A neural network equalization method with embedded signal-correlated noise variance

Abstract

This invention discloses a neural network equalization method embedding signal-related noise variance. The method includes: removing the cyclic prefix from the received time-domain signal, performing a fast Fourier transform, and removing Hermitian symmetry to obtain N frequency-domain signals; obtaining the photon count variance detected by a single SPAD in the nth sampling period based on the N frequency-domain signals, and then obtaining the photon count variance detected by the array; modeling the time-domain signal equalization as a DNN-SDN network, using the photon count variance as the input data of the DNN-SDN network; after offline training of the DNN-SDN network, deploying the network in a receiver for signal equalization. This invention can effectively suppress signal distortion caused by SPAD nonlinearity and underwater channel attenuation, thereby significantly reducing the bit error rate, increasing the communication distance of optical signals, and simplifying the complexity of the receiver.

Description

Technical Field

[0001] This invention relates to the field of underwater wireless optical communication (UWOC) and artificial intelligence, and in particular to a neural network equalization method with embedded signal-related noise variance. Background Technology

[0002] With the rapid development of marine science and underwater exploration technology, underwater wireless communication plays an irreplaceable role in autonomous underwater vehicles (AUVs), seabed sensor networks, and environmental monitoring. Compared with currently used underwater communication technologies such as underwater acoustic communication and radio frequency communication, underwater wireless optical communication (UWOC) has advantages such as high bandwidth, low latency, and good environmental security, thus becoming a key technology path for achieving high-speed data backhaul.

[0003] Typically, the receiving performance of a UWOC system is highly dependent on the sensitivity and linearity of the photodetector. In Geiger mode, single-photon avalanche diodes (SPADs) possess detection capabilities on the order of a single photon, and have therefore been widely used in long-distance, low-power UWOC systems in recent years. However, SPADs also exhibit some non-ideal characteristics, such as dead time, dark counting, and afterpulse, as well as limited photon detection efficiency (PDE). These factors cause the output photon count of SPADs to exhibit significant nonlinearity, and their noise statistics are strongly dependent on the incident light power, i.e., they exhibit signal-dependent noise (SDN). Furthermore, the exponential attenuation of the optical signal by water further deteriorates the signal-to-noise ratio of the received signal, especially during long-distance transmission, where signal distortion is severe, and traditional equalization methods based on the additive white Gaussian noise (AWGN) assumption are ineffective.

[0004] To address these challenges, researchers have proposed various compensation strategies. For example, to reduce dead-time effects and improve photon counting capabilities, Acconcia G et al. [1] A receiving scheme using a SPAD array to receive incident photons was proposed; while Huang S et al. [2] This paper proposes a combined scheme integrating photon counting and photon arrival time information, while introducing joint predistortion and noise normalization methods to mitigate the nonlinear distortion of SPADs. Early equalization studies often employed classical digital signal processing methods, such as Volterra nonlinear equalizers or decision feedback equalizers, to suppress signal distortion by modeling the nonlinear response of SPADs. However, these methods typically require prior knowledge of the precise parameters of the SPAD and channel state information, which is often difficult to obtain in practical deployments. Furthermore, the model complexity increases dramatically with data rates, thus limiting the practicality of these methods.

[0005] In recent years, deep learning technology has been introduced into the field of UWOC equalization due to its powerful nonlinear fitting capabilities. For example, radial basis function neural networks (RBFNNs) can directly recover the original symbols from the received signal, which alleviates nonlinear distortion to some extent. [3] However, this method treats the channel and noise as a black box and does not consider the impact of signal-dependent noise (SDN) generated by the SPAD physical mechanism, thus its generalization ability is insufficient under low signal-to-noise ratio or unknown channel conditions.

[0006] To improve the adaptability of models, researchers have recently attempted to introduce external auxiliary information to enhance the generalization performance of equalizers. For example, patent (CN202510254829.2). [4] This paper proposes inserting a fixed-pattern Prior Transmission (PT) sequence at the signal transmitter and comparing the difference between PT and the received sequence PR at the receiver. Then, a Transformer network is used to extract the Channel Embedding (CE), which is subsequently fused with the received data sequence Rx and input into an improved U-Net network for compensation. While this method demonstrates strong generalization ability under unknown channel conditions, it faces significant limitations in UWOC applications. First, the PT sequence itself does not carry any user data, and its transmission consumes valuable time-frequency resources, thus reducing the system's spectral efficiency—a cost that is particularly unacceptable in bandwidth-constrained underwater optical communication. Second, the adopted Transformer and U-Net joint architecture has high computational complexity and a large number of parameters, placing high demands on the hardware resources of the embedded underwater platform.

