Composite terahertz channel parameter high-precision estimation method based on particle swarm optimization

Abstract

The invention discloses a composite terahertz channel parameter high-precision estimation method based on particle swarm optimization, and the method comprises the steps: carrying out the initialization of a position, a local record and a global record vector of a PSO algorithm through employing an output result of a decomposition estimator; the global record vector is used for recording the highest log-likelihood function value generated in all particles and taking the value as the current optimal composite channel parameter. In each iteration of the particle swarm optimization process, taking a calculation result of a log-likelihood function as particle fitness and updating the particle fitness; when the termination condition is met, the variance surrounded in the iteration process is returned to obtain the channel parameter of the composite terahertz channel model generated by the particle swarm optimization algorithm, namely the channel parameter optimal solution meeting the maximum likelihood estimation criterion. According to the method, the joint maximum likelihood estimation problem is directly processed without decomposition, high-precision and high-efficiency parameter estimation is realized, and a flexible and adjustable optimization mechanism is provided.

Description

Technical Field

[0001] The present invention relates to channel modeling and optimization, and particularly to a method for high-precision estimation of composite terahertz channel parameters based on particle swarm optimization. This method can be applied to key technologies of 6G and belongs to the technical field of channel modeling using intelligent optimization algorithms in wireless communication. Background Art

[0002] Facing the rapid development of the sixth-generation (6G) wireless communication technology, it is urgent to explore new frequency bands that can support wireless data transmission rates of terabits per second (Tbps). Among the candidate frequency bands, the terahertz (THz) spectrum (0.1 - 10 THz) has attracted wide attention due to its rich unlicensed bandwidth resources. Terahertz wireless communication has significant advantages such as ultra-high data rate and ultra-low latency, and is particularly suitable for supporting future intelligent communication services. However, the unique propagation characteristics of the terahertz channel, such as high path loss, molecular absorption loss, short transmission distance, and quasi-optical behavior, bring new challenges to the design and analysis of wireless systems. Recent research has been dedicated to constructing analytical models that not only maintain mathematical tractability but also accurately characterize terahertz channel impairments. Among them, the composite terahertz channel model, as an effective tool, can comprehensively characterize random effects such as channel small-scale fading, shadowing, and frequency-selective attenuation, and has been widely used in the performance analysis of terahertz communication.

[0003] Although the performance analysis research based on the composite terahertz channel model is increasing, existing work generally assumes that the exact channel parameters are known (such as the parameters controlling molecular absorption, shadowing, and small-scale fading), without specifically clarifying the actual estimation methods for these parameters. This oversight deserves attention because the accuracy of channel parameter estimation directly affects the reliability of system performance analysis and optimization results. How to achieve a practical balance between estimation accuracy and computational efficiency remains the core challenge when using the composite terahertz channel model.

[0004] That is, the composite terahertz (THz) channel model has been widely adopted and recognized as an effective tool for capturing the unique behavioral characteristics of terahertz wireless channels and analyzing the performance of communication systems under the terahertz spectrum. However, the accurate parameter estimation for this composite channel model remains an open problem. So far, the maximum likelihood (ML) estimation criterion has been proposed as a theoretical principle to guide the estimation of free parameters of the composite THz channel model. Although ML estimation has information-theoretic optimality, its implementation in a non-linear high-dimensional parameter space often faces the problem of high computational complexity. The existence of this problem is not conducive to the practical deployment of ML-based channel parameter estimators in networks with high real-time requirements or resource constraints. Summary of the Invention

[0005] Aiming at the problems of high computational complexity and low accuracy existing in the existing parameter estimation methods, the purpose of the present invention is to propose a high-precision estimation method for composite terahertz channel parameters based on particle swarm optimization (PSO). The present invention realizes high-precision and high-efficiency parameter estimation by directly processing the joint maximum likelihood (ML) estimation problem without decomposition, and provides a flexible and adjustable optimization mechanism.

[0006] The technical solution of the present invention is realized as follows:

[0007] A high-precision estimation method for composite terahertz channel parameters based on particle swarm optimization. Suppose there are S independent samples of the internal channel power gain which are expressed as The expression of the composite terahertz channel model is

[0008]

[0009] where K v (·) represents the modified Bessel function of the second kind of order v, and C1(d,f)~C4(d,f) are auxiliary functions, and their specific expressions are defined as

[0010]

[0011] In the formula, m(d,f), σ(d,f) and ψ(d,f) are the channel parameters to be estimated, d is the transmitter-receiver distance; f is the carrier frequency; m(d,f) is the multipath fading coefficient, reflecting the complexity of the scattering environment of multipath propagation; σ(d,f) is the shadow intensity; ψ(d,f) is the path attenuation factor that jointly characterizes the spread and molecular absorption loss of THz radio propagation;

[0012] This method estimates the channel parameters based on the particle swarm optimization algorithm, and the specific steps are as follows.

