Performance evaluation method of single-radio frequency polarization spatial modulation system under radio frequency hardware impairment

Abstract

This invention provides a method for performance evaluation of a single-RF polarization spatial modulation system under RF hardware impairment. The method includes constructing an RF hardware impairment model to obtain a non-ideal system transmission model; expressing the bit error rate (BER) as a weighted sum of paired error probabilities using a joint upper bound method, decoupling the influence of the channel matrix and phase noise to construct a stable BER analysis framework; processing the BER analysis framework using piecewise approximation functions, reconstructing the BER analysis framework using image approximation, and calculating an approximate analytical expression for the BER; further deriving an asymptotic lower bound expression for the BER of the single-RF polarization spatial modulation system when the signal-to-noise ratio (SNR) approaches infinity, to determine the system performance evaluation results, thus achieving a comprehensive and accurate performance evaluation of the single-RF polarization spatial modulation system under complex RF hardware impairment.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for evaluating the performance of a single-radio polarization spatial modulation system under radio frequency hardware impairment. Background Technology

[0002] Single-radio polarization spatial modulation (SPM) technology is a key means to improve the spectral efficiency of wireless communication. Among them, spatial modulation (SM) and its derivative technologies, such as polarization shift keying (PolarSK) modulation systems and dual-polarization spatial modulation (DP-SM), have attracted widespread attention due to their good balance between spectral efficiency and implementation complexity. However, in practical deployments, the RF links of communication equipment inevitably have non-ideal characteristics, i.e., hardware impairments, such as I / Q imbalance, power amplifier nonlinearity, and phase noise. These impairments are exacerbated by device aging or the use of low-cost components, leading to decreased system performance, increased bit error rate, increased network operation and maintenance costs, and the introduction of security risks.

[0003] Currently, some research has been conducted to assess the impact of hardware impairments on single-RF polarization spatial modulation systems, but existing technologies still have significant shortcomings in this area: First, there is a lack of a unified framework that can comprehensively characterize the combined impact of various complex hardware impairments, including I / Q imbalance, amplifier nonlinearity, and phase noise, on the performance of RF polarization spatial modulation systems. Secondly, existing methods have the following main shortcomings: First, due to the introduction of complex random variables in damage modeling, the analytical expression for bit error rate is difficult to solve, and existing methods cannot provide a stable and reliable means of predicting bit error rate performance. Second, after being affected by RF hardware damage, it is difficult to quantify the bit error rate performance limit that the hardware damage can achieve. Third, it fails to discover that for a dual-polarized spatial modulation system with a set of polarized antennas, its bit error rate performance limit is not sensitive to channel changes.

[0004] Therefore, how to achieve a comprehensive and accurate performance evaluation of a single-RF polarization spatial modulation system under complex RF hardware impairments, and provide a theoretical basis and specific design guidance for the low-cost and high-reliability deployment of the system in complex communication scenarios where the channel changes rapidly or is difficult to estimate accurately, is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a method for performance evaluation of a single-RF polarization spatial modulation system under RF hardware damage, so as to achieve a comprehensive and accurate performance evaluation of the single-RF polarization spatial modulation system under complex RF hardware damage.

[0006] On one hand, the present invention provides a method for performance evaluation of a single-RF polarization spatial modulation system under RF hardware impairment, comprising: A radio frequency hardware impairment model that simultaneously includes power amplifier nonlinearity, I / Q imbalance and phase noise is constructed, and the impairment model is integrated into an ideal single radio frequency polarization spatial modulation system to form a non-ideal system transmission model. Based on the aforementioned non-ideal system transmission model, the bit error rate is expressed as a weighted sum of paired error probabilities using a joint upper bound method, and the influence of the channel matrix and phase noise is decoupled to construct a bit error rate analysis framework. The bit error rate analysis framework is processed by a piecewise approximation function to obtain a reconstructed bit error rate analysis framework. The reconstructed bit error rate analysis framework is then analyzed using an image approximation method to calculate an approximate analytical expression for the bit error rate. Based on the bit error rate analysis framework and the approximate analytical expression, the lower bound expression of the asymptotic bit error rate of the single-RF polarization spatial modulation system under the condition that the signal-to-noise ratio tends to infinity is derived. Based on the expression for the asymptotic lower bound of the bit error rate, the performance evaluation result of the single-RF polarization spatial modulation system is determined.