[0007] In summary, current equalization techniques for SPAD-UWOC systems face three core contradictions: First, traditional equalization methods rely excessively on precise device parameters and channel state information, making them ill-suited for dynamic underwater channels. Second, while purely data-driven deep learning models possess nonlinear fitting capabilities, they neglect the inherent signal-dependent noise (SDN) of SPADs, resulting in insufficient generalization ability in low signal-to-noise ratio scenarios. Third, while introducing prior transmission sequences (PTs) to enhance channel awareness improves adaptability, it comes at the cost of sacrificing spectral efficiency and increasing computational complexity, conflicting with the resource constraints of underwater platforms. Therefore, there is an urgent need to develop a new equalization paradigm that unifies the equalizer's strong generalization capability under unknown channel conditions with its engineering deployability, providing reliable technical support for the practical application of high-speed SPAD-UWOC systems.

[0008] References

[0009] [1]Acconcia G, Giudici A, Smith JA, et al. Toward high-performanceSPAD arrays for space-based atmosphere and ocean profiling LiDARs [J]. Journal of Applied Remote Sensing, 2021,15: 017501.

[0010] [2]Huang S, Patanwala SM, Kosman J, et al. Optimal photon countingreceiver for sub-dead-time signal transmission [J] Journal of Lightwave Technology, 2020, 38: 5225–5235.

[0011] [3]He C, Collins S. Signal demodulation using a radial basis functionneural network (RBFNN) in a silicon photomultiplier-based visible lightcommunication system [J]. IEEE Photonics Journal, 2022,14(4): 7337814.

[0012] [4] Huang Tao, Lu Xingyu. A signal equalization method based on neural network equalizer: CN120110851A[P]. 2025-06-06. Summary of the Invention

[0013] This invention provides a neural network equalization method with embedded signal-dependent noise variance. By using the signal-dependent noise (SDN) variance as the input feature of the neural network, this invention can effectively suppress signal distortion caused by SPAD nonlinearity and underwater channel attenuation without requiring precise channel state information. This significantly reduces the bit error rate, increases the communication distance of optical signals, and simplifies the complexity of the receiver. See the description below for details:

[0014] A neural network equalization method embedding signal-related noise variance, the method comprising:

[0015] The received time-domain signal is subjected to a cyclic prefix removal, a fast Fourier transform, and Hermitian symmetry removal to obtain N frequency-domain signals.

[0016] The variance of the single SPAD photon count detected in the nth sampling period is obtained based on N frequency domain signals. This allows us to obtain the variance of the array photon count during detection. ;

[0017] The time-domain signal equalization is modeled as a DNN-SDN network, and the array photon count variance is used. As input data for DNN-SDN networks;

[0018] After training the DNN-SDN network offline, the network is deployed in a receiver for signal equalization.

[0019] The photon count variance for:

[0020]

[0021] in, The variance of the photon count detected by a single SPAD in the array during the nth sampling period Ts; The modulated signal symbol transmitted by the transmitter at the nth sampling time; The number of photons that a single SPAD is expected to detect within this sampling period. This refers to the dead zone time.

[0022] The array photon count variance for:

[0023]

[0024] in, This represents the number of SPADs in the array.

[0025] The signal equalization is as follows:

[0026] The frequency domain symbols obtained after FFT processing at the receiving end SDN variance with corresponding subcarrier The input symbols are preprocessed and concatenated according to the input format and used as input to the trained network equalizer. The equalized complex constellation symbols are then fed into the standard m-QAM hard decision demodulation module, where each equalized symbol is mapped to its nearest constellation point to recover the original transmitted bit sequence.

[0027] The DNN-SDN network consists of one input layer, four hidden layers, and one output layer.

