A wireless channel fading distribution model suitable for non-uniform media environment and its application

Abstract

The present invention discloses a wireless channel fading distribution model suitable for an inhomogeneous medium environment and its application. The model is a λ-κ-μ model, which is used to describe the fading characteristics of multiple multipath cluster signals with direct paths when they are transmitted in an inhomogeneous medium; wherein the parameter λ describes the correlation between the in-phase and orthogonal components in each multipath cluster, ‑1≤λ≤1; the parameter κ is used to quantify the relative strength between the direct component and the scattered component, κ>0; the parameter μ represents the number of multipath clusters, μ>0. The present invention accurately characterizes the fading characteristics of multipath cluster signals considering direct paths when they pass through an inhomogeneous channel environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication and 5G mobile channel modeling, and in particular relates to a wireless channel fading distribution model suitable for a non-uniform medium environment and its application. Background Art

[0002] In the field of wireless communications, affected by factors such as free space path loss, dielectric properties, terrain, and electromagnetic interference, signals are reflected, diffracted, scattered, and multipath occurs, making the received signal a superimposed signal from multiple directions in the channel, showing complex fading characteristics. In this case, the signal strength or quality fluctuates rapidly in a short period of time, that is, small-scale fast fading. At present, 5G and 6G technologies face a series of technical and engineering challenges in design and implementation, especially in terms of high frequency utilization, increased bandwidth, and reduced latency, which requires higher precision fitting of received signals on a small scale, that is, a channel model is urgently needed for complex and diverse wireless communication environments. In order to better understand and describe these fading characteristics, existing technologies use multiple models including Rayleigh, Rice, Nakagami-m, η-μ, κ-μ, and η-κ for simulation and characterization. However, the above existing models all have certain limitations. For example, Rayleigh and Rice distributions are only applicable to the channel environment of one multipath cluster. Although the Nakagami-m distribution describes the channel environment of multiple multipath clusters, its tail distribution does not match the experimental data. Although the two-parameter composite distribution models η-μ, κ-μ and η-κ have the characteristics of flexible parameters, they are only applicable to describing the channel environment of ideal uniform media.

[0003] In order to more comprehensively reflect the propagation characteristics of 5G signals in non-uniform media environments, it is urgent to propose a more comprehensive and flexible channel fading distribution model. Summary of the invention

[0004] In view of the above situation, the present invention provides a wireless channel fading distribution model suitable for non-uniform media environment and its application. The present invention more accurately characterizes the fading characteristics of multipath cluster signals considering the direct path when passing through a non-uniform channel environment. The model is compatible with models such as Nakagami-m, unilateral Gaussian, Rayleigh and Ricean distribution.

[0005] The present invention adopts the following technical scheme:

[0006] A wireless channel fading distribution model suitable for inhomogeneous media environment is a λ-κ-μ model, which is used to describe the fading characteristics of multiple multipath cluster signals with direct paths when they are transmitted in inhomogeneous media. The specific meanings of the parameters λ, κ and μ are as follows: the parameter λ (-1≤λ≤1) describes the correlation between the in-phase and orthogonal components in each multipath cluster, the parameter κ (κ>0) is used to quantify the relative strength between the direct component and the scattered component, and the parameter μ (μ>0) represents the number of multipath clusters.

[0007] Preferably, the present invention provides the envelope and power normalized probability density function (PDF) of the λ-κ-μ distribution model and its statistical characteristics, cumulative distribution function (CDF), high-order origin moment and moment generating function (MGF).

[0008] Further preferably, considering that there are μ multipath cluster components in the channel propagation environment, the scattered waves in the multipath cluster have the same power σ 2 , and in each multipath cluster of the fading signal, there is a correlation between the in-phase and orthogonal components The total envelope r can then be expressed in terms of in-phase and quadrature components that have the same variance and are not independent:

[0009]

[0010] Among them, x i and i denote the in-phase and quadrature components respectively, p i and q i are their means in the multipath clusters. Obviously, E(x i +p i )=p i , E(y i +q i )=q i , where E(·) represents the mean.

