Digital communication error fast detection method based on new gaussian q function

Abstract

The application discloses a new Gauss Q function digital communication error fast detection method. The steps of the application are as follows: S1: the channel modulation method and the channel model are determined, the model corresponding PDF is obtained, and the fading factor m is input; 2: the detection equipment is used to obtain the digital signal to be detected; 3: the digital signal to be detected is preprocessed, and the complex white noise information average signal-to-noise ratio of the multipath channel is calculated; 4: a probability density registration module is set, and the corresponding Gauss Q function approximate expression is automatically output according to the input approximate term number N; 5: the SEP module is executed, the ASEP is calculated, and the transmission signal performance condition is obtained. The application can improve the situation that the parameter calculation time used by the approximate Gauss Q function increases exponentially with the term number, compared with the approximate formula pursuing high precision, the calculation speed of the application is faster, and the precision is also good; compared with the approximate formula pursuing calculation efficiency, the calculation precision of the application is higher, and the calculation speed is in the same order of magnitude.

Description

Technical Field

[0001] This invention belongs to the field of communication and electronic information technology, and mainly relates to the field of computer simulation. It proposes a fast digital communication error detection method based on a new Gaussian Q function, specifically involving a method for measuring the channel transmission signal performance based on the Gauss-Q function approximation of the Gauss-Kronrod approximation formula. Background Technology

[0002] The approximation problem of the Gaussian Q-Function (GQF) has been widely applied in signal processing and communication principles, playing a crucial role in the Symbol Error Probability (SEP) of digital modulation schemes to measure the performance of channel transmission signals. Furthermore, the Gaussian Q-Function has also been applied to additive white Gaussian noise, fading channels, and bit error rate estimation for various digital modulation schemes.

[0003] The metric for measuring the accuracy of data transmission within a specified time is the Average Symbol Error Probability (ASEP). Its calculation formula is shown below:

[0004] ρ(·) is the probability density function (PDF) of the signal-to-noise ratio (SEP) in the fading channel. The calculation of SEP depends on different modulation methods. For example, the formula for DE-QPSK modulation in the additive white noise channel is:

[0005] r is the instantaneous signal-to-noise ratio (SNR), and Q(·) is the right-tail function of the Gaussian Q-function, which is the standard normal distribution. The expression for the one-dimensional Gaussian Q-function is shown below: erfc(·) is the error function.

[0006] The Q-function is an important tool in probability theory and statistics. Since it is not an elementary function, it is often approximated by elementary functions for computational convenience. To more effectively control approximation errors, it is usually necessary to determine the upper and lower bounds of the Q-function, thereby limiting the approximation method. This helps ensure reliable results are obtained within acceptable error ranges in practical applications. Currently, with the development of 5G communication, the Internet of Things, and other fields, there are increasingly higher requirements for approximation accuracy. Improving the approximation error of Q(x) is becoming increasingly important for enhancing the performance analysis of communication systems. In recent years, many documents and patents have provided corresponding approximation Q-functions according to their respective application needs, such as approximation expressions that mainly improve approximation accuracy:

[0007]

[0008]

[0009]

[0010]

[0011] Another example is an approximate expression that primarily ensures computational efficiency:

[0012]

[0013]

[0014]

[0015] Among them (1) is The methods proposed by J et al. in 2017, (2) by Wu MW et al. in 2018, (3) by Chen XD et al. in 2021, (4) by Tanash IM et al. in 2021, (5) by Tanash IM et al. in 2021, (6) by Sadhwani D et al. in 2017, and (7) by Powari A et al. in 2022 are as follows. Currently, the first type of method suffers from an exponential increase in the time required to optimize the parameters with the number of terms, thus creating an efficiency bottleneck; while the second type of method has a lower approximation accuracy than the first type of method.

[0016] In practical communication systems, accurate estimation of the bit error rate (BER) is crucial to system performance. Signal-to-noise ratio (SNR) is related to the Gaussian distribution characteristics of the received signal, and the Gaussian probability density function, by modeling the signal distribution, provides the foundation for the design and optimization of various communication systems. Therefore, solving the Q-function approximation problem not only directly relates to the reliability of the communication system but also provides strong support for performance evaluation and optimization in practical applications.

