Complex unmanned aerial vehicle communication signal recovery method based on waveform generative adversarial network

Abstract

The invention relates to the technical field of wireless communication, and discloses a complex unmanned aerial vehicle communication signal recovery method based on a waveform generative adversarial network, and the method comprises the steps: obtaining a damaged waveform of a receiving end and a corresponding channel estimation value; the damaged waveform and the channel estimation value are jointly used as input and are sent into a pre-trained generator of a waveform generative adversarial network adopting a U-Net architecture; the generator outputs a recovery waveform highly similar to the ideal waveform through forward propagation calculation; and finally, the recovered waveform is used for subsequent symbol judgment. The generator is obtained through offline training, a course learning strategy based on the signal to interference plus noise ratio is innovatively adopted in the training process of the generator, and a simple task with the high signal to interference plus noise ratio is gradually transited to a complex task with the low signal to interference plus noise ratio, so that the stability and generalization ability of model training are improved. According to the invention, through an end-to-end waveform generation mode, the signal recovery performance and communication reliability of the unmanned aerial vehicle in a complex communication environment are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a method for recovering complex UAV communication signals based on waveform generation adversarial networks. Background Technology

[0002] With the increasing prevalence of unmanned aerial vehicle (UAV) technology in fields such as military reconnaissance, environmental monitoring, logistics transportation, and emergency communications, stringent challenges have been posed to the reliability and robustness of their mobile communication systems. UAV communication links, especially in complex environments such as cities, typically operate at high speeds, facing problems such as complex and variable signal propagation paths, significant multipath effects, and frequent non-line-of-sight transmissions. This results in severe, time-varying fading of the received signal.

[0003] To cope with stringent size, weight, and power consumption constraints, the transmitter power amplifiers on UAVs often operate in the saturation or near-saturation region to achieve higher energy efficiency. This inevitably introduces significant nonlinear distortion, causing distortion of the signal constellation diagram and out-of-band spread in the spectrum. Therefore, the receiver signal is not only affected by additive white Gaussian noise, but also suffers from combined damage caused by fast time-varying channel fading and power amplifier nonlinearity, sometimes further compounded by non-Gaussian noise components such as co-channel interference. These damages are intertwined and coupled, making signal recovery exceptionally difficult.

[0004] Traditional signal recovery techniques typically employ a separate processing framework, such as performing channel equalization first, followed by nonlinear compensation. However, linear equalization algorithms, designed for linear channels, experience a sharp performance decline in scenarios with significant nonlinear distortion. While model-based nonlinear compensation methods can theoretically compensate for specific nonlinearities, they require extremely high accuracy from both the nonlinear and channel models. In the complex, dynamically changing scenarios of UAVs, establishing accurate mathematical models that can track changes in real time is very difficult, leading to severe model mismatch problems, limited practical compensation effects, and often accompanied by extremely high computational complexity.

[0005] In recent years, with the development of artificial intelligence technology, deep learning has been introduced into the field of communication signal processing. Some methods attempt to replace traditional equalization modules with deep neural networks. However, most existing methods are discriminative models, which typically classify or regress distorted constellation points after signal sampling to determine their original symbol affiliation. While these methods can learn and combat nonlinear impairments to some extent, they are essentially black-box classifiers, lacking not only physical interpretability but also discarding rich information inherent in the complete waveform during processing, thus limiting their upper limit of recovery performance. Furthermore, these methods are often sensitive to the accuracy of channel state information or fail to fully consider the actual impact of channel estimation errors on system performance during training and deployment.

[0006] Therefore, in the complex communication scenarios of UAVs, how to design an efficient signal recovery method that can resist the combined damage such as power amplifier nonlinearity and fast time-varying channel fading in an end-to-end and integrated manner, maintain robustness under imperfect channel information, and also has physical interpretability is a technical problem that urgently needs to be solved in the field of wireless communication. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for recovering complex UAV communication signals based on waveform generation adversarial networks. This method solves the problem that existing communication signal recovery technologies suffer from poor signal recovery performance and insufficient robustness when faced with multiple combined impairments in UAV communication links, such as power amplifier nonlinearity, fast time-varying channel fading, and inaccurate channel estimation.