[0013] 1) Suppose the number of particles in the particle swarm is N, and initialize the position vector p n of each particle, the velocity vector v n and the local recording vector

[0014] as well as the global recording vector r and the global recording vector r * , the global recording vector r * is used to record the highest log-likelihood function value generated among all particles and serve as the current optimal composite channel parameter;

[0015] 2) In each iteration of the particle swarm optimization process, calculate the result according to Equation (8) as the particle fitness; and update according to Equation (13);

[0016]

[0017] where a1 and a2 are the internal individual acceleration and swarm acceleration respectively; rand([0,1],1×3) returns a 1×3 vector whose elements are randomly generated values between 0 and 1; ⊙ represents the Hadamard product;

[0018] 3) When the following conditions are simultaneously satisfied Var{·} returns the variance enclosed during the iteration process; ∈ is a preset termination threshold; i is the number of iterations experienced, and λ is the preset protection window size used to prevent premature convergence;

[0019] 4) Finally, the channel parameter estimation of the composite terahertz channel model generated by the particle swarm optimization algorithm is given by the following formula:

[0020]

[0021] When ∈ → 0, will converge to with probability, that is, the optimal solution of the channel parameters satisfying the maximum likelihood estimation criterion is obtained.

[0022] The initialization in step 1) is specifically carried out as follows

[0023] 1.1) Calculate to obtain according to the following formula

[0024]

[0025] where is calculated according to formula (9),

[0026]

[0027] 1.2) Initialize the position, local record, and global record vectors of the particle swarm optimization algorithm according to the obtained as follows

[0028]

[0029] where is a randomly generated integer between 1 and S, used to distinguish the initial positions of N particles to prevent premature convergence in the early stage of the PSO process;

[0030] 1.3) Based on the initialized p n , r n and r * , the velocity vector v n is initialized as follows

[0031] v n ←a1rand([0,1],1×3)⊙(r n-p n )

[0032] +a2rand([0,1],1×3)⊙(r * -p n ),(12).

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The present invention realizes high-precision and high-efficiency parameter estimation by directly dealing with the joint maximum likelihood (ML) estimation problem without decomposition, and provides a flexible and adjustable optimization mechanism. Compared with the decomposed estimator, the present invention can achieve higher estimation accuracy; compared with the exhaustive search (ES) estimator, its computational complexity remains within a reasonable range.

[0035] 2. The present invention maintains strong robustness under different system configurations, thus ensuring its reliable performance in diverse terahertz communication application scenarios.

[0036] 3. The estimator based on the particle swarm optimization algorithm exhibits powerful estimation and fast convergence in a wide range of hyperparameter configurations, highlighting its adaptability and effectiveness in solving the composite terahertz channel parameter estimation problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 - Flowchart of the method for high-precision estimation of composite terahertz channel parameters based on particle swarm optimization of the present invention.

[0038] Figure 2 - Schematic diagram of the variance of the highest LLF and iteration for three typical terahertz communication scenarios in the embodiments of the present invention.

[0039] Figure 3 - Comparison diagram of PDFs and CDFs generated by different channel parameter estimators for three typical terahertz communication scenarios in the embodiments of the present invention.

[0040] Figure 4 - Number of iterations required for algorithm convergence using different PSO hyperparameter sets in Scenario 1 of the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The implementation manner and principle of the present invention will be further described in detail below with reference to the accompanying drawings.

[0042] I. Terahertz Wireless Communication Composite Channel Model and Problem Modeling

[0043] 1.1 Composite Terahertz Channel Model

[0044] Consider a pair of point-to-point terahertz transceiver pairs, whose end-to-end equivalent channel can be characterized by both deterministic and random factors. The deterministic factors include the transmit / receive antenna gains (G T (f) and G R (f)), the carrier frequency f, and the propagation distance d; the random factors cover molecular absorption, dynamic shadowing effects, and multipath fading gains, and these random effects can be characterized by the composite internal channel power gain . The composite channel power gain of the terahertz wireless channel can be modeled as:

[0045]

[0046] Excluding the deterministic factors of the antenna system, the gamma-gamma composite channel model can be used to characterize the internal power gain of the terahertz channel. Its cumulative distribution function (CDF) and probability density function (PDF) (x≥0) are defined as:

[0047]

[0048] where: Γ(·) and γ(·,·) represent the gamma function and the incomplete gamma function, respectively. is the dynamic shadow factor, which characterizes the time-varying characteristics of the channel shadowing effect. m(d,f) is the multipath fading coefficient, which reflects the complexity of the scattering environment of multipath propagation.

