Application of improved P-BEM in time varying channel prediction in 5G high-speed mobile communication system

2.1 Analysis of TVN of wireless channels in HSMC systems

The TVNs of wireless channels are the main cause of channel variability. Orthogonal frequency technology is a technique that can combat interference and signal fading in communication networks, but its application range is limited due to the low efficiency of spectrum resource utilization [12,13]. OFDMA is a multi-access technology proposed by combining orthogonal frequency technology and frequency division multiplexing technology. This technology divides the signal transmission bandwidth into multiple orthogonal subcarrier sets and allocates resources according to user needs, making it the current mainstream multiple access solution. The structure of the transmitting and receiving ends of this scheme is shown in Figure 1 [5,14].

Figure 1

OFDMA structure.

At the transmitting end, communication participants are assigned to different sub-carriers, and then adaptive modulators are selected based on user needs to select the pairing method with the highest compatibility between sub-carriers and user channel conditions. The matched sub-carriers are first subjected to high-order modulation, and then, consistent with traditional orthogonal frequency techniques, the signal is transmitted. The operation of the receiving end and the transmitting end is opposite. Channel prediction is the process of predicting future states through the historical state of a channel during signal transmission. The core content of channel prediction is the acquisition of historical states, which rely on the CSI estimated by pilot symbols. The pilot symbols of different pilot structures are different, and channel prediction is directly related to the number and position of pilots. Pilot structures can reflect the number and position of pilots. The pilot structure includes comb shaped pilots inserted at intermediate intervals in the frequency domain, block-shaped structures distributed at intermediate intervals in the time domain, and lattice structures inserted at intermediate intervals in the time and frequency domains, as shown in Figure 2 [15,16].

Figure 2

Pilot structure design.

In a comb-shaped pilot structure, the pilot is continuously distributed in the time domain. In a block like structure, pilots are continuously distributed in the frequency domain. The pilot in the lattice structure is discontinuous in both domains. In comb-like structures, signals have strong resistance to time selective fading and have better performance in HSMC scenarios [17,18].

In block like structures, signals have strong resistance to frequency selective fading. When obtaining signal state information in HSMC scenarios, this structure requires more pilots, which can increase computational complexity and reduce system efficiency. The lattice structure has weak resistance to signal fading, but when obtaining historical CSI using this structure, intelligent algorithms can be used to calculate the position of data symbols, improving the performance of communication systems. The TVNs of wireless channels include multi-path effects and Doppler frequency shift (DFS) effects, as shown in Figure 3.

Figure 3

Multi-path effect and the DFS effect. (a) Multipath effect. (b) Frequency shift benefits.

Multi-path effect refers to the change in the transmission path of electromagnetic waves caused by the reflection or refraction of signals in contact with obstacles during transmission, resulting in the signal received by the terminal being a multi-path superimposed signal. After the superposition of signal paths, the amplitude and phase of the signal change, resulting in channel attenuation. The DFS effect is a phenomenon where the phase and frequency alter because of the difference in propagation distance when the wave source moves in a certain direction at a constant rate. The DFS can be calculated using Eq. (1).

where f d represents DFS. v represents the relative movement speed between the transmitting end and the receiving end. c is the light speed. f c denotes the carrier frequency. θ represents the angle between the direction of movement of the transmitting end and the receiving end. In high-speed mobile scenarios, the DFS effect is the main cause of channel changes. The communication scenario during high-speed rail operation is the most common HSMC scenario in daily life. The wireless communication channel (WCC) model in this scenario is the Rice channel of the scenic spot. The signals of this type of channel has two types: sight line and non-line of sight propagation. The latter component is a constant with Doppler frequency offset, which is complex fading under the influence of Doppler. In communication systems, the channel representation for transmitting signals is given in Eq. (2).

where i represents the signal transmission sub-frame index. m represents the symbol index on the sub-frame. n represents the channel sampling point index. c i represents the line-of-sight propagation component of the channel. ε i , m represents normalized Doppler frequency offset. N represents the length of Fourier transform and inverse Fourier transform. L is the number of channel paths. τ l p is the normalized delay of the l p th path. N S represents the sum of the loop length and N . δ represents a constant. a i , l p ( m , n ) represents the scattering path. The normalized Doppler frequency offset can be calculated using Eq. (3).

where f d represents the DFS between the transmitter and receiver in the communication system. Δ f represents the sub-carrier spacing. There are two different expressions for the Rice factor of the Rice channel. The first one represents the entire channel, as shown in Eq. (4).

where k represents the Rice factor. P s represents the sum of the covariance of the scattering components. The second method is the ratio of the line-of-sight propagation component to the non-line-of-sight propagation component on the first path, as shown in Eq. (5).

where var [ ⋅ ] represents the covariance of the scattering component. var [ α i , 0 ] represents the component of non-line-of-sight propagation on the first path.

