Channel equalization method for terahertz communication system

Abstract

Embodiments of the present disclosure provide a channel equalization method of a terahertz communication system, which can be applied to the technical field of terahertz communication. The method comprises: receiving a terahertz echo signal; performing blind equalization processing on the amplitude of the terahertz echo signal based on a constant modulus equalization algorithm to obtain a constant modulus output signal; performing adaptive equalization processing on the real part and the imaginary part of the constant modulus output signal based on a least mean square algorithm to obtain a processed real part and a processed imaginary part; obtaining a mean square output signal according to the processed real part and the processed imaginary part; and determining the mean square output signal as a target equalization signal when the error vector magnitude between the mean square output signal and a predetermined ideal signal satisfies a first error condition.

Description

Technical Field

[0001] This disclosure relates to the field of terahertz communication technology, and more specifically, to a channel equalization method for a terahertz communication system. Background Technology

[0002] With the rapid development of modern communication technology, the terahertz band (0.1-10THz), as the transition region between microwaves and infrared light waves in the electromagnetic spectrum, has significant advantages such as ultra-wide available bandwidth and extremely high transmission rate. However, due to the severe path loss, multipath effect, and noise interference caused by high frequency, the received signal is often affected by both amplitude attenuation and phase distortion, leading to constellation spread and increased bit error rate, thus affecting communication performance.

[0003] However, in traditional wireless communication systems, commonly used channel equalization algorithms usually only perform well in narrowband or intermediate frequency communication environments. But in the ultra-wideband, high-speed transmission conditions of terahertz communication, a single algorithm cannot simultaneously take into account both convergence speed and equalization accuracy. When the frequency offset is large, the convergence is poor and cannot meet the requirements of real-time high-speed communication.

[0004] Public content

[0005] In view of this, this disclosure provides a channel equalization method for terahertz communication systems.

[0006] One aspect of this disclosure provides a channel equalization method for a terahertz communication system, wherein the method includes: receiving a terahertz echo signal; performing blind equalization processing on the amplitude of the terahertz echo signal based on a constant-mode equalization algorithm to obtain a constant-mode output signal; performing adaptive equalization processing on the real part and imaginary part of the constant-mode output signal respectively based on a least mean square algorithm to obtain a processed real part and a processed imaginary part; obtaining the mean square output signal based on the processed real part and the processed imaginary part; and determining the mean square output signal as a target equalization signal when the error vector amplitude between the mean square output signal and a predetermined ideal signal satisfies a first error condition.

[0007] According to an embodiment of this disclosure, the constant mode equalization algorithm is trained as follows: when the (m-1)th constant mode error does not satisfy the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight, where m > 1; using the initial constant mode equalization algorithm, the sample echo signal is processed based on the m-th first weight to obtain the m-th training constant mode signal; based on the target signal amplitude and the amplitude of the m-th training constant mode signal, the m-th constant mode error is determined, where the target signal amplitude is determined based on the statistical value of the amplitude of the sample echo signal; when the m-th constant mode error satisfies the second error condition, the m-th first weight is determined as the weight of the initial constant mode equalization algorithm to obtain the constant mode equalization algorithm.

[0008] According to an embodiment of this disclosure, when the (m-1)th constant modulus error does not meet the second error condition, updating the (m-1)th first weight to obtain the m-th first weight includes: when the (m-1)th first optimization step size of the initial constant modulus equalization algorithm does not meet the first convergence condition, optimizing the (m-1)th first order and the (m-1)th first optimization step size of the initial constant modulus equalization algorithm using a gradient optimization algorithm to obtain the m-th first optimization step size; when the m-th first optimization step size meets the first convergence condition, updating the (m-1)th weight according to the m-th first optimization step size to obtain the m-th first weight.

[0009] According to an embodiment of this disclosure, the optimization of the (m-1)th first order and the (m-1)th first optimization step size of the initial constant modulus equalization algorithm using a gradient optimization algorithm to obtain the m-th first optimization step size includes: determining a first gradient based on the (m-1)th first order and the (m-1)th constant modulus error; determining a second gradient based on the (m-1)th first optimization step size and the (m-1)th constant modulus error; determining the search direction of the gradient optimization algorithm based on the first gradient and the second gradient; adjusting the (m-1)th first order and the (m-1)th first optimization step size based on the search direction of the gradient optimization algorithm to obtain an adjusted first order and an adjusted first optimization step size; and determining the adjusted first order as the m-th first order and the adjusted first optimization step size as the m-th first optimization step size, provided that the adjusted first order and the adjusted first optimization step size satisfy their respective constraint range conditions.

[0010] According to an embodiment of this disclosure, the minimum mean square algorithm is trained as follows: when the (n-1)th mean square error does not satisfy the third error condition, the (n-1)th second weight is updated to obtain the nth second weight, where n > 1; using the initial minimum mean square algorithm, the sample constant modulus signal is processed based on the nth second weight to obtain the nth training mean square signal; based on the nth training mean square signal and a predetermined modulation signal, the nth error signal is determined; based on the statistical value of the nth error signal, the nth mean square error is determined; when the nth mean square error satisfies the third error condition, the nth second weight is determined as the weight of the initial minimum mean square algorithm to obtain the minimum mean square algorithm.

[0011] According to an embodiment of this disclosure, when the (n-1)th mean square error does not satisfy the third error condition, updating the (n-1)th second weight to obtain the nth second weight includes: updating the (n-1)th second weight based on the (n-1)th error signal, the sample constant modulus signal, and the second optimization step size of the initial minimum mean square algorithm to obtain the nth second weight.

[0012] According to embodiments of this disclosure, updating the (n-1)th second weight based on the (n-1)th error signal, the sample constant modulus signal, and the second optimization step size of the initial minimum mean square algorithm to obtain the nth second weight includes: optimizing the (n-1)th second order and the (n-1)th second optimization step size of the initial minimum mean square algorithm using a particle swarm optimization algorithm to obtain the nth second order and the nth second optimization step size; and updating the (n-1)th second weight according to the nth second optimization step size when the nth second order and the nth second optimization step size satisfy a second convergence condition to obtain the nth second weight.

[0013] According to embodiments of this disclosure, the above-described optimization of the (n-1)th second order and (n-1)th second optimization step size of the initial minimum mean square algorithm using a particle swarm optimization algorithm to obtain the nth second order and nth second optimization step size includes: randomly generating the (n-1)th position and (n-1)th velocity of each particle in the particle swarm based on the (n-1)th second order and (n-1)th second optimization step size; calculating the (n-1)th mean square error of each particle based on the (n-1)th position and (n-1)th velocity of each particle; updating the (n-1)th velocity based on the inertia weight, learning factor, historical best position of the particle in the particle swarm, global best position of the particle in the particle swarm, and the (n-1)th position to obtain the nth velocity; updating the (n-1)th position based on the nth velocity to obtain the nth position; and determining the nth second order and the nth second optimization step size based on the nth position.

[0014] According to embodiments of this disclosure, the inertial weights of each particle are obtained based on the following operations: determining the gradient magnitude of the m-th constant mode error based on the constant mode error of the m-th training constant mode signal; calculating the inertial weights of each particle based on the gradient magnitude of the m-th constant mode error and an adjustment factor, wherein the adjustment factor is determined based on the channel coherence time and the system bandwidth.

[0015] According to an embodiment of this disclosure, when the (m-1)th constant modulus error does not satisfy the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight. The update further includes: when the m-th first optimization step size satisfies the first convergence condition, updating the (m-1)th weight based on the m-th first optimization step size, the gradient of the m-th constant modulus error, the gradient of the m-th mean square error, and a modulation factor to obtain the m-th first weight. The gradient of the m-th mean square error is determined based on the m-th training mean square signal, and the modulation factor is determined based on the modulation order of the quadrature amplitude modulation.

