ICACT20230070 Slide.29
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Thank you for listening.
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ICACT20230070 Slide.28
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Signal detection and channel estimation using independent component analysis were also studied in large-scale MIMO, where the number of both transmitting and receiving antennas is 10 or more for the deep unfolding uplink.
Signal detection and channel estimation by applying deep unfolding to ICA are effective.
This was demonstrated by utilizing DU's advantage of convergence acceleration in the design of iterative signal processing algorithms.
In addition, channel estimation with regular matrices was found to be an effective means of channel estimation when deep decomposition is used.
There are three possible future prospects.
The first is to improve the accuracy of BER characteristics on downlink lines using DU.
The second is to improve the accuracy of BER characteristics and channel estimation by increasing the number of intermediate layers.
The third is to design circuits with loss functions that take into account the modules in the later stages.
These three points are the main focus of this study from now on.
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ICACT20230070 Slide.27
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First, signal detection and channel estimation using ICA were conducted.
We investigated signal detection and channel estimation using independent component analysis (ICA) in large-scale MIMO, where the number of both transmit and receive antennas is 10 or more for the uplink.
It was shown that signal detection and channel estimation can be performed without problems when the number of transmit antennas is set to 16.
Moreover, when the number of base station antennas is increased, the diversity effect becomes more pronounced, and the accuracy of both signal detection and channel estimation are improved.
Next, MIMO communication was performed on the downlink using the channel obtained on the uplink.
The results showed that the channel was recovered with high accuracy when the number of base station antennas was increased by using precoding during the communication.
There are three future prospects.
First, when the communication channel is known, the BER characteristics using MMSE estimation, for example, should be compared to determine the amount of SNR degradation.
The second point is to conduct simulations in an environment where the communication channel is under correlated fading.
The third point is to use different modulation schemes, such as 16QAM, 64QAM, etc.
With these three points as considerations, I intend to continue my research.
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ICACT20230070 Slide.26
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Finally, conclusions are provided and future prospects are presented.
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ICACT20230070 Slide.25
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In Figure 8, we show the channel estimates for an environment with 16 UEs and 16 BS antennas, using the deep expansion.
The channel estimation accuracy is evaluated using the mean square error of the channel estimates.
The channel MSE shown in Figure 8 represents the average of all the estimated elements of the channel coefficient matrix 𝑯.
Figure 8 shows that DUICA improves the accuracy of channel estimation compared to the system with only ICA.
It is also confirmed that the accuracy of channel estimation improves as the SNR value increases.
Therefore, it is confirmed that DUICA improves the accuracy of channel estimation and that channel estimation is effective.
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ICACT20230070 Slide.24
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The channel matrix estimated for the uplink line was used for the downlink line, and simulation was performed with precoding required for transmission.
Figure 7 shows the BER characteristics for the case of 16 terminals.
Figure 7 shows that the estimation accuracy is high for the downlink except for the case where the number of transmitting and receiving antennas is the same.
Considering these results, intercommunication using ICA is considered to be effective in large-scale MIMO systems.
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ICACT20230070 Slide.23
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Table 2 shows the simulation parameters for the system using Deep Unfolding.
It is important to note the pilot sequence length.
In the ICA simulation described earlier, the pilot sequence length was 6 symbols, whereas only 4 symbols are required for DU.
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ICACT20230070 Slide.22
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Next, I describe simulation results from a system using Deep Unfolding.
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ICACT20230070 Slide.21
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Next, the accuracy of the channel estimation was evaluated by the mean squared error of the channel estimate.
Figure 6 shows the mean squared error when the number of base station antennas is 16, 24, and 32, respectively, with the ideal characteristic being the case where signal detection is performed correctly.
Here, all elements of the channel estimation matrix H were estimated and their average was taken as the channel MSE.
From Figure 6, it can be read that when the number of base station antennas is increased to 24, the SNR is more than 8 dB and the estimation accuracy is equivalent to the ideal characteristic.
Furthermore, when the number of base station antennas is increased up to 32, the estimation accuracy becomes equivalent to that of the ideal characteristic when the SNR is 4 dB or higher.
The above results confirm that channel estimation accuracy improves in a system with many terminal antennas connected simultaneously, indicating that channel estimation using ICA is effective.
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ICACT20230070 Slide.20
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The channel matrix estimated for the uplink line was used for the downlink line, and simulation was performed with precoding required for transmission.
Figure 5 shows the BER characteristics for the case of 16 terminals.
Figure 5 shows that the estimation accuracy is high for the downlink except for the case where the number of transmitting and receiving antennas is the same.
Considering these results, we believe that intercommunication using ICA is effective in large-scale MIMO systems.
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ICACT20230070 Slide.19
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Simulations of signal detection and channel estimation using independent component analysis were performed on the uplink line.
Table 1 shows the simulation parameters for the uplink.
Focusing on the number of terminals (16), a series length of at least 16 symbols is required to perform channel estimation.
However, by using ICA, the number of symbols in the preamplifier was only 5.
In addition, in ICA, the process of equation (7,8) needs to be repeated.
