CN114006794B - Complex value neural network-based channel estimation method and system - Google Patents
Complex value neural network-based channel estimation method and system Download PDFInfo
- Publication number
- CN114006794B CN114006794B CN202111178108.6A CN202111178108A CN114006794B CN 114006794 B CN114006794 B CN 114006794B CN 202111178108 A CN202111178108 A CN 202111178108A CN 114006794 B CN114006794 B CN 114006794B
- Authority
- CN
- China
- Prior art keywords
- complex
- neural network
- valued
- value
- pilot
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/0254—Channel estimation channel estimation algorithms using neural network algorithms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/08—Learning methods
Abstract
The invention discloses a channel estimation method and a system based on a complex value neural network, wherein the method comprises the following steps: s1, constructing a complex-valued neural network; s2, extracting pilot frequency at a receiving end, and estimating a CFR value of a pilot signal to obtain a training set and a test set; s3, taking the CFR value of the pilot signal in the training set as an input to perform offline training on the complex-valued neural network to obtain a trained complex-valued neural network; s4, testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal; and S5, recovering the original transmission signal according to the CFR value of the data signal. The Complex Value Neural Network (CVNN) -based channel estimation method and the system have high sensitivity and can effectively resist the influence of optical fiber dispersion.
Description
Technical Field
The invention relates to the technical field of optical fiber communication, in particular to a channel estimation method based on a complex value neural network.
Background
With the explosive growth of the internet of things and virtual/real applications, the demand for large-capacity, low-latency mobile communication services is increasing nowadays. To meet the demand of high-speed wireless networks, a flexible optical transmission network with high spectral efficiency, multi-user diversity, and simple equalization is essential for a mobile fronthaul platform. Among them, the multi-carrier technology is extremely competitive in meeting the above requirements. Optical Orthogonal Frequency Division Multiplexing (OFDM) has been widely studied by researchers because of its advantages such as its ability to resist the effects of fiber dispersion, high spectral efficiency, and the use of simple equalizers. However, some inherent disadvantages hinder its development in fifth generation mobile communications. First, in OFDM, a Cyclic Prefix (CP) is used as a guard interval to reduce inter-symbol interference (ISI), which introduces an unavoidable overhead. Meanwhile, OFDM signals are particularly susceptible to synchronization errors, which can destroy the orthogonality between subcarriers, thereby introducing severe inter-carrier interference (ICI). In addition, the rectangular filters used in OFDM produce out-of-band leakage.
FBMC/OQAM has been considered as an alternative to OFDM because it has advantages such as robustness against synchronization errors, no need for additional CP overhead, and suppression of out-of-band leakage due to the introduction of a good prototype filter. These advantages make FBMC widely used in optical and wireless communication systems. In addition, the asynchronous characteristic makes the FBMC particularly suitable for being applied to an uplink communication system for transmitting a plurality of users in an IM/DD Passive Optical Network (PON). Like the OFDM signal, the FBMC signal has advantages and disadvantages. The sub-carriers of the FBMC signal are no longer orthogonal in the complex domain but only in the real domain, which results in inherent imaginary interference between the sub-carriers and the symbols. When FBMC signals are transmitted in channels with complex-valued responses, it becomes very challenging to eliminate the inherent imaginary interference and accurately estimate their channel response values. Therefore, it is of great significance to provide a channel estimation method with low computational complexity and high performance in an optical FBMC system.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a complex-valued neural network-based channel estimation method which is high in sensitivity and can effectively resist the influence of optical fiber dispersion.
In order to solve the above problems, the present invention provides a Complex Value Neural Network (CVNN) based channel estimation method, which comprises the following steps:
s1, constructing a complex-valued neural network;
s2, extracting pilot frequency at a receiving end, and estimating a CFR value of a pilot frequency signal to obtain a training set and a test set;
s3, taking the CFR value of the pilot signal in the training set as an input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
s4, testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal;
and S5, restoring the original transmission signal according to the CFR value of the data signal.
As a further improvement of the invention, the complex-valued neural network comprises an input layer, a hidden layer and an output layer, wherein an input signal is transmitted forward among the input layer, the hidden layer and the output layer through nonlinear transformation; and updating parameters in the complex-valued neural network by using a learning algorithm to complete back propagation according to an error value between the output value of the output layer and the label value of the forward propagation.
As a further development of the invention, the nonlinear transformation is realized by an activation function.
As a further development of the invention, the activation function is a complex tanh function.