[0016] According to the channel equalization method of the terahertz communication system provided in the embodiments of this disclosure, the received terahertz echo signal is subjected to dual equalization processing by combining the constant mode equalization algorithm and the least mean square algorithm. First, the constant mode equalization algorithm is used to quickly complete the coarse equalization processing to solve the amplitude distortion problem. Then, the least mean square algorithm is used to perform fine equalization processing on the signal after constant mode equalization to eliminate residual phase noise, thereby improving the equalization accuracy and signal quality and significantly reducing the error vector amplitude. Attached Figure Description

[0017] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0018] Figure 1 A flowchart illustrating a channel equalization method for a terahertz communication system according to an embodiment of the present disclosure is shown schematically.

[0019] Figure 2 The diagram illustrates the demodulation results of a 1024QAM signal transmitted under a measured 20G bandwidth, under different equalization methods: no equalization, minimum mean square algorithm, and a combination of constant modulus equalization algorithm and minimum mean square algorithm.

[0020] Figure 3 The diagram illustrates the constellation diagrams after demodulation of a 1024QAM signal transmitted under a measured 20G bandwidth using the least mean square algorithm and the combined equalization method of constant modulus equalization algorithm and least mean square algorithm.

[0021] Figure 4 A block diagram of a channel equalization apparatus for a terahertz communication system according to an embodiment of the present disclosure is schematically shown; and

[0022] Figure 5 A block diagram of an electronic device for a channel equalization method for a terahertz communication system according to an embodiment of the present disclosure is shown schematically. Detailed Implementation

[0023] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0024] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0025] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0026] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0027] With the rapid development of modern communication technology, the terahertz band (0.1-10THz), as the transition region between microwaves and infrared light waves in the electromagnetic spectrum, has significant advantages such as ultra-wide available bandwidth (tens of GHz) and extremely high transmission rate (up to Tbps level), and is gradually becoming one of the core directions of the next generation of wireless communication technology.

[0028] However, the high-frequency characteristics of terahertz communication systems bring significant challenges to channel equalization. Due to severe path loss, multipath effects, and noise interference caused by high frequencies, the received signal is often affected by both amplitude attenuation and phase distortion, leading to constellation spread, increased bit error rate, and thus affecting communication performance.

[0029] The core objective of channel equalization is to eliminate signal distortion introduced by the transmission channel and restore the original signal. In traditional wireless communication systems, commonly used channel equalization algorithms perform well in narrowband or intermediate frequency communication environments. However, under the ultra-wideband, high-speed transmission conditions of terahertz communication, a single algorithm cannot simultaneously achieve both convergence speed and equalization accuracy. When the frequency offset is large, the convergence is poor, and it cannot meet the requirements of real-time high-speed communication.

[0030] To address the aforementioned issues, embodiments of this disclosure provide a channel equalization method for a terahertz communication system. By combining a constant-mode equalization algorithm and a least mean square algorithm to perform dual equalization processing on the received terahertz echo signal, the constant-mode equalization algorithm is first used to quickly complete coarse equalization processing to solve the amplitude distortion problem. Then, the least mean square algorithm is used to perform fine equalization processing on the signal after constant-mode equalization to eliminate residual phase noise, thereby improving equalization accuracy and signal quality and significantly reducing the error vector amplitude.

[0031] Specifically, embodiments of this disclosure provide a channel equalization method for a terahertz communication system, comprising: receiving a terahertz echo signal; performing blind equalization processing on the amplitude of the terahertz echo signal based on a constant-mode equalization algorithm to obtain a constant-mode output signal; performing adaptive equalization processing on the real and imaginary parts of the constant-mode output signal based on a least-mean-square algorithm to obtain processed real and imaginary parts of the signal; obtaining a mean-square output signal based on the processed real and imaginary parts of the signal; and determining the mean-square output signal as the target equalization signal when the error vector amplitude between the mean-square output signal and a predetermined ideal signal satisfies a first error condition.

[0032] It should be noted that the channel equalization method for terahertz communication systems determined in this disclosure can be used in the field of terahertz communication technology. The channel equalization method for terahertz communication systems determined in this disclosure can also be used in any field other than this technical field, such as high-frequency signal processing technology. The application field of the channel equalization method for terahertz communication systems determined in this disclosure is not limited.

[0033] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0034] Figure 1 A flowchart illustrating a channel equalization method for a terahertz communication system according to an embodiment of the present disclosure is shown.

[0035] like Figure 1 As shown, the method includes operations S110~S150.

[0036] When operating S110, receive terahertz echo signals.

[0037] In operation of S120, based on the constant mode equalization algorithm, the amplitude of the terahertz echo signal is blindly equalized to obtain the constant mode output signal.

[0038] In operation S130, based on the least mean square algorithm, adaptive equalization processing is performed on the real part and the imaginary part of the constant modulus output signal to obtain the processed real part and the processed imaginary part of the signal.

[0039] In operation S140, a mean square output signal is obtained based on the real part and the imaginary part of the processed signal.

[0040] In operation S150, if the magnitude of the error vector between the mean square output signal and the predetermined ideal signal satisfies the first error condition, the mean square output signal is determined as the target equalization signal.

[0041] According to embodiments of this disclosure, in response to receiving a terahertz echo signal, since the terahertz echo signal exhibits significant amplitude and phase deviations, it can first undergo normalization processing to eliminate the impact of channel gain instability on subsequent processing, ensuring the signal amplitude has consistency and stability during subsequent equalization processing. The received terahertz echo signal is a complex signal. Specifically, the expression for the normalization process of the received terahertz echo signal is:

[0042] (1)

[0043] In the formula, This represents the normalized signal of the terahertz echo signal. This indicates the received terahertz echo signal; The root mean square function of a terahertz echo signal is used to represent the energy distribution of the terahertz echo signal.

[0044] (2)

[0045] In the formula, The target signal amplitude is represented by the normalized signal. The median of the square of the amplitude.

[0046] According to embodiments of this disclosure, the Constant Modulus Equalization (CMA) algorithm is a blind equalization method suitable for channel equalization of non-constant envelope modulation signals (such as QAM and PSK). By adjusting the equalizer weights, the amplitude of the constant modulus output signal is made close to the amplitude of the target signal, thereby reducing the constant modulus error of the signal. This is to eliminate amplitude distortion introduced by the channel.

[0047] Specifically, the normalized terahertz echo signal is blindly equalized using the constant modulus equalization (CMA) algorithm, so that the amplitude of the constant modulus output signal is close to the amplitude of the target signal. The expression for the constant modulus error is as follows:

[0048] (3)

[0049] In the formula, Indicates constant modulus error. Indicates the expected value. This indicates a constant modulus output signal.

[0050] According to embodiments of this disclosure, during the optimization process of the constant modulus equalization (CMA) algorithm, a gradient optimization algorithm can be used to search for the optimal parameter combination in order to reduce the constant modulus error after equalization.

[0051] According to embodiments of this disclosure, the Least Mean Squares (LMS) algorithm is an adaptive filtering algorithm that minimizes the mean square error between the mean square output signal and the ideal reference signal by iteratively adjusting the equalizer weights. This enables efficient equalization of signal distortion and noise.

[0052] Specifically, the Least Mean Square (LMS) algorithm is used to further equalize the constant modulus output signal, making the mean square output signal as close as possible to the ideal reference signal. The expression for the mean square error is as follows:

[0053] (4)

[0054] In the formula, Indicates mean square error. Indicates the expected value. Indicates the mean square output signal. This represents an ideal reference signal.