2.2 TVCP combining P-BEM and BPNN

In HSMC systems, the prediction of TVCs faces the complexity of rapid signal changes and multipath effects. Although the traditional P-BEM method can capture the nonlinear and time-varying characteristics of the channel through polynomial function fitting, its fixed basis function may not accurately reflect the dynamic changes of the channel in high-speed moving environments. The advantage of P-BEM lies in its ability to use polynomial functions to fit and capture the nonlinear and time-varying characteristics of the channel. However, traditional P-BEM has limited predictive ability when facing rapid channel changes in high-speed mobile environments. BPNN can learn and extract the characteristics of channel changes from a large amount of historical data, which can be used as parameters for polynomial fitting in P-BEM, enabling the basic function of P-BEM to dynamically adapt to channel changes. Therefore, the study proposes to combine P-BEM with BPNN to improve the accuracy of TVCP. This model includes receiving antennas N r and transmitting antennas N t , and different antenna pilots need to maintain orthogonality. The pilot structure is a comb like structure. The o th symbol received by the system receiver is given by Eq. (6).

where o represents the symbol index. R represents the symbol received by the receiving end. S represents the symbol of the transmitting end. W represents a Gaussian white noise vector. H represents the frequency domain channel matrix. The expression of H is given by Eq. (7).

The [ H o ( r , t ) ] in Eq. (7) can be calculated using Eq. (8).

where h represents the sampling point channel, and r is the receiving antenna index. t represents the index of the transmitting antenna. l represents the path index. BEM can simulate wireless channels using basis functions. Therefore, when conducting prediction research on WCCs, BEM is used to model the wireless channels. The solution based on the BEM principle is calculated using Eq. (9) [19,20].

where b p , q represents the q th element of the p th basis function. c represents the basis coefficient corresponding to the basis function. ε represents the error in channel modeling by BEM. When modeling wireless channels using BEM, the frequency domain channel matrix H o r , t can be expressed using Eq. (10).

where diag { ⋅ } is the operation of converting a vector into a diagonal matrix. M q represents a matrix of N × N dimensions. F represents the Fourier transform matrix. c is the basis coefficient vector. The method of using P-BEM combined with BPNN for TVCP is to model the channel using P-BEM, and then calculate the estimated base coefficients of the past channel based on the received signal at the pilot using the least squares method. Using the estimated value of the base coefficient to construct the base coefficient sample as the training data of BPNN. Finally, using the estimated values of the past base coefficients of the channel as input for the trained prediction model, the future time-domain channel coefficients are predicted. The specific process can be divided into three steps. First, the historical basis coefficients for wireless channels based on P-BEM are estimated. Second is the training of neural networks. Finally, the wireless channel information are predicted. Traditional P-BEM is fixed in practical applications and cannot reflect the changing wireless channels in high-speed mobility. This study proposes to improve P-BEM and optimize its channel modeling [21,22]. The improvement of P-BEM is mainly reflected in the acquisition of wireless channel matrix. The improved P-BEM constructs a channel correlation matrix based on past channel information, and then extracts basis functions from the channel correlation matrix to model the wireless channel. In the improved P-BEM, assume that the ideal frequency domain channel information at time t is H o and the channel correlation matrix is P o , to perform singular value decomposition P o , as shown in Eq. (11).

where ∧ o represents a diagonal matrix composed of the eigenvalues of P o in descending order. J o represents the eigenvector matrix. At this point, the optimal basis function matrix B o is the first Q column of J o . Using B o , the wireless channel is modeled and the base coefficients are estimated, as shown in Eq. (12).

where R ˜ o represents the pilot signal received on the frequency domain OFDMA symbol. Γ ˜ o represents the sub-matrix of Γ o at the pilot position. After obtaining the basis coefficients based on the optimal basis function matrix B o , the training of BPNN can begin. When training BPNN, it is necessary to obtain the estimated base coefficients of past moments according to Eq. (12) and construct a training sample set, as calculated using Eq. (13).

where U means the quantity of training samples. X ( 1 ) denotes the input sample constructed by past base coefficient estimation. Y ( 1 ) represents the output sample. After constructing the training set, the BPNN can be trained using the conventional training method. After completing the training, the estimated base coefficients of any of the first G moments in the WCC are used as inputs for predicting the future channel. Figure 4 shows the TVCP process of the HSMC system constructed by combining improved P-BEM and BPNN.

