A method for modeling a low earth orbit satellite propagation channel

Abstract

The application discloses a low-orbit satellite propagation channel modeling method, comprising the following steps: generating an optimal signal propagation path from a satellite to a target receiving point by using an RRT algorithm; simulating the propagation of a direct path component and a multipath component according to a Corazza model; simulating the attenuation of the direct path component according to a Lognormal distribution; simulating the time delay distribution of the multipath component, and simulating the reflection, refraction and scattering in an actual space environment to determine the amplitude and phase changes; synthesizing the direct path component and the multipath components; calculating the Doppler frequency shift, and simulating the distribution of the Doppler frequency shift by using a Gaussian distribution; and constructing a low-orbit satellite propagation channel model based on the synthesis result of the direct path component and the multipath components and an additive white Gaussian noise. The application accurately simulates the multipath effect and the Doppler frequency shift, provides an important theoretical basis and practical guidance for the design and optimization of a wireless communication system, and significantly improves the performance and reliability of the system in a complex environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of low-orbit satellite communication, and particularly relates to a low-orbit satellite propagation channel modeling method. BACKGROUND

[0002] In modern satellite communication systems, the application of low-orbit satellites (LEO) is becoming more and more widespread, especially in the fields of global communication coverage, remote sensing monitoring and navigation. Due to its low orbital height, low-orbit satellites can provide higher signal strength and lower transmission delay, but at the same time, they also face complex signal propagation environments. These environments include the unevenness of the atmosphere, terrain obstacles (such as buildings, mountains), and the relative motion between the satellite and the receiver, all of which can have a significant impact on signal propagation.

[0003] Traditional satellite communication channel models usually assume an idealized signal propagation environment, ignoring complex factors such as multipath effects and Doppler frequency shifts. These models can provide some accuracy in simple environments, but in actual applications, especially in complex environments such as cities and mountains, the propagation characteristics of the signal differ significantly from the ideal model. Multipath effects can cause signal reflection, refraction and scattering, while the relative motion between the satellite and the receiver causes Doppler frequency shifts, all of which can affect the quality and reliability of the signal.

[0004] Although existing channel models can describe the basic propagation characteristics of the signal to some extent, they have deficiencies in handling multipath effects and Doppler frequency shifts. In particular, in dynamic environments and multi-task scenarios, these models cannot accurately predict the propagation behavior of the signal, making the design and optimization of communication systems challenging. Therefore, developing a model that can accurately simulate the propagation channel of low-orbit satellites is of great significance for improving the performance and reliability of satellite communication systems. SUMMARY

[0005] In view of this, the present application proposes a low-orbit satellite propagation channel modeling method, which accurately simulates multipath effects and Doppler frequency shifts, providing important theoretical basis and practical guidance for the design and optimization of wireless communication systems, significantly improving the performance and reliability of the system in complex environments.

[0006] To achieve the above purpose, the present application provides the following technical solutions:

[0007] The low-orbit satellite propagation channel modeling method provided by the present application comprises:

[0008] Step S1, using the RRT algorithm to plan the path to generate the optimal signal propagation path from the satellite to the target receiving point;

[0009] Step S2, simulating the propagation of the direct path component and the multipath component according to the Corazza model;

[0010] Step S3, simulating the attenuation of the direct path component according to the Lognormal distribution;

[0011] Step S4, for the multipath component, simulating the time delay distribution based on the propagation distance and the propagation speed of the signal, and determining the amplitude and phase changes according to the reflection, refraction and scattering in the actual space environment;

[0012] Step S5, synthesizing the direct path component and the plurality of multipath components according to the respective time delay, amplitude and phase;

[0013] Step S6, calculating the Doppler shift according to the relative motion speed of the satellite and the receiver, and simulating the distribution of the Doppler shift by using the Gaussian distribution;

[0014] Step S7, constructing the low-orbit satellite propagation channel model based on the synthesis result of the direct path component and the plurality of multipath components and the additive white Gaussian noise.