[0008] To achieve the above objectives, the first aspect of the present invention provides a method for recovering complex UAV communication signals based on waveform generation adversarial networks. This method directly maps and reconstructs the received damaged waveform into a high-quality ideal waveform through end-to-end learning, thereby effectively combating multiple complex damages.

[0009] In one embodiment, the method includes: first, acquiring the damaged digital baseband waveform obtained after processing by the radio frequency front-end at the receiving end, and the corresponding channel estimate obtained using pilot information. Then, the damaged waveform and the channel estimate are fed together as input into a pre-trained waveform generative adversarial network (GAN). The generator performs one forward propagation calculation and outputs a recovered waveform that is highly similar in size and structure to the ideal waveform. Finally, the recovered waveform is sent to a subsequent symbol decision unit, where the original bit information is recovered through sampling and decision-making. This method achieves real-time processing capability for fast time-varying channels through a symbol-by-symbol waveform recovery mechanism.

[0010] To enable the generator to recover ideal waveforms from complex damage, offline model training is required. In one embodiment, this offline training phase includes the following core steps:

[0011] Building the training dataset: First, generate a large number of ideal baseband modulation waveforms. Subsequently, by simulating impairments in a real communication link using a precise mathematical model, the ideal waveform is transformed into a paired impaired waveform. The simulated damage specifically includes:

[0012] Nonlinear distortion of power amplifiers: Nonlinear transfer characteristics of power amplifiers using a memoryless polynomial model. Modeling:

[0013] ;

[0014] Nakagami-m fading channel impairment: The Nakagami-m distribution, which can flexibly characterize multipath and line-of-sight components, is used to assess channel amplitude. The probability density function is as follows:

[0015] ;

[0016] Channel estimation error: To adapt the model to real, non-ideal channel conditions, channel estimates with errors are introduced into the training dataset. .

[0017] Constructing the network and conducting adversarial training: The waveform generation adversarial network consists of a generator. and discriminator In one embodiment, the generator The U-Net architecture is adopted to effectively extract deep features and preserve waveform details; the discriminator The PatchGAN architecture is employed to improve the local quality of the generated waveforms. The training process utilizes an adversarial mechanism and introduces a course learning strategy based on the signal-to-interference plus-noise ratio. This strategy starts with high SINR training samples, allowing the model to first learn to resist deterministic distortion, and then gradually transitions to low SINR samples to learn signal recovery in environments with strong noise and interference. During training, the generator... The optimization objective is to minimize the total loss function. This function is composed of adversarial loss. and hybrid reconstruction loss Weighted composition:

[0018] ;

[0019] in, The aim is to enable the generator to produce realistic waveforms sufficient to deceive the discriminator, while By combining L1 and L2 losses, it is ensured that the generated waveform accurately approximates the ideal waveform at the sampling point level.

[0020] By employing the above method, this invention transforms the signal recovery problem into a conditional waveform generation task. Because the model learns channel estimates as conditional inputs rather than fixed parameters, it possesses inherent robustness to channel estimation errors. Furthermore, the generative framework provides interpretable physical meaning for signal recovery through an intuitive waveform refinement process.

[0021] A second aspect of the present invention provides a complex unmanned aerial vehicle (UAV) communication signal recovery system designed to perform the aforementioned method.

[0022] In one embodiment, the system is deployed at the receiving end and mainly includes:

[0023] Signal reception and channel estimation module: Its function is to receive radio frequency signals transmitted through complex channels, and after down-conversion, filtering and analog-to-digital conversion, output the damaged waveform of digital baseband, and output the corresponding channel estimation value using pilot information.

[0024] Signal recovery module: As the core of the system, it contains a generator of a waveform generative adversarial network pre-trained according to the method described in the first aspect of the present invention. This module receives the damaged waveform and channel estimate from the preceding module, and outputs a high-quality recovered waveform through forward propagation calculation by the generator.

[0025] Symbol decision module: This module receives the recovered waveform from the signal recovery module and demodulates it into the original binary bit sequence through sampling and hard decision, thus completing the entire communication reception process.