In this study, the weight matrix was sufficiently converged by iterating 30 times.
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ICACT20230070 Slide.18
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From here, I will explain the results of the computer simulations.
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ICACT20230070 Slide.17
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Finally, the channel estimation method for MIMO is presented.
Using the output 𝒀 of the ICA after phase compensation and ordering, the received signal S, and the channel matrix estimated from the pilot sequence, we can express it as in Equation (8).
In this study, the channel coefficients are evaluated based on the Mean Square Error (MSE) of the estimated values of the channel coefficients.
Let ℎ_𝑛𝑚 be one element of the channel coefficient matrix and ℎ ̃_𝑛𝑚 be one element of the estimated channel coefficient matrix, the MSE is given by (9).
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ICACT20230070 Slide.16
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Both the signal flow graph in Figure 5 and the deep network model in Figure 4 are iterative algorithms.
They are considered to be similar, with 〖𝒘_𝑚^H 𝒍[𝑘] corresponding to the linear layer and the symmetric orthogonalization and fast immovable point algorithms corresponding to the activation function layer.
By optimizing the learnable parameters introduced in the fast fixed point algorithm, we improve the accuracy of ICA for short data series lengths.
The evolution structure of the iterative process of ICA with learnable parameters 𝛼 can be regarded as an FFNN.
However, the learnable parameters are adjusted by applying standard deep learning techniques (error back propagation, stochastic gradient method).
This approach of treating an iterative algorithm as an FFNN by expanding it is called deep expansion.
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ICACT20230070 Slide.15
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Next, we will discuss Feed-Forward Neural Networks.
An FFNN is a network in which information is propagated only in one direction from the input to the output.
It has an input layer, an intermediate layer, and an output layer, each of which is composed of multiple nodes connected by edges.
The intermediate layer of 𝑘 can have multiple layers, and the learning of a network with a particularly deep intermediate layer is called deep learning.
In the intermediate layer, the linear layer and the activation function layer are alternately connected. Edges have "weights" and the value of each node is calculated from the value of the node in the previous layer connected to it.
That is, it is computed from the values of the nodes in the previous layer, the weights of the connected edges, and the activation function of the layer.
The 〖𝒘_𝑚〗^H 𝒍[𝑘] in equation (6) of the fast immovable point algorithm can be represented as a linear layer since it performs linear operations.
Equation (7) of the target orthogonalization is a nonlinear operation, and the fast immovable point algorithm is a nonlinear operation by incorporating the learnable parameter 𝛼 in the exponential part for equation (5-3), which can be represented as the activation function layer.
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ICACT20230070 Slide.14
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Here, Figure 3 shows the algorithm diagram for updating the weight matrix.
From Equation (6), the immovable point algorithm can be divided into linear and nonlinear operations.
The red part is the linear operation, and the rest is the nonlinear operation.
Therefore, the iterative algorithm of the weight matrix is derived by repeating the linear and nonlinear operations.
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ICACT20230070 Slide.13
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In Figure 2, the MIMO system model is shown with M transmit antennas and N receive antennas.
Transmit signals are sent from each antenna, and the multiple signals are combined in space.
Therefore, when the signals are received at the base station, they must be correctly separated.
In MIMO communications, the phase of the signals is rotated when they are transmitted.
Therefore, after the signals are received, the order of the signals is rearranged by ICA to correct the phase rotation.
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ICACT20230070 Slide.12
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From here, I will discuss our research objectives.
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ICACT20230070 Slide.11
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First, there are two problems in applying ICA to MIMO.
The first is that the amount of arithmetic operations required to derive a large MIMO channel matrix becomes large.
The second is that a long data series is required to evaluate the non-Gaussianity of signals by ICA.
Therefore, we propose a method.
It is to improve the accuracy of ICA by applying independent component analysis to MIMO for signal detection and applying deep expansion to ICA to evaluate non-Gaussianity even with a short data series.
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ICACT20230070 Slide.10
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Here is a description of the research objectives.
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ICACT20230070 Slide.09
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ICA separates signals by exploiting the non-Gaussianity of each signal.
Negentropy is used as a measure of non-Gaussianity, which measures non-Gaussianity using entropy.
In order to calculate the expected value, if the number of samples is small, it may not converge to the expected value due to the theorem of large numbers.
Therefore, if the data series length is short, non-Gaussianity cannot be evaluated sufficiently, and convergence of 〖𝒘^′〗_𝑚 in equation (5-1) becomes difficult, and the accuracy of ICA may be reduced.
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ICACT20230070 Slide.08
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Next, the algorithm for updating the weight matrix 𝑾 by the immovable point algorithm is described.
In the updating procedure, we first determine the initial values of 𝑤_𝑖 and perform Equation (6) for each component.
Then, symmetric orthogonalization of the matrix is performed using Eq. (7), and Eq. (6) is repeated if the matrix 𝑾 has not converged.
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ICACT20230070 Slide.07
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Therefore, independent component analysis can be considered as a problem of searching for the direction with the maximum non-Gaussianity.