[0007] The present invention provides a method for performance evaluation of a single-RF polarization spatial modulation system under RF hardware impairment. This method constructs an RF hardware impairment model that simultaneously incorporates power amplifier nonlinearity, I / Q imbalance, and phase noise, and integrates this impairment model into an ideal single-RF polarization spatial modulation system to form a non-ideal system transmission model. Based on this non-ideal system transmission model, a joint upper bound method is used to represent the bit error rate as a weighted sum of paired error probabilities, decoupling the influence of the channel matrix and phase noise to construct a stable bit error rate analysis framework. Subsequently, the bit error rate analysis framework is processed by a piecewise approximation function to obtain a reconstructed bit error rate analysis framework, and then... The reconstructed bit error rate (BER) analysis framework is analyzed using an image approximation method, and an approximate analytical expression for the BER is calculated. Based on the BER analysis framework and the approximate analytical expression, an asymptotic lower bound expression for the BER of a single-RF polarization spatial modulation system when the signal-to-noise ratio (SNR) approaches infinity is further derived. Finally, the system performance evaluation result is determined based on this lower bound expression, thereby achieving a comprehensive and accurate performance evaluation of the single-RF polarization spatial modulation system under complex RF hardware impairments. This provides a theoretical basis and specific design guidance for the low-cost, high-reliability deployment of the system in complex communication scenarios where the channel changes rapidly or is difficult to estimate accurately. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating the performance evaluation method for a single-RF polarization spatial modulation system under RF hardware damage provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the image approximation method; Figure 3 This is a schematic diagram of the device for evaluating the performance of a single-radio-frequency polarization spatial modulation system under radio-frequency hardware damage, provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0011] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0012] Figure 1 This is a flowchart illustrating the performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment provided in an embodiment of the present invention.

[0013] like Figure 1 As shown, the performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment provided in this embodiment of the invention is introduced using the PolarSK system as an example. The method mainly includes the following steps: 101. Construct an RF hardware impairment model that simultaneously includes power amplifier nonlinearity, I / Q imbalance, and phase noise, and integrate the impairment model into an ideal single-RF polarization spatial modulation system to form a non-ideal system transmission model; In a specific implementation process, the original PolarSK system model under ideal hardware conditions is as follows: PolarSK is a single-RF polarization spatial modulation system that enhances spatial multiplexing gain by expanding the degrees of freedom in the polarization domain, thereby improving spectral efficiency. Specifically, it uses... The PolarSK system consists of a single-radio dual-polarization link, with vertical and horizontal dual-polarization antennas at the input and a receiver using... For dual-polarized antennas.

[0014] The signal constellation diagram at the PolarSK system transmitter includes two adjustable parameters: polarization order K and phase modulation order M, which together control the data transmission rate. Once the polarization parameter K is selected, a constant matrix of a specific dimension can be defined. (when Time is a scalar quantity. (when it is a vector), where each element Corresponding to the k-th polarization angle; in addition, the phase modulation order and The polarization phase parameters are determined by mapping the modulation index of the M-PSK to its position on a Poincaré sphere. Transmitted signal. Specifically expressed as equation (1): (1); in, Through polarization state index get, and These represent the indices of the modulation signals for the vertically polarized antenna and the horizontally polarized antenna, respectively.

[0015] In the PolarSK system, the transmitting antenna and the first The basic channel matrix corresponds to a 2×2 polarized antenna element composed of a group of receiving antennas. As shown in equation (2): (2); In the formula The polarization characteristics are a comprehensive parameter derived from cross-polarization discrimination (XPD), which combines the cross-polarization isolation (XPI) of the antenna array and the cross-polarization ratio (XPR) of the propagation channel in the actual scenario. It can be set based on measured or empirical values, for example, obtained from measurements at 2.8 GHz. Subscript The corresponding number of characters is represented. A receive antenna channel matrix, the four components of which are defined as follows: (1) Homopolarization component and , respectively characterizing the ideal transmission path of vertical polarization and the ideal transmission path of horizontal polarization, specifically representing two modes: vertical-vertical and horizontal-horizontal. (2) Cross-polarization components and , , respectively represent the transmission paths of polarization leakage, namely the vertical-horizontal transmission component and the horizontal-vertical transmission component.

[0016] Basic Channel The matrix is ​​represented by concatenating columns sequentially according to the order of the receiving antennas as follows: The dimension is obtained as The complete channel matrix.

[0017] Under ideal hardware conditions, the transmitted signals corresponding to the PolarSK signal constellation diagram After the channel fades, the receiver receives the signal. Represented as In the formula Let represent Gaussian white noise, where each element in the vector follows a complex Gaussian distribution. The average received signal-to-noise ratio for each symbol is defined as . , Energy per symbol represents the average energy carried by each transmitted symbol. It is the noise power spectral density.

[0018] Signal detection is a key technology for the receiver to reconstruct the transmitted signal and obtain the binary bit sequence based on the modulation method. Maximum likelihood estimation is widely recognized as the optimal signal detection algorithm. Under ideal hardware conditions, the corresponding maximum likelihood detection method based on the PolarSK system scheme is given below: ; In the transmitted symbol field, all transmitted signal combinations are selected and compared with the signals at the receiver to obtain estimated combinations. M represents the modulation order; for example, in 4psk, M=4.

[0019] Based on the above ideal system model, this step can be implemented as follows: a1. The nonlinearity of the power amplifier is modeled using the Saleh model to obtain the distorted signal; Specifically, the widely used Saleh model can be employed, which uses two functions to characterize nonlinearity: one function (AM / AM conversion) describes the nonlinear relationship between the input signal amplitude and the output signal amplitude, for example, it can be expressed as... ; This is the amplitude of the input signal, which is set to 1 by default. This indicates the degree of amplitude distortion. Another function (AM / PM conversion) describes the additional phase distortion of the output signal caused by the input signal amplitude; for example, it can be expressed as... , This indicates the degree of phase distortion. Among them, and It is an AM / AM parameter. and These are parameters characterizing AM / PM, and you can refer to typical parameters of the Saleh model in relevant literature, for example, =2.1587, =1.1517, =4.0033, =9.1040. The transmitted signal... This model allows us to obtain distorted signals that have undergone nonlinear transformation. .in, Nonlinear distortion signal real part and the virtual part They can be represented as follows: ; .