[0026] The modules work together to achieve efficient and reliable recovery from damaged radio frequency signals to the final bit stream.

[0027] This invention provides a method for recovering complex UAV communication signals based on waveform generative adversarial networks. It has the following beneficial effects:

[0028] 1. This invention employs a waveform generative adversarial network to directly learn the end-to-end mapping from the damaged waveform to the ideal waveform. This generative recovery paradigm can comprehensively combat various complex damages such as power amplifier nonlinearity and multipath fading, achieving high-fidelity reconstruction of the signal. Compared with traditional methods that rely on specific channel or noise models, this invention can more effectively purify the signal, thereby significantly improving communication reliability under dynamic and complex channels.

[0029] 2. This invention uses channel estimation as a conditional input to the generator, rather than fixed, perfect system parameters. Through a data-driven approach, the network can learn the intrinsic correlation between channel information and waveform impairments and adapt to errors in channel estimation. Therefore, even under conditions of imperfect or rapidly changing channel state information, this method can still maintain stable signal recovery performance and exhibit strong robustness, making it particularly suitable for high-speed mobile communication scenarios such as UAVs.

[0030] 3. By adopting a symbol-by-symbol waveform processing method, this invention naturally possesses the potential for low latency and real-time processing, effectively addressing fast time-varying channels. Meanwhile, its core generator module design allows it to function as a pluggable front-end signal processing unit, seamlessly replacing or cooperating with traditional equalization, filtering, and other modules. This modular design greatly enhances the system's flexibility and scalability, facilitating integration and deployment within existing communication systems. Attached Figure Description

[0031] Figure 1 This is a flowchart of the method of the present invention;

[0032] Figure 2 This is a system architecture diagram of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example:

[0035] Please see the appendix Figure 1 This invention provides a method for recovering complex UAV communication signals based on waveform generative adversarial networks, comprising the following steps:

[0036] S1. Obtain the damaged waveform received by the receiver and the corresponding channel estimate.

[0037] In this embodiment, the specific implementation method for step S1, namely, obtaining the damaged waveform and the corresponding channel estimation value within the current symbol period, is as follows.

[0038] This step is the data preparation stage for subsequent signal recovery procedures. Its core function is to accurately capture and characterize the physical signal that carries the original information and has been distorted after transmission through complex channels, while providing crucial bypass information about the channel state for the recovery process. This step is performed by the signal reception and channel estimation module deployed at the receiver front end.

[0039] First, the antenna deployed on the UAV platform is responsible for receiving electromagnetic wave signals from the air. During propagation, this signal has already suffered combined damage from various physical effects. The radio frequency front-end unit of the signal reception and channel estimation module processes this high-frequency signal, preferably including a series of standard operations such as low-noise amplification, filtering, down-conversion, and analog-to-digital conversion, ultimately outputting a digital baseband signal stream.

[0040] To facilitate subsequent processing by the generative model, the continuous digital baseband signal stream is segmented into waveform segments, each segment representing a symbol. Specifically, the damaged waveform obtained in this invention is denoted as... , is corresponding to the first A discrete-time complex sequence of transmitted symbols containing multiple sampling points. The damaged waveform... The mathematical model can accurately characterize the complex damage it contains, which at any time... instantaneous value It can be represented as:

[0041] ;

[0042] The right-hand side of the equation details the sources of the damage:

[0043] This represents the original ideal baseband modulated signal generated by the transmitter and is the ultimate goal of signal recovery.

[0044] This represents the nonlinear transfer function of the transmitter's power amplifier. Due to the strict limitations on power consumption and cost in UAV communication systems, their power amplifiers often operate in the nonlinear region. To characterize the resulting signal distortion, in this embodiment, the function is modeled as a memoryless polynomial, specifically in the form:

[0045] ;

[0046] This model can effectively characterize nonlinear impairments such as amplitude compression, phase rotation, and out-of-band spectrum regeneration caused by power amplifier saturation effects. These are key technical challenges that signal recovery in nonlinear channels must address.

