A wireless channel fading distribution model suitable for complex environments

Abstract

The present invention relates to the field of wireless communication technology, and discloses a wireless channel fading distribution model suitable for complex environments. The model is an α-λ-κ-μ distribution model, which obtains the distribution characteristics of the signal envelope and signal-to-noise ratio of the wireless channel in a complex environment including nonlinear media, non-uniform environments, and multipath propagation characteristics according to the four parameters α, λ, κ, and μ of the wireless channel in a complex environment, so as to obtain the fading distribution characteristics of the wireless channel in a complex environment; wherein α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, ‑1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a wireless channel fading distribution model suitable for complex environments. Background Art

[0002] In the field of wireless communications, accurately describing the propagation characteristics of signals is the key to understanding their interaction with the environment. Signals are affected by diffraction, scattering, and reflection during propagation, forming multipath propagation. When multipath signals are superimposed at the receiving end, interference occurs due to path differences, resulting in rapid fluctuations in signal strength, i.e., short-term fading, which affects communication quality. Moreover, with the development of communication technology, especially in scenarios such as satellite communications, signals are also affected by nonlinear media and non-uniform environments, causing changes in signals during propagation due to the nonlinear characteristics of the medium and the non-uniform characteristics of the environment. However, current channel models cannot accurately describe the propagation characteristics of signals in the above-mentioned complex channel environments. Summary of the invention

[0003] The purpose of the present invention is to provide a wireless channel fading distribution model suitable for complex environments, which can accurately characterize the fading characteristics of signals under the influence of multipath propagation and nonlinear media.

[0004] To solve the above technical problems, an embodiment of the present invention provides a wireless channel fading distribution model suitable for complex environments, the model is an α-λ-κ-μ distribution model, including: a signal envelope analysis module and a signal-to-noise ratio analysis module;

[0005] The signal envelope analysis module is used to obtain the probability density function and cumulative distribution function of the signal envelope according to the four parameters α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics, and obtain the distribution characteristics of the signal envelope of the wireless channel in a complex environment;

[0006] Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are then combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattered component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0;

[0007] The signal-to-noise ratio analysis module is used to obtain the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio according to the four parameters of the wireless channel α, λ, κ and μ, and obtain the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment;

[0008] The distribution characteristics of the signal envelope in a complex environment and the distribution characteristics of the signal-to-noise ratio in a complex environment are used to indicate the fading distribution characteristics of the wireless channel in a complex environment.

[0009] Optionally, the signal envelope analysis module is also used to obtain the probability density function of the signal envelope under the second-order moment and the higher-order moment according to the four parameters α, λ, κ and μ of the wireless channel, and to obtain the cumulative distribution function of the signal envelope under the second-order moment and the higher-order moment.

[0010] Optionally, the signal-to-noise ratio analysis module is further used to obtain the asymptotic results of the probability density function and the cumulative distribution function of the signal-to-noise ratio according to the four parameters α, λ, κ and μ of the wireless channel, so as to obtain the distribution characteristics of the signal-to-noise ratio under specific channel conditions.

[0011] Optionally, the signal envelope analysis module is further used to obtain the level crossing rate, average fading duration and fading amount of the wireless channel in a complex environment according to the probability density function and cumulative distribution function of the signal envelope.

[0012] Optionally, the signal-to-noise ratio analysis module is also used to obtain the interruption probability, average bit error rate and ergodic capacity of the wireless channel under the optimal rate adaptation strategy, channel inversion and fixed rate strategy in a complex environment based on the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio.

[0013] Optionally, in the α-λ-κ-μ distribution model, the scattered components in each multipath cluster signal have the same power , and the correlation between the in-phase component and the orthogonal component in each multipath cluster signal , envelope R λκμ It is expressed in the form of in-phase and quadrature components with the same variance and that are not independent:

[0014] ;

[0015] In the formula, and for , , Gaussian variables;

[0016] Signal envelope of λ-κ-μ distribution in α-λ-κ-μ distribution model The probability density function PDF is:

[0017] ;

[0018] In the formula, , , , represents the gamma function, is the Kummer confluence hypergeometric function, is the ratio of the total power of the line-of-sight path to the total power of the scattering path, , , ;

[0019] By transforming , , the PDF of the signal envelope of the λ-κ-μ distribution is obtained as:

[0020] ;

[0021] The envelope k-order moment of the λ-κ-μ distribution is:

[0022] ;

[0023] In the formula, is the Gaussian confluence hypergeometric function;

[0024] Considering signal envelopes affected by nonlinear media , and define ,but:

[0025] ;

[0026] Let the PDF of the envelope of the λ-κ-μ distribution signal be , the PDF of the signal envelope of the α-λ-κ-μ distribution model is obtained as:

[0027] ;

[0028] In the formula, ;

[0029] If we define the mean value of the signal envelope , then the PDF of the signal envelope of the α-λ-κ-μ distribution model is:

[0030] ;

[0031] By definition , the cumulative distribution function CDF of the signal envelope under the second-order moment and the higher-order moment are respectively:

[0032] ;

[0033] ;

[0034] Where Φ2 is the binary confluence Appel function;

[0035] according to , the PDF of the signal-to-noise ratio is:

[0036] ;

[0037] according to , the CDF of the signal-to-noise ratio is:

[0038] ;

[0039] according to , the k-order origin moment of the signal-to-noise ratio can be obtained as follows:

[0040] ;

[0041] according to , the moment generating function MGF of the signal-to-noise ratio can be obtained as follows:

[0042] ;

[0043] In the formula, is the Fox H function.

