A joint FTN waveform optimization method based on deep learning receiver

Abstract

The present invention discloses a joint FTN waveform optimization method based on a deep learning receiver, which belongs to a single carrier communication technology in the field of communication. The present invention optimizes the position of the constellation point and the PSD of the transmitted signal at the transmitting end, and adopts a BiLSTM network to perform signal detection at the receiving end, and maximizes SE and achieves BER performance improvement under the constraints of average transmission power and SEM. Combined with the deep learning BiLSTM detector, the present invention realizes the joint optimization of the FTN system transceiver, further improves the spectrum efficiency under the same time domain compression factor τ, and optimizes the system performance at the same time. Compared with the previous deep learning method that only performs receiving end optimization, the present invention performs joint optimization of the transceiver to obtain better spectrum efficiency performance and BER performance.

Description

Technical Field

[0001] The present invention belongs to single-carrier communication technology in the field of communications, and specifically relates to a joint FTN (Faster-Than-Nyquist) waveform optimization method based on a deep learning receiver. Background Art

[0002] Compared with 4G (the fourth generation of mobile communication technology), the service objects of 5G have expanded from the past communication between people to communication between people and between people and between things. It is predicted that with the continuous growth of user demand, the mobile communication network will face: 1000 times the growth of data capacity, 10 to 100 times the user rate demand, etc. in the next 10 years. In order to achieve higher transmission rates, there are generally two methods. One is to increase the spectrum bandwidth. At present, 4G is mainly concentrated in the spectrum below 2GHz, and the service band is very crowded. The high frequency band of 6 to 100GHz has more abundant idle spectrum resources and can be used as an auxiliary band for 5G. However, the frequency band above 30GHz belongs to the category of millimeter waves, and its biggest characteristic is that it has large attenuation in the air, weak diffraction ability, and poor propagation characteristics. The second is to increase the spectrum utilization rate, so that the system can transmit more data in the same bandwidth band, and greatly improve the system capacity under the premise of limited spectrum resources. Around this goal, how to further increase the spectrum efficiency several times under the condition of increasingly scarce spectrum resources is one of the key issues in future communication technology research.

[0003] Most existing communication system designs are based on the Nyquist first criterion, that is, orthogonal modulation is used to avoid inter-symbol interference (ISI), and the receiver implements low-complexity symbol-by-symbol demodulation. Under this system architecture, a direct way to improve spectral efficiency is to use high-order modulation (such as 256-QAM), that is, each transmitted symbol carries more information bits. However, high-order modulation is very sensitive to channel characteristics (multipath fading) and nonlinear factors (phase noise). At the same time, to achieve the same demodulation performance as low-order modulation, a higher demodulation signal-to-noise ratio (SNR) is required, which reduces the system power efficiency.

[0004] The FTNs were first proposed by Mazo. By abandoning orthogonality, that is, further reducing (or compressing) the symbol interval (that is, the interval between two consecutive shaped pulses) in the time direction, more symbols can be transmitted in the same time. However, inter-symbol interference is also introduced. In order to compensate for the ISI introduced by FTN and complete signal detection, many methods have been proposed, but single-module optimization is difficult to achieve a good performance-complexity compromise under high-order modulation conditions. Therefore, in order to obtain a better performance-complexity compromise, a pre- and post-equalization hybrid method is required, but traditional transceiver design and optimization rely on the establishment of mathematical models. In the case of non-orthogonal transmission, it is difficult to establish a suitable mathematical model to solve complex multi-module optimization problems.

[0005] In recent years, deep learning, as a hot research field, is often used as data-driven parameter optimization, so it is easier to achieve simultaneous optimization of multiple modules and solve complex optimization problems. If a neural network (NN) is used to replace the traditional transmitter and receiver, the transmitter NN learns to convert data into a transmission signal, while the receiver NN learns to recover data from the received signal. A large number of results show that data-driven methods can improve and supplement traditional model-driven methods, such as improving SE (spectral efficiency). However, these algorithms do not consider the power spectral density (PSD) of the transmitted signal during the optimization process, which makes it unable to meet the spectrum mask (SEM) requirements of existing communication standards. At present, some methods have adopted deep learning to deal with FTN, such as a fully connected deep neural network (DNN) was proposed for symbol estimation; and successive interference cancellation (SIC) was proposed to eliminate FTN-ISI; bidirectional long short-term memory (BiLSTM) was applied to FTN receiver design; an enhanced deep learning-based factor graph method was applied to signal recognition, but these methods only use deep learning to design receivers. Extensive data show that when the system is severely affected by FTN-ISI, the BER performance of these receivers is comparable to MLSE / BCJR in low-order modulation, but the performance is severely degraded in high-order modulation. Summary of the invention

[0006] The present invention provides a joint FTN waveform optimization method based on deep learning receiver to improve the SE performance of the FTN system.