[0015] Preferably, the step S1 comprises:

[0016] Step S11, taking the current position of the satellite as the starting point of the path planning, taking the position of the target receiving point as the end point, and taking the starting point as the root node of the random tree;

[0017] Step S12, randomly generating a target point in the space region between the satellite and the receiving point;

[0018] Step S13, finding the nearest node to the target point in the existing random tree, and generating a new node within a preset range to connect the nearest node and the target point by linear interpolation or interpolation method based on the physical model;

[0019] Step S14, checking whether the new node intersects with the obstacle, wherein the obstacle includes the uneven region of the atmosphere, the mountain and the ground building;

[0020] Step S15, when the new node intersects with the obstacle, returning to step S12, and if not, adding the new node to the random tree to form a new path;

[0021] Step S16, using the polynomial interpolation or spline interpolation method to smooth the path to reduce the jitter and unnecessary turning of the path, and optimizing the path length and shape based on the rewiring operation of the RRT algorithm, so as to find the optimal path.

[0022] Preferably, the step S3 comprises:

[0023] Based on the propagation of the direct path component simulated by the Corazza model, considering the shading effect on the direct path component, attenuation simulation is performed according to the Lognormal distribution to determine its corresponding probability density function f. Z (z):

[0024]

[0025] Where μ represents the mean of the logarithmic values ​​in the Lognormal distribution, σ represents the standard deviation of the logarithmic values ​​in the Lognormal distribution, and z represents the amplitude of the direct path component.

[0026] Preferably, step S4 includes:

[0027] Based on the obstacle distribution and signal propagation characteristics in the actual environment, multiple multipath components are generated;

[0028] The time delay distribution of multipath components is approximated by exponential or Rayleigh distribution, and its amplitude and phase changes are determined by simulating reflection, refraction and scattering in the actual space environment.

[0029] Constructing a representation model for multipath components:

[0030]

[0031] Where d(t) represents the multipath component, α n Let τ be a random variable determined by path loss and shadow fading. n (t) represents the signal path transmission delay for different paths, e is the natural logarithm, and j is the imaginary unit. r n (t) represents the signal propagation distance along the nth path, c represents the speed of light, u(t) represents the equivalent baseband signal, and φ n (t) represents the Doppler phase shift:

[0032]

[0033] Among them, f c Indicates the carrier frequency of the signal. This represents the Doppler phase shift of the nth path. The value is the Doppler frequency shift of the nth path.

[0034] The preferred low-Earth orbit satellite propagation channel model is expressed as follows:

[0035]

[0036] Where r(t) represents the received signal at the receiver, z(t) represents the direct path component, N(t) represents the number of resolvable multipath components at time t, n(t) represents additive white Gaussian noise, and f D Indicates Doppler frequency shift Where v represents the relative speed between the satellite and the receiver, c represents the speed of light, and f0 represents the frequency of the transmitted signal;

[0037] The distribution of the Doppler frequency shift is approximately Gaussian, and its probability density function is:

[0038]

[0039] in, It is expressed as the probability density function of the Doppler frequency shift. This represents the mean of the Doppler frequency shift. The standard deviation of the Doppler frequency shift;

[0040] Additive white Gaussian noise n(t) follows a Gaussian distribution, and its probability density function is:

[0041]

[0042] Among them, f N (n) represents the probability density function of additive white Gaussian noise, σ N This represents the standard deviation of the noise.

[0043] Preferably, the probability density function of the satellite communication signal that determines the signal arriving at the receiving end is expressed as:

[0044] f RS (r, s) = f R (r)·f S (s)

[0045] Among them, f RS (r, s) represents the probability density function of the satellite communication signal arriving at the receiver, f R (r) represents the probability density function of the received signal envelope, which follows a Rician distribution and:

[0046]

[0047] Where r represents the envelope of the received signal, ρ represents the amplitude of the direct path component of the received signal, and σ 2 Let i0 represent the average multipath power, and i0 be the first-order zero-order modified Bessel function.

[0048] f S (s) is the probability density function of the phase of the received signal, which follows a uniform distribution and:

[0049]

[0050] Where s is the phase of the received signal, s∈[0, 2π].

[0051] The present invention has achieved at least the following beneficial effects:

[0052] 1. The model can comprehensively simulate multipath effects, shadowing effects, Doppler effects, and additive white Gaussian noise in low-Earth orbit satellite communication channels, providing a reference for the performance evaluation and optimization of low-Earth orbit satellite communication systems.