As a further improvement of the present invention, the data input by the input layer is a CFR value of a pilot signal, which is as follows:
X＝[X 1 ，X 2 ，…，X m ] T
output H of the hidden layer j (j =1,2, \8230;, p) is as follows:
wherein, W ij And b j 1 Respectively, the complex-valued weights and offsets from the input layer to the hidden layer, f (-) being a complex tanh function;
final output Y of the output layer k (k =1,2, \8230;, n) is as follows:
wherein, W jk And b k 2 Respectively complex-valued weights and offsets from the hidden layer to the output layer.
As a further improvement of the present invention, the back propagation is a training process of the complex-valued neural network, the training is performed by a learning algorithm and a cost function, and the cost function is minimized by continuously updating the complex weights and the bias.
As a further improvement of the present invention, the cost function is as follows:
wherein the content of the first and second substances,
for the tag, i.e., the CFR value of the data signal, (·) denotes the conjugate of the complex-valued vector.
As a further improvement of the invention, the learning algorithm is an L-BFGS algorithm.
As a further improvement of the present invention, the CFR value of the pilot signal is calculated by the following formula:
wherein X p (k) And Y p (k) Pilot signals of a sending end and a receiving end are respectively; h LS (k) Is the channel response at the pilot in the frequency domain, i.e., the CFR value of the pilot signal.
The invention also provides a channel estimation system based on the complex value neural network, which comprises the following steps:
the network construction module is used for constructing a complex-valued neural network;
the pilot signal calculation module is used for extracting pilot frequency at a receiving end and estimating a CFR value of the pilot signal to obtain a training set and a test set;
the off-line training module is used for taking the CFR value of the pilot signal in the training set as input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
the test module is used for testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal; and restores the original transmission signal according to the CFR value of the data signal.
The invention has the beneficial effects that:
the Complex Value Neural Network (CVNN) -based channel estimation method and the system have high sensitivity and can effectively resist the influence of optical fiber dispersion.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are specifically described below with reference to the accompanying drawings.
Drawings
FIG. 1 is an architecture diagram of an FBMC transmission system;
FIG. 2 is a block pilot structure diagram;
FIG. 3 is an architecture diagram of a channel estimation method for a complex-valued neural network (CVNN);
FIG. 4 is a diagram of a three-layer complex-valued neural network (CVNN) architecture;
FIG. 5 is a graph of the change in MSE for three layers CVNN and RVNN;
FIG. 6 is a diagram of an experimental setup of a 12.5Gd/s IM/DD FBMC 64QAM transmission system under SSMF with different lengths;
FIG. 7 is a graph of measured BER versus received optical power for the CVNN and RVNN methods;
FIG. 8 is a graph and constellation of measured BER versus received optical power for three different channel estimation methods;
FIG. 9 is a graph of measured BER versus received optical power for different channel estimation methods for different pilot redundancy;
fig. 10 is a graph of measured BER versus received optical power for different channel estimation methods over different transmission distances.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Fig. 1 shows an architecture diagram of an FBMC transmission system. At the transmitting end, the binary bit stream is first mapped into QAM signals, and then formed into OQAM signals with inserted pilots. Unlike QAM signals, OQAM signals convert the real and imaginary parts of a complex QAM signal into real in-phase and imaginary quadrature components by multiplying by different phase factors, and then transmit them in sequence every half symbol period (T/2). When the real part of a symbol is transmitted, adjacent symbols are the imaginary parts of the symbol, which can remove ISI. Next, after the OQAM signal is allocated to each data subcarrier and subjected to the IFFT operation, the time domain signal on each subcarrier is filtered by a filter bank. Here, the filter bank is implemented by performing a series of frequency offsets on the basis of a prototype low-pass filter bank.
In the present invention, a Square Root Raised Cosine (SRRC) function is used as a prototype low-pass filter, and the time domain impulse response f (t) thereof can be expressed as:
wherein the roll-off factor alpha is 0.5. Finally, the data on each data subcarrier is superposed and converted into serial data for transmission, and the obtained transmission signal x (t) can be expressed as,
wherein N and N s Respectively represent the number of data subcarriers and the number of FBMC symbols, a m,n Indicating the nth data symbol on the mth subcarrier. At the receiving end, the corresponding inverse operation is performed. First, the received serial signal is converted into Nc-line parallel signals. And then, carrying out matched filtering and FFT operation on the N paths of data to obtain a frequency domain OQAM signal. And then, converting the OQAM signal into a QAM signal by removing the influence of a phase factor corresponding to the transmitting end. And finally, extracting the pilot signal inserted at the transmitting end for channel estimation and carrying out QAM demapping to recover the originally transmitted bit stream.