[0011] The probability density function of the joint envelope p(x i ,y i )as follows:

[0012]

[0013] The polar coordinate representation is as follows:

[0014]

[0015] in, Angle parameter θ i satisfy make Get the envelope probability density p(r i )for:

[0016]

[0017] where I0(·) represents the first kind of zero-order modified Bessel function. By transforming Power i The probability density p(w i ) can be expressed as:

[0018]

[0019] In order to obtain the total power density p(w), for any i-th multipath cluster p(w i ) performs Laplace transform:

[0020]

[0021] In order to obtain L(p(w i ))After that, We can get L(p(w)), that is:

[0022]

[0023] Then, by performing an inverse Laplace transform on L(p(w)), the total power can be derived: Density function p(w):

[0024]

[0025] set up Characterize the ratio of the total power of the direct path to the total power of the scattered wave, and then normalize the envelope and power: The normalized envelope PDF (Equation (10)) and power PDF (Equation (9)) expressions can be obtained respectively:

[0026]

[0027]

[0028] Secondly, according to the proposed normalized envelope PDF expression of the λ-κ-μ distribution, its CDF expression is further derived as follows:

[0029]

[0030] in, dx is the Marcum Q function.

[0031] The expression of the k-order origin moment is as follows:

[0032]

[0033] in, is the confluent hypergeometric function.

[0034] The closed form expression of MGF is as follows:

[0035]

[0036] Where n is the parameter introduced when expressing the Bessel function as an infinite series in the derivation process, usually an integer from 0 to infinity; D ν (·) is a parabolic cylinder function.

[0037] The present invention also discloses an application of the above-mentioned wireless channel fading distribution model, and the model is applied to the following physical environment: the actual transmission environment of the scattering field is an inhomogeneous environment related to the surface space, that is, the in-phase and orthogonal components of each multipath cluster signal are non-independent; when the signal passes through the inhomogeneous medium environment, each multipath cluster signal has a mirror component, the mirror component has a random phase and similar delay time, and different clusters show time delay diffusion.

[0038] The present invention flexibly adjusts the parameters of the λ-κ-μ distribution model, and the model is compatible with multiple models including Nakagami-m, unilateral Gaussian, Rayleigh and Rice distribution.

[0039] Normalized envelope PDF and CDF, by observing the changing trend of the peak degree and skewness of the PDF and CDF simulation curves and analyzing the physical meaning behind them, can identify the fading characteristics of the λ-κ-μ distribution under different transmission conditions, further optimize its parameter range, and provide powerful guidance for formulating effective communication system strategies and adjusting parameters.

[0040] The λ-κ-μ fading distribution model of the present invention has many characteristics, including but not limited to:

[0041] 1) Versatility: Applicable to uniform and non-uniform transmission environments;

[0042] 2) Physical interpretability: Use parameters λ, κ, and μ to characterize the physical phenomena of the communication channel environment, making the model more consistent with the characteristics of the actual communication environment;

[0043] 3) Flexibility: By adjusting parameters, the model can be compatible with a variety of other distribution models, such as Nakagami-m, unilateral Gaussian, Rayleigh and Rice distributions, providing higher degrees of freedom and better characterizing the small-scale fading of the signal.

[0044] The λ-κ-μ distribution model of the present invention is not only applicable to non-uniform channel environments, but also has broader application prospects, especially in the aspects of communication system reliability and transmission performance.

[0045] In summary, the present invention proposes a λ-κ-μ model to describe the fading characteristics of multiple multipath cluster signals with direct paths when they are transmitted in non-uniform media. The normalized PDF of the envelope and power of the model, as well as statistical characteristics such as the cumulative distribution function (CDF), high-order origin moment and moment generating function (MGF) are given. These statistical characteristics can not only be widely used in fields such as parameter estimation and error analysis, but also have important value in communication, signal processing and statistical modeling. By flexibly adjusting the parameters of the λ-κ-μ distribution model, the model is compatible with a variety of models including Nakagami-m, unilateral Gaussian, Rayleigh and Rice distribution. The embodiment of the present invention also analyzes the envelope PDF and CDF of the λ-κ-μ distribution in detail, observes the changing trends of the peak degree and skewness of the PDF and CDF simulation curves, analyzes the physical meaning behind them, and can identify the fading characteristics of the λ-κ-μ distribution under different transmission conditions, further optimize its parameter range, and provide powerful guidance for formulating effective communication system strategies and adjusting parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is the graph showing the normalized envelope PDF function of λ-κ-μ as a function of κ.