[0044] Optionally, by performing variable substitution on the CDF of the signal envelope at the second-order moment, , the PDF of the signal envelope is obtained, and the level penetration rate LCR of the α-λ-κ-μ distribution model is obtained as:

[0045] ;

[0046] In the formula, is the maximum Doppler frequency;

[0047] According to the definition , the average fading time AFD of the α-λ-κ-μ distribution model can be obtained as:

[0048] ;

[0049] The k-th moment of the signal envelope is:

[0050] ;

[0051] According to the definition of k-th moment and attenuation , the fading amount AoF can be obtained as:

[0052] ;

[0053] In the formula, ;

[0054] From the PDF of the signal-to-noise ratio, by replacing the variables , the outage probability OP under the α-λ-κ-μ distribution model is obtained as:

[0055] ;

[0056] In the formula, is the lower incomplete gamma function;

[0057] The average bit error rate under the α-λ-κ-μ distribution model is:

[0058] ;

[0059] In the formula, is the G-function;

[0060] The ergodic capacity of CIFA and the ergodic capacity of EC under the optimal rate adaptation strategy ORA, channel inversion and fixed rate strategy are respectively:

[0061] ;

[0062] ;

[0063] Depend on , It can be obtained that the asymptotic results of the PDF and CDF of the signal-to-noise ratio under high average signal-to-noise ratio conditions are:

[0064] ;

[0065] ;

[0066] And the asymptotic results of outage probability, average bit error rate, and ergodic capacity under high average signal-to-noise ratio conditions are:

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] In the formula, .

[0072] An embodiment of the present invention further provides a method for analyzing fading distribution of a wireless channel in a complex environment, comprising the following steps:

[0073] Obtain the values ​​of the four parameters α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics;

[0074] Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are then combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattered component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0;

[0075] Input the values ​​of the four parameters α, λ, κ and μ of the wireless channel into the above-mentioned wireless channel fading distribution model applicable to complex environments; wherein the wireless channel fading distribution model applicable to complex environments is an α-λ-κ-μ distribution model, including a signal envelope analysis module and a signal-to-noise ratio analysis module;

[0076] Through the signal envelope analysis module, the probability density function and cumulative distribution function of the signal envelope are obtained, and the distribution characteristics of the signal envelope of the wireless channel in a complex environment are obtained;

[0077] Through the signal-to-noise ratio analysis module, the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio are obtained, and the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment are obtained;

[0078] The fading distribution characteristics of the wireless channel in a complex environment are obtained by combining the distribution characteristics of the signal envelope of the wireless channel in a complex environment and the distribution characteristics of the signal-to-noise ratio in a complex environment.

[0079] The wireless channel fading distribution model applicable to complex environments provided by the present invention has at least the following beneficial effects:

[0080] Wireless signals will fade under the influence of nonlinear media, non-uniform environments and multipath propagation conditions. The wireless channel fading distribution model suitable for complex environments of the present invention, namely the α-λ-κ-μ distribution model, uses parameters α, λ, κ and μ to respectively represent the nonlinear strength of the nonlinear medium, the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, the strength of the line-of-sight component relative to the scattered component, and the number of multipath cluster signals. Then, the probability density function and the cumulative distribution function of the signal envelope are obtained through the above channel parameters to describe the distribution characteristics of the signal envelope and obtain the signal-to-noise ratio. The probability density function, cumulative distribution function, high-order origin moment and moment generating function are used to describe the distribution characteristics of the signal-to-noise ratio. Therefore, the signal propagation characteristics in nonlinear media, non-uniform environments and complex propagation environments formed by multipath propagation are accurately characterized by combining the signal envelope and the distribution characteristics of the signal-to-noise ratio. The interaction between the signal and the above-mentioned complex propagation environment is comprehensively analyzed, so that the α-λ-κ-μ distribution model can describe the fading characteristics of wireless signals containing line-of-sight components in nonlinear media, non-uniform environments and multipath propagation (i.e. complex propagation environments), which has broad application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] One or more embodiments are exemplarily described by the pictures in the corresponding drawings, and these exemplary descriptions do not constitute limitations on the embodiments.