[0020] a2. Based on the distorted signal, the I / Q imbalance is modeled using a matrix model that includes amplitude deviation parameters, phase deviation parameters, and DC offset components, resulting in a distorted signal. Specifically, after establishing the nonlinear distortion mechanism, the combined damage caused by I / Q imbalance and DC offset can be quantified. By substituting the amplitude and phase errors caused by I / Q imbalance and DC offset, the mathematical model can be expressed as equation (3): (3); in, and These represent the amplitude and phase deviations, respectively. and These are the two components of the DC offset. The distortion signal is then written as... . This represents the real part of the signal considering IQ imbalance and amplifier nonlinear distortion. This represents the imaginary part of the signal, taking into account IQ imbalance and amplifier nonlinear distortion.

[0021] a3. Based on the distorted signal, the constellation rotation caused by the phase noise is modeled using a Gaussian distribution with zero mean to obtain the damaged signal at the transmitting end; Specifically, unlike the idealized assumptions in communication theory, it is difficult for oscillators that generate signals to produce perfect sine waves in practical applications; therefore, Gaussian variables can be used instead. The constellation rotation caused by phase noise is modeled as follows: ; It can be controlled The magnitude of phase noise is represented by variations in order to simulate different degrees of damage to radio frequency devices.

[0022] a4. Based on the damaged signal at the transmitting end, construct the radio frequency hardware damage model.

[0023] Specifically, the signal at the receiver in the radio frequency hardware impairment model can be expressed as: .

[0024] in, This is the distorted signal after passing through the nonlinearity of the power amplifier and the I / Q imbalance. For phase noise, For the channel matrix, It is Gaussian white noise. The signal-to-noise ratio is given by the above formula, which represents the complete received signal model of the PolarSK system considering hardware impairments established in this invention. Subsequent bit error rate performance evaluations are all based on this model.

[0025] 102. Based on the aforementioned non-ideal system transmission model, the bit error rate is expressed as a weighted sum of paired error probabilities using a joint upper bound method, and the influence of the channel matrix and phase noise is decoupled to construct a bit error rate analysis framework. In a specific implementation, based on a non-ideal system transmission model, a joint upper bound method is used to decompose the bit error rate (BER). The overall BER is expressed as a weighted sum of the pairwise error probabilities between all transmitted and decision signal pairs, with the weight being the number of bit errors corresponding to each error condition. In the decomposed expression, the conditional probabilities that depend on both the channel matrix and phase noise are decoupled. First, the channel matrix is ​​fixed to obtain the conditional pairwise error probabilities that only consider phase noise. Then, these probabilities are transformed into Q-function form, and the global pairwise error probabilities are determined by calculating the expectation and statistical averaging. Substituting these probabilities back into the BER upper bound expression completes the construction of the BER analysis framework. This framework effectively separates the influence of the channel matrix and phase noise, reducing the complexity of subsequent BER calculations.

[0026] Specifically, this step can be achieved as follows: b1. The upper bound of the bit error rate is expressed as a weighted sum of the pairwise error probabilities between all transmitted and decision signal pairs using the joint upper bound method; where the weight is the number of bit errors corresponding to each error case. Specifically, due to the difficulty of calculating multiple integrals in irregular regions, the joint bound method can be used to determine the upper bound of the bit error rate, and its expression is Equation (4): (4); in This represents the global pairwise error probability for each detection error scenario, specifically corresponding to the probability when the transmitted signal combination is... At that time, the receiving end incorrectly judged as The probability of. This represents the number of bit errors in the encoded sequence under each error condition, typically calculated using the Hamming distance. , ; b2. Decompose the conditional probability in the expression for the upper bound of bit error rate that depends on the channel matrix and phase noise. First, fix the channel matrix to obtain the expression for the conditional pairwise error probability under given channel conditions. Specifically, the difficulty in accurately solving the expression for the upper bound of the bit error rate lies in the computation. The expectation is specifically expressed as equation (5): (5); The expected expression also depends on the channel matrix. and phase noise To ensure mathematical feasibility, the channel matrix can be fixed first. Eliminate channel matrix The influence of variables is used to obtain the conditional pairwise error probability under given channel conditions. Its expression is equation (6): (6); in For signals received by a non-ideal system, , To account for the distortion signal and its estimate due to IQ imbalance and amplifier nonlinearity, this expression retains only the phase noise. It is a unique variable.