[0028] The number of neurons in the four hidden layers are 512, 256, 128 and 30 respectively. The input layer contains 48 neurons, namely the real and imaginary parts corresponding to 16 subcarriers and the SDN variance corresponding to the subcarriers, and receives data from the subcarriers and SDN variance information.

[0029] The output layer contains 30 neurons, each containing the real and imaginary parts of 15 subcarriers of information, and uses the sigmoid activation function.

[0030] The beneficial effects of the technical solution provided by this invention are:

[0031] 1. Significantly improves the reliable transmission distance of underwater channels: Compared with traditional equalization methods, this method can support longer communication distances in both clear water and near-shore turbid waters, and maintains stable and reliable signal recovery capabilities while meeting the forward error correction threshold (FEC) of the bit error rate.

[0032] 2. By using the variance of signal-related noise as the network input feature, the bit error rate performance of the system is significantly improved: Traditional deep learning-based receivers ignore the strong correlation between noise variance and signal strength during SPAD detection, which makes noise modeling inaccurate in low optical power or long distance scenarios. This invention embeds the dynamically calculated SDN variance into the DNN training process, enabling it to adaptively perceive the current signal-to-noise state and adjust the equalization strategy in a timely manner.

[0033] 3. Strong robustness: This invention does not rely on precise channel state information and can obtain efficient and accurate equalization results through offline training, thus exhibiting stronger robustness.

[0034] 4. Strong architectural versatility and portability to other optical communication systems: The core idea of ​​this invention is to use physical layer noise characteristics as explicit input features of the neural network. It is not only applicable to SPAD-UWOC systems, but can also be extended to scenarios with signal-dependent noise, such as silicon photomultiplier tube (SiPM) visible light communication and free space optical communication (FSO), and has good technical scalability. Attached Figure Description

[0035] Figure 1 The diagram shows the block diagram of the DCO-OFDM UWOC system using the DNN-SDN scheme.

[0036] Figure 2 This is a diagram of the DNN-SDN network architecture.

[0037] Figure 3 Flowchart for training strategy;

[0038] Figure 4 This diagram illustrates the performance evolution comparison between DNN-SDN and DNN-only solutions.

[0039] Figure 5 This is a performance comparison diagram between DNN-SDN and traditional equalization schemes. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0041] Example 1

[0042] This invention relates to a UWOC (Ultra-WOC) receiving signal processing method that uses a single-photon avalanche diode (SPAD) as a photodetector. This signal processing method uses the variance of signal-related noise (SDN) as an input feature of a neural network to construct a deep equalizer for the output symbols, significantly improving symbol recovery accuracy and reducing the bit error rate of subsequent signal demodulation.

[0043] This invention proposes a deep neural network DNN-SDN (deepneural networks with embedded SDN variance). The core idea is to use the SDN variance that can be calculated at the physical layer as an auxiliary input to guide the neural network to adaptively compensate for signal correlation distortion and provide high-quality complex symbols for subsequent signal demodulation and decoding.

[0044] A neural network equalization method embedding signal-related noise variance is proposed, applicable to SPAD-UWOC systems that employ m-ary orthogonal amplitude frequency division multiplexing (m-QAM-OFDM) modulation. The method includes the following steps:

[0045] Step 101: Frequency domain signal acquisition;

[0046] The receiver removes the cyclic prefix (CP) from the received time-domain signal, performs a Fast Fourier Transform (FFT), and after removing Hermitian symmetry, obtains N frequency-domain subcarrier symbols:

[0047] (1)

[0048] Among them, the effective data is carried only by k=1∼N-1. To transmit subcarriers, It is a complex field.

[0049] Step 102: SDN variance calculation;

[0050] 1) Assuming channel loss is ξ, the average received signal optical power is determined by... Give, and These represent the signal power at the receiving end and the signal power at the transmitting end, respectively. For the SPAD receiver, the rate at which it detects and receives photons is:

[0051] (2)

[0052] in, Indicates the photon detection efficiency (PDE) of SPAD; It is photon energy; Indicates the background photon velocity; , and These represent the dark count rate (DCR), afterpulse probability, and crosstalk probability of the SPAD array, respectively, and the photon rate. In the formula This indicates the background light power received by the SPAD array.