[0007] The technical solution adopted by the present invention is:

[0008] A joint FTN waveform optimization method based on a deep learning receiver, the method comprising the following steps:

[0009] Step 1, initialize the modulation constellation and perform center normalization processing on it to obtain a normalized constellation C. Preferably, the initial position of the initialized modulation constellation is an M-QAM (multi-level quadrature amplitude modulation) position of Gray code mapping;

[0010] Initialize the coefficients of the linear filter p, the coefficients of the linear filter p are The order of the linear filter p is 2L, where k represents a symbol identifier and L represents a preset symbol length;

[0011] Initialize the network parameters of the bidirectional BiLSTM detector, including weight W and bias γ;

[0012] Initialize two weights with values ​​between 0 and 1, denoted as the first weight λ and the second weight η respectively;

[0013] The network structure of the bidirectional BiLSTM detector includes: a D-layer bidirectional LSTM network, a linear layer, and a softmax layer, where D is an integer greater than or equal to 2;

[0014] Step 2: Perform symbol mapping based on the current constellation C, and send the mapped symbols to the linear filter p to introduce specific memory for the transmitted symbols, thereby obtaining the transmitted symbol sequence {x[k]} after precoding processing, thereby completing the precoding of the symbols;

[0015] Step 3, after performing signal modulation on the transmission symbol sequence {x[k]} using the FTN modulation method, a corresponding receiving signal is obtained through channel simulation processing;

[0016] Step 4: Perform matched filtering on the received signal obtained in step 3 and then input it into the bidirectional BiLSTM detector for signal detection:

[0017] A set of matched filtered received signals is extracted according to the specified length N as the input signal r of the bidirectional BiLSTM detector, and each symbol of the input signal is decomposed into real and imaginary parts to obtain an input vector with a dimension of N×2 and input it into the D-layer bidirectional LSTM network of the bidirectional BiLSTM detector; the output of the D-layer bidirectional LSTM network is converted to a dimension of 2×log by the linear layer of the bidirectional BiLSTM detector. 2 The data of M is then passed through the softmax layer to output the probability of each symbol being a transmitted bit 0 or 1; where M represents the size of the constellation C;

[0018] The log-likelihood ratio of signal detection is obtained based on the probability of the softmax layer output, that is, the soft information output LLR;

[0019] Step 5: By minimizing the loss function Iteratively update the constellation C, the coefficients of the linear filter p, and the network parameters of the bidirectional BiLSTM detector;

[0020] in, Represents the cross entropy of the output of the softmax layer of the bidirectional BiLSTM detector, that is, the total binary cross entropy;

[0021] S beyond represents the spectrum mask constraint, and BW represents the allocated normalized bandwidth, S mask (f) represents the spectrum mask, S(f) represents the power spectrum density, and f represents the frequency;

[0022] Preferably, the above object can be iteratively updated using a gradient descent method based on the currently calculated loss function value;

[0023] Step 6, iteratively update the first weight λ and the second weight η in sequence:

[0024] First update λ: According to the formula λ-ηS beyond Get the updated first weight λ;

[0025] Update η again: obtain the updated second weight η according to the formula κη, where κ is a constant greater than 1 and the deviation from 1 is within a specified range;

[0026] Step 7, check whether the iterative convergence condition is met, if so, stop, and obtain the waveform optimization result based on the current constellation C, the coefficient of the linear filter p and the network parameters of the bidirectional BiLSTM detector; thus, the signal transmission stage processing can be performed based on the constellation C and the linear filter p in the optimization result; the bidirectional BiLSTM detector in the optimized structure performs signal detection processing on the filtered received signal;

[0027] If not, continue to execute steps 2-7 based on the updated constellation C, the coefficients of the linear filter p, and the network parameters of the bidirectional BiLSTM detector;

[0028] The iterative convergence condition is: the spectrum template constraint S beyond The value of approaches 0 and the value of the loss function Loss is stable; it is known that the number of iterations reaches the set upper limit.