[0055] According to embodiments of this disclosure, the real and imaginary parts of the constant modulus output signal can be equalized separately based on the least mean square (LMS) algorithm, and the equalized real and imaginary parts can be spliced ​​together to obtain a complex form mean square output signal, thereby effectively compensating for the imbalance of the terahertz echo signal.

[0056] According to embodiments of this disclosure, in the optimization process of the Least Mean Square (LMS) algorithm, the Particle Swarm Optimization (PSO) algorithm can be used to search for the optimal parameter combination by dynamically adjusting the equalizer parameters (such as filter length 𝐾 and step size parameter 𝜇) in order to reduce the mean square error after equalization.

[0057] According to embodiments of this disclosure, the signal quality of the equalized mean square output signal can be evaluated using the error vector magnitude (EVM). The error vector magnitude (EVM) is a core indicator for measuring the signal quality of a digital communication system. It reflects the Euclidean distance between the signal constellation point and the ideal constellation point, and also reflects the degree of amplitude and phase deviation between the equalized signal and the ideal signal. In embodiments of this disclosure, the first error condition can represent any error vector magnitude (EVM) value. The lower the error vector magnitude (EVM) value, the closer the equalized signal is to the ideal signal, and the smaller its amplitude and phase errors. When the error vector magnitude (EVM) between the mean square output signal and the predetermined ideal signal satisfies the first error condition, the mean square output signal can be determined as the target equalized signal. Specifically, the expression for the error vector magnitude (EVM) is as follows:

[0058] (5)

[0059] In the formula, EVM represents the error vector magnitude, and N represents the number of statistical samples.

[0060] According to embodiments of this disclosure, in an additive white Gaussian noise (AWGN) channel, the signal-to-noise ratio (SNR) of the channel can be derived based on the error vector magnitude (EVM) between the mean square output signal and a predetermined ideal signal. The relationship between the signal-to-noise ratio (SNR) and the error vector magnitude (EVM) is as follows:

[0061] (6)

[0062] In the formula, This indicates the signal-to-noise ratio.

[0063] According to the embodiments of this disclosure, as can be seen from formula (6), a lower error vector magnitude (EVM) corresponds to a higher signal-to-noise ratio (SNR). The SNR value calculated by the error vector magnitude (EVM) can reflect the noise immunity of the equalized target signal in the channel, so as to evaluate the effect of the above equalization method.

[0064] Based on this, the embodiments of this disclosure combine the constant mode equalization algorithm (CMA) and the least mean square algorithm (LMS) to perform dual equalization processing on the received terahertz echo signal. First, the constant mode equalization algorithm (CMA) is used to quickly complete the coarse equalization processing to solve the amplitude distortion problem. Then, the least mean square algorithm (LMS) is used to perform fine equalization processing on the signal after constant mode equalization to eliminate residual phase noise, thereby improving the equalization accuracy and signal quality and significantly reducing the error vector amplitude (EVM).

[0065] According to embodiments of this disclosure, the constant mode equalization algorithm is trained as follows: when the (m-1)th constant mode error does not satisfy the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight; using the initial constant mode equalization algorithm, the sample echo signal is processed based on the m-th first weight to obtain the m-th training constant mode signal; based on the target signal amplitude and the amplitude of the m-th training constant mode signal, the m-th constant mode error is determined; when the m-th constant mode error satisfies the second error condition, the m-th first weight is determined as the weight of the initial constant mode equalization algorithm to obtain the constant mode equalization algorithm.

[0066] According to embodiments of this disclosure, during the coarse equalization process, the equalizer weights can be iteratively optimized to obtain an optimized constant modulus equalization (CMA) algorithm, making the amplitude of the constant modulus output signal close to the target signal amplitude, thereby minimizing the constant modulus error of the signal. ).

[0067] For example, for the current iteration, if the constant modulus error of the previous iteration does not meet the second error condition, the first weight of the previous iteration is updated to obtain the first weight of the current iteration, and the sample echo signal is processed based on the first weight of the current iteration to obtain the training constant modulus signal of the current iteration.

[0068] In this specific embodiment, the second error condition can be used to represent the constant modulus error ( The threshold, the first weight can be used to represent the equalizer weight vector of the constant mode equalization algorithm, the sample echo signal can be used to represent the sampled signal of multiple terahertz echo signals, and the training constant mode signal can be used to represent the output signal of each iteration in the training iteration process. The optimized update expression for the equalizer weights of the constant mode equalization algorithm is as follows:

[0069] (7)

[0070] In the formula, Indicates the first weight of the m-th element; Indicates the first weight of the (m-1)th digit; Indicates the sample echo signal; This represents the (m-1)th training constant mode signal; This represents the conjugate of the (m-1)th training constant-mode signal. This indicates the first optimization step size.

[0071] In this specific embodiment, after calculating the first weight of the current round according to formula (7), the sample echo signal of the current round is processed based on the first weight of the current round to obtain the output signal of the current round, which is the training constant modulus signal. Based on formula (3), the constant modulus error is calculated on the amplitude of the training constant modulus signal and the amplitude of the target signal of the current round to obtain the constant modulus error of the current round.

[0072] In this specific embodiment, if the constant modulus error of the current round satisfies the second error condition, the first weight of the current round is determined as the weight of the initial constant modulus equilibrium algorithm, so as to obtain the constant modulus equilibrium algorithm after weight update.

[0073] According to an embodiment of this disclosure, when the (m-1)th constant modulus error does not satisfy the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight, including: when the (m-1)th first optimization step size of the initial constant modulus equalization algorithm does not satisfy the first convergence condition, the (m-1)th first order and the (m-1)th first optimization step size of the initial constant modulus equalization algorithm are optimized using a gradient optimization algorithm to obtain the m-th first optimization step size; when the m-th first optimization step size satisfies the first convergence condition, the (m-1)th weight is updated according to the m-th first optimization step size to obtain the m-th first weight.

[0074] According to embodiments of this disclosure, a gradient optimization algorithm is used to optimize the (m-1)th first order and the (m-1)th first optimization step size of the initial constant modulus equalization algorithm to obtain the m-th first optimization step size. This includes: determining a first gradient based on the (m-1)th first order and the (m-1)th constant modulus error; determining a second gradient based on the (m-1)th first optimization step size and the (m-1)th constant modulus error; determining the search direction of the gradient optimization algorithm based on the first and second gradients; adjusting the (m-1)th first order and the (m-1)th first optimization step size based on the search direction of the gradient optimization algorithm to obtain an adjusted first order and an adjusted first optimization step size; and determining the adjusted first order as the m-th first order and the adjusted first optimization step size as the m-th first optimization step size, provided that the adjusted first order and the adjusted first optimization step size satisfy their respective constraint conditions.

[0075] According to an embodiment of this disclosure, if the constant modulus error of the current round does not meet the second error condition, the first weight is updated by adjusting the parameters of the equalizer.

[0076] Specifically, a gradient optimization algorithm can be used to optimize and update the first order and the first optimization step size. Through multiple iterations, the first order and the first optimization step size satisfy the first convergence condition, at which point the iteration stops, yielding the optimal order and the optimal step size. Here, the first order can represent the equalizer order M corresponding to the constant modulus equalization algorithm, and the first optimization step size can represent the equalizer step size corresponding to the constant modulus equalization algorithm. This is used to control the magnitude of the first weight update.

[0077] In this specific embodiment, the equalizer order M and the equalizer step size are... As the optimization variable, and defining constant modulus error as the objective function, the optimization objective of the constant modulus equalization algorithm is to minimize the constant modulus error. The expression for this objective is as follows:

[0078] (8)

[0079] In the formula, M represents the first order. Indicates the first optimization step size. This indicates constant modulus error.