[0047] This represents the instantaneous channel fading coefficient of the UAV communication link. In complex environments such as cities, signal propagation is affected by reflection, diffraction, and scattering from buildings, leading to multipath effects and deep fading. To accurately model this complex fading channel, this embodiment preferably uses the Nakagami-m fading model. The channel amplitude of this model... The probability density function is expressed as:

[0048] ;

[0049] Among them, parameters It can flexibly characterize the severity of fading, thus covering a variety of channel scenarios, from severe Rayleigh fading to Rice fading with strong line-of-sight components.

[0050] and These represent the sum of co-channel interference signals and additive white Gaussian noise present in the link, respectively.

[0051] Meanwhile, to assist in the subsequent signal recovery process, the signal receiving and channel estimation module also needs to provide information about the current channel state. This is achieved by processing the preset pilot symbols in the transmitted signal frame. This module extracts and calculates the received pilot signals to obtain information about the current channel state. The estimated value of the channel coefficients for each symbol is denoted as . .

[0052] In practical communication systems, channel estimation inevitably contains errors due to noise, interference, and the time-varying nature of the channel. This invention fully considers this reality and does not assume that the channel estimation is perfect. Channel estimation value. Modeled as true channel values With one error term The sum of:

[0053] ;

[0054] The quality of channel estimation can be quantified by the normalized mean square error, which is a major reason for the performance degradation of traditional equalization techniques.

[0055] Finally, when step S1 is completed, the data pair is output. Among them, the damaged waveform The main object that needs to be recovered is the channel estimate, which contains errors. This serves as conditional information or guiding features. Both of these will be used as input to the waveform generation adversarial network generator in the next step, enabling the network to perform more targeted and efficient recovery operations on the damaged waveform, given an understanding of the general state of the current channel.

[0056] S2. The damaged waveform and the channel estimate are used as inputs and fed into the generator of the pre-trained waveform generative adversarial network for forward propagation calculation.

[0057] In this embodiment, step S2, which involves inputting the damaged waveform and the channel estimate together into the generator of a pre-trained waveform generation adversarial network and outputting the recovered waveform through forward propagation, is the core technical step in achieving signal recovery in this invention.

[0058] This step follows the data obtained in step S1. It utilizes a deep neural network model that has been trained offline, specifically the generator in a waveform generative adversarial network. For damaged waveforms Perform end-to-end cleanup and reconstruction. This process is completed in the receiver's signal recovery module, which essentially transforms the complex signal recovery problem into a conditional image-to-image conversion task.

[0059] Specifically, generator It is a carefully designed deep convolutional neural network. In this embodiment, the U-Net architecture is preferred. A key feature of this architecture is its symmetrical encoder-decoder structure. The encoder part extracts the damaged waveform step-by-step through downsampling and convolution operations. The mid-to-deep, multi-scale abstract features aim to understand and encode complex impairment information such as nonlinear distortion and fading modes. The decoder then uses upsampling and convolution operations to progressively decode and reconstruct these abstract features into the dimensions of the target waveform.

[0060] The key innovation of the U-Net architecture lies in the introduction of skip connections between the encoder and decoder. These connections directly pass feature maps extracted by the encoder at different levels and concatenate them to the input of the corresponding levels in the decoder. This design allows the network to directly utilize shallow features containing high-resolution details from the encoder during the decoding and reconstruction process. Therefore, the generator... It can effectively learn and reverse deep and complex damage while accurately preserving and recovering the fine structural and phase information in the waveform that is crucial for sign determination.

[0061] During the execution of this step, the damaged waveform acquired in the previous step... With imperfect channel estimates Collectively used as generators The input. The channel estimate here. It plays the role of conditional information, providing the generator with bypass information about the current channel state and guiding the generator to adjust its recovery strategy according to specific channel conditions. In other words, the mapping relationship learned by the generator is not a fixed function, but an adaptive recovery function conditional on the channel state.

[0062] This process can be mathematically represented as a single forward propagation calculation:

[0063] ;

[0064] in, This represents a generator model with fixed network parameters. The computation process is one-time and non-iterative, involving a series of pre-learned linear transformations and non-linear activations of the input data across different network layers, ultimately yielding a reconstructed waveform at the output layer that perfectly matches the ideal waveform size and structure. .