[0053] 2) In this embodiment of the invention, it is assumed that the transmitter and receiver are precisely synchronized in time. For each SPAD in the array receiver, its sampling period T s The average number of detected photons within is:

[0054] (3)

[0055] in, This represents the number of SPADs in the array. Dead time; To detect the average photon arrival rate (in photons / s) received at the nth sampling time; is the time-dependent photon rate function; n is the discrete-time index.

[0056] The corresponding photon count variance is:

[0057] (4)

[0058] in, The variance of the photon count detected by a single SPAD in the array during the nth sampling period; The modulated signal symbol transmitted by the transmitter at the nth sampling time; The average number of photons that a single SPAD is expected to detect during this sampling period.

[0059] 3) The average detectable photon count of the array receiver can be expressed as:

[0060] (5)

[0061] in, This is the number of photons that the SPAD array is expected to detect during this sampling period.

[0062] Since the photon counts detected by each SPAD in the array are independent, the variance of the photon counts detected by the array is:

[0063] (6)

[0064] Substituting equation (3) into equation (6) and rearranging, we get:

[0065] (7)

[0066] Step 103: Network Construction;

[0067] 1) In this embodiment of the invention, the signal equalization in the receiver is modeled as a DNN-SDN network. The input layer is the first layer of the DNN-SDN network, and its input is the training data, i.e. With SDN variance The final layer of the network is the output layer, where the output data is signed data that approximates the expected value. The Adam optimization algorithm is used to optimize the network parameters to achieve efficient convergence.

[0068] 2) The mean squared error is used as the loss function, which is defined as:

[0069] (8)

[0070] In the formula, S n The expected value, i.e., the data to be transmitted. This is the network's estimate (or predicted output) for the nth symbol. The loss function is used to evaluate the difference between the actual output and the expected output of the DNN network.

[0071] Step 104: Signal equalization and demodulation;

[0072] After completing the offline training of the DNN-SDN network, the network is deployed in a receiver for signal equalization. The specific process is as follows:

[0073] First, the frequency domain symbols obtained after FFT processing at the receiving end are... SDN variance with corresponding subcarrier The input format defined in step 103 is preprocessed and concatenated as input to the trained network equalizer; subsequently, through forward propagation calculation, the network outputs the equalized complex constellation symbols. This includes only valid data subcarriers k=1~N-1. Finally, the complex constellation symbols... The signal is fed into a standard m-QAM hard-decision demodulation module, which maps each equalized symbol to its nearest constellation point, thereby recovering the original transmitted bit sequence.

[0074] Example 2

[0075] like Figure 1 As shown, the SPAD-based UWOC system proposed in this embodiment of the invention employs DC-biased optical orthogonal frequency division multiplexing (DCO-OFDM) modulation technology. At the transmitter, a random binary bit sequence is modulated using 4-QAM, satisfying conjugate symmetry. After inverse fast Fourier transform (IFFT) and the addition of a cyclic prefix (CP), the signal is converted to the real number domain and DC biased, finally being converted into an optical signal for transmission. The optical signal is transmitted via an underwater channel based on Beer-Lambert's law and detected by the SPAD array at the receiver. After removing the CP and performing an FFT at the receiver, the resulting frequency domain symbol is directly input into the DNN-SDN network proposed in this embodiment of the invention for equalization processing.

[0076] like Figure 2 As shown, the DNN-SDN network consists of an input layer, four hidden layers (with 512, 256, 128, and 30 neurons respectively), and an output layer. The input layer contains 48 neurons (real and imaginary parts corresponding to 16 subcarriers + SDN variance corresponding to the subcarriers), receiving data from the subcarriers and SDN variance information. The hidden layers use fully connected layers, batch normalization, and the ReLU activation function. The output layer contains 30 neurons (containing the real and imaginary parts corresponding to 15 subcarriers) and uses the sigmoid activation function. Finally, the equalized data is demodulated to recover the original transmitted data.