[0029] Furthermore, the total binary cross entropy is specifically:

[0030]

[0031] in, Represents the i-th received symbol output by the softmax layer To send bit bi The probability of i is 0 or 1, and r represents the input signal of the bidirectional BiLSTM detector.

[0032] In the symbol mapping stage, the method of the present invention designs a trainable constellation C, and introduces specific memory, i.e., precoding, for the transmitted symbols by passing the mapped symbols through a trainable linear filter p. At the receiving end, the symbols are sequentially matched filtered and down-sampled, and then signal detection is performed through a BiLSTM system, and several trainable parts are jointly optimized to improve the spectrum efficiency.

[0033] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0034] The present invention optimizes the position of the constellation points and the PSD of the transmitted signal at the transmitting end, and uses the BiLSTM network to perform signal detection at the receiving end, maximizing SE and achieving BER performance improvement under the constraints of average transmit power and SEM. Combined with the deep learning BiLSTM detector, the present invention realizes the joint optimization of the FTN system transceiver, further improves the spectrum efficiency under the same time domain compression factor τ, and optimizes the system performance at the same time. Compared with the previous deep learning method that only optimizes the receiving end, the present invention can obtain better spectrum efficiency performance and BER performance by performing joint optimization of the transceiver. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0036] Figure 1 A system implementation structure block diagram of a joint FTN waveform optimization method based on a deep learning receiver provided in an embodiment of the present invention;

[0037] Figure 2 The figure is a schematic diagram of the structure of a receiving-end detector (bidirectional BiLSTM detector) based on a bidirectional LSTM neural network in an embodiment of the present invention.

[0038] Figure 3 Schematic diagram of the structure of the LSTM block in an embodiment of the present invention.

[0039] Figure 4 1 is a power spectrum density diagram of different FTN signals when the modulation order is 1024 in an embodiment of the present invention.

[0040] Figure 5The BER performance curve of the transceiver based on the method of the present invention when the modulation order is 256 in the embodiment of the present invention.

[0041] Figure 6 The BER performance curve of the transceiver based on the method of the present invention when the modulation order is 1024 in the embodiment of the present invention.

[0042] Figure 7 In the embodiment of the present invention, the constellation obtained by learning the scheme of the present invention when the modulation order is 256, the time acceleration factor is 7 / 9, and the bit signal-to-noise ratio is 10 dB.

[0043] Figure 8 In the embodiment of the present invention, the constellation obtained by learning the scheme of the present invention when the modulation order is 1024, the time acceleration factor is 7 / 9, and the bit signal-to-noise ratio is 13dB. DETAILED DESCRIPTION

[0044] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0045] The embodiment of the present invention provides a joint FTN waveform optimization method based on a deep learning receiver. The present invention is a joint FTN waveform optimization strategy based on a deep learning receiver instead of optimizing only the neural network in the receiver. And the joint design of the transmitter and receiver is transformed into a joint optimization problem, and the constellation geometry, linear precoder, and bidirectional LSTM signal detector are trained simultaneously under the constraints of average transmission power and SEM to maximize the spectrum efficiency. That is, in the symbol mapping stage, a trainable constellation C is designed, and the mapped symbols are passed through a trainable linear filter to introduce specific memory for the transmitted symbols, that is, precoding. At the receiving end, the symbols are matched filtered in turn. After downsampling, a BiLSTM system (detector built based on BiLSTM) is used for signal detection, and several trainable parts are jointly optimized to achieve improvements in spectrum efficiency and BER performance under high-order modulation.

[0046] In order to achieve the above objectives, compared with the traditional method of only optimizing the receiver at the receiving end or optimizing the precoding at the transmitting end, the spectrum efficiency performance improvement in the present invention can be decomposed into three parts, namely, from the design of the constellation diagram, from the design of the precoder coefficients at the transmitting end, and from the parameter design of the bidirectional LSTM receiver at the receiving end.

[0047] Given the spectrum efficiency improvement target and the number of constellation symbols, precoder length, signal detector input length, etc., the design schemes that meet the spectrum efficiency improvement target are infinite. Therefore, there are degrees of freedom in the design scheme. This degree of freedom can be used to optimize system performance. The criterion is to maximize the system's achievable capacity, which can be converted into minimizing binary cross entropy through derivation. On the other hand, the present invention also takes into account some constraints, such as spectrum templates. For different scenario requirements, other constraints can also be added, including: transmit power constraints; constellation and transmit filter energy constraints; peak-to-average power ratio (PAPR) constraints to improve power amplifier efficiency; passband ripple constraints, etc.