[0049] In the composite modeling, , as a potential random factor, its statistical characteristics can be modeled by another gamma distribution for x≥0, and the corresponding CDF and PDF are:

[0050]

[0051] where ξ1(d,f) = exp(σ(d,f) 2 ) - 1, ξ2(d,f) = exp(σ(d,f) 2 / 2) are two auxiliary coefficients related to the shadow intensity σ(d,f); Ψ(d,f) is the path attenuation factor that jointly characterizes the spread and molecular absorption loss of THz radio propagation, and can be expressed by the Friis and Beer-Lambert theorems as:

[0052]

[0053] where c, α, κ(f) represent the speed of light, the propagation loss exponent, and the medium absorption coefficient, respectively.

[0054] According to Equations (2) and (3), the PDF of the gamma-gamma composite terahertz channel model can be obtained through the marginalization method (marginalization is a method in probability theory that requires summing over the possible values of a variable to determine the marginal contribution of another variable).

[0055]

[0056] where K v (·) represents the modified Bessel function of the second kind of order v, and C1(d,f)~C4(d,f) are auxiliary functions, and their specific expressions are defined as

[0057]

[0058] 1.2 Formulating the channel parameter estimation problem

[0059] According to the description of the composite THz channel model given above, there is a set of unknown channel parameters m(d,f), σ(d,f), and κ(f), which are estimated through repeated channel measurements. For ease of processing, define Therefore, when ψ(d,f) is determined, κ(f) = -(log(ψ(d,f))) / d can be obtained.

[0060] Let there be S independent samples of the internal channel power gain which are expressed as Theoretically, the ML estimation criterion can be used to process these S measurement samples to generate information-theoretically optimal estimates of m(d,f), σ(d,f), and ψ(d,f) by solving the following formulated estimation problem:

[0061]

[0062] where

[0063]

[0064] is a log-likelihood function (LLF).

[0065] It can be clearly seen from Equations (5) and (8) that due to the non-convex and non-linear nature of the LLF, solving the ML estimation problem in Equation (7) is analytically intractable and computationally challenging. This objective involves evaluating and optimizing the composition of transcendental functions, including Bessel functions, gamma functions, and incomplete gamma functions, as well as coupled parameters, which makes standard gradient-based optimization methods prone to converge to local maxima. In addition, when the number of samples S is large or when the input data samples When high variability is exhibited, the likelihood surface becomes more distorted, which may lead to computational overflow. These difficulties not only increase the risk of convergence failure but also reduce the practicality of maximum likelihood (ML)-based channel parameter estimators in real-time or resource-constrained deployment scenarios.

[0066] II. DESIGN OF PARAMETER ESTIMATOR BASED ON PARTICLE SWARM OPTIMIZATION

[0067] To address the tractability and computational challenges described above, an intuitive but less accurate solution has been proposed: First, decompose the original maximum likelihood (ML) estimation problem given by Equation (7) into S sub-problems at the sample level (as shown in Equation (9)), and then approximate the solution of the original ML estimation problem by weighted averaging the sample-level parameter estimates. The specific process is as follows:

[0068]

[0069] Although this decomposed estimator improves tractability and computational convenience, this method has fundamental limitations from a statistical estimation perspective. Specifically, the decomposition process ignores the joint likelihood structure inherent in the original problem of Equation (7), which is crucial for capturing the overall statistical behavior of the sample set. Therefore, the S sub-problems solved separately cannot fully utilize the complete information contained in the sample distribution, which may lead to bias or inconsistency in channel parameter estimation. In addition, the weighted averaging step lacks a rigorous statistical theory support and it is difficult to ensure that the estimator converges to the optimal solution . It can be seen that this decomposed estimator may reduce the estimation accuracy and reliability, especially for the scenarios of heterogeneous fading and shadow dynamic characteristics existing in practical terahertz channels, this problem is more prominent.

[0070] To overcome the above problems, this method proposes a particle swarm optimization (PSO) channel parameter estimator that directly solves the original joint ML estimation problem. As a population-based metaheuristic method, PSO does not require explicit gradient calculation and is particularly suitable for maximizing complex log-likelihood functions (LLFs) that contain special functions and non-linear parameter couplings. Given N particles, each particle can be characterized by a position vector p n , a velocity vector v n and a local record vector The global record vector r * is used to record the current optimal composite channel parameters that produce the highest LLF value among all particles.