[0053] 2. Based on the stepwise construction and optimization of random trees, and through real-time obstacle detection and avoidance, the generated path is not only feasible, but also efficient and smooth, which significantly improves the efficiency and reliability of path planning, and is particularly suitable for dynamic path planning in complex environments.

[0054] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0055] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0056] Figure 1 This is a flowchart illustrating the steps of a low-Earth orbit satellite propagation channel modeling method in an embodiment of the present invention.

[0057] Figure 2 This is a flowchart illustrating the steps of the optimal signal propagation path generation algorithm in an embodiment of the present invention. Detailed Implementation

[0058] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0059] This invention provides a method for modeling low-Earth orbit satellite propagation channels, referring to... Figure 1 ,include:

[0060] Step S1: Use the RRT algorithm to perform path planning and generate the optimal signal propagation path from the satellite to the target receiving point;

[0061] Step S2: Simulate the propagation of the direct path component and the multipath component based on the Corazza model;

[0062] Step S3: Simulate the attenuation of the direct path component according to the Lognormal distribution;

[0063] Step S4: For multipath components, perform time delay distribution simulation based on signal propagation distance and propagation speed, and simulate reflection, refraction and scattering in the actual space environment to determine their amplitude and phase changes;

[0064] Step S5: Combine the direct path component and multiple multipath components according to their respective time delay, amplitude, and phase.

[0065] Step S6: Calculate the Doppler frequency shift based on the relative motion velocity between the satellite and the receiver, and use a Gaussian distribution to simulate the distribution of the Doppler frequency shift;

[0066] Step S7: Construct a low-Earth orbit satellite propagation channel model based on the synthesis results of the direct path component and multiple multipath components, as well as additive white Gaussian noise.

[0067] The working principle and beneficial effects of the above technical solution are as follows: The RRT algorithm is used for path planning to generate the optimal signal propagation path from the satellite to the target receiving point. The RRT algorithm can quickly generate paths in complex environments, considering factors such as satellite orbital characteristics, Earth's curvature, atmospheric effects, and potential ground obstacles, ensuring the feasibility and efficiency of the path. The propagation of the direct path component and multipath components is simulated based on the Corazza model. The Corazza model is a fully shadowed model that can effectively describe the direct and multipath effects of signals during propagation. The attenuation of the direct path component is simulated according to the Lognormal distribution. The direct path component is affected by the shadowing effect, and the Lognormal distribution can accurately describe this attenuation characteristic, improving the accuracy of the model. The time delay distribution is simulated based on the signal propagation distance and speed. The time delay of the multipath component can be calculated by dividing the propagation distance by the speed of light. Reflection, refraction, and scattering in the actual space environment are simulated to determine the amplitude and phase changes of the multipath component. These changes affect the signal strength and phase, thus affecting the quality of the received signal. The direct path component and multiple multipath components are synthesized according to their respective time delays, amplitudes, and phases. The synthesized signal comprehensively reflects various effects during signal propagation, improving the model's comprehensiveness and accuracy. The Doppler frequency shift is calculated based on the relative velocity of the satellite and receiver, and a Gaussian distribution is used to simulate its distribution. The Doppler frequency shift affects the signal frequency, and the Gaussian distribution accurately describes this change, improving the model's precision. Based on the synthesis results of the direct path component and multipath components, along with additive white Gaussian noise, a low-Earth orbit (LEO) satellite propagation channel model is constructed. This model comprehensively simulates multipath effects, shadowing effects, Doppler effects, and additive white Gaussian noise in LEO satellite communication channels, providing a reference for performance evaluation and optimization of LEO satellite communication systems.

[0068] In a preferred embodiment, refer toFigure 2 Step S1 includes:

[0069] Step S11: Take the current position of the satellite as the starting point of the path planning, take the position of the target receiving point as the ending point, and take the starting point as the root node of the random tree.