[0048] Therefore, the constellation diagram, the precoder coefficients at the transmitting end, and the parameters of the bidirectional LSTM receiver at the receiving end are jointly designed and converted into an optimization problem. By constructing a suitable loss function through deep learning to solve the optimization problem, the above parameters can be obtained. At the same time, the joint optimization design problem of the transmitting and receiving ends in the present invention is solved by offline training and then deployed in the FTN system to further reduce the complexity.

[0049] Therefore, when the joint FTN waveform optimization method based on deep learning receiver of the present invention is used for communication, the specific processing process of the transmitting end, the receiving end and the receiving end is as follows:

[0050] Transmitter processing steps:

[0051] Forward error correction coding: Forward error correction coding (FEC) is performed on the binary information bit sequence to be sent to obtain the coded bit sequence b.

[0052] Symbol mapping: The coded sequence is grouped into M groups; each group containing M bits is mapped to obtain a symbol a[k], where k represents the kth symbol, and each a[k] comes from the constellation C. Then, the symbol sequence {a[k]} is input to the precoder module. The present invention will optimize the transmitted modulation constellation C.

[0053] Precoding: In this specific implementation, the precoder is implemented as a finite-order filter with a filter coefficient of Where L represents the precoder length (i.e., symbol length), and the output of the precoder is The filter order is 2L. Then the sequence {x[k]} is sent to the FTN mapper to obtain the FTN signal. Where ρ = 1 / ||p|| 2 is the normalization constant.

[0054] FTN modulation: This is achieved through the FTN shaping filter. It is a T-orthogonal unit energy root raised cosine filter (RRC), the time acceleration factor τ satisfies 0<τ≤1, and the symbol time interval is τT. The expression of FTN signal can be described as:

[0055]

[0056] The signal given by equation (1) corresponds to sending a symbol {x[k]} every τT seconds, and the symbol rate is 1 / τT. In contrast, in the Nyquist system, τ = 1, and the symbol rate is 1 / T. Therefore, in the FTN system, by artificially reducing the upsampling multiple of the symbol sequence {x[k]}, the symbol interval can be reduced from T in the Nyquist system to τT, so that more symbols can be transmitted in the same time and bandwidth, and the system spectrum efficiency is improved.

[0057] The symbol for the sender can also be expressed like this:

[0058] s(t)=∑ k a[k]φ(t-kτT) (2)

[0059] in Since the time interval n≠0, E[a[k]a * [k+n]]=0, so the power density function of the transmitted symbol s(t) depends only on φ(t), and the power density function of s(t) is:

[0060]

[0061] Here, f represents frequency.

[0062] From (3), we can see that the power spectrum density of the transmitted signal is When determining, it is completely determined by p. The present invention will avoid bandwidth expansion and improve spectrum efficiency by selecting a suitable p.

[0063] Processing steps at the receiving end:

[0064] Receive signal: The RF front end receives the signal from the channel interference and obtains the baseband signal s through down conversion r (t). Then s r (t) is sent to the FTN demodulation module.

[0065] FTN demodulation: This is achieved by an FTN demapper, which contains a matched filter (with a response of ) and down sampler. In this specific implementation, considering the AWGN (Additive White Gaussian Noise) channel, the noise variance is The expression of the output signal of the FTN demapper module is:

[0066]

[0067] in,

[0068]

[0069] At this time, the noise {ω[n]} is colored noise, and its autocorrelation function is:

[0070]

[0071] Among them, N 0 is the power density of the noise, and n represents the signal sampling time.

[0072] Signal detection: Since the received symbol r(n) at time n is subject to interference from the moments before and after the symbol, the embodiment of the present invention adopts a bidirectional BiLSTM detector (a detector built based on BiLSTM, also known as a BiLSTM system) to perform FTN-ISI elimination and signal detection. A group of signals are input into the LSTM-based detector every N (preset value) moments. Each symbol is decomposed into real and imaginary parts as inputs with a dimension of N×2. The D-layer (greater than or equal to 2) bidirectional LSTM network is passed through a linear layer, and the result at each moment is converted into a 2×log 2 M's signal, and then transforms the signal detection into a classification problem. Finally, a softmax layer is used to obtain the probability of sending a bit 0 or 1, and then the LLR is obtained:

[0073]

[0074] Among them, LLR i represents the i-th received symbol Soft information, Respectively represent the i-th received symbol output by the softmax layer is the probability of sending a bit as 0 or 1.

