPA antenna array with M = 32 antennas. Therefore, with N = 4 BSs serving the same user simultaneously, the dimension of the integrated omni-directional signal [TeX:] $$\mathbf{r}^{\text {omni }}$$ equaled 128×1. Before training the neural network, [TeX:] $$\mathbf{r}^{\text {omni }}$$ was normalized by the maximum and minimum values of the vector. In the deep learning simulation, we adopt the DNN described in Section III-A, with [TeX:] $$\mathcal{L}=3,4, \cdots, 7$$ and [TeX:] $$n_{l}=2048$$ neurons per layer. This DNN is trained using the datasets for the channel estimation. The other hyper-parameters are summarized in Table 2. In the LSTM, the learning rate is set to 0.001, and the batch size is 30. We construct our DNN and LSTM network in Keras [32] with a tensorFlow [33] backend. The rest of the simulation is implemented on MATLAB.

We adopt the NMSE to test the difference between the estimated channel vector and predicted channel vector and thereby evaluated the performance of the proposed machine learning

system. It is defined as

where [TeX:] $$\hat{\mathbf{h}}$$ is the predicted channel vector and [TeX:] $$\hat{\mathbf{h}}$$ is the actual channel vector

In Fig. 7, we investigate the performance of the DNN-based channel estimation with different number of layers. The performance first improves and then degrades as the number of layers [TeX:] $$\mathcal{L}$$ increases. Fig. 6 shows that the optimal number of layers is [TeX:] $$\mathcal{L}$$ =6, which is the default value of [TeX:] $$\mathcal{L}$$ in our simulations. Theoretically, the learning capability of the DNN improves as the number of layers increases. Owing to the vanishing gradient and pathology degradation, the training of the DNN becomes more challenging as the network deepens [34].

Fig. 8 illustrates our investigation of the performance of the LSTM-based channel tracking with a different type of LSTM (with three hidden layers and three time slots) for the

estimated channel sequence. Based on Fig. 8, we adopt BiLSTM rather than unidirectional LSTM (Uni-LSTM) because Bi-LSTM causes the LSTM to converge faster

Fig. 9 shows the NMSE performance of Bi-LSTM with different numbers of time slots. The time slots of the Bi-LSTM input shorten as the vehicular UE speeds up. Furthermore, the performance degrades as the time slot of Bi-LSTM increases, even for high vehicular UE speed. This is because the estimated channel was outdated and the long-predictions inaccurate. Based on Fig. 9, we adopt the numbers of time slots according to the vehicular environment. For example, Bi-LSTM adopts one time slot in a high-speed environment such as a freeway, and three time slots in a dense urban environment.

To demonstrate that our algorithm can reduce the pilot overhead, we introduce the beam coherence time and effective achievable rate, which is a recent concept in mmWave communications to represent the average beam training time [15]. The effective achievable rate can be characterized as

where [TeX:] $$N_{\mathrm{tr}}, T_{\mathrm{p}}$$ and [TeX:] $$T_{\mathrm{B}}$$ are the number of training pilot, beam training pilot sequence time, and beam coherence time, respectively. We compare our algorithm to a prior work [22]. The algorithm in [22] estimates the channel vectors using the traditional method and then designs the beamformer in the first beam coherence time. Rather than estimating the channel vectors, the BSs design the beamformer using our proposed system in the second beam coherence time. They reduced the overhead of two beam coherence times to half of the original value. Fig. 10 shows the achievable rate. The algorithm in [22], which incurs a higher overhead, has a lower effective achievable rate than that of our algorithm. When the number of training pilots is increased, the performance difference increases. This clearly illustrates the capability of the proposed deep learning-based al-

gorithm in supporting highly-mobile mmWave applications with negligible training overhead.

In this study, we proposed a novel method integrating deep learning and channel estimation/tracking, and develop its deep learning modeling for vehicular mmWave communications. More specifically, a DNN was leveraged to learn the mapping function between an omni-beam pattern and mmWave channel, with negligible overhead. Following the channel estimation, BiLSTM was leveraged to track the channel. Bi-LSTM employes the past channel to promote the prediction of the user’s channel. We use accurate 3D ray-tracing to analyze a performance of the proposed deep learning algorithm of massive MIMO in vehicular communications. The simulation results demonstrated that the proposed algorithm estimated and tracked the mmWave channel efficiently, incurring a negligible training overhead.

Sangmi Moon received the B.S., M.S., and Ph.D. degrees in Electronics & Computer Engineering from Chonnam National University, Gwangju, Korea, in 2012, 2014, and 2017 respectively. She was a Visiting Scholar in the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, from September 2017 to February 2019. She is currently a Postdoctoral Researcher at Chonnam National University, Gwangju, Korea from 2018. Her research interests include 3D-MIMO, 3DBeamforming, V2X, deep learning, and Next generation wireless communication systems.

Hyeonsung Kim received his B.S. degree in Electron- ics & Computer Engineering from Chonnam National University, Gwangju, Korea in 2020. He is currently a Master’s Student in the Department of Electronics & Computer Engineering at Chonnam National Univer- sity, Gwangju, Korea from 2020. His research inter- ests include mobile and next generation wireless com- munication systems; MIMO, OFDM and deep learning.

Intae Hwang received a B.S. degree in Electronics Engineering from Chonnam National University, Gwangju, Korea in 1990 and a M.S. degree in Electronics Engineering from Yonsei University, Seoul, Korea in 1992, and a Ph.D. degree in Electrical & Electronics Engineering from Yonsei University, Seoul, Korea in 2004. He was a Senior Engineer at LG Electronics from 1992 to 2005. He is currently a Professor in the Department of Electronic Engineering at Chonnam National University, Gwangju, Korea from 2006. His current research activities are in digital & wireless communication systems, mobile terminal system for next generation applications; physical layer software for mobile terminals, efficient algorithms for MIMO-OFDM, Relay, ICIM, CoMP, D2D, SCE, MTC, V2X, IoE, and NR MIMO schemes for wireless communication.

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