[0070] Step S12: Randomly generate a target point in the space region between the satellite and the receiving point;

[0071] Step S13: Find the node closest to the target point in the existing random tree, and generate a new node within a preset range using linear interpolation or a physical model-based interpolation method to connect the nearest node and the target point;

[0072] Step S14: Check whether the new node intersects with obstacles, including uneven areas of the atmosphere, mountains, and ground buildings;

[0073] Step S15: If the new node intersects with an obstacle, return to step S12; if it does not intersect, add the new node to the random tree to form a new path.

[0074] Step S16: Use polynomial interpolation or spline interpolation methods to smooth the path to reduce path jitter and unnecessary turns, and optimize the path length and shape based on the rewiring operation of the RRT algorithm to find the optimal path.

[0075] The working principle and beneficial effects of the above technical solution are as follows: Step S11 sets the current position of the satellite as the starting point of path planning, the position of the target receiving point as the ending point, and uses this starting point as the root node of the random tree. This step lays the foundation for path planning, clarifying the start and end positions of the path. Next, in step S12, a target point is randomly generated in the spatial region between the satellite and the receiving point, serving as an intermediate guiding point in the path planning process. Then, in step S13, the node closest to the target point is found in the existing random tree, and a new node is generated within a preset range using linear interpolation or a physical model-based interpolation method, thus connecting the nearest node and the target point. After generating the new node, in step S14, the system checks whether the node intersects with any obstacles, which may include uneven areas of the atmosphere, mountains, and ground buildings. If the new node intersects with an obstacle, step S15 returns to step S12, regenerates the target point, and repeats the above process; if they do not intersect, the new node is added to the random tree, forming a new path. Finally, in step S16, polynomial interpolation or spline interpolation methods are used to smooth the path, reducing path jitter and unnecessary turns. The path length and shape are further optimized through the rewiring operation of the RRT algorithm to find the optimal path. This technical solution works based on the stepwise construction and optimization of random trees. By detecting and avoiding obstacles in real time, it ensures that the generated path is not only feasible but also efficient and smooth, significantly improving the efficiency and reliability of path planning. It is particularly suitable for dynamic path planning in complex environments. This method can effectively address satellite communication, navigation, and other applications requiring precise path planning, providing strong support for the development of modern aerospace and communication technologies.

[0076] In a preferred embodiment, step S3 includes:

[0077] Based on the propagation of the direct path component simulated by the Corazza model, considering the shading effect on the direct path component, attenuation simulation is performed according to the Lognormal distribution to determine its corresponding probability density function f. Z (z):

[0078]

[0079] Where μ represents the mean of the logarithmic values ​​in the Lognormal distribution, σ represents the standard deviation of the logarithmic values ​​in the Lognormal distribution, and z represents the amplitude of the direct path component.

[0080] The working principle and beneficial effects of the above technical solution are as follows: Step S3 focuses on simulating the propagation of the direct path component and its shadowing effect. Specifically, this step simulates the propagation characteristics of the direct path component based on the Corazza model, and considers the shadowing effect that the direct path component may experience during propagation. To accurately describe this attenuation phenomenon, the step uses the Lognormal distribution for simulation, which is a statistical distribution commonly used to describe signal strength attenuation. By determining the probability density function of the Lognormal distribution, the attenuation characteristics of the direct path component amplitude can be quantified, where parameters μ and σ represent the mean and standard deviation of the logarithm in the Lognormal distribution, respectively, and A represents the amplitude of the direct path component. The working principle of this technical solution is based on the simulation of the propagation of the direct path component using the Corazza model, combined with the Lognormal distribution to describe the signal attenuation caused by the shadowing effect. The Corazza model provides a theoretical basis for understanding and predicting the propagation behavior of the direct path component in complex environments. The Lognormal distribution is used to simulate the random attenuation of signal strength caused by obstacles such as buildings and terrain. This attenuation usually exhibits nonlinear characteristics and is related to the distribution of obstacles on the signal propagation path. By calculating the probability density function of the Lognormal distribution, the probability distribution of amplitude attenuation of the direct path component under specific environmental conditions can be evaluated, providing important reference for the design and optimization of wireless communication systems. Combining the Corazza model and the Lognormal distribution allows for more accurate prediction of the propagation characteristics of the direct path component in complex environments, including signal strength attenuation. This provides a more precise signal attenuation model for wireless communication system design, helping to optimize system parameters and improve communication quality and reliability. Accurate prediction of signal attenuation allows for more rational network layout planning, optimization of base station locations and power configurations, and improved utilization efficiency of spectrum resources.