[0075] Joint optimization of transmitter and receiver:

[0076] Due to the constraints of the spectrum template, the available bandwidth is fixed, so the embodiment of the present invention takes maximizing the achievable rate of the system as the optimization goal. This goal can be converted into minimizing the total binary cross entropy. Since it is difficult to quantify it mathematically, the Monte Carlo sampling method is used to give an estimate:

[0077]

[0078] Where W and γ are the trainable weights and bias terms in the bidirectional BiLSTM detector.

[0079] In order to meet actual needs, the power spectral density of the transmission signal must meet the constraints of the spectrum mask to limit the out-of-band emission level. Generally speaking, such regulations are given by international regulatory agencies. The embodiment of the present invention considers the spectrum mask specified by the European Telecommunications Standards Institute (ETSI), which requires that the power spectral density of the transmission signal is located under the spectrum mask of all frequencies in the specified frequency band:

[0080]

[0081] Where BW is the standardized bandwidth allocated by the regulatory agency, S mask is the spectrum mask. This constraint can be rewritten as:

[0082] S beyond =0 (10)

[0083] in In addition, the transmit signal average power is constrained to 1, and the constellation C and transmit filter are constrained to unit energy.

[0084] ∫|φ(t)| 2 dt=1 (11)

[0085] E C[k]～U[C] [C[k]]=1 (12)

[0086] Among them, U[C] represents the uniform distribution on C. Therefore, the optimization problem can be expressed as:

[0087]

[0088]

[0089] Example

[0090] Figure 1 The structural block diagram of the system implementation of the joint FTN waveform optimization method based on the deep learning receiver of this embodiment is shown in FIG. The source end inputs the binary information bit stream to be sent. The information bit first passes through the forward error correction (FEC) coding module, and then the coded symbol b is modulated onto a string of baseband symbols a, where each symbol is obtained from a trainable M-dimensional constellation C, and then a is filtered by a precoder p to obtain a sequence {x[k]}. Finally, the FTN mapper generates a transmit FTN signal and sends it to the channel.

[0091] The receiver RF front end receives the transmitted signal contaminated by the channel. Then, the FTN demodulator completes matched filtering and downsampling of the received signal to obtain the symbol sequence {r[n]}, which is sent to the BiLSTM detector, and the LLR of each symbol bit is obtained through the detector, and finally passed through the forward error correction (FEC) decoding module.

[0092] In this embodiment, before optimizing the constellation C, it is assumed that the constellation set Contains M complex numbers. In order to ensure energy normalization and no DC offset, the constellation C needs to be center normalized:

[0093]

[0094] Figure 2 The structure diagram of the receiving end detector based on the bidirectional LSTM neural network (i.e., the bidirectional BiLSTM detector). First, the complex symbol r[n] is converted into the input O of the first layer. 1 [n] = [Re{r[n]}, Im{r[n]}], assuming that the input is the symbol of N moments, then the input to BiLSTM is a tensor An N×2 vector. Figure 2 As shown, each column represents a moment, O d The two parts contained in [n] correspond to the real part and imaginary part of the input respectively. Each layer of LSTM network is divided into two parts, forward and backward LSTM, which transmit the information in the memory unit at different times in the same layer, where d = 1, 2, ..., D. After the D-layer LSTM network is a linear layer, the result at each moment will be converted into a dimension of 2×log 2 M data, and finally passes through a softmax layer to obtain the probability of sending a bit 0 or 1, and obtain LLRs.

[0095] Figure 3 This is the structure diagram of the LSTM block. First, the top line from c[n-1] to c[n] is the LSTM's summary of all previous input information, passing on "memory". Then the leftmost sigmoid neural layer below is the forget gate, which is responsible for controlling whether to forget some previous components. The sigmoid in the middle and the tanh next to it together form the memory gate, which is responsible for deciding how much current information to add to the memory. The output gate is the rightmost part, which determines the output at the current moment.