[0027] b3. Transform the expression for the conditional pairwise error probability into a Q-function with decision variables; the decision variables are obtained based on channel gain, hardware impairment factor, and phase noise; Specifically, we can further analyze equation (6) and derive equation (7) using phase noise: (7); in Based on the inequality structure obtained in the formula, and introducing the right-tail function Q-function corresponding to the Gaussian distribution, we obtain the following formula: ; For ease of subsequent analysis and mathematical implementation, the following is defined: ,in, It is the Gaussian Q-function. It is a decision variable that integrates channel gain, hardware impairment factor and phase noise, and its expression can be rewritten as equation (8): (8) in, ; In the formula The signal-to-noise ratio is represented by intermediate variables A, B, and C, which are determined by system parameters (indexed modulation scheme, hardware impairment factor) and the channel matrix. Representing complex numbers phase angle, express The amplitude. Ultimately, it can be transformed into the following Q function: .

[0028] b4. Based on the Q function, determine the global pairwise error probability; Specifically, the problem of solving the global pairwise error probability is transformed into a double expectation problem, with the inner layer first dealing with phase noise. Calculate the expectation, and then the outer layer calculates the channel. Calculate the expected value. Use the following two-step expectation method: (1) Regarding phase noise Calculate the expectation: for a given channel matrix ,calculate The calculation formula can be expressed as formula (9): (9).

[0029] (2) Calculate the expectation of the channel: calculate the channel matrix for all channels. The expectation is to obtain the global The formula for its calculation is: .

[0030] In a specific implementation, the expected calculation can be performed based on the channel type: For pure line-of-sight (LOS) channels: Channel matrix If it is a deterministic matrix, then The expression is simplified to The global pairwise error probability is obtained by directly using the approximate analytical expression provided later.

[0031] If the channel has a scattering path: Channel matrix Due to its randomness and complex statistical distribution, it is difficult to directly find a closed-form solution. In this case, the Monte Carlo ensemble averaging method can be used for numerical estimation. For each randomly generated channel sample, the corresponding analytical expression is called to calculate the solution. Then, the average of all samples is taken, using the following formula: .

[0032] Where T represents the number of Monte Carlo simulations, which approximates the real channel by averaging a large number of randomly generated channel samples. .

[0033] b5. Substitute the obtained global pairwise error probability into the bit error rate upper bound expression to complete the construction of the bit error rate analysis framework.

[0034] Specifically, the calculated global pairwise error probability can be... Substitute back to the original expression for the upper bound of the bit error rate, and replace the expression with... This yields a bit error rate expression containing only phase noise, hardware impairment parameters, and modulation parameters, thus completing the construction of the bit error rate analysis framework. This framework effectively decouples the channel matrix and phase noise variables, and the bit error rate can be solved subsequently through the analysis and calculation of the Q function.

[0035] 103. The bit error rate analysis framework is processed by a piecewise approximation function to obtain a reconstructed bit error rate analysis framework. The reconstructed bit error rate analysis framework is then analyzed using the image approximation method to calculate an approximate analytical expression for the bit error rate. In a specific implementation, the process of processing the bit error rate analysis framework using a piecewise approximation function may include: c1. Construct a piecewise approximation function to handle the two cases where the input value of the Q function in the bit error rate analysis framework is non-negative and negative; wherein, when the input value is non-negative, it is approximated by an exponential sum; when the input value is negative, it is approximated by 1 minus the exponential sum. Specifically, the core of calculating the bit error rate using the above bit error rate analysis framework lies in analyzing and solving... In this formula It exists in the global expected integral. This situation, though rare, significantly reduces the accuracy of the widely used Craig Q-function approximation method, necessitating special handling of the negative value region. To address this, the following piecewise expression can be introduced to reconstruct the Q-function, resulting in: Its expression can be found in equation (10): (10).

[0036] in, The coefficients in this formula .

[0037] c2. Substitute the piecewise approximation function into the expectation calculation of the Q function, and decompose the overall expectation into a combination of three integral terms; wherein, the three integral terms include: the positive integral corresponding to the non-negative input value, the negative integral corresponding to the negative input value, and the probability integral corresponding to the negative input value. Substitute the piecewise function , Rewritten as the following equation (11): (11); Integral of the probability term Quantified probability Once determined The probability can be calculated using the Q function once the distribution range is determined.

[0038] c3. For the exponential integral terms with the same structure in the positive and negative integrals, by introducing auxiliary variables and parameter transformations, the positive and negative integrals are rewritten as a linear combination of the normal probability density functions, so as to transform the integral calculation problem into the evaluation problem of the normal cumulative distribution function.

[0039] Specifically, in equation (11), the positive and negative integrals have the same integral structure, which can be obtained by using Theorem 1 (Reconstructing the Normal Distribution Probability Density Function). and The same integral structure can be reformulated using a unified normal distribution probability density function as equation (12): (12); in, ; ; ; ; ; ; In the above formula, It is a normal distribution The probability density function, This means that the original integral term is transformed into an integral term of the normal distribution probability density function. This is to reconstruct the original integral into a constant term extracted from the normal distribution probability density function. It is the mean of the newly constructed normal distribution probability density function. Let V be the variance of the newly constructed normal probability density function. , , All are intermediate variables.

[0040] Through this transformation, the original integral is reformulated as a normal distribution probability density function. The key advantage of Theorem 1 lies in simplifying the integral calculation problem into a problem based on... Symbols and the process of numerical calculation using the Q function.

[0041] Using Theorem 1, The overall expectation calculation is significantly simplified. For and In the case of equation (11), the expressions are represented as equations (13) and (14) respectively: (13).