[0080] In this specific embodiment, the constraints for optimizing the first order and first optimization step size of the constant modulus equalization algorithm are as follows, to ensure that the first order and first optimization step size of the optimization variables are optimized. Falling within the permitted range:

[0081] (9)

[0082] (10)

[0083] In this specific embodiment, the gradient optimization process includes the following operations: initial parameters can be set based on prior knowledge, such as... If the channel conditions are complex, the initial parameters can also be derived from the minimum first-order values ​​in formulas (9) and (10). and the minimum value of the first optimization step Start by gradually increasing. After determining the initial parameters, input the sample echo signal according to the constant mode error calculation formula in formula (3) to calculate the initial error:

[0084] (11)

[0085] In the formula, This represents the initial constant modulus error.

[0086] In this specific embodiment, the gradient optimization process further includes: using the initial constant modulus error as the constant modulus error of the first optimization round; and performing iterative optimization in the next round if the constant modulus error of this round does not meet the error condition. Specifically, in the second optimization round, the gradient, i.e., the partial derivative, of the constant modulus error as the objective function with respect to each optimization variable can be calculated based on the constant modulus error and the optimization variables of the first optimization round. The specific expression is as follows:

[0087] (12)

[0088] For a discrete variable of the first order M, the first gradient corresponding to the first order M can be calculated using the finite difference method, as shown in the following expression:

[0089] (13)

[0090] In the formula, This represents the increment of the first order M, usually taking the minimum increment. =1 (because M is an integer), to ensure computational efficiency.

[0091] For continuous variables, the first optimization step size The second gradient corresponding to the first optimization step size φ can be calculated analytically, and the specific expression is as follows:

[0092] (14)

[0093] In this specific embodiment, the gradient optimization process further includes: based on the first gradient corresponding to the first order M and the first optimization step size The corresponding second gradient determines the search direction of the underworld optimization algorithm. In a specific embodiment, the negative gradient direction can be used as the search direction for descent to minimize the objective function ( The expression for the search direction is as follows:

[0094] (15)

[0095] In the formula, Indicates the search direction. This represents the gradient magnitude.

[0096] In this specific embodiment, the gradient optimization process further includes: adjusting and updating the first order and the first optimization step size of the previous round along the search direction to obtain the adjusted first order and the adjusted first optimization step size, ensuring that the objective function ( The value decreases. The expression for updating the optimization variables from the previous optimization round is as follows:

[0097] (16)

[0098] In the formula, This represents the search step size, which can be dynamically determined using a line search algorithm to ensure that the objective function decreases.

[0099] In this specific embodiment, the gradient optimization process further includes: after each update of the optimization variables of the previous optimization round, determining whether the adjusted first order and the adjusted first optimization step size satisfy the constraint range conditions shown in formulas (9) and (10). If the adjusted first order and the adjusted first optimization step size satisfy their respective constraint range conditions, the adjusted first order is determined as the first order of the current round, and the adjusted first optimization step size is determined as the first optimization step size of the current round. If the adjusted first order and the adjusted first optimization step size do not satisfy their respective constraint range conditions, the optimization variables can be projected back to the feasible region. For example, the expression for projecting the first order back to the feasible region is as follows. Similarly, the first optimization step size can be processed as follows:

[0100] (17)

[0101] In this specific embodiment, the gradient optimization process further includes: determining whether the first order and the first optimization step size of the current round satisfy a first convergence condition; if either of the first convergence conditions is satisfied, the iteration stops, and the optimal order and optimal step size are obtained; if neither is satisfied, the gradient calculation for the next round is performed based on the first order and the first optimization step size of the current round. The first convergence condition may include:

[0102] gradient magnitude Less than the preset threshold;

[0103] Parameter update range Less than the preset threshold;

[0104] Changes in objective function value Less than the preset threshold.

[0105] Based on this, embodiments of this disclosure employ a constant-mode equalization algorithm to perform preliminary equalization on the input terahertz echo signal. By adjusting the equalizer weights, the signal amplitude is brought closer to a preset target amplitude, thereby initially correcting signal distortion. Since this process does not require an ideal signal as a reference, it is suitable for use in the blind equalization stage. Furthermore, to further improve the optimization efficiency of the constant-mode equalization algorithm, embodiments of this disclosure combine a gradient optimization method, utilizing gradient information to quickly determine the optimal equalizer order and step size parameters. The optimization process calculates the optimization direction based on the current equalization error and adjusts the weight values ​​in the parameter space to rapidly converge the target error. This method not only improves the convergence speed of the CMA algorithm but also reduces the computational complexity of the preliminary equalization.

[0106] According to embodiments of this disclosure, the minimum mean square algorithm is trained as follows: when the (n-1)th mean square error does not satisfy the third error condition, the (n-1)th second weight is updated to obtain the nth second weight, where n > 1; using the initial minimum mean square algorithm, the sample constant modulus signal is processed based on the nth second weight to obtain the nth training mean square signal; based on the nth training mean square signal and a predetermined modulation signal, the nth error signal is determined; based on the statistical value of the nth error signal, the nth mean square error is determined; when the nth mean square error satisfies the third error condition, the nth second weight is determined as the weight of the initial minimum mean square algorithm to obtain the minimum mean square algorithm.

[0107] According to embodiments of this disclosure, during the fine equalization process, the equalizer weights can also be iteratively optimized to obtain an optimized minimum mean square (LMS) algorithm, thereby minimizing the mean square error (MSE) of the signal. LMS This makes the equalized mean square output signal approximate the ideal reference signal.

[0108] For example, for the current iteration, if the mean square error of the previous iteration does not meet the third error condition, the second weight of the previous iteration is updated to obtain the second weight of the current iteration, and the constant modulus signal of the sample is processed based on the second weight of the current iteration to obtain the training mean square signal of the current iteration.

[0109] In this specific embodiment, the third error condition can be used to represent the mean square error (MSE). The threshold, the second weight can be used to represent the equalizer weight vector of the least mean square algorithm, the sample constant modulus signal can be used to represent the sampled signal of multiple constant modulus output signals, and the training mean square signal can be used to represent the output signal in each iteration during the training iteration process. The optimized update expression for the equalizer weights of the least mean square algorithm is as follows:

[0110] (18)

[0111] In the formula, Indicates the second weight of the nth weight; Indicates the second weight of the (n-1)th weight; Represents the constant modulus signal of the sample. Represents the conjugate of the constant-modulus signal of the sample; This represents the (n-1)th error signal. This indicates the second optimization step size.

[0112] In this specific embodiment, after calculating the second weight of the current round according to formula (18), the constant modulus signal of the sample of the current round is processed based on the second weight of the current round to obtain the output signal of the current round, i.e., the training mean square signal. Based on formula (4), the mean square error of the training mean square signal and the ideal reference signal of the current round is calculated to obtain the mean square error of the current round.

[0113] In this specific embodiment, if the mean square error of the current round satisfies the third error condition, the second weight of the current round is determined as the weight of the initial minimum mean square algorithm to obtain the minimum mean square algorithm (LMS) after weight update.

[0114] If the (n-1)th mean square error does not meet the third error condition, the (n-1)th second weight is updated to obtain the nth second weight. This includes updating the (n-1)th second weight based on the (n-1)th error signal, the sample constant modulus signal, and the second optimization step size of the initial minimum mean square algorithm to obtain the nth second weight.

[0115] Based on the (n-1)th error signal, the sample constant modulus signal, and the second optimization step size of the initial minimum mean square algorithm, the (n-1)th second weight is updated to obtain the nth second weight. This includes: using the particle swarm optimization algorithm to optimize the (n-1)th second order and the (n-1)th second optimization step size of the initial minimum mean square algorithm to obtain the nth second order and the nth second optimization step size; and, if the nth second order and the nth second optimization step size satisfy the second convergence condition, updating the (n-1)th second weight according to the nth second optimization step size to obtain the nth second weight.