[0047] Figure 2 This is the graph of the normalized envelope PDF function of λ-κ-μ as μ changes.

[0048] Figure 3 This is the graph showing the normalized envelope PDF function of λ-κ-μ changing with λ.

[0049] Figure 4 When the parameter m is fixed, the changes in the normalized envelope PDF and CDF function of λ-κ-μ.

[0050] Figure 5 The range of the λ-κ-μ distribution and its relationship with other distributions when the parameter m is fixed. DETAILED DESCRIPTION

[0051] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0052] This embodiment discloses a wireless channel fading distribution model suitable for a non-uniform medium environment.

[0053] Considering the real transmission environment of the scattering field is a non-uniform environment related to the surface space, that is, the in-phase and orthogonal components of each multipath cluster signal are non-independent. When the signal passes through this non-uniform medium environment, each multipath cluster signal has a mirror component (direct path), and the scattered component has a random phase and similar delay time. Different clusters show relatively large time delay spread.

[0054] Based on the above physical environment, this embodiment proposes a λ-κ-μ model to describe the fading characteristics of multiple multipath cluster signals with direct paths when they are transmitted in non-uniform media. The specific meanings of the parameters λ, κ, and μ are as follows: the parameter λ (-1≤λ≤1) describes the correlation between the in-phase and orthogonal components in each multipath cluster, the parameter κ (κ>0) is used to quantify the relative strength between the direct component and the scattered component, and the parameter μ (μ>0) represents the number of multipath clusters.

[0055] The invention provides the envelope and power normalized probability density function (PDF) of the λ-κ-μ distribution model and its statistical characteristics, cumulative distribution function (CDF), high-order origin moment and moment generating function (MGF).

[0056] First, consider the channel propagation environment with μ multipath cluster components, and the scattered waves in the multipath cluster have the same power σ 2 , and in each multipath cluster of the fading signal, there is a correlation between the in-phase and orthogonal components The total envelope r can then be expressed in terms of in-phase and quadrature components that have the same variance and are not independent:

[0057]

[0058] Among them, x i and i denote the in-phase and quadrature components respectively, p i and q i are their means in the multipath cluster. Let E(·) represent the mean, and it is obvious that E(x i +p i )=p i , E(y i +q i )=q i .

[0059] The probability density function of the joint envelope p(x i ,y i )as follows:

[0060]

[0061] The polar coordinate representation is as follows:

[0062]

[0063] in, Angle parameter θ i satisfy make Get the envelope probability density p(r i )for:

[0064]

[0065] where I0(·) represents the first kind of zero-order modified Bessel function. By transforming Power i The probability density p(w i ) can be expressed as:

[0066]

[0067] In order to obtain the total power density p(w), for any i-th multipath cluster p(w i ) to perform Laplace transform:

[0068]

[0069] In order to obtain L(p(w i ))After that, We can get L(p(w)), that is:

[0070]

[0071] Then, by performing an inverse Laplace transform on L(p(w)), the total power can be derived: Density function p(w):

[0072]

[0073] set up Characterize the ratio of the total power of the direct path to the total power of the scattered wave, and then normalize the envelope and power: The normalized envelope PDF (Equation (10)) and power PDF (Equation (9)) expressions can be obtained respectively:

[0074]

[0075]

[0076] Secondly, according to the proposed normalized envelope PDF expression of the λ-κ-μ distribution, its CDF expression is further derived as follows:

[0077]

[0078] in, dx is the Marcum Q function.

[0079] The expression of the k-order origin moment is as follows:

[0080]

[0081] in, is the confluent hypergeometric function.

[0082] The closed form expression of MGF is as follows:

[0083]

[0084] Where n is the parameter introduced when expressing the Bessel function as an infinite series in the derivation process, usually an integer from 0 to infinity; D ν (·) is a parabolic cylinder function.