[0082] Figure 1 is a schematic diagram of an α-λ-κ-μ distribution model provided according to an embodiment of the present invention;

[0083] Figure 2 is a flow chart of derivation of an α-λ-κ-μ distribution model provided according to an embodiment of the present invention;

[0084] Figure 3 It is a schematic diagram of the change of the signal-to-noise ratio PDF function of an α-λ-κ-μ distribution model with κ and μ according to an embodiment of the present invention;

[0085] Figure 4 It is a schematic diagram of the change of the signal-to-noise ratio PDF function of an α-λ-κ-μ distribution model with α and λ according to an embodiment of the present invention;

[0086] Figure 5 It is a schematic diagram of the change of LCR and AFD functions of an α-λ-κ-μ distribution model according to an embodiment of the present invention with respect to α and λ;

[0087] Figure 6 It is a schematic diagram of changes in the signal-to-noise ratio PDF and CDF functions of the α-λ-κ-μ distribution model when the fading amount AoF is fixed according to an embodiment of the present invention;

[0088] Figure 7 It is a schematic diagram of the change of the interruption probability function of an α-λ-κ-μ distribution model with α and λ provided in accordance with an embodiment of the present invention;

[0089] Figure 8 It is a schematic diagram of the variation of the average bit error rate function of an α-λ-κ-μ distribution model with α and λ provided according to an embodiment of the present invention;

[0090] Fig. 9 It is a schematic diagram of the change of the average bit error rate function of an α-λ-κ-μ distribution model with the modulation mode according to an embodiment of the present invention;

[0091] Fig.10 It is a schematic diagram of the change of ergodic capacity function of an α-λ-κ-μ distribution model with α and λ provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0092] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. However, it will be appreciated by those skilled in the art that in the embodiments of the present invention, many technical details are proposed in order to enable the reader to better understand the present invention. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present invention can be implemented. The division of the following embodiments is for the convenience of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined and referenced with each other without contradiction.

[0093] An embodiment of the present invention relates to a wireless channel fading distribution model suitable for complex environments. The implementation details of the wireless channel fading distribution model suitable for complex environments of this embodiment are specifically described below. The following content is only the implementation details provided for easy understanding and is not necessary for implementing this solution.

[0094] The wireless channel fading distribution model applicable to complex environments in this embodiment is the α-λ-κ-μ distribution model, such as Figure 1 As shown, the α-λ-κ-μ distribution model includes: a signal envelope analysis module and a signal-to-noise ratio analysis module.

[0095] Specifically, the signal envelope analysis module is used to obtain the probability density function and cumulative distribution function of the signal envelope according to the four parameters of α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics, and obtain the distribution characteristics of the signal envelope of the wireless channel in a complex environment. Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattering component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the strength of the line-of-sight component relative to the scattering component, κ>0; μ represents the number of multipath cluster signals, μ>0.

[0096] The signal-to-noise ratio analysis module is used to obtain the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio according to the four parameters of the wireless channel α, λ, κ and μ, and obtain the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment.

[0097] The distribution characteristics of the signal envelope in a complex environment and the distribution characteristics of the signal-to-noise ratio in a complex environment obtained above are used to indicate the fading distribution characteristics of the wireless channel in a complex environment.

[0098] In the specific implementation, the signal envelope analysis module is also used to obtain the probability density function of the signal envelope under the second-order moment and the higher-order moment according to the four parameters α, λ, κ and μ of the wireless channel, and to obtain the cumulative distribution function of the signal envelope under the second-order moment and the higher-order moment.

[0099] The signal-to-noise ratio analysis module is also used to obtain the asymptotic results of the probability density function and the cumulative distribution function of the signal-to-noise ratio according to the four parameters α, λ, κ and μ of the wireless channel, and obtain the distribution characteristics of the signal-to-noise ratio under specific channel conditions.

[0100] The signal envelope analysis module is also used to obtain the level crossing rate, average fading duration and fading amount of the wireless channel in a complex environment according to the probability density function and cumulative distribution function of the signal envelope.

[0101] The signal-to-noise ratio analysis module is also used to obtain the interruption probability, average bit error rate and ergodic capacity of the wireless channel under the optimal rate adaptation strategy, channel reversal and fixed rate strategy in a complex environment according to the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio.

[0102] Based on the above content, the distribution characteristics of the signal envelope of the wireless channel in a complex environment and the distribution characteristics of the signal-to-noise ratio in a complex environment can be more comprehensively described, so that the fading distribution characteristics of the wireless channel in a complex environment can be more accurately described.

[0103] In this embodiment, the wireless signal will fade under the influence of nonlinear media, non-uniform environment and multipath propagation conditions. The wireless channel fading distribution model applicable to complex environments of the present invention, namely, the α-λ-κ-μ distribution model, uses parameters α, λ, κ and μ to respectively represent the nonlinear strength of the nonlinear medium, the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, the strength of the line-of-sight component relative to the scattered component, and the number of multipath cluster signals. Then, the probability density function and the cumulative distribution function of the signal envelope are obtained through the above channel parameters to describe the distribution characteristics of the signal envelope, and the signal The probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio are used to describe the distribution characteristics of the signal-to-noise ratio. Then, combined with the signal envelope and the distribution characteristics of the signal-to-noise ratio, the propagation characteristics of the signal in nonlinear media, non-uniform environments and complex propagation environments formed by multipath propagation are accurately characterized. The interaction between the signal and the above-mentioned complex propagation environment is comprehensively analyzed, so that the α-λ-κ-μ distribution model can describe the fading characteristics of wireless signals containing line-of-sight components under nonlinear media, non-uniform environments and multipath propagation (i.e., complex propagation environments), and has broad application potential.