In the FBMC transmission system, the FBMC signals are only orthogonal in the real domain since the introduction of the filter bank destroys the orthogonality between the subcarriers. However, the response of the fibre channel is complex-valued, and the transmitted signal is subject to imaginary interference from adjacent data symbols. Therefore, in order to recover the transmitted signal at the receiving end, an accurate channel estimation technique is particularly important. Channel estimation is an algorithm for estimating a channel response from a received signal, and the estimated value can be further used in channel equalization to eliminate the influence of a channel on a transmission signal, so as to more accurately recover an original transmission signal. At the receiving end, the received signal y (t) in the time domain can be expressed as:
wherein h (t) represents the impulse response of the channel, and w (t) is white gaussian noise. Then, the frequency domain signal Y (k) can be expressed as:
Y(k)＝X(k)H(k)+W(k)
wherein, Y (k), X (k), H (k) and W (k) are the result of FFT transformation of Y (t), X (t), H (t) and W (t), respectively. Channel estimation is a method for estimating H (k) in the frequency domain.
The invention adopts a block pilot-based channel estimation algorithm, which is suitable for a slowly-changing optical fiber channel. The block pilot structure is shown in fig. 2, where black and white circles represent block pilots and data, respectively. In block pilots, pilots are loaded on all data subcarriers and inserted periodically into the data. Since the sequence and location of the inserted pilots are known at the transmitting and receiving ends, it is feasible to extract the pilots at the receiving end for computing the channel response and to perform interpolation to obtain the channel response for all data. There are many algorithms for calculating the channel response values at the pilots, of which LS and LMMSE are two classical methods. To describe the channel estimation algorithm, we first define some relevant parameters, where the total number of inserted pilots is P, and the redundancy (OH) of the pilots is the percentage of the total data. X p (k) And Y p (k) Which are pilot signals of the transmitting end and the receiving end, respectively. In the LS algorithm, the channel response at the pilot in the frequency domainShould H LS (k) Can be defined as:
as can be seen from the above equation, the LS calculation method is simple, but the influence of the noise W is not considered. Thus calculated H LS Including noise information. When the noise power increases, the estimation performance of LS deteriorates.
The LMMSE algorithm is based on the LS algorithm, and the influence of noise W, the channel response value H of which at the pilot frequency is in consideration of the calculation process LMMSE (k) It can be defined as the number of,
wherein R is HH Beta is the autocorrelation matrix of the channel and is related to the selected modulation scheme, and I is the identity matrix. Its performance is superior to the LS algorithm. Unfortunately, LMMSE requires a priori information of the fibre channel to calculate the inverse of the matrix, and the calculation complexity is high. In order to obtain higher estimation precision with lower computation complexity, the invention provides a new method for channel estimation based on a complex-valued neural network.
Referring to fig. 3, the channel estimation method based on the complex-valued neural network in the preferred embodiment of the present invention includes the following steps:
s1, constructing a complex-valued neural network;
s2, extracting pilot frequency at a receiving end, and estimating a CFR value of a pilot signal to obtain a training set and a test set; optionally, the CFR value of the pilot signal is calculated by the following formula:
wherein X p (k) And Y p (k) Pilot signals of a sending end and a receiving end are respectively; h LS (k) For channels at pilots in the frequency domainThe response, i.e., the CFR value of the pilot signal.
S3, taking the CFR value of the pilot signal in the training set as an input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
s4, testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal;
and S5, restoring the original transmission signal according to the CFR value of the data signal.
As shown in fig. 4, the complex-valued neural network of the present invention has a three-layer structure, including an input layer, a hidden layer, and an output layer, where an input signal is transmitted forward through nonlinear transformation among the input layer, the hidden layer, and the output layer; and updating parameters in the complex-valued neural network by using a learning algorithm to complete back propagation according to an error value between the output value of the output layer and the label value of the forward propagation. The purpose of back propagation is to minimize the error value between the output of the CVNN and the tag value.
In the forward propagation process, data X = [ X ] input by an input layer 1 ，X 2 ，…，X m ] T Is the CFR value at the pilot. From the input layer to the hidden layer, the output of the hidden layer can be obtained by nonlinear variation of X multiplied by the complex-valued weight plus the complex-valued bias. Here, the non-linear variation is realized by an activation function. There are many types of activation functions, such as sigmoid and tanh functions, among others. It is worth mentioning that CVNN uses complex-valued activation functions to process the complex values of the inputs, unlike RVNN (real-valued neural network). Furthermore, since complex-valued channel responses have negative numbers in both the real and imaginary parts, the output values of the sigmoid and tanh functions vary between 0-1 and-1, respectively. We select a complex tanh function as the activation function.