[0081] In a preferred embodiment, step S4 includes:

[0082] Based on the obstacle distribution and signal propagation characteristics in the actual environment, multiple multipath components are generated;

[0083] The time delay distribution of multipath components is approximated by exponential or Rayleigh distribution, and its amplitude and phase changes are determined by simulating reflection, refraction and scattering in the actual space environment.

[0084] Constructing a representation model for multipath components:

[0085]

[0086] Where d(t) represents the multipath component, α nLet τ be a random variable determined by path loss and shadow fading. n (t) represents the signal path transmission delay for different paths, e is the natural logarithm, and j is the imaginary unit. r n (t) represents the signal propagation distance along the nth path, c represents the speed of light, u(t) represents the equivalent baseband signal, and φ n (t) represents the Doppler phase shift:

[0087]

[0088] Among them, f c Indicates the carrier frequency of the signal. This represents the Doppler phase shift of the nth path. The value is the Doppler frequency shift of the nth path.

[0089] The working principle and beneficial effects of the above technical solution are as follows: Step S4 focuses on simulating multipath effects, an important phenomenon in wireless signal propagation. Specifically, Step S4 first generates multiple multipath components based on the obstacle distribution and signal propagation characteristics in the actual environment. These multipath components are caused by reflection, refraction, and scattering phenomena resulting from the signal encountering obstacles such as buildings and terrain during propagation. Next, the time delay distribution of the multipath components is approximated by an exponential or Rayleigh distribution, which helps simulate the signal propagation characteristics in the actual spatial environment and determine the amplitude and phase changes of the multipath components. These changes are due to the differences in propagation distance and speed of the signal along different paths. To more accurately describe the multipath components, a representation model is constructed, in which each multipath component consists of parameters such as random variables determined by path loss and shadow fading, signal path transmission delay, natural logarithm, imaginary unit, signal propagation distance, speed of light, equivalent baseband signal, and Doppler phase shift. The Doppler phase shift is further determined by the carrier frequency of the signal and the Doppler frequency shift of each path, reflecting the frequency changes of the signal along different paths.

[0090] In one specific embodiment, the low-Earth orbit satellite propagation channel model is represented as follows:

[0091]

[0092] Where r(t) represents the received signal at the receiver, z(t) represents the direct path component, N(t) represents the number of resolvable multipath components at time t, n(t) represents additive white Gaussian noise, and f D Indicates Doppler frequency shift Where v represents the relative speed between the satellite and the receiver, c represents the speed of light, and f0 represents the frequency of the transmitted signal;

[0093] The distribution of the Doppler frequency shift is approximately Gaussian, and its probability density function is:

[0094]

[0095] in, It is expressed as the probability density function of the Doppler frequency shift. This represents the mean of the Doppler frequency shift. The standard deviation of the Doppler frequency shift;

[0096] Additive white Gaussian noise n(t) follows a Gaussian distribution, and its probability density function is:

[0097]

[0098] Among them, f N (n) represents the probability density function of additive white Gaussian noise, σ N This represents the standard deviation of the noise.

[0099] The working principle and beneficial effects of the above technical solution are as follows:

[0100] In one specific embodiment, the probability density function for determining the satellite communication signal arriving at the receiver is expressed as:

[0101] f RS (r, s) = f R (r)·f S (s)

[0102] Among them, f RS (r, s) represents the probability density function of the satellite communication signal arriving at the receiver, f R (r) represents the probability density function of the received signal envelope, which follows a Rician distribution and:

[0103]

[0104] Where r represents the envelope of the received signal, ρ represents the amplitude of the direct path component of the received signal, and σ 2 Let I0 represent the average multipath power, and I0 be the first-order zero-order modified Bessel function.

[0105] f S (s) is the probability density function of the phase of the received signal, which follows a uniform distribution and:

[0106]

[0107] Where s is the phase of the received signal, s∈[0, 2π].