[0104] The following is a specific embodiment to describe the wireless channel fading distribution model applicable to complex environments of the present invention:

[0105] Assume that the wireless signal received by the wireless channel is the result of the combination of multiple multipath components (i.e., multipath cluster signals) through nonlinear functions (i.e., nonlinear media). Among them, the environment of the wireless channel scattering field is non-uniform, which means that the in-phase component and the orthogonal component of each multipath cluster signal do not exist independently, but are interrelated. During the signal transmission process, each multipath cluster signal contains a line-of-sight component (i.e., direct path), and its scattered components have random phases and similar delays, while different multipath cluster signals show large time delay spread.

[0106] Based on the above physical assumptions, this embodiment proposes an α-λ-κ-μ distribution model to describe the fading behavior of multipath cluster signals in nonlinear media and non-uniform environments. Among them, each parameter in the α-λ-κ-μ distribution model has a specific meaning: α (α>0) is used to characterize the nonlinear strength of the nonlinear medium; λ (-1≤λ≤1) represents the correlation between the in-phase component and the orthogonal component in the multipath cluster signal; κ (κ>0) is used to quantify the intensity of the line-of-sight component relative to the scattered component; μ (μ>0) defines the number of multipath cluster signals.

[0107] Based on the above-mentioned α-λ-κ-μ distribution model, this embodiment proposes an envelope distribution function based on the second-order moment and high-order moment of the envelope, and uses the derived formula to give the statistical characteristics of the signal-to-noise ratio, including the analytical expressions of the probability density function (PDF), the cumulative distribution function (CDF), the high-order origin moment and the moment generating function (MGF). And based on the envelope statistical characteristics of the channel model, the accurate closed-form expressions of important performance indicators such as the level crossing rate (LCR), the average fade duration (AFD) and the amount of fading (AoF) are derived. In addition, the statistical characteristics of the signal-to-noise ratio are used to analyze the outage probability (OP), the average bit error rate (BER) under different modulation modes, and the ergodic capacity (EC) under the optimal rate adaptation (ORA), channel inversion and fixed rate strategy (CIFA), and the corresponding high signal-to-noise ratio asymptotic results are given. The derivation process is as follows: Figure 2 shown.

[0108] First, consider the channel propagation environment with μ multipath cluster components, and the scattered waves in the multipath cluster have the same power , and in each multipath cluster of the fading signal, there is a correlation between the in-phase and orthogonal components , then the total envelope R λκμ It can be expressed in terms of in-phase and quadrature components that have the same variance and are dependent:

[0109] ;

[0110] In the formula, and for , , Gaussian variables of

[0111] It can be obtained that the normalized envelope of the λ-κ-μ distribution in the α-λ-κ-μ distribution model is The PDF is:

[0112] ;

[0113] In the formula, , , , represents the gamma function, is the Kummer confluence hypergeometric function, is the ratio of the total power of the line-of-sight path to the total power of the scattering path, , , ;

[0114] By transforming , , the envelope PDF of the λ-κ-μ distribution is obtained as:

[0115] ;

[0116] The envelope k-order moment of the λ-κ-μ distribution is:

[0117] ;

[0118] In the formula, is the Gaussian confluence hypergeometric function;

[0119] Considering the envelope of wireless signals affected by nonlinear media , and define ,but:

[0120] ;

[0121] Let the envelope k-order moment of the λ-κ-μ distribution be , the envelope PDF of the α-λ-κ-μ distribution model is obtained as:

[0122] ;

[0123] In the formula, ;

[0124] If we define the mean of the envelope , then the envelope PDF of the α-λ-κ-μ distribution model is:

[0125] ;

[0126] By definition , the CDFs of the envelope second-order moment and higher-order moment are obtained as follows:

[0127] ;

[0128] ;

[0129] Where Φ2 is the binary confluence Appel function;

[0130] according to , the PDF of the instantaneous signal-to-noise ratio is:

[0131] ;

[0132] according to , the CDF of the instantaneous signal-to-noise ratio is:

[0133] ;

[0134] according to , the k-order origin moment of the instantaneous signal-to-noise ratio can be obtained as follows:

[0135] ;

[0136] according to , the MGF of the instantaneous signal-to-noise ratio can be obtained as follows:

[0137] ;

[0138] In the formula, is the Fox H function.

[0139] By substituting variables in the CDF including the second moment , the PDF of the normalized envelope is obtained, and the level penetration rate LCR of the α-λ-κ-μ distribution model is obtained as follows:

[0140] ;

[0141] In the formula, is the maximum Doppler frequency;

[0142] According to the definition , the average fading time AFD of the α-λ-κ-μ distribution model can be obtained as:

[0143] ;

[0144] The k-th moment of the envelope is:

[0145] ;

[0146] According to the definition of k-th moment and attenuation , the fading amount AoF can be obtained as:

[0147] ;

[0148] In the formula, .