[0071] When initializing the PSO algorithm, it is necessary to reasonably configure the state vectors of N particles, which has a decisive impact on the convergence efficiency.

[0072] The initialization process needs to satisfy the parameter constraint conditions: m(d,f) ≥ 0, σ(d,f) ≥ 0, 0 ≤ ψ(d,f) ≤ 1. Ideally, the initial position should be as close as possible to the global optimal solution. Considering the above optimization objectives and the characteristics of the ML estimation problem, the output results of the decomposition estimator described in Equation (10) are used to initialize the position, local record, and global record vectors of the PSO algorithm. The specific method is as follows:

[0073]

[0074] where is a randomly generated integer between 1 and S, used to distinguish the initial positions of N particles to prevent premature convergence in the early stage of the PSO process. Based on the initialized p n , r n and r * , the velocity vector can be initialized as

[0075]

[0076] where a1 and a2 are the internal individual acceleration and swarm acceleration respectively; rand([0,1],1×3) returns a 1×3 vector whose elements are randomly generated values between 0 and 1; ⊙ represents the Hadamard product.

[0077] In each iteration of the PSO process, the particle fitness is quantified by the LLF given in Equation (8), and the relevant vectors will be updated according to the following rules

[0078]

[0079] When are all satisfied, Var{·} returns the variance enclosed during the iteration process; ∈ is a preset precision control threshold; i is the number of iterations experienced, and λ is a preset protection window size used to prevent premature convergence.

[0080] Finally, the estimation of the composite THz channel model generated by the PSO-based estimator is given by the following formula:

[0081]

[0082] When ∈ → 0, will converge to with probability, that is, the optimal solution of the original ML estimation problem given in Equation (7).

[0083] For clarity, the process of parameter estimation of the composite THz channel model based on the particle swarm algorithm is summarized below.

[0084]

[0085]

[0086] To verify the estimation accuracy and computational efficiency of the proposed PSO-based composite channel parameter estimator, the g s (d,f) dataset corresponding to different spreading loss exponents α was used. The dataset was organized on a two-dimensional spatial frequency grid, covering the entire THz band with carrier frequencies f ranging from 0.1 THz to 1 THz and transmitter-receiver distances d between 0.1 m and 10 m, which correspond to different far-field communication scenarios using THz radio. In the extended environment characterized by α, for each spatial frequency state (d,f), there are S = 1000 randomized data samples For ease of study, the following classic THz communication scenarios were defined and studied:

[0087] Scenario 1: d = 0.1 m, f = 0.68 THz, α = 3.88

[0088] Scenario 2: d = 1 m, f = 0.41 THz, α = 2.11

[0089] Scenario 3: d = 10 m, f = 0.36 THz, α = 2.68

[0090] For the following PSO calculations, unless otherwise stated, the parameters were set as N = 100, a1 = a2 = 1, ∈ = 0.5, λ = 100. At the same time, the channel parameter estimators (schemes) based on exhaustive search (ES) and simple decomposer were used as the comparison groups.

[0091] Figure 2 The convergence characteristics of the PSO-based parameter estimator proposed in the present invention in three typical terahertz communication scenarios are shown. The variance of the highest log-likelihood function (LLF) value in each iteration shows a continuous and rapid downward trend, indicating that the algorithm has stable convergence performance. It is worth noting that, as Figure 2 shown, the PSO estimator achieved a significant improvement in the LLF value in all scenarios (the specific gains are shown in the labels of each curve). These experimental results confirm that: compared with the decomposable estimator, the PSO-based estimator can achieve higher estimation accuracy; at the same time, compared with the exhaustive search (ES) estimator, its computational complexity remains within a reasonable range.

[0092] To further evaluate the estimation quality, Figure 3The estimated distributions generated by different estimators using the empirical PDFs and CDFs were compared for all three scenarios. The PSO-based estimator generated corresponding PDF and CDF curves that were closely aligned with those of the ES benchmark, confirming its statistical reliability. In contrast, the decomposition-based estimators showed significant biases in the tail and body regions of the distribution. This further demonstrates the advantage of joint optimization over the full likelihood space, as in the PSO method, rather than relying on decomposed single-sample estimates. Figure 2 and Figure 3 The results shown together highlight the accuracy and robustness of the proposed PSO estimator in estimating composite channel parameters that capture complex THz channel dynamics while maintaining high computational feasibility.