Output H of the hidden layer j (j =1,2, \8230;, p) is as follows:
wherein, W ij And b j 1 Respectively, the complex-valued weights and offsets from the input layer to the hidden layer, f (-) being a complex tanh function; from the hidden layer to the output layer, the same operations are performed as from the input layer to the hidden layer.
Final output Y of the output layer k (k =1,2, \8230;, n) is as follows:
wherein, W jk And b k 2 Respectively complex-valued weights and offsets from the hidden layer to the output layer.
The back propagation is a training process of a complex-valued neural network, the training is completed by a learning algorithm and a cost function, and the cost function is minimized by continuously updating complex weights and biases. An L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) algorithm with the learning rate of 0.005 is selected as a learning algorithm, and the learning algorithm has a fast convergence rate.
MSE was chosen as the cost function to evaluate the performance of the training as follows:
wherein the content of the first and second substances,
for the tag, i.e., the CFR value of the data signal, (·) denotes the conjugate of the complex-valued vector. The ultimate goal of network training is to minimize MSE.
Since the fibre channel response is complex valued, it is suitable to use CVNN for direct processing rather than RVNN. In the present invention, we compare RVNN and CVNN in terms of both network complexity and training convergence speed. If a three-layer CVNN is used to handle the same problem, the number of input and output layer neurons is known in advance. Then, the fewer the number of hidden layer neurons, the lower the network complexity, given the same performance achieved. A large number of pilots wastes valuable spectral resources, and therefore it is very helpful to achieve accurate channel estimation under as few pilot conditions as possible. To compare the MSE of CVNN and RVNN, we chose 5% of the pilot OH for analysis. There are 64 symbols in total, with the number of pilot and data symbols being 3 and 61, respectively. The input and output of CVNN are CFR values at pilot and data symbols, respectively. Therefore, CVNN has 3 input neurons and 61 output neurons. However, RVNN requires processing of the complex numbers into real and imaginary parts, resulting in twice the number of input and output neurons as CVNN. Since the three-layer network structure used is relatively simple and the number of neurons in the input and output layers is determined, the difference between networks depends mainly on the number of neurons in the hidden layer. Fig. 5 is a graph of the MSE change for three layers CVNN and RVNN. As can be seen in fig. 5, for CVNN,5 hidden layer neurons can get a good MSE curve, as shown by the dashed line in fig. 5. In contrast, the MSE performance of RVNN depends largely on the number of hidden layer neurons. When the number of neurons in the hidden layer is increased from 5 to 15, the convergence rate of the network and the performance of the MSE are both improved, as shown by the solid line in FIG. 5. Furthermore, CVNN requires only 50 iterations to reach the minimum MSE value compared to 90 iterations of RVNN. Thus, CVNN with fewer neurons in the hidden layer may reach the best MSE performance faster than RVNN.
FIG. 6 is a diagram of an experimental setup of a 12.5Gd/s IM/DD FBMC 64QAM transmission system under SSMF with different lengths. At the FBMC transmitting end, firstly, a serial FBMC 64QAM complex signal X (t) is generated off-line. Then, the real and imaginary parts of X (t) are concatenated to obtain a serial real-valued signal. Next, the real-valued signal is loaded to an Arbitrary Waveform Generator (AWG) with a sampling rate of 50GSa/s to realize digital-to-analog conversion. Then, the output of the AWG is modulated into a Continuous Wave (CW) by a Mach-Zehnder modulator (MZM). The continuous wave is generated at 1550.112nm and transmitted through SSMF at 30 km or 50 km. After the SSMF transmission, the optical signal reaches the FBMC receiving end, wherein a Photodetector (PD) converts the received optical signal into an electrical signal, and a Variable Optical Attenuator (VOA) is used to adjust the input power of the PD. Finally, a real-time oscilloscope with a sampling rate of 50GSa/s is used for analog-to-digital conversion to acquire data for offline digital signal processing. In addition, an additional noise control stage is inserted in front of the FBMC receiving end, which is composed of two parts, VOA and erbium-doped fiber amplifier (EDFA), for measuring BER to simulate various noise levels. In the off-line digital signal processing process, firstly, the acquired digital signals are subjected to inverse concatenation, and the real part signals and the imaginary part signals are recombined into complex signals. Then, the original transmission signal is restored by performing channel estimation and demapping operations on the complex signal. In the experimental process, the total number of subcarriers and the number of data subcarriers are 512 and 128 respectively.