[0042] (14).

[0043] The given constant in the formula and normal probability density function By determining and corresponding Within a given range, numerical calculations are performed.

[0044] In a specific implementation, under given channel conditions, the decision variable is described as a cosine function with a constant term; the process of analyzing the key parameter relationships in the piecewise approximation function using the image approximation method to calculate the approximate analytical expression of the bit error rate may include: Analyze the zero-crossing points of the decision variable, design an image approximation method, and transform the sign determination of the decision variable into the positional relationship between a straight line and a cosine function curve in a two-dimensional coordinate system. The positional relationship includes three cases: the straight line is below the cosine function curve, the straight line passes through the cosine function curve, and the straight line is above the cosine function curve. For each of the three cases, determine the sign distribution of the Q function input value, and obtain the calculation results of the positive integral, the negative integral, and the probability integral in each case. Based on the calculation results, the approximate analytical expression is determined.

[0045] Specifically, due to Embedded in The term exhibits periodic oscillation characteristics and cannot be determined by simply solving algebraic equations. The symbol cannot be determined by the periodicity of the symbol itself, but must be analyzed to determine its complete periodicity. For better analysis... and Given the range of the interval, the problem can be transformed into a geometric problem and solved using the graphical approximation method. Figure 2 This is a schematic diagram of the image approximation method.

[0046] First, it can be done through Analyzing the zero-crossing points of the decision variable is equivalent to finding a secant line. With a trigonometric function The intersecting roots transform the sign determination of the decision variable into the positional relationship between a straight line and the cosine function curve in a two-dimensional coordinate system. The position of this straight line determines the number and distribution of its intersection points with the cosine function curve, thereby determining the sign of the intersection. Symbol change pattern within the base period: Given a channel matrix Under these conditions, three typical cases can be identified, see equation (15): (15); Scenario 1 (The straight line is below the cosine function curve): At this point, the entire red line is at Below the image (not shown in the figure), the equation takes values. .

[0047] In Scenario 1 , and The calculation result is shown in equation (16): (16); Scenario 2 (A straight line passes through a cosine function curve): When The cut-off line passes through The image shows the corresponding dark enclosed area above the red line. The range of values ​​satisfies Sometimes, The area below the straight line corresponds to The range of values ​​indicates .

[0048] In scenario two , and The calculation result is shown in equation (17): (17); The intersection of the straight line and the cosine function curve is expressed by equations (18)-(19): (18); (19); in, ; Scenario 3 (The straight line is above the cosine function curve): When At that time, the red line is always located at Below the image, satisfying .

[0049] Scenario 3 , and The calculation result is shown in equation (20): (20); The calculation results for each case can be summed to obtain the approximate analytical expression, see equation (21): (twenty one); 104. Based on the bit error rate analysis framework and the approximate analytical expression, derive the lower bound expression for the asymptotic bit error rate of the single-radio multiple-input multiple-output under the condition that the signal-to-noise ratio tends to infinity; In a specific implementation process, this step can be implemented in the following way: d1. In the bit error rate analysis framework, the limit value of the approximate analytical expression when the signal-to-noise ratio approaches infinity is defined as the asymptotic lower bound of the bit error rate; In a specific implementation process, to further clarify the theoretical limit of the system, based on the above work, the asymptotic lower bound of the bit error rate of the PolarSK system under hardware impairment is further derived. This lower bound can be used as a benchmark for evaluating the approximation of the actual system performance. Among them, when the single-RF polarization spatial modulation system is affected by hardware impairment, the bit error rate will stop decreasing after the signal-to-noise ratio exceeds a certain level. To clarify the performance limit under hardware impairment, an asymptotic analysis of PolarSK can be performed under high signal-to-noise ratio conditions to derive the asymptotic lower bound of the bit error rate. Specifically, the asymptotic lower bound of the bit error rate can be defined as the limit value of the approximate analytical expression of the bit error rate when the signal-to-noise ratio tends to infinity, denoted as Equation (22): (twenty two); d2. Based on the three scenarios, determine the value rule for the lower bound of the asymptotic bit error rate in each scenario, and obtain the expression for the lower bound of the asymptotic bit error rate; wherein, the value rule directly corresponds to the relative position of the straight line and the cosine function curve; Image approximation can be used. The expression depends only on The symbol. Through image approximation, Figure 2 The area below the midline represents the effective region for each cycle. Based on the previous analysis, each pair of points corresponds to a bell-shaped curve of a normal distribution (…). Figure 2 On the curve below, The region corresponding to each cycle The sum of the areas intercepted by the bell-shaped curve is the required value. The area of ​​this region can be calculated using equation (23): (twenty three); The final expression for the lower bound of the asymptotic bit error rate can be found in equation (24): (twenty four); That is, when the straight line is below the cosine function curve, the lower bound of the asymptotic bit error rate is 0; when the straight line passes through the cosine function curve, the lower bound of the asymptotic bit error rate is the probability that the decision variable is less than 0; when the straight line is above the cosine function curve, the lower bound of the asymptotic bit error rate is 1.