In other words, in independent component analysis with non-Gaussianity, the algorithm to update the weight matrix 𝑾 is important,
A quantitative measure of the non-Gaussianity of the random variable is needed.
Let us denote a random variable as y.
In this study, we apply negentropy as a measure of non-Gaussianity.
However, since the computation of negentropy is complicated by the need to estimate the probability density function, we use a non-quadratic function g, which can be expressed by the approximation equation 4-1
where E represents the expected value calculation, Equation 4-2 is used for the non-quadratic function g, and 𝑣 is a Gaussian variable with y standardized to mean 0 and variance 1.
From the above, when maximizing negentropy, the fastest algorithm, fast independent component analysis (fast ICA), can be obtained by using an immovable point with excellent convergence characteristics.
Therefore, the algorithm for updating the weight matrix using the fixed point algorithm can be expressed as in Equation 5.
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ICACT20230070 Slide.06
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Independent Component Analysis is a computational method for separating a multivariate signal into multiple independent components
When applied to MIMO communications, ICA can be described as a computational method for estimating the mixed variable matrix and the transmitted signal by observing only the observed signal.
For simplicity, we assume that noise is not considered, and the estimation of 𝑿 is based on the directly observable 𝑺 with respect to equation (2-2).
The estimate of the transmitted signal 𝑿 ̂ can be expressed as Equation 4 using the weight matrix 𝑾^𝑯.
The components 𝑥_𝑚 [𝑘] of the transmission matrix 𝑿 follow a discrete distribution, but when H is multiplied and several independent signals are mixed, their probability density distribution approaches a Gaussian distribution by the central limit theorem.
When 𝒘_𝑚 is adjusted so that the non-zero element of the vector composed by 〖𝒘_𝑚〗^𝑯 𝑯 becomes one, the central limit theorem does not hold and the discrete distribution of the transmitted symbols appears as is .
In other words, when 𝒘𝒘_𝑚 is determined so that the non-Gaussianity of 〖𝒘_𝑚〗^𝑯𝑺 is maximized, 𝒙 ̂_𝑚 can be considered one independent component and BSS is realized [4].
Thus, independent component analysis can be considered as a problem of searching for the direction with the maximum non-Gaussianity.
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ICACT20230070 Slide.05
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In MIMO communications, channel estimation is required for signal detection at the receiver.
In the case of large-scale MIMO (with an increased number of antennas), if the channel matrix is derived by inverse matrix operations, the length of the series becomes longer, and the amount of operations increases exponentially with the number of antennas.
When the measured signal is known, LSCE (Least Square Channel Estimation), which is based on the minimization of the mean square error, is used to estimate the channel matrix.
→When LSCE is used, there is a problem that the throughput is reduced due to overhead preambles.
If the probing signal is not known, LSCE cannot be used.
On the other hand, when the transmitted signal is unknown, signal detection using ICA, a type of BSS, is attracting attention
→This method is useful when the signals are independent of each other, the number of signal sources is less than the number of observed data, and the probability distribution of the signals is not Gaussian.
→The ICA algorithm using the fixed-point iterative method converges quickly.
→Short preamble length compared to the preamble length required for conventional channel estimation.
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ICACT20230070 Slide.04
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If each element of Equation 1 is a matrix, the channel matrix can be represented by Equation 3 above.
The black letters are represented as known signals and the red letters as unknown signals.
In this study, since the transmitted signal x and the received signal s are known signals, the channel matrix H is obtained from s and x.
This is used as an application of the MIMO detection problem to detect the transmit signal from the known received signal and the channel matrix, and the research to find the channel matrix and the transmit signal with high accuracy with low computational complexity has been going on for a long time and until now.
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ICACT20230070 Slide.03
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MIMO (Multiple-Input Multiple-Output) transmission, a key technology for 5G, enables large-scale connections by spatially multiplexing signals at the same time and frequency, thereby contributing to higher capacity and speed in communications.
MIMO also enables precoding, eigenmode transmission, and signal detection.
In order to obtain these advantages, the channel must be accurately estimated from the received signal at the base station.
Once an accurate channel is obtained, it is possible to maximize network throughput by precoding the transmitted signal on the downlink or to completely separate the received signal on the uplink.
Generally, spatial multiplexed signals are separated by estimating the channel information from the pilot signal and applying spatial filtering based on the estimated channel information.
In principle, as the number of spatial multiplexes becomes large, the pilot length should be increased for the channel estimation.
However, while the accuracy of channel estimation improves when long pilot sequences are added, the overhead also increases, which is undesirable from the viewpoint of transmission efficiency.
Therefore, in large-scale MIMO, a system that can estimate the channel from relatively short pilot sequences with unknown channel matrices is currently required.
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ICACT20230070 Slide.02
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First, let me give you some background technology and research background.
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ICACT20230070 Slide.01
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I will proceed with this table of contents.
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ICACT20230070 Slide.00
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Hello, everyone. I’m Yuya Takahashi from Meiji University in Japan. Today I'm going to talk about my conference paper：Large MIMO Channel Estimation Study Based on Independent Component Analysis.
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