To verify the proposed method and evaluate the performance of CVNN-based channel estimation, we measured BER curves of the channel estimation algorithms (i.e. CVNN, RVNN, LS and LMMSE) in different scenarios, respectively. For CVNN, in an IM/DD FBMC transmission system, an experiment is repeatedly performed to collect data for processing under different Received Optical Power (ROP) conditions, wherein a part of the data is used as training data, and a part of the data is used as test data. A plurality of groups of data with receiving optical power of-3 dBm to-15 dBm are selected as training data, and data with receiving optical power of-16 dBm to-22 dBm are tested. Take 5% pilot and 64 symbols as an example, i.e. 3 pilots and 61 data symbols per subcarrier. Thus, during the training process, the data size of the CVNN input layer is 3 × 3328, and the data size of the output layer and label is 61 × 3328. During the test, the data sizes of the input and output layers were 3 × 128 and 61 × 128, respectively, for each different ROP.
Next, the present invention verifies that the MSE performance of RVNN depends largely on this simulation result of the number of hidden layer neurons. To verify the above simulation results, we measured the BER performance of CVNN and RVNN experimentally. Therein, the channel estimation performance of CVNN with 5 hidden layer neurons and RVNN with 5, 10 and 15 hidden layer neurons were measured, respectively. FIG. 7 is a graph plotting CVNN and RVNN based channel estimation techniques measured with 5% pilot redundancy in back-to-back (BTB) conditions as receivedGraph of BER variation versus optical power variation. As shown in fig. 7, for RVNN, as the number of hidden layer neurons increases, the corresponding BER performance is improved. When the number of the hidden layer neurons is 5 or 10, the BER curve is always higher than the HD-FEC threshold value by 3.8 x 10 -3 As shown by the lower triangular mark curve and the diamond mark curve in fig. 7. The BER performance of the RVNN only approximates that of a CVNN with 5 hidden layer neurons when the number of hidden layer neurons increases to 15, as shown by the square labeled curve and the upper triangular labeled curve in FIG. 7. Furthermore, it can be observed that the BER curve shown in fig. 7 substantially coincides with the simulated MSE curve trend in fig. 5. Here, the number of training times of RVNN and CVNN is set to 90 and 50, respectively.
Furthermore, to compare various channel estimation algorithms, we also measured BER curves for LS and LMMSE based channel estimation techniques, as shown in fig. 8. As expected, LMMSE achieves better BER performance than LS, as shown by the upper triangular and circular labeled curves in fig. 8. Here, the LMMSE algorithm can achieve better BER performance since it takes into account channel noise and channel statistics. CVNN, on the other hand, is trained on a large number of a priori fibre channel data, so that the network can learn the specific distribution of the fibre channels. Compared to the LS and LMMSE algorithms, CVNN achieves approximately 3dB and 1dB receive sensitivity improvement at the HD-FEC threshold, respectively, as can be derived from the BER curves measured in fig. 8. In fig. 8, (a), (b), and (c) are constellation diagrams obtained after the receiving end 64QAM signal uses LS, LMMSE, and CVNN to perform channel estimation respectively when the receiving optical power is-12 dBm. From fig. 8 (a) to (c), it can be observed that the constellation is converging, which is consistent with the performance variation of BER.
Generally, the larger the pilot redundancy, the better the performance of channel estimation, but the large number of pilots wastes valuable spectrum resources. Therefore, it is desirable to achieve accurate channel estimation with a small number of pilots. To verify the feasibility and performance of CVNN-based channel estimation at low pilot redundancy in IM/DD FBMC 64QAM transmission systems, we plot the BER curves for three different channel estimation algorithms at 10%, 5% and 1% pilot redundancy for the BTB case in fig. 9. When the pilot redundancy is changed from 10% to 1%, the estimated performance of CVNN is always better than LS and LMMSE, as shown by the black and grey curves in fig. 9. CVNN achieves approximately 2.5dB and 2dB receive sensitivity improvement at the HD-FEC threshold when pilot redundancy is 10%, compared to LS and LMMSE, respectively. Similarly, CVNN achieves approximately 3dB and 1dB receive sensitivity improvement at the HD-FEC threshold compared to LS and LMMSE, respectively, when only 5% pilot redundancy is used. When pilot redundancy is reduced to 1%, LS, LMMSE and CVNN approach the HD-FEC threshold at-16 dBm, -17dBm and-18 dBm, respectively. In such low pilot redundancy, CVNN can still achieve approximately 2dB and 1dB receive sensitivity improvement at the HD-FEC threshold, respectively, compared to LS and LMMSE. Therefore, for the CVNN-based channel estimation method, even though pilot redundancy is reduced, channel characteristics can be estimated.