[0077] To more clearly demonstrate the technical advantages of the embodiments of the present invention, a typical comparative scheme—the DNN-only equalizer—is further described here. This scheme adopts the same network structure as the embodiments of the present invention, but its input only contains the real and imaginary parts (32 dimensions in total) of the received frequency domain symbols, without introducing SDN variance as an auxiliary feature. In other words, the DNN-only model treats channel and detector noise as a black box, relying entirely on data-driven learning of the equalization mapping, and cannot explicitly perceive the instantaneous noise state of each subcarrier. Since the noise variance of the SPAD detector dynamically changes with the received optical power, in long-distance or low signal-to-noise ratio scenarios, the same constellation points may correspond to significantly different noise levels. The DNN-only model, lacking the ability to model this physical characteristic, struggles to adaptively adjust its equalization strategy, leading to decreased symbol recovery accuracy and increased bit error rate. In contrast, the embodiments of the present invention, by using SDN variance as an explicit input feature, enable the network to dynamically correct the response of each subcarrier according to the current channel conditions, thereby achieving a more robust and accurate equalization effect with the same network complexity.

[0078] The training process of the network is as follows Figure 3 The following is stated:

[0079] Step 201: Generate training data;

[0080] This invention utilizes a pre-established underwater channel model and a SPAD photon detection model to simulate and generate a large number of training samples. For each input signal, its corresponding expected output, i.e., the original 4-QAM modulation symbol, is obtained. Simultaneously, the SDN variance under this signal condition is calculated.

[0081] Step 202: Data preprocessing;

[0082] In this embodiment of the invention, the generated training data is normalized to ensure that the numerical range of different features is on the same order of magnitude, thereby improving training efficiency and stability.

[0083] Step 203: Initialize network parameters;

[0084] In this embodiment of the invention, all weights and biases of the DNN-SDN network are randomly initialized.

[0085] Step 204: Forward propagation;

[0086] In this embodiment of the invention, the preprocessed input data (including symbolic data and SDN variance data) is sent into the network, and the output is obtained through the operation of each layer.

[0087] Step 205: Calculate the loss function;

[0088] Step 206: Backpropagation and parameter update.

[0089] The Adam optimization algorithm is employed to update the network's weights and biases based on the calculated loss function. The Adam algorithm adaptively adjusts the learning rate by estimating the first and second moments of the gradient, thus handling complex nonlinear problems more effectively than a fixed learning rate.

[0090] The update forms for weight w and bias b are as follows:

[0091] (9)

[0092] in, The network's first Layer, the p-th neuron of the input, the q-th neuron of the output; The learning rate is k; the current iteration number is k. It is a very small constant used to prevent division by zero errors; For the k-th iteration, the weights The first moment estimate of the gradient; For the k-th iteration, the weights The second moment estimate of the gradient; This is the first-order moment estimate after bias correction; This is the second-order moment estimate after bias correction; For the first The bias value of the layer and the q-th neuron in the k-th iteration; For the first The layer, the weights from the p-th input to the q-th output at the k-th iteration.

[0093] Step 207: Iterative training.

[0094] In this embodiment of the invention, steps 204 to 206 are repeated, using mini-batch data for iterative training until the network converges. After training, the entire pre-trained DNN-SDN network is integrated into the receiver for real-time processing of the received signal.

[0095] Example 3

[0096] Figure 4 This diagram compares the performance of DNN-SDN and DNN-only approaches during training. The horizontal axis represents the number of training epochs, the left vertical axis represents the loss function value, and the right vertical axis represents the bit error rate (BER). The forward error correction threshold is also marked. ).from Figure 4As can be seen, the loss value of DNN-SDN decreases faster, significantly lower than that of DNN-only after about 40 rounds, and stabilizes at a lower plateau (approximately 0.0055) around 100 rounds. In contrast, DNN-only converges more slowly and has a higher plateau value (approximately 0.0068), with a slight increase later, indicating a tendency towards overfitting. Correspondingly, the BER of DNN-SDN decreases rapidly in the early stages of training, dropping below the FEC threshold around 60 rounds and stabilizing thereafter. Around 100; while DNN-only converges more slowly, only approaching the threshold around the 120th round, and finally stabilizing at 100. The performance of the latter is significantly inferior to the former. Especially in the middle of training, the two curves diverge significantly, and the gap widens as training progresses. This fully demonstrates that introducing the variance of signal-related noise (SDN) as an input feature enables the network to adaptively adjust the equalization strategy based on physical priors, effectively improving symbol recovery accuracy and training stability. This result intuitively verifies the significant advantages of the embodiment of the present invention over the method using only DNN in terms of convergence speed, final performance, and robustness.