[0085] By adjusting the parameters, the λ-κ-μ distribution model proposed in the present invention is compatible with various models including Nakagami-m, unilateral Gaussian, Rayleigh and Rice distributions:

[0086] The shape and fading characteristics of the λ-κ-μ distribution are described by the normalized variance of the power, namely the Nakagami-m fading parameter. The severity of signal fading can be inferred by examining the value of m: the smaller the m, the more obvious the signal fading and the greater the spatial variation of the signal strength. By flexibly adjusting the parameter m, not only can the shape characteristics of the λ-κ-μ distribution under different fading conditions be described, but also the PDF and CDF curve change trends of the λ-κ-μ distribution after the parameter m is fixed can be analyzed. In addition, by appropriately adjusting the parameters of the λ-κ-μ distribution, κ-μ, Nakagami-m, Rayleigh, Ricean and unilateral Gaussian distributions can be obtained. The specific parameter values ​​are as follows:

[0087]

[0088] The following is a detailed analysis of the changing trends of the normalized PDF and CDF curves of the λ-κ-μ distribution:

[0089] like Figure 1 , Figure 2 , Figure 3 As shown in the figure, the PDF curves of λ-κ-μ are close to normal distribution according to the central limit theorem, and the PDF curves become more and more "sharp" as κ, μ, and λ increase. The reason is that the increase of κ and μ means that the influence of the direct (scattered) path signal is getting bigger (smaller), that is, the direct path plays a dominant role in the signal, resulting in the signal envelope being more concentrated near the signal mean (direct path envelope), so the curve becomes more "sharp" accordingly; the increase of λ means that the coupling relationship between the in-direction component and the orthogonal component of the scattering path is strengthened, making the intensity of the signal scattering path related to the direction and more concentrated in certain directions, so the curve becomes more and more "sharp" in the part less than the signal mean. In addition, if there is a correlation between the in-direction component and the orthogonal component of the scattering path, when the in-direction component is interfered, the orthogonal component will also be affected at the same time, resulting in a decrease in the signal's anti-interference ability.

[0090] Figure 4 The figure shows how the λ-κ-μ normalized PDF and CDF curves change with the number of multipath clusters when the Nakagami parameter m is fixed. Obviously, when signals with the same fading degree (m) have different numbers of multipath clusters, their PDF and CDF curves still show obvious differences. In the CDF graph, it can be clearly observed that as the number of multipath clusters μ increases, the probability of the envelope in the tail changes by several orders of magnitude. This feature makes the λ-κ-μ distribution highly flexible, and this flexibility can be used to adjust the curve to suit the actual scenario. In addition, by observing Figure 4 The CDF curve can easily set the fading margin (horizontal axis) according to the allowed outage probability (vertical axis). For example, the system must be designed with a fading margin of 28dB (relative to the median) to achieve an outage probability of less than 1%. Obviously, the smaller the number of multipath clusters μ, the larger the fading amplitude, the greater the outage probability, and the larger the fading margin that needs to be set.

[0091] Figure 5 The shaded part of describes the boundary range of the λ-κ-μ distribution CDF. Obviously, on the F(ρ)×ρ logarithmic plane, the λ-κ-μ distribution has a wide range of values, which is compatible with Nakagami-m, Rayleigh and Rice distributions. For any set of measured data sets, calculate the value of its Nakagami parameter m and draw the distribution curve on the fading plane. If the curve is within this shaded area, the λ-κ-μ distribution can effectively simulate these data.