[0093] Taking Scenario 1 as an example, Figure 4 An assessment of the convergence efficiency of the proposed PSO-based composite channel estimator was provided by presenting the number of iterations required under different PSO hyperparameter settings. The figure illustrates how the algorithm performance is affected by different combinations of the acceleration coefficients a1 and a2, the particle swarm size N, and the precision threshold ∈. As shown in the figure, increasing the number of particles generally leads to faster convergence. Conversely, overly aggressive acceleration or too tight an accuracy threshold may result in extended convergence times due to oscillatory behavior or reduced updates. This assessment emphasizes the importance of choosing appropriate PSO hyperparameters to balance estimation accuracy and computational efficiency.

[0094] Overall, the estimator based on the particle swarm optimization algorithm demonstrated strong estimation and fast convergence across a wide range of hyperparameter configurations, highlighting its adaptability and effectiveness in solving the composite terahertz channel parameter estimation problem.

[0095] Finally, it should be noted that the above examples of the present invention are merely examples for illustrating the present invention and are not limitations on the embodiments of the present invention. Although the applicant has described the present invention in detail with reference to the preferred embodiments, for those of ordinary skill in the art, other different forms of changes and modifications can be made based on the above description. It is not possible to enumerate all the embodiments here. Any obvious changes or modifications derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A high-precision estimation method for composite terahertz channel parameters based on particle swarm optimization. Suppose there are S independent samples of the internal channel power gain , which are expressed as The expression of the composite terahertz channel model is where K v (·) represents the modified Bessel function of the second kind of order v, and C1(d,f) to C4(d,f) are auxiliary functions, whose specific expressions are defined as Where \(m(d,f)\), \(\sigma(d,f)\) and \(\psi(d,f)\) are the channel parameters to be estimated, \(d\) is the transmitter-receiver distance; \(f\) is the carrier frequency; \(m(d,f)\) is the multipath fading coefficient, reflecting the complexity of the scattering environment of multipath propagation; \(\sigma(d,f)\) is the shadow intensity; \(\psi(d,f)\) is the path attenuation factor that jointly characterizes the spread of THz radio propagation and molecular absorption loss; It is characterized in that: This method estimates the channel parameters based on the particle swarm optimization algorithm, and the specific steps are as follows. 1) Let the number of particles in the particle swarm be N, and initialize the position vector p of each particle n , velocity vector v n , and local record vector , as well as the global record vector r * . The global record vector r * is used to record the highest log-likelihood function value generated among all particles and serve as the current optimal composite channel parameter; 2) In each iteration of the particle swarm optimization process, the calculation result according to Equation (8) is used as the particle fitness; and the update is performed according to Equation (13). Where \(a1\) and \(a2\) are the internal individual acceleration and swarm acceleration respectively; \(rand([0,1],1\times3)\) returns a \(1\times3\) vector whose elements are randomly generated values between 0 and 1; \(\odot\) represents the Hadamard product. 3) When both and i > λ are satisfied, Var{·} returns the variance enclosed during the iterative process; ∈ is a preset termination threshold; i is the number of iterations experienced, and λ is the size of a preset protection window used to prevent premature convergence; 4) Finally, the channel parameter estimation of the composite terahertz channel model generated by the particle swarm optimization algorithm is given by the following formula: When ∈ → 0, will converge to with probability That is, the optimal solution of the channel parameters satisfying the maximum likelihood estimation criterion is obtained.

2. The high-precision estimation method for composite terahertz channel parameters based on particle swarm optimization according to claim 1, wherein: The initialization of step 1) is specifically carried out as follows. 1.1) Calculate according to the following formula to obtain Among them, It is calculated according to formula (9). s.t., \(m(d,f)\geq0\), \(\sigma(d,f)\geq0\), \(0\lt\psi(d,f)\leq1\), \(1\leq s\leq S\) 1.2) According to the obtained Initialize the position, local record, and global record vectors of the particle swarm optimization algorithm according to the following formula wherein is a randomly generated integer between 1 and S, used to distinguish the initial positions of N particles to prevent premature convergence in the early stage of the PSO process; 1.3) Based on the initialized p n , r n and r * , the velocity vector v n is initialized as follows 3. A high-precision estimation method for composite terahertz channel parameters based on particle swarm optimization according to claim 1, characterized in that: The initialization process needs to satisfy the parameter constraint conditions: \(m(d,f)\geq0\), \(\sigma(d,f)\geq0\), \(0\leq\psi(d,f)\leq1\).

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