In summary, the estimation performance of CVNN is always better than LS and LMMSE under the same pilot redundancy condition. And it can be observed from fig. 10 that the CVNN-based channel estimation algorithm only needs to use 5% of pilot redundancy to achieve the BER performance achieved with 10% of pilot redundancy in LS. In addition, under the condition of low pilot redundancy, the CVNN-based channel estimation algorithm still shows the superiority and good performance. Also, it can be observed from fig. 10 that the CVNN-based channel estimation algorithm only needs to use 1% of pilot redundancy to achieve the BER performance achieved with 5% of pilot redundancy in LS.
In order to evaluate the feasibility of different channel estimation algorithms in fiber transmission, the present invention measures the BER curves of the three algorithms in the case of transmitting the SSMF at BTB, 30 km and 50 km, respectively, as shown in fig. 10. The losses incurred over 30 km and 50 km fiber transmission are negligible compared to BTB transmission, as shown by the labeled curves in fig. 10. These results demonstrate that the IM/DD FBMC transmission system is very resistant to the effects of fiber dispersion.
Finally, the invention comparatively analyzes the computation complexity of the four channel estimation methods. For ease of analysis, only the channel estimate for each subcarrier is calculatedThe total number of real multiplications is shown in table 1. Wherein, N s Denotes the number of FBMC symbols. The LS and LMMSE algorithms respectively need to carry out N s And (N) s ) 2 The next complex multiplication operation. Then, the number of complex multiplication operations multiplied by 4 is converted into the number of real multiplication operations. As can be seen from the third section, CVNN and RVNN are tested using a network structure that is trained offline in advance, and therefore, the computational complexity depends on the number of real multiplications used in the test process. In the test process, the weights and the offsets are well known, so that the final result can be obtained by simple multiplication and addition operations among three layers. The number of real multiplications required for CVNN is 4 x (m) 1 *p 1 +p 1 *n 1 ) RVNN requires separate processing of the real and imaginary parts of the complex numbers, requiring real multiplication times of 2m 1 *p 2 +p 2 *2n 1 . Wherein m is 1 ，p 1 ，n 1 The number of the neurons of the CVNN input layer, the hidden layer and the output layer is respectively. For the same reason, 2m 1 ，p 2 ，2n 1 The numbers of neurons of the RVNN input layer, the hidden layer and the output layer are respectively. According to the above discussion, m 1 ＝3，n 1 ＝61，p 1 ＝5，p 2 And (5) =15.CVNN requires a real number of multiplications of 4 (3 + 5+ 61) =1280. While RVNN requires real number of multiplications of 2 x 3 x 15+2 x 15 x 61=1920. Thus, the number of real number multiplications required to obtain CVNN is less than RVNN. We can conclude that the computational complexity of CVNN, RVNN and LS is of the same order of magnitude, whereas LMMSE is higher.
TABLE 1 computational complexity comparison
In the invention, a CVNN-based channel estimation algorithm in an IM/DD FBMC transmission system with the transmission rate of 12.5GBd/s is provided and verified through experiments. Compared with LS, LMMSE and RVNN algorithms, the superiority of CVNN algorithm is verified by experimentally measuring BER curve. Compared to the RVNN algorithm, CVNN requires only one third of its number of hidden layer neurons to achieve near RVNN BER performance. Meanwhile, the CVNN is also superior to LS and LMMSE in BER performance, and achieves about 3dB and 1dB of receiving sensitivity improvement at the HD-FEC threshold under the conditions of BTB transmission and 5% pilot redundancy, respectively. In addition, CVNN is very resistant to fiber dispersion when transmitting 30 km and 50 km SSMF. Finally, the complexity of the CVNN test phase and LS are of the same order in terms of computational complexity and are lower than LMMSE. We can conclude that CVNN is a promising and suitable channel estimation method for use in IM/DD FBMC transmission systems.
The preferred embodiment of the invention also discloses a channel estimation system based on the complex value neural network, which comprises the following modules:
the network construction module is used for constructing a complex-valued neural network;
the pilot signal calculation module is used for extracting pilot frequency at a receiving end and estimating a CFR value of the pilot signal to obtain a training set and a test set;
the off-line training module is used for taking the CFR value of the pilot signal in the training set as input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
the test module is used for testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal; and restores the original transmission signal according to the CFR value of the data signal.