[0017] With the continuous evolution of communication technologies, emerging fields such as 5G and IoT communication have presented new challenges and opportunities for the research of Q-functions. In these fields, the demand for faster and more reliable communication is more urgent, making accurate modeling and approximation methods for Q-functions a research hotspot. Summary of the Invention

[0018] This invention addresses the bottlenecks in efficiency and accuracy of channel transmission signal performance evaluation in wireless communication technology by proposing a fast digital communication error detection method based on a novel Gaussian Q-function. Currently, Gaussian Q-function approximation methods, as described above, mainly suffer from problems such as the time required to optimize parameters increasing exponentially with the number of terms, or insufficient approximate accuracy. The purpose of this invention is to achieve fast digital communication error detection and improve detection accuracy by creating a new Gaussian Q-function approximation method. The primary application area of ​​this invention is fast fading channels in the field of wireless communication.

[0019] The specific steps of the technical solution provided by this invention are as follows:

[0020] Step S1: Define the channel modulation method and channel model, obtain the corresponding PDF, and input the fading factor m. The fading factor characterizes the rate at which the signal changes in the channel. The faster the signal changes, the larger m is, and the more difficult it is to recover the original signal. Different modulation methods and channel models have different PDFs, but they are all related to the fading factor m and the average signal-to-noise ratio r. Therefore, it is also necessary to determine the average signal-to-noise ratio of the signal.

[0021] Step S2: Acquire the digital signal to be detected. The digital signal to be detected is obtained through the signal storage module or digital signal sensor of the detection equipment in the application scenario. The detection equipment can obtain the following parameter information of the digital signal to be detected: total signal energy E s The power spectral density of the noise, N0, and the symbol period of the signal, T. sym and sampling interval T samp .

[0022] Step S3: Preprocess the digital signal to be detected by calculating the average signal-to-noise ratio using the sampled parameters.

[0023] The average signal-to-noise ratio r of the complex white noise information of the multipath channel is calculated using the parameter information of the digital signal to be detected, as follows:

[0024]

[0025] Step S4: Set up the probability density registration module to automatically output the corresponding Gaussian Q-function approximation expression based on the input number of approximation terms N. The probability density registration module uses the Gauss-Kronrod integral to approximate the Q-function. For the integral expression... Numerical integration approximates it as the sum of N weighted terms f(x), i.e. Where A i x represents the approximation coefficients for the corresponding approximation nodes. i These are the selected approximation nodes. For N-term approximations, Gaussian integrals offer the best approximation results because they achieve the highest algebraic accuracy of 2N+1 degrees.

[0026] Step S41: Since the integration domain of the Gauss-Kronrod integral is [-1, 1], it is first necessary to modify the original expression. Perform variable substitution, let Then there is Where e is the natural index and t is the independent variable of the mathematical model, which has no physical meaning at present.

[0027] Step S42: Then, based on the size of the input N, use Legendre polynomials to solve for N pairs of approximate nodes x. i and approximation coefficient A i , i = 1, 2, ..., N.

[0028] Step S43: Use the Stieltjes polynomial to add N+1 pairs of approximate nodes x i and approximation coefficient A i To adjust the approximate effect, i = 1, 2, ..., 2N+1.

[0029] Step S44: Substitute the obtained 2N+1 pairs of approximate nodes x i and approximation coefficient A i To the expression Q(x)≈A i f(x i Obtain an approximate expression and output it.

[0030] Step S5: Execute the SEP module to calculate ASEP. SEP characterizes the probability of symbol errors in a communication system and directly reflects the system's performance and reliability. For multipath fading, since it is impossible to control all channels to maintain the same signal-to-noise ratio, ASEP calculation is often used to characterize the performance of the combined system. Different modulation methods correspond to different SEP modules, thus allowing for comparison of ASEP results obtained from different methods and models, enabling analysis and improvement of the methods. SEP(r) is the combination function of the Gaussian Q function, and p(r) is the PDF of the signal-to-noise ratio in the range of [0,∞]. The PDF of different models is also different, but they are all related to the fading factor m and the average signal-to-noise ratio r.