[0050] 105. Based on the expression for the asymptotic lower bound of the bit error rate, determine the performance evaluation result of the single-radio frequency polarization spatial modulation system.

[0051] Specifically, the calculation result of the asymptotic lower bound expression can be used as the theoretical lower limit of the system's bit error rate, presenting the system's performance limit, and output together with the approximate bit error rate result to form a performance evaluation result that can be used to guide system design, hardware selection, and performance optimization.

[0052] In a specific implementation, the single-RF polarization spatial modulation system may also include a DP-SM system. To facilitate understanding of the improvements of this invention, an ideal DP-SM system without considering hardware impairments will first be briefly introduced as the basis for subsequent analysis.

[0053] exist In the DP-SM system, The transmission signal and the decision signal are represented as follows: Among them, the channel matrix The dimension is noise vector It is A complex Gaussian vector of dimension 1. The signal-to-noise ratio is denoted as... Defined as .in, Energy per symbol represents the average energy carried by each transmitted symbol. This refers to the noise power spectral density. In practical dual-polarization systems, the transmission of both vertically and horizontally polarized signals is affected by two key factors: cross-polarization interference (XPI) caused by imperfect antenna utilization, and cross-polarization ratio (XPR) during propagation. In summary, these effects collectively constitute the noise power spectral density of each signal. This is the 2×2 dimensional unit polarization channel vector corresponding to the antenna pair indexed. It can be expressed as equation (25): (25); in, The polarization characteristics are a comprehensive parameter derived from cross-polarization discrimination (XPD), which combines the cross-polarization isolation (XPI) of the antenna array and the cross-polarization ratio (XPR) of the propagation channel in the actual scenario. For example, the measured results at a carrier frequency of 2.8 GHz are... Subscript The corresponding number of characters is represented. A receiver antenna channel matrix, with co-polarized components. and , respectively characterizing the ideal transmission path of vertical polarization and the ideal transmission path of horizontal polarization, specifically representing two modes: vertical-vertical and horizontal-horizontal. Cross-polarization components and , , respectively represent the transmission paths of polarization leakage, namely the vertical-horizontal transmission component and the horizontal-vertical transmission component.

[0054] By systematically stacking Unit polarization channel vector of each receiving antenna The channel matrix is ​​constructed. This yields the channel matrix of the DP-SM system. , DP-SM is a dual-polarization spatial modulation, a type of indexed modulation. It transmits signals using only one antenna at a time, meaning it selects one of two polarized antennas, either in the vertical (v) or horizontal (h) direction. For simplicity in the subsequent model, this is used... This represents the channel vector for transmitting signals when the antenna in the vertical direction is selected, i.e., Represents the vertical polarization channel vector. This refers to the channel vector for signals transmitted using a horizontally oriented antenna, i.e. This represents the horizontal polarization channel vector. In the original signal reception model, the transmitted signal... It adheres to the constraint of single-polarization activation, meaning that a single transmission activates either a horizontally or vertically polarized antenna. Specifically, when the horizontal polarization component... When transmitted, the vertical component It is zero, and vice versa. This makes Simplify to scalar ,in Represents the activated polarization mode, where if p takes a value in the set... This indicates =1, =[1,0], if p takes the value H in the set, then it indicates that... =1, =[0,1]. Therefore, the received signal can be restated as Accordingly, Representative channel matrix The column vectors associated with the active polarization mode.

[0055] Maximum likelihood detection (MLD) is widely considered an ideal signal detection algorithm. In a DP-SM system under idealized hardware assumptions, an MLD-based detector can be expressed as equation (26): (26); In the transmitted symbol field, all transmitted signal combinations are selected and compared with the signals at the receiver to obtain estimated combinations. . For the above The estimated value. For modulation symbol index. This is an estimate of the modulation symbol. M represents the modulation order; for example, in 4PSK, M=4.

[0056] It should be noted that the main difference between the PolarSK system and the DP-SM system lies in the signal input. They are different. The PolarSK system is multipolar, with a richer polarization domain than a dual-polarization system. The calculation steps are different. The relevant evaluation process of the DP-SM system can be referred to the aforementioned records, and will not be repeated here.

[0057] In a specific implementation process, based on the aforementioned asymptotic lower bound solution method, it can be revealed that the performance limit of a DP-SM system with a single set of polarized antennas is "channel independent". For the DP-SM system, when At this stage, the error component of polarized antenna detection is negligible, and the error only occurs in the coding and demodulation stages. When the system has hardware impairments, this lower limit exhibits characteristics independent of specific channel fading, and the channel matrix... The dimension and value of have no effect on the asymptotic lower bound of the bit error rate. Therefore, the expression for the lower bound can be rewritten as equation (27): (27); Equation (27) shows that the "channel independence" of the DP-SM system is decoupled into two dimensions: Dimension 1: Under the influence of hardware damage and thermal noise, the error components of polarized antenna detection remain at a negligible level. Therefore, system error analysis only needs to focus on the error components of the encoding and demodulation stages.

[0058] Dimension 2: The asymptotic bit error rate lower bound, determined by the coding and demodulation error components, remains independent of the specific channel fading implementation.

[0059] Therefore, it can be determined that the performance evaluation results of the single-RF polarization spatial modulation system include bit error rate performance limits that are independent of channel fading.