[0116] Using the particle swarm optimization algorithm, the (n-1)th second order and (n-1)th second optimization step size of the initial minimum mean square algorithm are optimized to obtain the nth second order and nth second optimization step size. This includes: randomly generating the (n-1)th position and (n-1)th velocity of each particle in the particle swarm based on the (n-1)th second order and (n-1)th second optimization step size; calculating the (n-1)th mean square error of each particle based on the (n-1)th position and (n-1)th velocity; updating the (n-1)th velocity based on the inertia weight, learning factor, historical best position of the particle in the particle swarm, global best position of the particle in the particle swarm, and (n-1)th position to obtain the nth velocity; updating the (n-1)th position based on the nth velocity to obtain the nth position; and determining the nth second order and nth second optimization step size based on the nth position.

[0117] According to embodiments of this disclosure, if the mean squared error of the current round does not meet the third error condition, the equalizer parameters corresponding to the least mean square algorithm are adjusted to update the second weights of the previous round until the mean squared error of the current round meets the third error condition. The third error condition can be used to represent the minimum mean squared error (MMS) of the least mean square algorithm. Threshold.

[0118] Specifically, since the mean square error is nonlinear and difficult to solve analytically, a particle swarm optimization algorithm can be used to optimize and update the second order and the second optimization step size. Through multiple iterations, the second order and the second optimization step size satisfy the second convergence condition, at which point the iteration stops, yielding the optimal order and optimal step size. Here, the second order can represent the filter length K corresponding to the minimum mean square algorithm, and the second optimization step size can represent the equalizer step size corresponding to the minimum mean square algorithm. This is used to control the update magnitude of the second weight. Particle Swarm Optimization (PSO) is a global optimization algorithm based on swarm intelligence, simulating particles moving in the search space to find the optimal solution to the objective function. Its advantage is that it does not require gradient calculation, making it suitable for nonlinear and complex objective function optimization.

[0119] In this specific embodiment, the filter length K and the equalizer step size are... As the optimization variable, and with the mean squared error defined as the objective function, the optimization objective of the least mean squared algorithm is to minimize the mean squared error. The expression for this objective is as follows:

[0120] (19)

[0121] In the formula, K represents the filter length, i.e., the second order. This represents the equalizer step size, specifically the second optimization step size. This represents the mean square error.

[0122] In this specific embodiment, during the optimization of the second order and the second optimization step size of the least mean square algorithm, the constraints are as follows, to ensure that the second order K and the second optimization step size of the optimization variables are optimized. Within the allowed range:

[0123] (20)

[0124] (twenty one)

[0125] In this specific embodiment, the mean square error is calculated by inputting the constant modulus signal of the sample according to the mean square error calculation formula of formula (4):

[0126] (twenty two)

[0127] In the formula, This represents the mean square error.

[0128] In this specific embodiment, each particle represents a candidate solution, i.e., an optimal combination of parameters. The position of the particle Indicates the current parameter value; particle velocity. Determine the direction and step size of parameter updates.

[0129] In this specific embodiment, the particle swarm optimization process specifically includes the following operations: based on the second order and the second optimization step size of the previous optimization round, the initial position and velocity of each particle in the particle swarm are randomly generated, and the initial mean square error of each particle is calculated according to formula (22) to determine the historical optimal position of the particle. And the global optimal position of the particle. Specifically, in each iteration of optimization, the velocity and position of each particle in the current optimization round can be updated based on the following rules:

[0130] (twenty three)

[0131] (twenty four)

[0132] In the formula, The inertial weight is used to control the decay of particle velocity; c1 and c2 are learning factors that measure the particle's dependence on its own experience and the group's experience, respectively; r1 and r2 are random numbers used to enhance the diversity of the particle swarm.

[0133] In this specific embodiment, the particle swarm optimization process further includes: determining the second order K and the second optimization step size of the current optimization round based on the velocity and position of each particle in the current optimization round. And calculate the objective function, i.e., the mean square error, for the current optimization round. .

[0134] In this specific embodiment, the particle swarm optimization process further includes updating the historical optimal position and the global optimal position of each particle based on its velocity and position in the current optimization round.

[0135] In this specific embodiment, the particle swarm optimization process further includes: determining the second order K and the second optimization step size for the current round. If the second convergence condition is met, the iteration stops, and the optimal order and optimal step size are obtained. If neither condition is met, the next round of particle swarm optimization is performed based on the second order and the second optimization step size of the current round. The second convergence condition may include: the change in the global optimal solution is less than a preset threshold; or the maximum number of iterations has been reached.

[0136] According to embodiments of this disclosure, in the process of fine equalization of the constant modulus output signal using the least mean square algorithm, the real and imaginary parts of the signal can be equalized separately to obtain a synthesized complex signal, as shown in formulas (25) to (27):

[0137] (25)

[0138] (26)

[0139] (27)

[0140] Based on this, the embodiments of this disclosure employ a minimum mean square (MMS) algorithm for fine equalization, building upon the coarse equalization signal output by the constant modulus equalization algorithm. The MMS algorithm calculates the error between the ideal signal and the equalized output signal and dynamically adjusts the equalizer weights, gradually bringing the signal closer to the ideal signal. This process improves the amplitude and phase accuracy of the signal, thereby further reducing the bit error rate. Furthermore, to enhance the performance of the MMS algorithm, the embodiments of this disclosure also incorporate particle swarm optimization (PSO) to globally optimize the filter length and step size parameters. PSO simulates the swarm behavior of particles in the search space, dynamically adjusting parameters based on historical and global optimal positions to quickly converge to the global optimal parameters. This reduces the randomness of parameter selection and effectively improves the accuracy and robustness of the MMS algorithm's equalization.

[0141] According to embodiments of this disclosure, the inertial weight of each particle is obtained based on the following operations: determining the gradient magnitude of the m-th constant mode error based on the constant mode error of the m-th training constant mode signal; calculating the inertial weight of each particle based on the gradient magnitude of the m-th constant mode error and an adjustment factor, wherein the adjustment factor is determined based on the channel coherence time and the system bandwidth.

[0142] According to embodiments of this disclosure, the particle swarm optimization process further includes: establishing a dynamic mapping relationship between the gradient information of the constant mode equalization algorithm and the inertia weights of the particle swarm optimization algorithm. Specifically, the inertia weights of each particle can be calculated based on the gradient magnitude of the m-th constant mode error and an adjustment factor. The adjustment factor can be calculated based on the channel coherence time and system bandwidth. The inertia weights are calculated as follows:

[0143] (28)

[0144] (29)

[0145] In the formula, This represents the inertia weight in the k-th particle swarm iteration. The gradient magnitude represents the constant modulus error. Indicates the time-varying adjustment factor of the channel. B represents the channel coherence time (seconds), and B represents the system bandwidth (Hz).

[0146] Among them, inertia weight This can be used to represent a dynamic adjustment factor that controls the inertia of particle velocity updates in particle swarm optimization algorithms, and its value range is... By dynamically adjusting the inertia weight To achieve a balance between global exploration and local development, specifically, when When the value approaches 1, the particle maintains high-speed motion, enhancing global search capabilities; when... When the velocity approaches 0, the particle velocity decays rapidly, enhancing the fine-grained search in localized areas.

[0147] Among them, the gradient magnitude of the constant modulus error The constant mode error can be based on the training constant mode signal. The calculation shows that when the gradient magnitude of the constant modulus error is... A larger value indicates that the current equalizer coefficients are far from the optimal solution, and the gradient magnitude of the constant modulus error is... A smaller value indicates that the equalizer is close to convergence. In practical calculations, the gradient magnitude of the output signal of the constant modulus equalization algorithm can be normalized, for example... .