[0031] The beneficial effects of this invention are:

[0032] The core technical feature of this invention is the creation of a novel Gaussian Q-function approximation method to achieve rapid detection of digital communication errors and improve detection accuracy. This method addresses the issue that the computation time for the parameters used in the Gaussian Q-function approximation increases exponentially with the number of terms. This invention incorporates the idea of ​​numerical integration, using Gauss-Kronrod integration to adaptively obtain an approximate expression for the Gaussian Q-function. This approximate expression is then substituted into the ASEP formula to efficiently obtain a highly accurate ASEP approximation value. Experiments show that compared to other Gaussian Q-function approximation methods for digital communication error detection, this method has more accurate and powerful performance. Furthermore, this method can also be used as a preprocessing method for other fitting algorithms to improve their fitting accuracy.

[0033] Compared with existing patents and papers, this invention has the following advantages: compared with approximate formulas that pursue high accuracy, this invention has a faster calculation speed and better accuracy; compared with approximate formulas that pursue calculation efficiency, this invention has higher calculation accuracy and the calculation speed is on the same order of magnitude. Attached Figure Description

[0034] Figure 1 The flowchart shows the calculation process for the symbol error probability of a digital modulation scheme.

[0035] Figure 2 The flowchart shows the new Gaussian Q-function approximation method.

[0036] Figure 3 The graph shows the index data results for each method.

[0037] Figure 4 The graph shows the index data results for each method.

[0038] Figure 5 The graph shows the index data results for each method. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the following embodiments are provided.

[0040] This method clarifies the channel modulation method and channel model, obtaining the corresponding PDF. Secondly, this method acquires the digital signal to be detected, which is obtained using the signal storage module or digital signal sensor of the device in the application scenario. Then, this method performs digital signal preprocessing to calculate the average signal-to-noise ratio. Next, the probability density registration module (adaptive) is set, automatically outputting the corresponding Gaussian Q-function approximation expression based on the number of input approximation terms N. Figure 2As shown. Finally, the SEP module is executed to calculate ASEP and obtain the transmission signal performance. The method described in this invention can improve the situation where the calculation time of the parameters used in the approximate Gaussian Q function increases exponentially with the number of terms. On the one hand, compared with the approximation formula that pursues high accuracy, the calculation speed of this invention is faster and the accuracy is also better. On the other hand, compared with the approximation formula that pursues computational efficiency, the calculation accuracy of this invention is higher and the calculation speed is on the same order of magnitude. At the same time, this method can also be used as a preprocessing method for other fitting algorithms to improve their fitting accuracy.

[0041] The present invention will be further described in detail below. The application background of the embodiments of the present invention is error probability detection of a nakagami-m fast fading channel based on DE-QPSK modulation technology. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0042] like Figure 1 and 2 The flowchart shown below illustrates an embodiment of the fast digital communication error detection method based on the new Gaussian Q function in SEP calculation. Details are as follows:

[0043] In step S1, the channel modulation method is specified as DE-QPSK modulation, the channel model is a nakagami-m fast fading channel, and its PDF is [PDF information missing]. Assume the fading factor m = 2.

[0044] In step S2, the digital signal to be detected is acquired. The received signal parameter information, such as the total signal energy E, can be obtained through the detection device. s The power spectral density of the noise, N0, and the symbol period of the signal, T. sym Sampling interval T samp .

[0045] In step S3, the average signal-to-noise ratio r of the multipath channel can be calculated using the parameters described above.

[0046] Step S4: Set up the probability density registration module, assuming the number of input approximation terms N = 2.

[0047] Step S41: Since the integration domain of the Gauss-Kronrod integral is [-1, 1], it is first necessary to modify the original expression. Perform variable substitution, let Then there is

[0048] Step S42: Then, based on the size of the input N, use Legendre polynomials to solve for N pairs of approximate nodes and coefficients A. i and x i ,i=1,2.

[0049] Step S43: Use the Stieltjes polynomial to add N+1 pairs of nodes and coefficients A i and x i i = 1, 2, 3, 4, 5 to adjust the approximate effect.

[0050] Step S44: Substitute the obtained 5 pairs of approximate nodes x i and approximation coefficient A i To the expression Q(x)≈A i f(x i The approximate expression is obtained and output as shown in Table 2.