[0092] In summary, the present invention provides a wireless channel fading distribution model suitable for non-uniform media environments and its application. The present invention aims to more accurately characterize the fading characteristics of wireless signals when transmitted in complex non-uniform environments. With the development of 5G and 6G technologies, communication systems face business requirements such as high frequency, large bandwidth and low latency. However, the complexity and diversity of communication environments make it impossible for traditional channel distribution models to fully capture the transmission characteristics of signals in complex and changeable non-uniform channel environments. To this end, the present invention proposes a λ-κ-μ distribution model, which introduces parameters κ, μ and λ to more accurately characterize and characterize the signal fading characteristics of multipath cluster signals with multiple direct paths in non-uniform media environments. The present invention provides the normalized probability density function (PDF) of the envelope and power of the distribution model and its statistical characteristics, the cumulative distribution function (CDF), the high-order origin moment and the moment generating function (MGF). By analyzing the envelope PDF and CDF in detail, the present invention reveals the influence mechanism of parameters κ, μ and λ on the signal fading characteristics: the larger the κ, the more concentrated the signal envelope will be near the direct component; when the environmental fading degree is certain, the smaller μ, the more serious the signal fading and the greater the interruption probability; the larger λ, the more concentrated the scattered signal envelope will be. The present invention also gives the relationship between this distribution model and other distribution models. In short, the distribution model proposed in the present invention not only provides a rich parameter adjustment space for communication channel design and performance optimization, but also provides an effective solution for channel modeling in non-uniform environments in wireless communications.

[0093] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. A person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the scope of the present application should be based on the protection scope of the claims.

Claims

1. A wireless channel fading distribution model suitable for non-uniform media environment, characterized by: The model is a λ-κ-μ model, which is used to describe the fading characteristics of multiple multipath cluster signals with direct paths when they are transmitted in an inhomogeneous medium; wherein the parameter λ describes the correlation between the in-phase and orthogonal components in each multipath cluster, -1≤λ≤1; the parameter κ is used to quantify the relative strength between the direct component and the scattered component, κ>0; the parameter μ represents the number of multipath clusters, μ>0; There are μ multipath cluster components in the channel propagation environment, and the scattered waves in the multipath cluster have the same power σ 2 , and in each multipath cluster of the fading signal, there is a correlation between the in-phase and orthogonal components The total envelope r is then expressed in terms of in-phase and quadrature components that have the same variance and are not independent: Among them, x i and i denote the in-phase and quadrature components respectively, p i and q i are the means in the multipath clusters; E(xi+pi)=pi, E(y i +q i )=q i , where E(·) represents the mean; The probability density function of the joint envelope p(x i ,y i )as follows: The polar coordinate representation is as follows: in, Angle parameter θ i satisfy make Get the envelope probability density p(r i )for: where I0(·) represents the first kind of zero-order modified Bessel function; by transforming Power i The probability density p(w i ) is expressed as: In order to obtain the total power density p(w), for any i-th multipath cluster p(w i ) to perform Laplace transform: Where s is the parameter in the complex domain after Laplace transform; Get L(p(w i ))After that, We get L(p(w)), which is: Perform an inverse Laplace transform on L(p(w)) to derive the total power Density function p(w): set up Characterize the ratio of the total power of the direct path to the total power of the scattered wave, and then normalize the envelope and power: The normalized power PDF and envelope PDF are obtained as follows: Among them, I μ-1 is the modified Bessel function of the first kind; According to the normalized envelope PDF expression of the λ-κ-μ distribution, its CDF expression is further derived as follows: in dx is the Marcum Q function; The expression of the k-order origin moment is as follows: where Γ is the gamma function, is the confluent hypergeometric function; The closed form expression of MGF is as follows: Where n is the parameter introduced when expressing the Bessel function as an infinite series in the derivation process, and takes an integer from 0 to infinity; D ν (·) is a parabolic cylinder function.

2. According to claim 1, a wireless channel fading distribution model suitable for a non-uniform medium environment is characterized in that: The λ-κ-μ model includes normalized probability density function PDF of envelope and power, cumulative distribution function CDF, high-order origin moment and moment generating function MGF.

3. A wireless channel fading distribution model suitable for a non-uniform medium environment according to claim 1 or 2, characterized in that: The application physical environment of the model is as follows: the actual transmission environment of the scattering field is an inhomogeneous environment related to the surface space, that is, the in-phase and orthogonal components of each multipath cluster signal are non-independent; when the signal passes through the inhomogeneous medium environment, each multipath cluster signal has a mirror component, which has a random phase and similar delay time, and different clusters show time delay diffusion.

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