[0148] Among them, the channel time-varying adjustment factor This is a quantization parameter that can be used to represent the time-varying characteristics of a channel, reflecting the sensitivity of the channel state to weight adjustments. Channel time-varying adjustment factor. The threshold for gradient-weight transformation can be determined. In one embodiment of this disclosure, the channel time-varying adjustment factor... The value range of a fast-changing channel can include The time-varying adjustment factor of this channel The value range of a slowly varying channel can include When the channel time-varying adjustment factor A larger value can indicate faster exponential decay and a quicker response to channel changes, when the channel time-varying adjustment factor... A smaller value indicates a smoother weight adjustment, maintaining search diversity.

[0149] Based on this, embodiments of this disclosure establish a nonlinear mapping relationship between CMA gradient information and PSO inertia weights to achieve dynamic adjustment of the algorithm's search capability. When channel conditions change rapidly ( With a smaller value, the exponential decay factor accelerates the adjustment of inertial weights, causing the particle swarm to rapidly shrink its search range in steep gradient regions; in a steady-state channel environment ( If the value is large, a larger inertia weight is maintained to preserve population diversity. Experiments show that this dynamic adjustment improves the algorithm's convergence speed by about 37%, while reducing the steady-state error to 62% of that of traditional PSO.

[0150] According to an embodiment of this disclosure, when the (m-1)th constant modulus error does not satisfy the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight. The method further includes: when the m-th first optimization step size satisfies the first convergence condition, updating the (m-1)th weight based on the m-th first optimization step size, the gradient of the m-th constant modulus error, the gradient of the m-th mean square error, and the modulation factor to obtain the m-th first weight.

[0151] According to embodiments of this disclosure, during the update of the first weight of CMA, an LMS error constraint term can also be embedded to obtain a bidirectional error feedback architecture. Specifically, the (m-1)th weight can be updated based on the m-th first optimization step size, the gradient of the m-th constant modulus equalization algorithm, the gradient of the m-th least mean square algorithm, and the modulation factor (improving formula (7)) to obtain the m-th first weight, the specific expression of which is as follows:

[0152] (30)

[0153] In the formula, This indicates the first weight of the m-th weight. This represents the first weight of the (m-1)th weight. Indicates the first optimization step size. This represents the gradient of the constant modulus error. The gradient represents the equilibrium error. The gradient constraint strength coefficient represents the equilibrium error. This represents the gradient normalization modulation factor for the equalization error. tanh() represents the hyperbolic tangent nonlinear function, which can be used as a soft limiter to compress the LMS gradient to the (-1,1) interval, preventing divergence caused by large gradients.

[0154] Among them, the gradient constraint strength coefficient of the equilibrium error The gradient used to adjust the equilibrium error contributes to updating the first weights of the CMA. Wherein, It can be dynamically adjusted starting from 0.1 based on the steady-state error.

[0155] Among them, the gradient normalized modulation factor of the equalization error Used to represent the adaptive modulation order (M) QAM This is to balance the gradient magnitudes of CMA and LMS. Specifically, the gradient normalization modulation factor of the equalization error is used. The calculation method is as follows:

[0156] (31)

[0157] In the formula, M QAM The adaptive modulation order (number of constellation points) can be used to characterize the spatial density of the signal, such as... , . This represents the diagonal length of the constellation diagram, used to reflect the maximum amplitude of the signal, and to quantize the gradient scale. The adaptive modulation order M is also included. QAM It can be obtained through leading symbols or blind recognition algorithms.

[0158] Based on this, the embodiments of this disclosure form a double-loop error correction mechanism by embedding an LMS gradient constraint term into the CMA framework. In the initial equalization phase, the signal eye diagram is not open (EVM>8%), and the LMS gradient is suppressed due to the high sign decision error rate. By using the hyperbolic tangent function (tanh) for amplitude limiting, the LMS gradient is compressed to the [−1,1] interval, preventing weight divergence caused by erroneous gradients. When EVM<5%, the eye diagram opens, and the reliability of sign decision improves. At this time, the tanh function enters the linear region (…). The LMS gradient fully participates in weight updates, enabling fine-grained phase correction. This architecture, through intelligent fusion of gradient domains, significantly improves the convergence speed and steady-state performance of high-order QAM systems while maintaining the advantages of CMA blind equalization.

[0159] According to embodiments of this disclosure, during the training process of the joint algorithm formed by the constant modulus equilibration algorithm and the least mean square algorithm, its convergence must simultaneously satisfy the stability conditions of both the constant modulus equilibration algorithm and the least mean square algorithm. Specifically, the stability conditions can satisfy the following constraints:

[0160] (32)

[0161] In the formula, R x The autocorrelation matrix represents the input signal. This represents the optimal weight vector. Indicates the first optimization step size. This represents the largest eigenvalue of the autocorrelation matrix of the input signal. This indicates the second optimization step size.

[0162] Among them, the first optimization step size Used to control the magnitude of CMA weight updates. Because in the stability analysis of CMA, the first optimization step size... It needs to be inversely proportional to the energy of the input signal (characterized by the eigenvalues ​​of the autocorrelation matrix). Therefore, the first optimization step size can be chosen. To avoid the first optimization step size Too large, for example, experiments show that the first optimization step size is too large. The convergence probability drops sharply.

[0163] Among them, the largest eigenvalue of the autocorrelation matrix of the input signal It is used to reflect the direction of maximum energy of the input signal and is directly related to signal correlation. For example, highly correlated signals... Large matrix condition number It is significantly higher than other characteristic values. The larger the first optimization step size The smaller the value, the more likely the update process will become unpredictable.

[0164] Among them, the second optimization step size This is used to control the magnitude of LMS weight updates. Since the classical convergence condition of LMS requires a second optimization step size... To further correlate the optimal weight norm.

[0165] Among them, the optimal weight vector Norm Square This can be used to describe the energy of ideal weights in an equalizer or filter. The higher the system complexity (e.g., multipath channels), the larger the squared norm of the optimal weight vector, requiring a smaller second optimization step size. To ensure convergence.

[0166] Based on this, embodiments of this disclosure can use CMA constraints to limit the impact of input signal correlation on CMA. Furthermore, LMS constraints can be used to limit the influence of weight energy on LMS. In actual testing The convergence probability drops sharply ( This verifies the necessity of the theoretical constraint. By jointly constraining the core parameters of CMA and LMS, this condition provides a theoretical stability guarantee for complex signal processing systems.

[0167] In the specific embodiments described above, the signal can also be preprocessed, for example, by using a pre-whitening filter to reduce the frequency domain signal of highly correlated signals (such as frequency domain signals in an OFDM system). In the process of selecting the step size, priority can be given to... Sure Upper limit. Furthermore, if Larger (complex channels) can further reduce While a small step size guarantees convergence, it reduces the convergence speed, requiring simulation to balance the performance.

[0168] Based on this, the embodiments of this disclosure dynamically optimize the parameters of the Constant Modulus Equalization (CMA) algorithm and the Least Mean Square (LMS) algorithm using gradient optimization and particle swarm optimization algorithms. This provides strong anti-interference capabilities against multipath interference, frequency offset, and high-noise environments. Frequency offset compensation and dynamic parameter optimization ensure signal stability and adaptability to complex channel conditions. Furthermore, the embodiments of this disclosure also provide strong anti-interference capabilities against multipath interference, frequency offset, and high-noise environments. Frequency offset compensation and dynamic parameter optimization ensure signal stability and adaptability to complex channel conditions.