[0108] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A method of modeling a low earth orbit satellite propagation channel, the method comprising: Comprise: Step S1, using RRT algorithm for path planning, generating the optimal signal propagation path from satellite to target receiving point; Step S2, according to Corazza model simulates direct path component and multipath component propagation; Step S3, according to Lognormal distribution to direct path component attenuation simulation; Step S4, for multipath component, based on the propagation distance and propagation velocity of signal delay distribution simulation, and simulate the actual space environment in the reflection, refraction and scattering to determine its amplitude and phase change; Step S5, the direct path component and multiple multipath components according to the respective time delay, amplitude and phase synthesis; Step S6, according to the relative motion velocity of satellite and receiver to calculate the Doppler shift, and using Gaussian distribution to simulate the distribution of Doppler shift; Step S7, based on the synthesis results of direct path component and multiple multipath components and additive white Gaussian noise to construct low earth orbit satellite propagation channel model; Low earth orbit satellite propagation channel model is expressed as: wherein denotes the received signal at the receiving end, denotes the direct path component, denotes the number of resolvable multipath components at time t, denotes the additive white Gaussian noise, denotes the Doppler shift wherein denotes the relative velocity of the satellite and the receiver, denotes the speed of light, denotes the transmitted signal frequency; Where the distribution of Doppler shift is approximately Gaussian distribution, and its probability density function is: wherein the probability density function of the Doppler shift, the mean value of the Doppler shift, the standard deviation of the Doppler shift; Additive white Gaussian noise obeys a Gaussian distribution with the probability density function wherein denotes the probability density function of an additive white Gaussian noise, is the standard deviation of the noise. 2.The method of claim 1, wherein, Step S1 includes: Step S11, the current position of the satellite as the starting point of path planning, the position of the target receiving point as the end point, the starting point as the root node of the random tree; Step S12, randomly generate a target point in the space between the satellite and the receiving point; Step S13, find the nearest node to the target point in the existing random tree, and generate a new node within the preset range to connect the nearest node and the target point by linear interpolation or interpolation method based on physical model; Step S14, check whether the new node intersects with the obstacle, wherein the obstacle includes the uneven region of the atmosphere, mountain and ground building; Step S15, when the new node intersects with the obstacle, return to step S12, if not intersected, then add the new node to the random tree, forming a new path; Step S16, using polynomial interpolation or spline interpolation method to smooth the path to reduce the jitter and unnecessary turning of the path, and based on the rewiring operation of RRT algorithm to optimize the path length and shape, so as to find the optimal path. 3.The method of claim 1, wherein, Step S3 includes: According to the propagation of the direct path component simulated by the Corazza model, considering the shadowing effect on the direct path component, the corresponding probability density function is determined by simulating the attenuation according to the Lognormal distribution : wherein, represents the mean of the log values in the Lognormal distribution, represents the standard deviation of the log values in the Lognormal distribution, represents the magnitude of the direct path component.

4. The method of claim 1, wherein, Step S4 includes: According to the distribution of obstacles in the actual environment and the signal propagation characteristics, a plurality of multipath components are generated; The delay distribution of multipath component is approximated by exponential distribution or Rayleigh distribution, and the amplitude and phase change of multipath component is determined by simulating the reflection, refraction and scattering in the actual space environment; The representation model of multipath component is constructed: wherein denotes a multipath component, is a random variable determined by path loss and shadow fading, is a signal path transmission delay of a different path, is the natural logarithm, is the imaginary unit, , denotes a signal propagation distance of the nth path, denotes the speed of light, denotes an equivalent baseband signal, denotes a Doppler phase shift: wherein denotes the carrier frequency of the signal, denotes the Doppler phase shift of the n-th path, is the Doppler frequency shift of the n-th path.

5. The method of claim 1, wherein, The satellite communication signal probability density function of the signal arriving at the receiving end is determined as: wherein denotes the probability density function of the satellite communication signal reaching the receiving end signal, denotes the probability density function of the received signal envelope, which is subject to a Rician distribution and: wherein denotes the envelope of the received signal, denotes the amplitude of the direct path component of the received signal, denotes the average multipath power, is a first kind zero order modified Bessel function; The probability density function of the received signal phase is uniform and: wherein is the phase of the received signal, .

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