[0060] Furthermore, the formulas used in the PolarSK system and DP-SM system are illustrated using a single set of polarized antennas as an example. Those skilled in the art will understand that a similar method can still be used to evaluate a single-radio frequency polarized spatial modulation system with multiple sets of polarized antennas. Examples will not be provided here.

[0061] Based on the same general inventive concept, this invention also protects a method and apparatus for evaluating the performance of a single-radio-polarized spatial modulation system under radio-frequency hardware damage. The method and apparatus for evaluating the performance of a single-radio-polarized spatial modulation system under radio-frequency hardware damage provided by this invention will be described below. The method and apparatus for evaluating the performance of a single-radio-polarized spatial modulation system under radio-frequency hardware damage described below can be referred to in correspondence with the method for evaluating the performance of a single-radio-polarized spatial modulation system under radio-frequency hardware damage described above.

[0062] Figure 3 This is a schematic diagram of the device for evaluating the performance of a single-RF polarization spatial modulation system under RF hardware impairment, as provided in an embodiment of the present invention. Figure 3 As shown, the performance evaluation method and apparatus for a single-radio polarization spatial modulation system under radio frequency hardware impairment in this embodiment includes a construction module 31, a decoupling module 32, an analysis module 33, a derivation module 34, and a determination module 35.

[0063] Among them, the construction module 31 is used to construct an RF hardware impairment model that simultaneously includes power amplifier nonlinearity, I / Q imbalance and phase noise, and integrate the impairment model into an ideal single RF polarization spatial modulation system to form a non-ideal system transmission model; The decoupling module 32 is used to construct a bit error rate analysis framework by representing the bit error rate as a weighted sum of paired error probabilities based on the non-ideal system transmission model and by using a joint upper bound method, and by decoupling the influence of the channel matrix and phase noise. Analysis module 33 is used to process the bit error rate analysis framework through a piecewise approximation function to obtain a reconstructed bit error rate analysis framework, and to analyze the reconstructed bit error rate analysis framework using an image approximation method. Derivation module 34 is used to derive the lower bound expression of the asymptotic bit error rate of the single-radio multiple-input multiple-output under the condition that the signal-to-noise ratio tends to infinity, based on the bit error rate analysis framework and the approximate analytical expression. The determination module 35 is used to determine the performance evaluation result of the single-radio polarization spatial modulation system based on the expression of the asymptotic bit error rate lower bound.

[0064] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440. The processor 410, communication interface 420, and memory 430 communicate with each other via the communication bus 440. The processor 410 can call logic instructions in the memory 430 to execute a performance evaluation method for a single-radio polarization spatial modulation system under radio frequency hardware impairment.

[0065] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0066] It should be noted that all relevant information that may be involved in the various embodiments of the present invention is processed in strict accordance with the requirements of laws and regulations, following the principles of legality, legitimacy, and necessity, based on the reasonable purpose of the business scenario, and is information that users actively provide or generate during the use of the product / service, as well as information obtained with user authorization.

[0067] The information processed by this invention may vary depending on the specific product / service scenario and should be based on the specific scenario in which the user uses the product / service. This may involve user account information, device information, or other related information. This invention will treat the relevant information and its processing with the utmost diligence.

[0068] This invention places great emphasis on the security of relevant information and has adopted reasonable and feasible security protection measures that comply with industry standards to protect user information and prevent unauthorized access, public disclosure, use, modification, damage or loss of relevant information.

[0069] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0070] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for performance evaluation of a single-RF polarization spatial modulation system under RF hardware impairment, characterized in that, include: A radio frequency hardware impairment model that simultaneously includes power amplifier nonlinearity, I / Q imbalance and phase noise is constructed, and the impairment model is integrated into an ideal single radio frequency polarization spatial modulation system to form a non-ideal system transmission model. Based on the aforementioned non-ideal system transmission model, the bit error rate is expressed as a weighted sum of paired error probabilities using a joint upper bound method, and the influence of the channel matrix and phase noise is decoupled to construct a bit error rate analysis framework. The bit error rate analysis framework is processed by a piecewise approximation function to obtain a reconstructed bit error rate analysis framework. The reconstructed bit error rate analysis framework is then analyzed using an image approximation method to calculate an approximate analytical expression for the bit error rate. Based on the bit error rate analysis framework and the approximate analytical expression, the lower bound expression of the asymptotic bit error rate of the single-RF polarization spatial modulation system under the condition that the signal-to-noise ratio tends to infinity is derived. Based on the expression for the asymptotic lower bound of the bit error rate, the performance evaluation result of the single-RF polarization spatial modulation system is determined.

2. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 1, characterized in that, A radio frequency hardware impairment model is constructed that simultaneously incorporates power amplifier nonlinearity, I / Q imbalance, and phase noise, including: The nonlinearity of the power amplifier is modeled using the Saleh model to obtain the distorted signal; Based on the distorted signal, the I / Q imbalance is modeled using a matrix model that includes amplitude deviation parameters, phase deviation parameters, and DC offset components, resulting in a distorted signal. Based on the distorted signal, the constellation rotation caused by the phase noise is modeled using a Gaussian distribution with zero mean, and the damaged signal at the transmitting end is obtained. Based on the damaged signal from the transmitter, the radio frequency hardware damage model is constructed.

3. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 1, characterized in that, Based on the aforementioned non-ideal system transmission model, a bit error rate (BER) is expressed as a weighted sum of paired error probabilities using a joint upper bound method. The influence of the channel matrix and phase noise is decoupled to construct a BER analysis framework, including: The upper bound of the bit error rate is expressed as a weighted sum of the pairwise error probabilities between all transmitted and decision signal pairs using a joint upper bound method; where the weights are the number of bit errors corresponding to each error case. The conditional probability in the expression for the upper bound of bit error rate, which depends on the channel matrix and phase noise, is decomposed. First, the channel matrix is ​​fixed to obtain the expression for the conditional pairwise error probability under given channel conditions. The expression for the conditional pairwise error probability is transformed into a Q-function with decision variables; these decision variables are obtained based on channel gain, hardware impairment factor, and phase noise. Based on the Q function, the global pairwise error probability is determined; Substituting the obtained global pairwise error probability into the upper bound expression of the bit error rate completes the construction of the bit error rate analysis framework.

4. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 3, characterized in that, Based on the Q-function, the global pairwise error probability is determined, including: The solution to the global pairwise error probability is transformed into a dual expectation problem, with the inner layer first calculating the expectation of the phase noise and the outer layer calculating the expectation of the channel matrix. For a given channel matrix, the average pairwise error probability under given channel conditions can be obtained by taking the expectation of the phase noise; The global pairwise error probability is determined based on the channel type: when the channel matrix is ​​a deterministic channel, the average pairwise error probability is directly used as the global pairwise error probability; when the channel matrix is ​​a random channel, the Monte Carlo method is used to sample the channel matrix multiple times, calculate the average pairwise error probability corresponding to each sample, and take the statistical average to obtain the global pairwise error probability.

5. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 4, characterized in that, The bit error rate analysis framework is processed using a piecewise approximation function, including: A piecewise approximation function is constructed to handle the two cases where the input value of the Q function in the bit error rate analysis framework is non-negative and negative; wherein, when the input value is non-negative, it is represented in the form of exponent sum; when the input value is negative, it is represented in the form of 1 minus the exponent sum. The piecewise approximation function is substituted into the expectation calculation of the Q function, and the overall expectation is decomposed into a combination of three integral terms; wherein, the three integral terms include: the positive integral corresponding to the non-negative input value, the negative integral corresponding to the negative input value, and the probability integral corresponding to the negative input value. For the exponential integral terms with the same structure in the positive and negative integrals, by introducing auxiliary variables and parameter transformations, the positive and negative integrals are rewritten as a linear combination of the normal probability density functions, so as to transform the integral calculation problem into the evaluation problem of the normal cumulative distribution function.

6. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 5, characterized in that, Under given channel conditions, the decision variable is described as a cosine function with a constant term; The reconstruction bit error rate analysis framework is analyzed using the image approximation method, and an approximate analytical expression for the bit error rate is calculated, including: Analyze the zero-crossing points of the decision variable and design an image approximation method to transform the sign determination of the decision variable into the positional relationship between the straight line and the cosine function curve in a two-dimensional coordinate system. The positional relationship includes three cases: the straight line is below the cosine function curve, the straight line passes through the cosine function curve, and the straight line is above the cosine function curve. For each of the three scenarios, the sign of the decision variable is determined, and the calculation results of the positive integral, the negative integral, and the probability integral are obtained in each scenario. Based on the calculation results, the approximate analytical expression is determined.

7. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 6, characterized in that, Based on the calculation results, the approximate analytical expression is determined, including: The calculation results for each case are summed to obtain the approximate analytical expression.

8. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 6, characterized in that, Based on the aforementioned bit error rate analysis framework and the approximate analytical expression, the lower bound expression for the asymptotic bit error rate of the single-RF polarization spatial modulation system under the condition that the signal-to-noise ratio approaches infinity is derived, including: In the bit error rate analysis framework, the limit of the approximate analytical expression when the signal-to-noise ratio approaches infinity is defined as the asymptotic lower bound of the bit error rate. Based on the three scenarios, a rule for determining the lower bound of the asymptotic bit error rate is established for each scenario, thereby obtaining an expression for the lower bound of the asymptotic bit error rate; wherein the rule for determining the lower bound directly corresponds to the relative position of the straight line and the cosine function curve.

9. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to claim 8, characterized in that, The rules for determining the value of the asymptotic bit error rate lower bound in each case include: When the straight line is located below the cosine function curve, the lower bound of the asymptotic bit error rate is 0; When the straight line crosses the cosine function curve, the lower bound of the asymptotic bit error rate is the probability that the decision variable is less than 0; When the straight line is above the cosine function curve, the lower bound of the asymptotic bit error rate is 1.

10. The performance evaluation method for a single-RF polarization spatial modulation system under RF hardware impairment according to any one of claims 1-9, characterized in that, The single-radio polarization spatial modulation system includes a polarization shift keying modulation system and / or a dual-polarization spatial modulation system.

Images