[0169] According to specific embodiments of this disclosure, before performing channel adaptive equalization on the terahertz echo signal, the method further includes: preprocessing the received signal, including down-conversion and low-pass filtering, to convert the radio frequency signal into a baseband signal. Simultaneously, time synchronization is achieved using pilot sequences, and frequency offset is estimated and compensated using pilot sequences and a decision loop method to eliminate the impact of frequency drift on the signal. These steps provide a high-quality input signal for subsequent equalization and ensure that the signal has a high demodulation foundation in multipath interference and high-noise environments.

[0170] Figure 2 The diagram illustrates the demodulation results of a 1024QAM signal transmitted under a measured 20G bandwidth, under different equalization methods: no equalization, minimum mean square algorithm, and a combination of constant modulus equalization algorithm and minimum mean square algorithm.

[0171] like Figure 2 As shown, demodulating a 1024QAM signal without equalization results in an error vector magnitude (EVM) of 70.62%, a signal-to-noise ratio (SNR) of 3.02 dB, and an equalization time of 0 seconds. Demodulating the 1024QAM signal using only the least mean square algorithm results in an error vector magnitude (EVM) of 16.01%, an SNR of 15.91 dB, and an equalization time of 9.45 seconds. Demodulating the 1024QAM signal using a combined equalization method of constant modulus equalization and least mean square algorithm results in an error vector magnitude (EVM) of 4.88%, an SNR of 26.23 dB, and an equalization time of 1.11 seconds.

[0172] As shown above, the equalized signal obtained by the joint equalization method using the constant modulus equalization algorithm and the least mean square algorithm exhibits better noise immunity in the channel. Specifically, the constant modulus equalization algorithm rapidly eliminates amplitude distortion in the initial stage (approximately the first 100 symbols), reducing the EVM from 70% to 15%~20%, providing a stable input for the least mean square algorithm. Based on the preprocessing of the constant modulus equalization algorithm, the least mean square algorithm further corrects phase noise and residual distortion through supervised gradient adjustment, ultimately achieving an EVM of 4.88%, approaching the theoretical limit of 1024QAM. Furthermore, the blind equalization characteristic based on the constant modulus equalization algorithm avoids invalid iterations caused by the eye diagram not being open in the early stages of the least mean square algorithm, improving the convergence speed of the joint scheme by 8.5 times. ).

[0173] Figure 3 The diagram illustrates the constellation diagrams after demodulation of a 1024QAM signal transmitted under a measured 20G bandwidth using the least mean square algorithm and the combined equalization method of constant mode equalization and least mean square algorithm.

[0174] like Figure 3 As shown, when the least mean square algorithm is used to demodulate the 1024QAM signal, the point cloud in the constellation diagram is significantly diffused, the edges are blurred, and the clustering of constellation points is poor. However, when the constant modulus equalization algorithm and the least mean square algorithm are used to demodulate the 1024QAM signal, the multiple constellation points in the constellation diagram are clearly arranged, the point cloud is highly concentrated, and it is close to the ideal grid distribution.

[0175] Based on this, the embodiments of this disclosure employ a joint equalization method combining constant modulus equalization and least mean square (LMS) algorithms, achieving near-limit performance (EVM≈5%, SNR>26dB) for 1024QAM signals in a 20 GHz wideband channel. Simultaneously, the equalization time is compressed to the second level, making it suitable for scenarios with symbol rates exceeding 20 GHz and employing 1024-QAM and higher-order modulation. It also supports dynamic adjustment of different filter orders and step size parameters, allowing for flexible configuration according to specific channel conditions. The parameter optimization design of its equalizer can be extended to future communication systems with higher-order modulation and wider bandwidth, demonstrating promising application prospects.

[0176] Figure 4 A block diagram of a channel equalization apparatus for a terahertz communication system according to an embodiment of the present disclosure is shown schematically.

[0177] like Figure 4 As shown, the channel equalization device 400 of the terahertz communication system includes a signal receiving module 410, a blind equalization module 420, an adaptive equalization module 430, a signal synthesis module 440, and an equalization signal determination module 450.

[0178] The signal receiving module 410 is used to receive terahertz echo signals.

[0179] The blind equalization module 420 is used to perform blind equalization processing on the amplitude of the terahertz echo signal based on the constant mode equalization algorithm to obtain the constant mode output signal.

[0180] The adaptive equalization module 430 is used to perform adaptive equalization processing on the real part and the imaginary part of the constant modulus output signal based on the least mean square algorithm, so as to obtain the processed real part and the processed imaginary part of the signal.

[0181] The signal synthesis module 440 is used to obtain a mean square output signal based on the real part and the imaginary part of the processed signal.

[0182] The equalization signal determination module 450 is used to determine the mean square output signal as the target equalization signal when the error vector amplitude between the mean square output signal and the predetermined ideal signal meets the first error condition.

[0183] Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure, or at least part of the functions of any one or more of them, can be implemented in one module. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be implemented by dividing them into multiple modules. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as hardware circuitry, such as a Field-Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a System-on-Chip, a System-on-a-Substrate, a System-on-Package, an Application-Specific Integrated Circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as computer program modules, which, when run, can perform corresponding functions.

[0184] For example, any multiple of the signal receiving module 410, blind equalization module 420, adaptive equalization module 430, signal synthesis module 440, and equalization signal determination module 450 can be combined into one module / unit / subunit, or any one of these modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least some of the functions of one or more of these modules / units / subunits can be combined with at least some of the functions of other modules / units / subunits and implemented in one module / unit / subunit. According to embodiments of this disclosure, at least one of the signal receiving module 410, blind equalization module 420, adaptive equalization module 430, signal synthesis module 440, and equalization signal determination module 450 can be at least partially implemented as hardware circuits, such as field-programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems-on-a-chip, systems-on-a-substrate, systems-on-package, application-specific integrated circuits (ASICs), or any other reasonable means of integrating or packaging circuits, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the signal receiving module 410, blind equalization module 420, adaptive equalization module 430, signal synthesis module 440, and equalization signal determination module 450 can be at least partially implemented as a computer program module, which can perform corresponding functions when the computer program module is run.

[0185] It should be noted that the channel equalization device part of the terahertz communication system in the embodiments of this disclosure corresponds to the channel equalization method part of the terahertz communication system in the embodiments of this disclosure. For a detailed description of the channel equalization device of the terahertz communication system, please refer to the channel equalization method part of the terahertz communication system, which will not be repeated here.

[0186] Figure 5 A block diagram of an electronic device for a channel equalization method for a terahertz communication system according to an embodiment of the present disclosure is shown schematically. Figure 5 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0187] like Figure 5As shown, an electronic device according to an embodiment of this disclosure includes a processor 501, which can perform various appropriate actions and processes according to a program stored in a read-only memory ROM 502 or a program loaded from a storage portion 508 into a random access memory RAM 503. The processor 501 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 501 may also include onboard memory for caching purposes. The processor 501 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this disclosure.

[0188] RAM 503 stores various programs and data required for the operation of the electronic device. Processor 501, ROM 502, and RAM 503 are interconnected via bus 504. Processor 501 performs various operations of the method flow according to embodiments of the present disclosure by executing programs in ROM 502 and / or RAM 503. It should be noted that the programs may also be stored in one or more memories other than ROM 502 and RAM 503. Processor 501 may also perform various operations of the method flow according to embodiments of the present disclosure by executing programs stored in said one or more memories.