[0149] From the PDF of the instantaneous signal-to-noise ratio, by replacing the variables , the outage probability OP under the α-λ-κ-μ distribution model is obtained as:

[0150] ;

[0151] In the formula, is the lower incomplete gamma function;

[0152] The definition of average bit error rate is:

[0153] ;

[0154] In the formula, represents the Gaussian Q function, δ 1 , δ 2,j , δ 3 Indicates different modulation schemes, and the specific parameters are shown in Table 1:

[0155] Table 1

[0156]

[0157] It can be obtained that the average bit error rate under the α-λ-κ-μ distribution model is:

[0158] ;

[0159] In the formula, is the G-function;

[0160] The ergodic capacity (EC) of CIFA under the optimal rate adaptation ORA, channel inversion and fixed rate strategies are:

[0161] ;

[0162] .

[0163] Depend on , It can be obtained that the asymptotic forms of the signal-to-noise ratio PDF and CDF under high average signal-to-noise ratio conditions are:

[0164] ;

[0165] ;

[0166] Substitute the above formula into the definition of outage probability, average bit error rate, and ergodic capacity, and the asymptotic formulas of outage probability, average bit error rate, and ergodic capacity under high average signal-to-noise ratio conditions are:

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] In the formula, .

[0172] By adjusting the parameters, the α-λ-κ-μ distribution model of this embodiment is compatible with λ-κ-μ, α-κ-μ, α-μ, κ-µ, λ-µ, Nakagami-m, unilateral Gaussian, Rayleigh and Rice distributions, and the specific parameters are shown in Table 2:

[0173] Table 2

[0174]

[0175] The PDF and CDF of the signal-to-noise ratio under the α-λ-κ-μ distribution and the changing trend of its performance curve are analyzed in detail, such as Figure 3 and Figure 4 As shown in the figure, with the increase of κ or μ, the single peak phenomenon of the curve becomes more and more obvious, and the extreme point moves to the upper right. This is because when κ and μ increase, ζ2 will increase or δ2 will decrease, which means the increase of the signal direct link (LOS) power or the decrease of the scattering link (NLOS). Therefore, the power distribution of the signal is more concentrated, and the probability that the signal power is close to the mean is greater, so the increase of κ or μ means the better the signal quality. Similar to the previous example, the increase of the nonlinear parameter α increases the kurtosis of the PDF curve and shows right skewness. This is because α can be regarded as an indicator that describes the nonlinear relationship of all path signals, that is, , α increases, which can be regarded as the power of the partial multipath signal actually received by the receiver is greater, then the total power of the actual received signal is greater, and the probability of a high signal-to-noise ratio increases, which means that the signal quality is better. In contrast to the effect of the increase in α, the increase in the correlation coefficient λ reduces the kurtosis of the PDF curve and shows a left skewness. This is because the larger |λ| is, the higher the correlation between the in-phase component and the orthogonal component of the signal. When the in-phase component of the signal is affected, the orthogonal component will also be affected, which means that the signal quality deteriorates.

[0176] Figure 5The normalized level crossing rate and normalized average decay time are plotted respectively. For α, as expected, when the signal stability is enhanced, the signal fluctuation frequency decreases, which means that the signal envelope exceeds or falls below the threshold less frequently during transmission, the time below the low threshold is shorter, and the time below the high envelope is longer. For λ, when the signal is in a low envelope, it means that the in-phase component and the orthogonal component of the signal are close to 0. When the correlation is enhanced, the probability that the in-phase component and the orthogonal component are close to 0 at the same time decreases. When the in-phase component increases, due to the enhanced correlation, the possibility of the orthogonal component increasing increases, and the possibility of the signal envelope increasing increases. Therefore, when the correlation coefficient λ is enhanced, the LCR and AFD of the signal decrease at the low threshold, and at the high threshold, the LCR increases and the AFD increases.

[0177] Figure 6 It shows how the PDF and CDF curves of the signal-to-noise ratio change with α when the fading amount is fixed. Obviously, when AoF, κ, and μ are fixed, if α increases (which means the signal quality described by the model is enhanced), then λ increases (which means the signal quality described by the model is deteriorated). Nevertheless, with the increase of α, the extreme value of the signal-to-noise ratio probability density curve becomes significantly higher and the extreme point moves to the right, and the signal is more stable, which means that when the degree of environmental fading is fixed, the PDF and CDF of the signal-to-noise ratio are more sensitive to α. When λ is close to its extreme value (λ=0 and λ→1), α varies between 1.3927 and 10.8055. At these points, the two curves spanning the widest range are selected as the boundaries of the α-λ-κ-μ distribution, as shown in Figure 6 The dotted line in is shown. The corresponding λ values ​​of different α are shown in Table 3:

[0178] Table 3

[0179]

[0180] The influence of α and λ on the interruption probability of α-λ-κ-μ distribution is as follows: Figure 7 As shown. As expected, when α increases, the signal quality improves and, therefore, the outage probability decreases. For λ, the effect on the outage probability depends on the signal-to-noise ratio (SNR). When the average SNR is low, an increase in λ leads to a higher outage probability. This phenomenon can be attributed to the inherent weakness of the signal in a low average SNR environment, where the increase in correlation makes the signal more susceptible to noise and reduces its noise immunity. On the contrary, under high average SNR conditions, an increase in λ leads to a decrease in the outage probability. This is because, in this case, an increase in correlation means a higher energy signal, thereby enhancing its ability to overcome noise more effectively.