Figure 4

Improvement of the TVCP process of P-BEM with BPNN.

The steps to predict the WCC of the HSMC system are as follows: Step 1 is to obtain the channel correlation matrix based on the historical information of WCC. Step 2 is to perform singular value decomposition on the channel correlation matrix to obtain the optimal basis function for P-BEM. Step 3 is to model WCC using P-BEM based on the optimal basis function. Step 4 is to use the pilot signals received in the past and the optimal basis function to calculate the estimated base coefficients at historical times. Step 5 is to calculate the ideal channel basis coefficient at time t . Step 6 is to construct a training dataset for BPNN based on the estimated base coefficients and ideal base coefficients. Step 7 is to set the training parameters for BPNN and train it. Step 8 is to input the estimated base coefficients from any of the first G moments and predict the CSI for future moments.

3.1 Experimental environment and parameter settings

A TVCP method for HSMC systems based on P-BEM and BPNN was studied and improved. To verify the feasibility of the designed channel prediction method (CPM) and its improvements, a simulation experimental environment was established. Simulation tests were conducted on the improved and unimproved CPMs. The experimental operating system is Windows 10 Professional, with Intel Core i9-10900K CPU, NVIDIA GeForce RTX 3080 GPU, and 32.0GB system memory. In the HSMC system, the symbol length, cyclic prefix length, carrier frequency, sub-carrier spacing, train speed, channel model, and number of basic functions of the transmitting antenna, receiving antenna, and OFDMA are important parameters. The number of hidden layer neurons, training error, and maximum number of iterations are important parameters of BPNN. Wang et al. and Ma et al. conducted research and analysis on TVCP schemes in different network environments, and achieved certain results. Therefore, the study referred to the relevant research of these scholars to design simulation test network parameters, as shown in Tables 1 and 2 [23,24].

In the BPNN model, the study selected 5 hidden layer neurons (improved) and 20 hidden layer neurons (pre improved) to balance the model’s learning ability and computational efficiency. Fewer neurons reduce model complexity and training time, while an appropriate number of neurons ensure the ability to capture channel changes. The maximum number of iterations and training error are set based on the model convergence speed and prediction accuracy, respectively, from 3,000 to 1,000 iterations, and from 1,000 to 3,000 iterations to achieve finer training stopping conditions. The sample size has been increased from 100 to 2,000 in order to improve the model’s generalization ability and prediction accuracy, especially in high-speed moving scenarios where the effect is significant. These choices take into account data diversity, training efficiency, and prediction accuracy. This study compared the performance of two improved CPMs from five aspects during simulation testing. The first method is the mean squared error (MSE) of two methods at different training sample sizes. The second type is the training time at different numbers of training samples. The third type is MSE with different training methods. The fourth type is MSE for different prediction methods, and the fifth type is analysis of computational complexity.

3.2 Analysis of channel prediction simulation results

The training samples have a significant impact on the training effectiveness of the model. This study compared the MSE of the two improved CPMs before and after the improvement under different training sample numbers, as shown in Figure 5.

Figure 5

Effect of the training samples on the model training. (a) The impact of sample size on the pre-improved CPM. (b) The impact of sample size on improved CPMs.

Figure 5(a) shows the MSE of the pre-improved prediction scheme under different training samples. When the signal-to-noise ratio (SNR) was the same, the higher the training samples, the lower the MSE of the model. When the training samples were 100 and 2,000, the maximum MSE was close to 1 and 0.01. As the training data increased, the prediction accuracy would also gradually increase. Figure 5(b) shows the MSE of the improved prediction scheme under different training samples. The impact of training samples on the improved CPM was consistent with the original scheme, and the model MSE increased with the increase in training samples. Table 3 shows the training time of the two CPMs before and after improvement under different training sample sizes.

In Table 3, the pre-improved CPM significantly increased training time as the number of training samples increased. When the training sample increased from 100 to 2,000, the training time increased from about 10 s to over 780 s. After improvement, the training time of the CPM would also increase with the rise of the training samples, but the rise speed would significantly decrease. When the training sample increased from 100 to 2,000, the training time increased from about 2 s to about 30 s. Figure 6 shows the impact of different training methods on channel prediction performance.