[0051] Table 1. Gauss-Krondrod integration nodes and corresponding quadrature coefficients when N=2

[0052] 1 0.1980 0.9258 2 0.4909 0.5774 3 0.6222 0 4 0.4909 -0.5774 5 0.1980 -0.9258

[0053] Substitute the obtained nodes and corresponding coefficients into the formula:

[0054] The approximate expression obtained is as follows:

[0055]

[0056] In step S5, the SEP module is executed. The SEP calculation formula for DE-QPSK modulation technology is:

[0057]

[0058] The Nakagami-m fast fading channel model

[0059] Suppose the approximate Gaussian Q-function expression is as follows: but

[0060]

[0061] Since a1, a2, b1, b2, m, Since everything is known, it can be calculated directly without further approximation, thus ensuring both accuracy and computational efficiency.

[0062] Table 2 below is a test comparison table showing the rapid digital communication error detection method based on the new Gaussian Q function of the present invention and various other methods, and provides a detailed description of the application effects of the present invention.

[0063] Table 2: Comparison of ASEP calculation errors using different Gaussian Q-function methods ( m=2)

[0064]

[0065]

[0066] In summary, as shown in Table 2, the method of the present invention has a smaller error than other methods and higher accuracy.

[0067] Table 3: Comparison of ASEP computation time for different Gaussian Q-function methods ( m=2)

[0068] In this invention, N=3 0.178299 Approximate (1) 1.301880 Approximate (2) 0.533468 Approximately (3), N = 4 3.133211 Approximate (4) 0.074613 Approximately (6), N = 4 0.273207 Approximately (7), N = 6 0.508081

[0069] In summary, as shown in Table 3, the computation time of this method is better than that of most other methods.

[0070] like Figure 3-5 As shown in Tables 1-3, the test results indicate that in digital communication error detection applications, compared to other algorithms, the ASEP calculation error of the method proposed in this invention can be improved by at least one order of magnitude on average, with a maximum improvement of three orders of magnitude. Furthermore, the calculation speed is superior to most methods and is roughly on par with the best method. Note that all experimental comparisons in this paper are based on Matlab simulation experiments, and the precise values ​​of Q and I are the results of numerical integration built into Matlab. In summary, this method, after testing, shows improvements in both accuracy and speed for digital communication error detection. The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fast digital communication error detection method based on the new Gaussian Q function, characterized in that, The specific steps are as follows: Step S1: Define the channel modulation method and channel model, obtain the probability density function PDF corresponding to the model, input the fading factor m, and determine the average signal-to-noise ratio of the signal; Step S2: Acquire the digital signal to be detected using the detection device. The following parameters of the digital signal to be detected are: total signal energy. Power spectral density of noise The symbol period of a signal and sampling interval ; Step S3: Preprocess the digital signal to be detected, and calculate the average signal-to-noise ratio of the complex white noise information of the multipath channel using the parameter information of the digital signal to be detected. as follows: ； Step S4: Set up the probability density registration module to automatically output the corresponding Gaussian Q-function approximation expression based on the input number of approximation terms N; the probability density registration module uses Gauss-Kronrod integration to approximate the Q-function; for the integral expression... Numerical integration approximates it as a sum of N weighted terms f(x), i.e. ,in These are the approximation coefficients for the corresponding approximation nodes. These are the selected approximate nodes; Step S5: Execute the SEP module to calculate ASEP. ,in It is a combination function of the Gaussian Q-function. For signal-to-noise ratio in The PDF varies across different models, but it is related to the fading factor m and the average signal-to-noise ratio. Regarding this, step 5 is implemented as follows: The SEP calculation formula for DE-QPSK modulation technology is: ； The Nakagami-m fast fading channel model ; Suppose the approximate Gaussian Q-function expression is as follows: but ； because Since everything is known, it can be calculated directly without further approximation, thus ensuring both accuracy and computational efficiency.

2. The method for rapid detection of digital communication errors based on the new Gaussian Q function according to claim 1, characterized in that, Step 4 is implemented as follows: Step S41: Since the integration domain of the Gauss-Kronrod integral is [-1, 1], it is first necessary to modify the original expression. Perform variable substitution, let Then there is , where e is the natural index and t is the independent variable of the mathematical model, which has no physical meaning at present; Step S42: Then, based on the size of the input N, use Legendre polynomials to solve for N pairs of approximate nodes. and approximation coefficients , ; Step S43: Use the Stieltjes polynomial to add N+1 pairs of approximate nodes. and approximation coefficients To adjust the approximate effect, ; Step S44: Substitute the obtained 2N+1 pairs of approximate nodes and approximation coefficients to expression Obtain an approximate expression and output it.

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