[0181] In order to verify the accuracy of the derived average bit error rate expression, simulations were performed using 16-QAM modulation, as shown in Figure 8As shown in Figure 2. The derived analytical and asymptotic expressions show good agreement with the Monte Carlo simulation results. As mentioned earlier, increasing α improves signal stability and reduces the average bit error rate. For λ, it can be observed that the average bit error rate during signal transmission increases as λ increases. This is due to the increased correlation between the in-phase and quadrature components, which means that the signal stability is reduced.

[0182] Fig. 9 The average bit error rate of the α-λ-κ-μ distribution under different modulation schemes and different α values ​​is shown. With the same number of symbol states (M), the signal has stronger anti-interference ability under PSK modulation compared with other modulation schemes. In addition, as M increases, the average bit error rate also increases. Regarding the effect of α, the observed trend is consistent with previous findings. An increase in α corresponds to a lower average bit error rate during signal transmission. It is worth noting that the effect of α is more significant for modulation schemes with fewer M.

[0183] Fig.10 The ergodic capacity for different α, λ, and transmission criteria is described in Figure 2. As expected, the ergodic capacity increases with The parameter α shows similar effects under both ORA and CIFR criteria. As the value of α increases, the ergodic capacity improves, which can be attributed to the enhanced stability and quality of the signal. On the other hand, an increase in λ leads to a more unstable signal, resulting in a decrease in the ergodic capacity during signal transmission. The impact of λ on the ergodic capacity is more significant under the ORA criterion than under the CIFR criterion. This difference can be attributed to the fact that within the ORA framework, λ plays a key role in determining the channel state, thereby having a substantial impact on the resource allocation decision. In contrast, the resource allocation strategy adopted by the CIFR criterion is inherently less sensitive to λ as it operates independently of the channel state.

[0184] In summary, this embodiment proposes an α-λ-κ-μ fading channel model, which can simultaneously characterize the nonlinearity of the medium, the inhomogeneity of the environment, the line-of-sight component, and the impact of multipath clusters on the signal. For different defined envelope averages, we derive the PDF and CDF analytical and asymptotic expressions of the instantaneous signal envelope and signal-to-noise ratio. Based on the application scenarios applicable to these statistical characteristics, we obtain closed-form expressions of the proposed model in terms of level penetration rate, average fading time, fading amount, outage probability, average bit error rate, and ergodic capacity. In addition, asymptotic expressions under high average signal-to-noise ratio are provided. The simulation results show that when the parameters α, κ, and μ increase or λ decreases, the signal stability improves. Accordingly, the signal performance is enhanced; however, at high SNR, the outage probability decreases with the increase of λ. In addition, under the condition of fixed fading amount, the parameter α shows a more significant effect than λ. And the validity of the derived expression is verified by comparison with the Monte Carlo simulation results.

[0185] The wireless channel fading distribution model of this embodiment, which is applicable to complex environments, has the following characteristics:

[0186] (1) Wide applicability: The model is applicable to linear and nonlinear, uniform and non-uniform transmission environments, and can be applied to envelope and energy-related performance analysis.

[0187] (2) Physical interpretability: The physical characteristics of the signal are described by the parameters α, λ, κ, and μ, which can more comprehensively analyze the interaction between the signal and the environment;

[0188] (3) Flexibility: By adjusting parameters, the proposed model is compatible with a variety of other distribution models, such as λ-κ-μ, α-κ-μ, α-μ, κ-µ, λ-µ, Nakagami-m, unilateral Gaussian, Rayleigh and Rice distributions.

[0189] Therefore, the α-λ-κ-μ distribution model is not only applicable to nonlinear and non-uniform channel environments, but also has a wide range of application potentials, especially in analyzing the performance of communication systems.

[0190] Another embodiment of the present invention relates to a fading distribution analysis method for a wireless channel in a complex environment. The implementation details of the fading distribution analysis method for a wireless channel in a complex environment of this embodiment are specifically described below. The following content is only for the convenience of understanding the implementation details provided, and is not necessary for implementing this solution. The fading distribution analysis method for a wireless channel in a complex environment of this embodiment includes the following steps:

[0191] Step 1: Obtain the values ​​of four parameters α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics.