[0065] generator Its powerful recovery capabilities stem from the adversarial learning paradigm it follows during offline training. During training, the generator... The goal is not only to minimize its output from the ideal waveform The pixel-level differences between them must also ensure that the generated waveform can deceive the adversary discriminator, which uses a PatchGAN architecture, in terms of structure and statistical properties. Its overall optimization objective can be expressed as minimizing the total loss. :

[0066] ;

[0067] By fully optimizing this minimax game problem under the guidance of a curriculum-based learning strategy, the final generator is obtained. It can implicitly learn the inverse function of complex channel impairments.

[0068] Therefore, the output of step S2, i.e., the recovered waveform, is... The recovered waveform is a high-fidelity estimate of the ideal waveform, purified end-to-end by a deep neural network. Nonlinear distortion, multipath fading, noise, and interference in this waveform have been significantly suppressed. This recovered waveform will serve as the direct basis for symbol decision in subsequent step S3, providing a high-quality signal foundation for ultimately achieving reliable communication.

[0069] S3. The generator outputs the recovered waveform, which is then used for subsequent symbol determination.

[0070] In this embodiment, step S3, which involves outputting the recovered waveform to subsequent units for symbol determination to recover the original information, constitutes the final step of the signal recovery method of the present invention.

[0071] This step follows the output of step S2, and its core task is to recover the high-quality waveform generated by the signal recovery module. The signal is transformed from a continuous analog domain representation into a discrete sequence of digital bits carrying the original information. This process is performed in the symbol decision module of the receiver, and its reliability and accuracy directly benefit from the deep cleansing and high-fidelity reconstruction of the signal performed in the preceding steps.

[0072] Specifically, the symbol decision module receives data from the generator. Output recovered waveform Because the waveform has undergone end-to-end nonlinear correction and channel equalization, its shape closely approximates the ideal transmit waveform under distortion-free conditions. Therefore, the subsequent decision-making process can be completed using standard digital demodulation techniques that are simple in structure and computationally efficient.

[0073] This step can be further broken down into the following two key operations:

[0074] First, there's the sampling operation. Then, the waveform is recovered. It is a continuous sequence in time. To extract discrete values ​​representing individual symbols, it is necessary to sample it at a specific time within each symbol period. This specific time is called the optimal sampling time, at which sampling maximizes symbol energy and minimizes the impact of inter-symbol interference. The timing synchronization unit in the receiver is responsible for determining this optimal sampling time. Since the waveform quality input to the symbol decision module has been significantly improved, the accuracy and robustness of timing synchronization have also been enhanced accordingly. The recovered waveform is then processed at the optimal sampling time. By sampling, a complex value can be obtained, which is the value for the current i-th... The estimated constellation points of each symbol are denoted as . .

[0075] Secondly, there is the decision operation. This involves obtaining discrete constellation point estimates. Next, it needs to be determined as an ideal constellation point in the constellation diagram specified by the modulation method. This process is also known as hard-decision demodulation or minimum-distance decision. Specifically, for a given... Metamodulation constellation diagram, which exists from A set of ideal constellation points The decision rule is to find the values ​​in the set that correspond to the estimated constellation points. The ideal constellation point with the smallest Euclidean distance. The judgment process can be represented by the following formula:

[0076] ;

[0077] in, It represents the Euclidean norm.

[0078] Because the recovered waveform output by the preceding step S2 has high fidelity, the constellation point estimate obtained after sampling... They will closely cluster at their respective ideal constellation points. The surrounding area forms a clear and separable cluster of constellations. This allows the aforementioned decision criterion based on minimum distance to operate with extremely high accuracy, effectively avoiding decision ambiguity and errors caused by noise, residual interference, or nonlinear distortion.

[0079] After determining the ideal constellation point for judgment Then, according to the bit-to-symbol mapping rules preset by the modulation method, the constellation point can be uniquely converted back to the original binary bit sequence it represents.