[0096] Among them, the forward propagation equation of any d-th layer in the D layer is:

[0097]

[0098]

[0099] Among them, W and γ are the trainable weights and bias terms in the BiLSTM system, that is, W iO Represents the weight between the input gate and the current layer input, W ih Represents the weight between the input gate and the hidden state at the previous moment, W fO Represents the weight between the forget gate and the current layer input, W fh Represents the weight between the forget gate and the hidden state of the previous moment, W cO Represents the weight between the memory gate and the current layer input, W ch Represents the weight between the memory gate and the hidden state of the previous moment, W oO Represents the weight between the output gate and the current layer input, W oh represents the weight between the output gate and the hidden state at the previous moment, γ i , γ f , γ c , γ o They represent the bias items of the input gate, forget gate, memory gate, and output gate respectively. i[n], f[n], and o[n] represent the input gate, forget gate, and output gate at time n respectively. and They represent the memory gate and hidden state of the forward propagation at time n, σ represents the sigmoid function, represents the Hadamard product.

[0100] The backward propagation equation for the dth layer is:

[0101]

[0102] After the output of the last LSTM layer, the forward and backward outputs are combined:

[0103]

[0104] in, They represent the memory gate and hidden state of the backward propagation at time n respectively.

[0105] The training steps are as follows:

[0106] Step 1: Parameter initialization:

[0107] Initialize the coefficients of the linear filter p, the constellation set The weight W and bias γ of the bidirectional BiLSTM detector, the two weights (first weight λ, second weight η) with a value range between 0 and 1, are denoted as η [0] and λ [0] , and the number of initializations u (the initial value is 0);

[0108] And the initial value of the modulation constellation C is calculated according to formula (14);

[0109] Step 2: The number of iterations u increases by 1;

[0110] Step 3: Update iteratively p, C, W, γ by minimizing the loss function, where the loss function is as follows:

[0111]

[0112] That is, based on the currently calculated loss function value, the coefficients of the linear filter p, the modulation constellation C, the weight W and the bias γ of the bidirectional BiLSTM detector are iteratively updated using the gradient descent method;

[0113] Step 4: Update the first weight λ: λ [u+1] =λ [u] -η [u] S beyond

[0114] Step 5: Update the second weight η: η [u+1] =κη [u] , where κ is a constant slightly larger than 1. That is, κ is a constant greater than 1 and the deviation from 1 is within a specified range. Preferably, the deviation from 1 does not exceed 0.1.

[0115] When the preset training end condition (S beyond When the value of approaches 0 and the Loss is stable (the value no longer decreases), or the number of iterations reaches a preset upper limit, a trained detector is obtained, and then the optimization processing of the FTN waveform is realized based on the detector.

[0116] The key parameters involved in the FTN system in this embodiment are shown in Table 1. In all subsequent simulations, the spectrum template with a bandwidth of 56 MHz specified by ETSI is selected.

[0117] Table 1 Simulation parameters

[0118]

[0119] Figure 4 The power spectral density of the FTN signal is shown when the constellation size is 1024. It can be seen that the learned waveform satisfies the constraints of the spectrum template, which proves the effectiveness of the PSD constraint in the optimization process. In addition, the learned waveform has a performance that is closer to the spectrum template than RRC, especially when τ is small (τ=7 / 9), which is more obvious.

[0120] Figure 5 and Figure 6The BER performance for high-order modulation (M=256, 1024) is given, and the BiLSTM receiver is also plotted as a benchmark. The waveform labeled "Proposed w / o const" shows the BER performance of the proposed method without constellation optimization. These results show that it is difficult to eliminate severe FTN-ISI with only LSTM receivers in high-order modulation. In the case of τ=7 / 9, when M=256 and 1024, the E-bandwidth of error-free transmission achieved by LSTM is 0.04477 W / m. b / N 0 11.9dB and 16dB respectively to achieve BER=10 -4 However, for the optimization method proposed in the present invention, the required E b / N 0 They are only 9.7dB and 12.8dB respectively. Even without constellation optimization, the performance gain of the method of the present invention is 0.4-1dB. If constellation optimization is considered, the performance gain is 1.3-1.5dB when τ=8 / 9, and the performance gain is 0.55-0.75dB when τ=7 / 9. When τ=8 / 9, the performance of the method of the present invention is even better than Nyquist transmission, proving that the constellation and waveform learned by the method of the present invention have higher capacity than traditional QAM and RRC. These results show that in high-order modulation, the joint optimization of the transceiver can significantly reduce the bit error rate compared with the optimization of the receiver alone, while the increase in complexity is negligible.