[0192] Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are then combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattered component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0;

[0193] Step 2: Input the values ​​of the four parameters α, λ, κ and μ of the wireless channel into the wireless channel fading distribution model suitable for complex environments as described in any of the above embodiments; wherein the wireless channel fading distribution model suitable for complex environments is an α-λ-κ-μ distribution model, including a signal envelope analysis module and a signal-to-noise ratio analysis module.

[0194] Step 3: Obtain the probability density function and cumulative distribution function of the signal envelope through the signal envelope analysis module to obtain the distribution characteristics of the signal envelope of the wireless channel in a complex environment.

[0195] Step 4: Obtain the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio through the signal-to-noise ratio analysis module to obtain the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment.

[0196] Step 5: Acquire the fading distribution characteristics of the wireless channel in the complex environment by combining the distribution characteristics of the signal envelope of the wireless channel in the complex environment and the distribution characteristics of the signal-to-noise ratio in the complex environment.

[0197] The steps of the above methods are divided only for clear description. When implemented, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of the present invention.

[0198] Those skilled in the art can understand that the above embodiments are specific embodiments of the present invention, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the embodiments of the present invention. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the embodiments of the present invention, so the protection scope of the embodiments of the present invention shall be based on the scope defined in the claims.

Claims

1. A wireless channel fading distribution model suitable for complex environments, characterized in that: The model is an α-λ-κ-μ distribution model, including: a signal envelope analysis module and a signal-to-noise ratio analysis module; The signal envelope analysis module is used to obtain the probability density function and cumulative distribution function of the signal envelope according to the four parameters α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics, and obtain the distribution characteristics of the signal envelope of the wireless channel in a complex environment; Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are then combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattered component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0; The signal-to-noise ratio analysis module is used to obtain the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio according to the four parameters of the wireless channel α, λ, κ and μ, and obtain the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment; The distribution characteristics of signal envelope and signal-to-noise ratio in complex environments are used to indicate the fading distribution characteristics of wireless channels in complex environments. The signal envelope analysis module is further used to obtain the probability density function of the signal envelope under the second-order moment and the higher-order moment according to the four parameters α, λ, κ and μ of the wireless channel, and to obtain the cumulative distribution function of the signal envelope under the second-order moment and the higher-order moment respectively; The signal-to-noise ratio analysis module is further used to obtain the asymptotic results of the probability density function and the cumulative distribution function of the signal-to-noise ratio according to the four parameters α, λ, κ and μ of the wireless channel, and obtain the distribution characteristics of the signal-to-noise ratio under specific channel conditions; In the α-λ-κ-μ distribution model, the scattered components in each multipath cluster signal have the same power σ 2 , and the correlation between the in-phase component and the orthogonal component in each multipath cluster signal Envelope R λκμ It is expressed in the form of in-phase and quadrature components with the same variance and that are not independent: Where, X i and Y i for Var(X i )=Var(Y i )=σ 2 Gaussian variables; Signal envelope of λ-κ-μ distribution in α-λ-κ-μ distribution model The probability density function PDF is: In the formula, A mn =μ+m+n, Γ(·) represents the gamma function, 1F1(·) is the Kummer confluence hypergeometric function, It represents the ratio of the total power of the line-of-sight path to the total power of the scattered path, By transforming The PDF of the signal envelope of the λ-κ-μ distribution is obtained as follows: The envelope k-order moment of the λ-κ-μ distribution is: Where 2F1(·) is the Gaussian confluence hypergeometric function; Considering signal envelopes affected by nonlinear media And define but: Let the PDF of the envelope of the λ-κ-μ distribution signal be The PDF of the signal envelope of the α-λ-κ-μ distribution model is obtained as follows: In the formula, If we define the mean value of the signal envelope Then the PDF of the signal envelope of the α-λ-κ-μ distribution model is: By definition The cumulative distribution functions (CDFs) of the signal envelope under the second-order moment and the higher-order moment are: Where Φ2(·) is the binary confluent Appel function; according to The PDF of the signal-to-noise ratio is: according to The CDF of the signal-to-noise ratio is: according to The k-order origin moment of the signal-to-noise ratio is as follows: according to The moment generating function MGF of the signal-to-noise ratio can be obtained as follows: Where H(·) is the Fox H function.

2. The wireless channel fading distribution model suitable for complex environments according to claim 1, characterized in that: The signal envelope analysis module is also used to obtain the level crossing rate, average fading duration and fading amount of the wireless channel in a complex environment according to the probability density function and cumulative distribution function of the signal envelope.

3. The wireless channel fading distribution model suitable for complex environments according to claim 2, characterized in that: The signal-to-noise ratio analysis module is also used to obtain the interruption probability, average bit error rate and ergodic capacity of the wireless channel under the optimal rate adaptation strategy, channel reversal and fixed rate strategy in a complex environment according to the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio.