The calculation steps involved in the present system are the same as those in the above method embodiments, and are not described herein again.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (8)
1. The channel estimation method based on the complex value neural network is characterized by comprising the following steps:
s1, constructing a complex-valued neural network;
s2, extracting pilot frequency at a receiving end, and estimating a CFR value of a pilot frequency signal to obtain a training set and a test set;
s3, taking the CFR value of the pilot signal in the training set as an input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
s4, testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal;
s5, recovering an original transmission signal according to the CFR value of the data signal;
the input data of the input layer is the CFR value of the pilot signal, and the CFR value is as follows:
X＝[X 1 ，X 2 ，…，X m ] T
output H of the hidden layer j (j =1,2, \8230;, p) is as follows:
wherein, W ij And b j 1 Respectively, the complex-valued weights and offsets from the input layer to the hidden layer, f (-) being a complex tanh function;
final output Y of the output layer k (k =1,2, \8230;, n) is as follows:
wherein, W jk And b k 2 Complex-valued weights and offsets from the hidden layer to the output layer, respectively;
back propagation is a training process of a complex-valued neural network, the training is completed by a learning algorithm and a cost function, and the cost function is minimized by continuously updating complex weights and biases;
the cost function is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for the tag, i.e., the CFR value of the data signal, (·) denotes the conjugate of the complex-valued vector;
the CFR value of the pilot signal is calculated by the following formula:
wherein, X p (k) And Y p (k) Pilot signals of a sending end and a receiving end are respectively; h LS (k) Is the channel response at the pilot in the frequency domain, i.e., the CFR value of the pilot signal.
2. The complex-valued neural network-based channel estimation method of claim 1, wherein the complex-valued neural network comprises an input layer, a hidden layer and an output layer, and an input signal is propagated in forward direction among the input layer, the hidden layer and the output layer through a nonlinear transformation; and updating parameters in the complex-valued neural network by using a learning algorithm to complete back propagation according to an error value between the output value of the output layer and the label value of the forward propagation.
3. The complex-valued neural network-based channel estimation method of claim 2, wherein said non-linear transformation is implemented by an activation function.
4. The complex-valued neural network-based channel estimation method of claim 3, wherein said activation function is a complex tanh function.
5. The complex-valued neural network-based channel estimation method of claim 1, characterized in that the learning algorithm is an L-BFGS algorithm.
6. A complex-valued neural network-based channel estimation system, comprising:
the network construction module is used for constructing a complex-valued neural network;
the pilot signal calculation module is used for extracting pilot frequency at a receiving end and estimating a CFR value of the pilot signal to obtain a training set and a test set;
the off-line training module is used for taking the CFR value of the pilot signal in the training set as input to carry out off-line training on the complex-valued neural network to obtain a trained complex-valued neural network;
the test module is used for testing the trained complex-valued neural network by taking the CFR value of the pilot signal in the test set as input to obtain the CFR value of the data signal; recovering the original transmission signal according to the CFR value of the data signal;
the input data of the input layer is the CFR value of the pilot signal, and the CFR value is as follows:
X＝[X 1 ，X 2 ，…，X m ] T
output H of the hidden layer j (j =1,2, \8230;, p) is as follows:
wherein, W ij And b j 1 Respectively, the complex-valued weights and offsets from the input layer to the hidden layer, f (-) being a complex tanh function;
final output Y of the output layer k (k =1,2, \8230;, n) is as follows:
wherein, W jk And b k 2 Complex-valued weights and offsets from the hidden layer to the output layer, respectively;
back propagation is a training process of a complex-valued neural network, the training is completed by a learning algorithm and a cost function, and the cost function is minimized by continuously updating complex weights and biases;
the cost function is as follows:
wherein the content of the first and second substances,
for the tag, i.e., the CFR value of the data signal, (·) denotes the conjugate of the complex-valued vector;
the CFR value of the pilot signal is calculated by the following formula:
wherein, X p (k) And Y p (k) Pilot signals of a sending end and a receiving end are respectively; h LS (k) Is the channel response at the pilot in the frequency domain, i.e., the CFR value of the pilot signal.
7. A complex-valued neural network-based channel estimation system as claimed in claim 6, characterized in that the non-linear transformation is implemented by an activation function.