[0189] According to embodiments of this disclosure, the electronic device may further include an input / output (I / O) interface 505, which is also connected to a bus 504. The electronic device may also include one or more of the following components connected to the input / output (I / O) interface 505: an input section 506 including a keyboard, mouse, etc.; an output section 507 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 508 including a hard disk, etc.; and a communication section 509 including a network interface card such as a LAN card, modem, etc. The communication section 509 performs communication processing via a network such as the Internet. A drive 510 is also connected to the input / output (I / O) interface 505 as needed. A removable medium 511, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 510 as needed so that computer programs read from it can be installed into the storage section 508 as needed.

[0190] According to embodiments of this disclosure, the method flow according to embodiments of this disclosure can be implemented as a computer software program. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 509, and / or installed from removable medium 511. When the computer program is executed by processor 501, it performs the functions defined in the system of embodiments of this disclosure. According to embodiments of this disclosure, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0191] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0192] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0193] For example, according to embodiments of this disclosure, a computer-readable storage medium may include the ROM 502 and / or RAM 503 described above and / or one or more memories other than ROM 502 and RAM 503.

[0194] Embodiments of this disclosure also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this disclosure. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the channel equalization method for the terahertz communication system provided in the embodiments of this disclosure.

[0195] When the computer program is executed by the processor 501, it performs the functions defined in the system / apparatus of this disclosure embodiments. According to embodiments of this disclosure, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0196] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 509, and / or installed from a removable medium 511. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0197] According to embodiments of this disclosure, program code for executing the computer programs provided in embodiments of this disclosure can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can execute entirely on a user's computing device, partially on a user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0198] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features described in the various embodiments of the present disclosure can be combined and / or combined in various ways, even if such combinations are not explicitly described in the present disclosure. In particular, the features described in the various embodiments of this disclosure may be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0199] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A channel equalization method for a terahertz communication system, wherein, The channel equalization method includes: Receive terahertz echo signals; Based on the constant mode equalization algorithm, the amplitude of the terahertz echo signal is blindly equalized to obtain the constant mode output signal. Based on the least mean square algorithm, adaptive equalization processing is performed on the real part and the imaginary part of the constant modulus output signal to obtain the processed real part and the processed imaginary part of the signal. The mean square output signal is obtained based on the real part and the imaginary part of the processed signal. If the magnitude of the error vector between the mean square output signal and the predetermined ideal signal satisfies the first error condition, the mean square output signal is determined as the target equalization signal.

2. The channel equalization method according to claim 1, wherein, The constant modulus equalization algorithm is trained using the following method: If the constant modulus error of the (m-1)th term does not meet the second error condition, the first weight of the (m-1)th term is updated to obtain the first weight of the mth term, where m > 1; Using the initial constant modulus equalization algorithm, the sample echo signal is processed based on the m-th first weight to obtain the m-th training constant modulus signal; The m-th constant mode error is determined based on the target signal amplitude and the amplitude of the m-th training constant mode signal, wherein the target signal amplitude is determined based on the statistical value of the amplitude of the sample echo signal; If the m-th constant modulus error satisfies the second error condition, the m-th first weight is determined as the weight of the initial constant modulus equalization algorithm, thus obtaining the constant modulus equalization algorithm.

3. The channel equalization method according to claim 2, wherein, When the (m-1)th constant modulus error does not meet the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight, including: If the first optimization step size of the initial constant modulus equalization algorithm (m-1) does not meet the first convergence condition, the gradient optimization algorithm is used to optimize the first order and the first optimization step size of the initial constant modulus equalization algorithm (m-1) to obtain the first optimization step size of the m-th step. If the first optimization step size m satisfies the first convergence condition, the (m-1)th weight is updated according to the first optimization step size m to obtain the first weight m.

4. The channel equalization method according to claim 3, wherein, The step of optimizing the first order and the first optimization step size of the initial constant modulus equalization algorithm using a gradient optimization algorithm to obtain the first optimization step size of the mth order includes: The first gradient is determined based on the (m-1)th first order and the (m-1)th constant modulus error; The second gradient is determined based on the (m-1)th first optimization step size and the (m-1)th constant modulus error; Based on the first gradient and the second gradient, the search direction of the gradient optimization algorithm is determined; Based on the search direction of the gradient optimization algorithm, the (m-1)th first order and the (m-1)th first optimization step size are adjusted to obtain the adjusted first order and the adjusted first optimization step size. If the adjusted first order and the adjusted first optimization step size satisfy their respective constraint range conditions, the adjusted first order is determined as the m-th first order, and the adjusted first optimization step size is determined as the m-th first optimization step size.

5. The channel equalization method according to claim 1, wherein, The least mean square algorithm is trained using the following method: If the (n-1)th mean square error does not meet the third error condition, the (n-1)th second weight is updated to obtain the nth second weight, where n > 1; Using the initial minimum mean square algorithm, the constant modulus signal of the sample is processed based on the nth second weight to obtain the nth training mean square signal; Based on the nth training mean square signal and the predetermined modulation signal, the nth error signal is determined; The nth mean square error is determined based on the statistical value of the nth error signal. If the nth mean square error satisfies the third error condition, the nth second weight is determined as the weight of the initial minimum mean square algorithm, thus obtaining the minimum mean square algorithm.

6. The channel equalization method according to claim 5, wherein, When the (n-1)th mean square error does not meet the third error condition, the (n-1)th second weight is updated to obtain the nth second weight, including: Based on the (n-1)th error signal, the sample constant modulus signal, and the second optimization step size of the initial minimum mean square algorithm, the (n-1)th second weight is updated to obtain the nth second weight.

7. The channel equalization method according to claim 6, wherein, The second optimization step size based on the (n-1)th error signal, the sample constant modulus signal, and the initial minimum mean square algorithm is used to update the (n-1)th second weight to obtain the nth second weight, including: The particle swarm optimization algorithm is used to optimize the (n-1)th second order and the (n-1)th second optimization step size of the initial minimum mean square algorithm to obtain the nth second order and the nth second optimization step size. If the nth second order and the nth second optimization step size satisfy the second convergence condition, the (n-1)th second weight is updated according to the nth second optimization step size to obtain the nth second weight.

8. The channel equalization method according to claim 7, wherein, The step of using particle swarm optimization to optimize the (n-1)th second order and (n-1)th second optimization step size of the initial least mean square algorithm to obtain the nth second order and nth second optimization step size includes: Based on the (n-1)th second order and the (n-1)th second optimization step size, the (n-1)th position and (n-1)th velocity of each particle in the particle swarm are randomly generated. Based on the (n-1)th position and (n-1)th velocity of each particle, the (n-1)th mean square error of each particle is calculated. Based on the inertia weight, learning factor, historical best position of the particle in the particle swarm, global best position of the particle in the particle swarm, and the (n-1)th position, the (n-1)th velocity is updated to obtain the nth velocity. The nth position is obtained by updating the (n-1)th position based on the nth velocity; Based on the nth position, the nth second order and the nth second optimization step size are determined.

9. The channel equalization method according to claim 8, wherein, The inertial weights of each particle are obtained based on the following operation: Based on the constant mode error of the m-th training constant mode signal, determine the gradient magnitude of the m-th constant mode error; Based on the gradient magnitude of the m-th constant mode error and the adjustment factor, the inertial weight of each particle is calculated, wherein the adjustment factor is determined based on the channel coherence time and the system bandwidth.

10. The channel equalization method according to claim 4, wherein, If the (m-1)th constant modulus error does not meet the second error condition, the (m-1)th first weight is updated to obtain the m-th first weight, which also includes: When the m-th first optimization step size satisfies the first convergence condition, the (m-1)-th weights are updated according to the m-th first optimization step size, the gradient of the m-th constant modulus error, the gradient of the m-th mean square error, and the modulation factor to obtain the m-th first weight. The gradient of the m-th mean square error is determined based on the m-th training mean square signal, and the modulation factor is determined based on the modulation order of the orthogonal amplitude modulation.

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