[0121] Figure 7 and Figure 8 The present invention is given in two cases (M = 256, τ = 7 / 9, E b / N 0 =10dB; M=1024, τ=7 / 9, E b / N 0 =13dB). The initialization before constellation optimization selects the QAM constellation mapped by Gray code, and uses the optimized constellation points to maintain the symmetry of the QAM constellation. However, compared with QAM, the present invention obtains some very similar constellation point combinations. Every four constellation points of M=256 and M=1024 almost overlap. In addition, when M=1024, the four groups of almost overlapping constellation points are relatively close.

[0122] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0124] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A joint FTN waveform optimization method based on deep learning receiver, It is characterized in that The following steps are involved: Step 1, initialize the modulation constellation and perform center normalization processing on it to obtain the normalized constellation C; Initialize the coefficients of the linear filter p, the coefficients of the linear filter p are The order of the linear filter p is 2L, where k represents a symbol identifier and L represents a preset symbol length; Initialize the network parameters of the bidirectional BiLSTM detector, including weight W and bias γ; Initialize two weights with values ​​between 0 and 1, denoted as the first weight λ and the second weight η respectively; The network structure of the bidirectional BiLSTM detector includes: a D-layer bidirectional LSTM network, a linear layer, and a softmax layer, where D is an integer greater than or equal to 2; Step 2: Perform symbol mapping based on the current constellation C, and send the mapped symbols to a linear filter p to obtain a transmitted symbol sequence {x[k]} after precoding processing; Step 3, after performing signal modulation on the transmission symbol sequence {x[k]} using the FTN modulation method, a corresponding receiving signal is obtained through channel simulation processing; Step 4: Perform matched filtering on the received signal obtained in step 3 and then input it into the bidirectional BiLSTM detector for signal detection: A set of matched filtered received signals is extracted according to the specified length N as the input signal r of the bidirectional BiLSTM detector, and each symbol of the input signal is decomposed into real and imaginary parts to obtain an input vector with a dimension of N×2 and input it into the D-layer bidirectional LSTM network of the bidirectional BiLSTM detector; the output of the D-layer bidirectional LSTM network is converted to a dimension of 2×log by the linear layer of the bidirectional BiLSTM detector. 2 The data of M is then passed through the softmax layer to output the probability of each symbol being a transmitted bit 0 or 1; where M represents the size of the constellation C; The log-likelihood ratio of signal detection is obtained based on the probability of the softmax layer output, that is, the soft information output LLR; Step 5: By minimizing the loss function Iteratively update the constellation C, the coefficients of the linear filter p, and the network parameters of the bidirectional BiLSTM detector; in, Represents the cross entropy of the output of the softmax layer of the bidirectional BiLSTM detector; S beyond represents the spectrum mask constraint, and BW represents the allocated normalized bandwidth, S mask (f) represents the spectrum mask, S(f) represents the power spectrum density, and f represents the frequency; Step 6, iteratively update the first weight λ and the second weight η in sequence: First update λ: According to the formula λ-ηS beyond Get the updated first weight λ; Update η again: obtain the updated second weight η according to the formula κη, where κ is a constant greater than 1 and the deviation from 1 is within a specified range; Step 7, check whether the iterative convergence condition is met, if so, stop, and obtain the waveform optimization result based on the current constellation C, the coefficient of the linear filter p and the network parameters of the bidirectional BiLSTM detector; If not, continue to execute steps 2-7 based on the updated constellation C, the coefficients of the linear filter p, and the network parameters of the bidirectional BiLSTM detector; The iterative convergence condition is: the spectrum template constraint S beyond The value of approaches 0 and the value of the loss function Loss is stable; or the number of iterations reaches the set upper limit.

2. The method according to claim 1, It is characterized in that Cross Entropy Specifically: in, Represents the i-th received symbol output by the softmax layer To send bit b i The probability of i Is 0 or 1.

3. The method according to claim 1, It is characterized in that In step 5, based on the currently calculated loss function value, the gradient descent method is used to iteratively update the constellation C, the coefficients of the linear filter p, and the network parameters of the bidirectional BiLSTM detector.

4. The method according to claim 1, It is characterized in that In step 1, the initial position of the initialized modulation constellation is the M-QAM position of the Gray code mapping.

Images