[0097] Figure 5 This paper presents a comparison of the bit error rate (BER) performance of the DNN-SDN scheme with traditional equalization algorithms, namely Least Mean Square (LMS) and Recursive Least Squares (RLS), under different underwater channel conditions. Figure 5 As can be seen, in clear water environments, DNN-SDN consistently falls below the FEC threshold when SNR ≥ 8 dB, and its BER is approximately 2.0 × 10⁻³ at SNR = 10 dB, significantly outperforming LMS and RLS. In turbid coastal waters, DNN-SDN still meets the FEC requirement at SNR ≥ 10 dB, with a minimum BER of 1.0 × 10⁻³, while LMS and RLS require SNR > 14 dB to achieve equivalent reliability, and their BER deteriorates sharply in the low SNR region (<10 dB). Notably, the DNN-SDN curve is generally flatter with a steeper descent slope, indicating stronger robustness to SNR variations; while traditional algorithms offer limited improvement in the high SNR region, limited by linear model assumptions and unable to compensate for the combined effects of SPAD nonlinearity and signal-related shot noise. This comparison fully demonstrates that by embedding physical layer noise characteristics (SDN variance) into a deep network, the present invention achieves joint modeling of complex underwater channels and detector nonlinearities, thereby significantly improving the system's reliable transmission capability and anti-interference performance without requiring channel state information.

[0098] In summary, this invention achieves equalization of the received signal by constructing a DNN network embedded with SDN variance. This method does not rely on precise channel state information and can achieve high performance through offline training. It effectively overcomes the challenges posed by SPAD nonlinearity, signal-dependent noise, and underwater channel attenuation, significantly improving the bit error rate performance and effective transmission distance of the UWOC system.

[0099] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0100] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A neural network equalization method embedding signal-related noise variance, characterized in that, The method includes: The received time-domain signal is subjected to a cyclic prefix removal, a fast Fourier transform, and Hermitian symmetry removal to obtain N frequency-domain signals. The variance of the single SPAD photon count detected in the nth sampling period is obtained based on N frequency domain signals. This allows us to obtain the variance of the array photon count during detection. ; The time-domain signal equalization is modeled as a DNN-SDN network, and the array photon count variance is used. As input data for DNN-SDN networks; After training the DNN-SDN network offline, the network is deployed in a receiver for signal equalization.

2. The neural network equalization method for embedded signal-correlation noise variance according to claim 1, characterized in that, The photon count variance for: ； in, The variance of the photon count detected by a single SPAD in the array during the nth sampling period Ts; The modulated signal symbol transmitted by the transmitter at the nth sampling time; The number of photons that a single SPAD is expected to detect within this sampling period. This refers to the dead zone time.

3. The neural network equalization method for embedded signal-correlated noise variance according to claim 1, characterized in that, The array photon count variance for: ； in, This represents the number of SPADs in the array.

4. The neural network equalization method for embedded signal-correlation noise variance according to claim 1, characterized in that, The signal equalization is as follows: The frequency domain symbols obtained after FFT processing at the receiving end SDN variance with corresponding subcarrier The input symbols are preprocessed and concatenated according to the input format and used as input to the trained network equalizer. The equalized complex constellation symbols are then fed into the standard m-QAM hard decision demodulation module, where each equalized symbol is mapped to its nearest constellation point to recover the original transmitted bit sequence.

5. The neural network equalization method for embedded signal-correlation noise variance according to claim 1, characterized in that, The DNN-SDN network consists of one input layer, four hidden layers, and one output layer.

6. The neural network equalization method for embedded signal-correlation noise variance according to claim 1, characterized in that, The number of neurons in the four hidden layers are 512, 256, 128 and 30 respectively. The input layer contains 48 neurons, namely the real and imaginary parts corresponding to 16 subcarriers and the SDN variance corresponding to the subcarriers, and receives data from the subcarriers and SDN variance information. The output layer contains 30 neurons, each containing the real and imaginary parts of 15 subcarriers of information, and uses the sigmoid activation function.

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