[0080] Through the above sampling and decision operations, step S3 completes the conversion from the high-quality recovered waveform to the final information bits, marking the end of the entire communication reception and signal recovery process. The architectural advantage of this invention lies in its centralized solution of the complex, nonlinear signal recovery task in the preceding step S2 using a generative model. This allows step S3 to employ a standard, low-complexity decision unit, ensuring not only overall recovery performance but also demonstrating the system design flexibility and engineering practicality of this invention as a pluggable front-end module.

[0081] Please see the appendix Figure 2 A complex unmanned aerial vehicle (UAV) communication signal recovery system, comprising:

[0082] The signal receiving and channel estimation module is used to receive and process signals from the antenna to output the damaged waveform and the corresponding channel estimation value.

[0083] The signal recovery module has a pre-trained waveform generative adversarial network generator inside. This signal recovery module is connected to the signal receiving and channel estimation module to receive the damaged waveform and channel estimation value, and output the recovered waveform.

[0084] The symbol decision module, connected to the signal recovery module, is used to receive the recovered waveform and make a decision on it to recover the original bit stream.

[0085] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for recovering complex UAV communication signals based on a waveform generative adversarial network, comprising the following steps: S1. Obtaining a damaged waveform received by a receiving end and a corresponding channel estimation value; S2. Inputting the damaged waveform and the channel estimation value together into a generator of a pre-trained waveform generative adversarial network for forward propagation calculation; S3. Outputting a recovered waveform from the generator, and using the recovered waveform for subsequent symbol decision.

2. The method of claim 1, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, and The waveform generative adversarial network is obtained through an offline model training stage, which includes constructing a training data set containing ideal waveforms, damaged waveforms, and channel estimation values, and using the data set to adversarially train the waveform generative adversarial network.

3. The method of claim 2, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, characterized in that, In the step of constructing the training data set, the process of generating the damaged waveform includes simulating at least one of the following damages: Nonlinear distortion of a power amplifier at a transmitting end; Channel damage of a Nakagami-m fading channel; Channel estimation process containing channel estimation error; Gaussian white noise at a receiver end.

4. The method of claim 2, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method. The generator in the waveform generative adversarial network adopts a U-Net architecture, and the discriminator in the waveform generative adversarial network adopts a PatchGAN architecture.

5. The method of claim 2, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, and The adversarial training adopts a strategy based on curriculum learning, which includes: Setting training courses from high signal-to-interference-and-noise ratio (SINR) to low SINR; In the early stage of training, using training samples with higher SINR to train the waveform generative adversarial network; As the training progresses, gradually using training samples with lower SINR until the training of all course stages is completed.

6. The method of claim 5, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, and In the adversarial training, the update of the generator is based on a total loss function obtained by weighted summation of an adversarial loss and a hybrid reconstruction loss; wherein the adversarial loss is used to evaluate the authenticity of the generated waveform, and the hybrid reconstruction loss is used to evaluate the difference between the generated waveform and the ideal waveform.

7. The method of claim 1, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method. The obtained damaged waveform is a waveform segment processed symbol by symbol, and the generator outputs a corresponding recovered waveform segment for the input damaged waveform segment.

8. The method of claim 1, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, and The damaged waveform is a composite damage waveform containing nonlinear distortion of a power amplifier at a transmitting end, Nakagami-m fading channel damage, channel estimation error, and Gaussian white noise.

9. The method of claim 1, wherein the waveform generation adversarial network is based on a complex drone communication signal recovery method, and The step of using the recovered waveform for subsequent symbol decision includes: Sampling the recovered waveform at the optimal sampling time to obtain discrete constellation point estimates; Mapping the constellation point estimates to the nearest ideal constellation points to recover the original binary bit sequence.

10. A complex UAV communication signal recovery system, the complex UAV communication signal recovery method based on a waveform generation GAN according to any one of claims 1-9, characterized in that, It includes: A signal receiving and channel estimation module for receiving signals from an antenna and processing to output a damaged waveform and a corresponding channel estimation value; A signal recovery module having a pre-trained generator of a waveform generative adversarial network deployed therein, which is connected with the signal receiving and channel estimation module, for receiving the damaged waveform and the channel estimation value, and outputting a recovered waveform; A symbol decision module connected with the signal recovery module, for receiving the recovered waveform and making a decision thereon to recover an original bit stream.

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