Figure 6

Effect of different training methods on the channel prediction performance. (a) The impact of sample size on the pre-improved CPM. (b) The impact of sample size on improved CPMs.

Figure 6(a) and (b) shows the impact of different training methods on the pre-improved and improved CPM. In Figure 6(a), when training with fixed SNR and training-based SNR, the MSE of the CPM was highest at around 0.01 and 0.009. The training-based SNR was slightly lower than the fixed SNR training method, and as the SNR increased, the difference between the two would also become larger. In Figure 6(b), as the SNR increased, the MSE of the two training methods gradually tended to be consistent. When the SNR was low, the MSE value of the training-based SNR method was smaller. To further analyze the feasibility of the proposed CPM, the improving path channel estimation (IPCE) in the research by Li and Mitra [21] and the membership filtering (MF) in the research by Zhao et al. [22] were compared with the research method. Meanwhile, this article also compared it with the dual channel transferable RUL model proposed by Guo et al. [25]. Figure 7 shows the comparison results of MES performance under normalized DFS using different prediction methods.

Figure 7

Change in the channel prediction performance with the normalized DFS.

In Figure 7, as the normalized DFS increased, the MSE of all methods increased. When the normalized DFS was 0.1, the MSE of all methods was below 0.001. After increasing the normalized DFS to 0.5, the MSE of the improved method was around 0.0001, while the MSE of other methods was above 0.001. As the Doppler shift continues to increase, the MSE values of different methods also increase slightly, but it can still be observed that the MSE value of the improved P-BEM model designed in the study remains at a low level. This indicates that the model designed for research is recognized to maintain good basic performance under the continuous increase of DFS. The normalized DFS had the least interference on the designed CPM, and the improved CPM performed the best in HSMS. The analysis of complexity was calculated. The complexity of historical information obtained, model training complexity, and prediction complexity were expanded into three dimensions.

Figure 8 shows the complexity comparison of obtaining historical information. In Figure 8(a), the complexity of the historical information obtained by the research method was much higher than that of the methods in the research by Li and Mitra [21] and Zhao et al. [22]. As the number of sub-carriers increased, the complexity of obtaining historical information would gradually increase. The changes in Figure 8(b) are consistent with Figure 8(a). Figure 9 shows a comparison of model training complexity.

Figure 8

Comparison of the complexity of obtaining historical information. (a) After improvement. (b) Before improvement.

Figure 9

Training complexity comparison. (a) After improvement. (b) Before improvement.

Figure 9 showed the comparison of training complexity between MF and the improved and pre-improved P-BEM-BPNN methods. In Figure 9(a), the training complexity of the P-BEM-BPNN method did not increase with the increase in the quantity of sub-carriers, which is always below 1 × 10⁻⁷, while the training complexity of MF would continue to increase with the increase in the number of sub-carriers. In Figure 9(b), the training complexity of both methods increased with the increase in the number of sub-carriers. When the number of sub-carriers was higher than 20, the training complexity of the P-BEM-BPNN method was lower. Figure 10 shows a comparison of model prediction complexity.

Figure 10

Predictive complexity comparison results. (a) After improvement. (b) Before improvement.

Figure 10 showed the comparison of prediction complexity between IPCE, MF, and P-BEM-BPNN methods before and after improvement. In Figure 10(a), the IPCE method had the lowest prediction complexity, followed by the improved P-BEM-BPNN method. The prediction complexity of these two methods did not increase with the number of sub-carriers. In Figure 10(b), the prediction complexity of the IPCE method was basically 0, while the prediction complexity of the other two methods increased with the number of sub-carriers.

The study further compared the prediction complexity of three models, IPCE, MF, and IP-BEM-BPNN, with the variation in device computing resources. The results are shown in Figure 11. Figure 11(a) shows the change in model prediction complexity with the increase in device computing resources before model optimization. As can be seen, with the continuous increase in device computing resources, the complexity of model prediction will gradually decrease. Figure 11(a) shows that after model optimization, with the continuous increase in device computing resources, the prediction complexity of the IP-BEM-BPNN model remains basically unchanged and at a lower level.

Figure 11

Prediction complexity changes with device computing resources. (a) After improvement. (b) Before improvement.