4. The wireless channel fading distribution model suitable for complex environments according to claim 3, characterized in that: By performing variable substitution on the CDF of the signal envelope at the second-order moment, By obtaining the PDF of the signal envelope, the level penetration rate LCR of the α-λ-κ-μ distribution model can be obtained as: In the formula, f m is the maximum Doppler frequency; According to the definition The average fading time AFD of the α-λ-κ-μ distribution model is obtained as follows: The k-th moment of the signal envelope is: According to the definition of k-th moment and attenuation The fading amount AoF can be obtained as: In the formula, From the PDF of the signal-to-noise ratio, by replacing the variables γ = γ th , the outage probability OP under the α-λ-κ-μ distribution model is obtained as: In the formula, is the lower incomplete gamma function; The average bit error rate under the α-λ-κ-μ distribution model is: Where G(·) is the G-function; The ergodic capacity of CIFA and the ergodic capacity of EC under the optimal rate adaptation strategy ORA, channel inversion and fixed rate strategy are respectively: Depend on It can be obtained that the asymptotic results of the PDF and CDF of the signal-to-noise ratio under high average signal-to-noise ratio conditions are: And the asymptotic results of outage probability, average bit error rate, and ergodic capacity under high average signal-to-noise ratio conditions are: In the formula, 5. A method for analyzing the fading distribution of wireless channels in complex environments, characterized in that: include: Obtain the values ​​of the four parameters α, λ, κ and μ of the wireless channel in a complex environment including nonlinear media, non-uniform environment and multipath propagation characteristics; Among them, the signal in the wireless channel forms multiple multipath cluster signals due to multipath propagation, and the multiple multipath cluster signals are then combined through the nonlinear medium; each multipath cluster signal contains a line-of-sight component and a scattered component, and the non-uniform environment makes the in-phase component and the orthogonal component in each multipath cluster signal correlated with each other; α represents the nonlinear strength of the nonlinear medium, α>0; λ represents the correlation between the in-phase component and the orthogonal component in each multipath cluster signal, -1≤λ≤1; κ is used to quantify the intensity of the line-of-sight component relative to the scattered component, κ>0; μ represents the number of multipath cluster signals, μ>0; Input the values ​​of the four parameters α, λ, κ and μ of the wireless channel into the wireless channel fading distribution model applicable to a complex environment as described in any one of claims 1 to 4; wherein the wireless channel fading distribution model applicable to a complex environment is an α-λ-κ-μ distribution model, including a signal envelope analysis module and a signal-to-noise ratio analysis module; Through the signal envelope analysis module, the probability density function and cumulative distribution function of the signal envelope are obtained, and the distribution characteristics of the signal envelope of the wireless channel in a complex environment are obtained; Through the signal-to-noise ratio analysis module, the probability density function, cumulative distribution function, high-order origin moment and moment generating function of the signal-to-noise ratio are obtained, and the distribution characteristics of the signal-to-noise ratio of the wireless channel in a complex environment are obtained; Combining the distribution characteristics of the signal envelope of the wireless channel in a complex environment and the distribution characteristics of the signal-to-noise ratio in a complex environment, the fading distribution characteristics of the wireless channel in a complex environment are obtained; Wherein, the method further comprises: Through the signal envelope analysis module, the probability density function of the signal envelope under the second-order moment and the higher-order moment, as well as the cumulative distribution function of the signal envelope under the second-order moment and the higher-order moment are obtained; Through the signal-to-noise ratio analysis module, the asymptotic results of the probability density function and cumulative distribution function of the signal-to-noise ratio are obtained, and the distribution characteristics of the signal-to-noise ratio under specific channel conditions are obtained; In the α-λ-κ-μ distribution model, the scattered components in each multipath cluster signal have the same power σ 2 , and the correlation between the in-phase component and the orthogonal component in each multipath cluster signal Envelope R λκμ It is expressed in the form of in-phase and quadrature components with the same variance and that are not independent: Where, X i and Y i for Var(X i )=Var(Y i )=σ 2 Gaussian variables; Signal envelope of λ-κ-μ distribution in α-λ-κ-μ distribution model The probability density function PDF is: In the formula, A mn =μ+m+n, Γ(·) represents the gamma function, 1F1(·) is the Kummer confluence hypergeometric function, It represents the ratio of the total power of the line-of-sight path to the total power of the scattered path, By transforming The PDF of the signal envelope of the λ-κ-μ distribution is obtained as follows: The envelope k-order moment of the λ-κ-μ distribution is: Where 2F1(·) is the Gaussian confluence hypergeometric function; Considering signal envelopes affected by nonlinear media And define but: Let the PDF of the envelope of the λ-κ-μ distribution signal be The PDF of the signal envelope of the α-λ-κ-μ distribution model is obtained as follows: In the formula, If we define the mean value of the signal envelope Then the PDF of the signal envelope of the α-λ-κ-μ distribution model is: By definition The cumulative distribution functions (CDFs) of the signal envelope under the second-order moment and the higher-order moment are: Where Φ2(·) is the binary confluent Appel function; according to The PDF of the signal-to-noise ratio is: according to The CDF of the signal-to-noise ratio is: according to The k-order origin moment of the signal-to-noise ratio is as follows: according to The moment generating function MGF of the signal-to-noise ratio can be obtained as follows: Where H(·) is the Fox H function.

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