8. The complex-valued neural network-based channel estimation system of claim 7, wherein the activation function is a complex tanh function.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111178108.6A CN114006794B (en) | 2021-10-09 | 2021-10-09 | Complex value neural network-based channel estimation method and system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111178108.6A CN114006794B (en) | 2021-10-09 | 2021-10-09 | Complex value neural network-based channel estimation method and system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114006794A CN114006794A (en) | 2022-02-01 |
| CN114006794B true CN114006794B (en) | 2022-11-25 |
Family
ID=79922425
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111178108.6A Active CN114006794B (en) | 2021-10-09 | 2021-10-09 | Complex value neural network-based channel estimation method and system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114006794B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114844749B (en) * | 2022-04-26 | 2023-06-09 | 电子科技大学 | Fiber channel estimation method based on neural network |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019191099A1 (en) * | 2018-03-26 | 2019-10-03 | Zte Corporation | Non-linear adaptive neural network equalizer in optical communication |
| CN112637093A (en) * | 2020-12-09 | 2021-04-09 | 齐鲁工业大学 | Signal detection method based on model-driven deep learning |
| CN112995892A (en) * | 2021-02-08 | 2021-06-18 | 东南大学 | Large-scale MIMO fingerprint positioning method based on complex neural network |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108566257B (en) * | 2018-04-27 | 2020-08-18 | 电子科技大学 | Signal recovery method based on back propagation neural network |
| KR20200143999A (en) * | 2019-06-17 | 2020-12-28 | 현대자동차주식회사 | Apparatus for compensating channel based on ann and method thereof |
| CN111510402B (en) * | 2020-03-12 | 2021-08-27 | 西安电子科技大学 | OFDM channel estimation method based on deep learning |
| CN111404849B (en) * | 2020-03-20 | 2021-01-12 | 北京航空航天大学 | OFDM channel estimation and signal detection method based on deep learning |
-
2021
- 2021-10-09 CN CN202111178108.6A patent/CN114006794B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019191099A1 (en) * | 2018-03-26 | 2019-10-03 | Zte Corporation | Non-linear adaptive neural network equalizer in optical communication |
| CN112637093A (en) * | 2020-12-09 | 2021-04-09 | 齐鲁工业大学 | Signal detection method based on model-driven deep learning |
| CN112995892A (en) * | 2021-02-08 | 2021-06-18 | 东南大学 | Large-scale MIMO fingerprint positioning method based on complex neural network |
Non-Patent Citations (1)
| Title |
|---|
| 5G高速移动系统中基于BP神经网络的多普勒频偏估计方法;王增浩等;《电信科学》;20200420(第04期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114006794A (en) | 2022-02-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104038465B (en) | A kind of many sub-block phase noise estimation compensation process suitable for CO ofdm systems | |
| Feng et al. | Performance-enhanced direct detection optical OFDM transmission with CAZAC equalization | |
| CN107171735B (en) | A kind of big line width CO-OFDM phase noise compensation method of time-frequency domain Kalman filtering | |
| CN109347562B (en) | CO-OFDM system phase noise optimization compensation method | |
| WO2019191099A1 (en) | Non-linear adaptive neural network equalizer in optical communication | |
| Barros et al. | Optimized dispersion compensation using orthogonal frequency-division multiplexing | |
| CN111865432B (en) | Blind phase noise compensation method in CO-FBMC/OQAM system | |
| CN115174330B (en) | Compensation method for distortion signal of multi-carrier access network and nonlinear equalizer | |
| CN113300779B (en) | Pilot-assisted CO-FBMC/OQAM system phase noise compensation method | |
| Chu et al. | Channel estimation based on complex-valued neural networks in IM/DD FBMC/OQAM transmission system | |
| CN105187345A (en) | Non-iterative blind phase noise compensation method suitable for CO-OFDM system | |
| Do et al. | Data-aided chromatic dispersion estimation for polarization multiplexed optical systems | |
| Li et al. | Channel equalization in optical OFDM systems using independent component analysis | |
| CN114006794B (en) | Complex value neural network-based channel estimation method and system | |
| CN114844749B (en) | Fiber channel estimation method based on neural network | |
| Chi et al. | AI based on frequency slicing deep neural network for underwater visible light communication | |
| Yang et al. | A modified convolutional neural network-based signal demodulation method for direct detection OFDM/OQAM-PON | |
| CN113612707B (en) | ANN_LS-based IM/DD-OFDM/OQAM-PON system channel estimation method | |
| CN114978837A (en) | Filter bank multi-carrier system signal transmission method, device and storage medium | |
| Guo et al. | 98.7-Gb/s optical SE-DMT transmission using an enhanced decision-directed algorithm with preconditions | |
| CN113300995A (en) | Channel estimation algorithm for IM/DD-OFDM/OQAM-PON system | |
| Bernhard et al. | Multicarrier transmission using Hadamard transform for optical communications | |
| Zhu et al. | Discrete cosine transform based pilot-aided phase noise estimation for high-order QAM coherent optical systems | |
| CN115173952B (en) | Optimized receiving method of optical universal filtering multi-carrier optical access network | |
| CN115001912B (en) | IFDMA-PON improvement method based on BiLSTM |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |