Binary phase shift keying signal detection method and system based on Gaussian kernel function

Abstract

The invention discloses a binary phase shift keying signal detection method and system based on a Gaussian kernel function, which can effectively suppress the influence of pulse interference on a judgment detector by introducing the Gaussian kernel function and utilizing the suppression effect of the kernel function on large-amplitude data, has excellent non-Gaussian noise resistance robustness, and can effectively improve the detection accuracy of the binary phase shift keying signal. The bit error rate performance superior to that of a traditional method can be provided, and possibility is provided for reliable data transmission in a noise-dominated communication environment. A systolic array architecture is designed, a complex judgment algorithm is decomposed into modularized and pipelined hardware units, a parallel operation mode is adopted, the defects that a traditional robust algorithm is large in calculation amount and difficult to achieve in real time can be overcome, the time complexity of double summation operation is reduced from O () to O (), and the calculation efficiency is improved. And the strict requirement of a high-data-rate communication system on real-time processing is met.

Description

Technical Field

[0001] This invention relates to the technical fields of signal processing, digital communication and programmable logic device (FPGA) hardware, and in particular to a binary phase shift keying signal detection method and system based on Gaussian kernel function. Background Technology

[0002] In modern communication, radar, sonar, and other core systems, reliable signal detection is crucial for ensuring information transmission quality and overall system performance. Binary Phase Shift Keying (BPSK), as a fundamental and commonly used digital modulation method, is widely applied in various digital communication scenarios due to its simple hardware implementation and theoretically optimal bit error rate performance in additive white Gaussian noise (AWGN) channels. In ideal communication environments, receivers typically use linear correlation detectors to determine signal characteristics: by performing correlation operations between the received signal and a pre-defined known matching signal, the modulation type of the received signal is determined based on the amplitude of the result. This scheme has been proven to be the theoretically optimal detection method in AWGN channels.

[0003] However, in real-world communication scenarios, the BPSK signal demodulation process is often affected by various types of impulse interference, and the performance deficiencies of traditional linear correlation detectors are becoming increasingly apparent—their optimal performance strictly relies on the assumption that "channel noise follows a Gaussian distribution," while the statistical characteristics of most channel noise in reality do not satisfy this assumption. For example, sudden impulse interference in urban environments, electromagnetic interference in shortwave communication systems, and environmental noise in underwater sonar transmission all exhibit "heavy tail" distribution characteristics, and their mathematical models are more closely aligned with the Laplace distribution. The probability density function of Laplace noise has a sharp peak at zero, and the decay rate of its tails is much slower than that of a Gaussian distribution. This means that this type of noise contains both a large number of small-amplitude interferences and occasional large-amplitude impulse spikes.

[0004] Traditional linear correlators, designed based on the least squares criterion, are extremely sensitive to the aforementioned pulse spike interference: a single large-amplitude noise sample can cause severe distortion in the correlator output, leading to decision errors. Especially in low signal-to-noise ratio environments, where signal energy is already weak, occasional strong impulse noise can completely drown out the useful signal, causing a sharp increase in the bit error rate of BPSK receivers based on the Gaussian assumption, or even complete failure. Furthermore, traditional correlators require precise modeling of the statistical characteristics of the received signal; once the channel noise model changes (e.g., from a Gaussian distribution to a Laplace distribution), their detection performance deteriorates significantly, making them unsuitable for complex and ever-changing real-world channel environments.

[0005] To address the signal detection problem under non-Gaussian noise, various technical solutions have been proposed, but all have significant limitations: 1) Nonlinear transformation method: This method uses devices such as limiting amplifiers to perform nonlinear processing on the received signal in an attempt to suppress the heavy tailing characteristics of noise and make its distribution approximate a Gaussian distribution. However, this method requires accurate statistical information of the noise in advance, and the nonlinear transformation is prone to introducing signal distortion and loss of key modulation information; when processing broadband signals, it may also distort the signal spectrum, further deteriorating the detection performance.

[0006] 2) Robust statistical method: Detectors are designed directly based on the probability density function of non-Gaussian noise, such as likelihood ratio detectors. Although this type of detector is theoretically the optimal solution, it requires complex nonlinear operations such as logarithmic and exponential operations in Laplace noise environments. This makes it difficult to implement in real time on hardware platforms such as FPGA and ASIC, resulting in extremely high computational complexity, which cannot meet the requirements of high data rate communication systems.

[0007] 3) Adaptive filtering method: The filter parameters are dynamically adjusted through an adaptive algorithm to suppress non-Gaussian noise. However, this method has a slow convergence speed and the filter parameters are difficult to match the noise characteristics in real time when the channel environment changes rapidly, resulting in poor detection performance stability.

[0008] Therefore, there is an urgent need for a BPSK signal detection technology that combines robustness against non-Gaussian noise, low computational complexity, and hardware feasibility to meet the requirements for reliable signal detection in complex channel environments. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a binary phase shift keying signal detection method and system based on Gaussian kernel function.

[0010] To achieve the above objectives, the technical solution provided by this invention is as follows: A binary phase-shift keying signal detection method based on a Gaussian kernel function includes: S1. Establish a mathematical model for the BPSK signal under Laplace noise: The digital signal modulated by BPSK is represented as the following binary hypothesis detection: , ; and These are two forms of BPSK signals. The amplitude of the carrier signal. The frequency of the carrier signal. The signal length; The signal model received by the receiver is: ; in, The signal received by the receiver. The modulation signal to be detected. For signal amplitude, It is Laplace noise; S2. Constructing a Gaussian kernel detector (GKD): ; in," "Indicates that it is defined as; and They are respectively The first in the signal sequence and the One sampling point; using middle The type, of which and To match the first in the signal sequence and the One sampling point; These are the parameters of the Gaussian kernel; S3. Based on the symmetry of the BPSK signal, a decision is made by combining the output value of the Gaussian kernel detector: when When >0, the decision is a digital signal 1; when When <0, the decision is a digital signal 0.

[0011] Furthermore, Laplace noise Follow the mean variance is The probability density function of the noise sample follows a Laplace distribution and is independent and identically distributed, satisfying the following condition: That is, it is symmetric about the mean 0.

[0012] Furthermore, Gaussian kernel parameters The value range is [0, 10], and the optimal value interval is [2, 3], within which the Gaussian kernel detector has the lowest bit error rate.

[0013] Furthermore, to achieve the above objectives, the present invention also provides a binary phase shift keying signal detection system based on a Gaussian kernel function, used to implement the above-mentioned BPSK signal detection method based on a Gaussian kernel function, including a memory DDR, a pulsating array, and an off-array processing unit; The memory DDR is used to store the original data and the calculation results; The pulsating array is used for rapid calculation. This yields the final summation result; The off-array processing unit receives the final accumulated result from the pulsating array and makes a decision.

[0014] Furthermore, the total size of the pulsating array is ,Depend on It consists of three processing units, including a first arithmetic unit, a second arithmetic unit, and a third arithmetic unit. The functions and configurations of each unit are as follows: The first processing unit: number of One port, fixed in the first row of the pulse array, has no accumulated result input port and receives raw input data. and Calculate the first intermediate result and pass it to the subsequent calculation unit; The second processing unit has the following quantity: 1, distributed in the second row to the 2nd row of the pulsating array. All lines Units and The unit is equipped with an accumulation input port and an output port; it receives input data and the accumulation result above, and after completing the calculation, it transmits the input data to the right and lower units and the accumulation result to the lower unit. The third processing unit has the following quantity: One, located in the last row of the pulsating array, except for Units outside the unit, that is, from arrive All units; two accumulation results and two input data input ports: two input ports from above, receiving the accumulation results and input data from above respectively; two horizontal input ports from the previous column, receiving the accumulation results and input data from the left respectively, merging intermediate results from different paths and performing accumulation operation.

[0015] Furthermore, the first arithmetic unit includes a first subtractor. Second subtractor First multiplication device Second multiplication device Third multiplication instrument First indexer and the first adder ; Among them, the second subtractor Receive input data and ,calculate The calculation result is then passed to the first multiplier. First multiplier Calculate based on input data and the calculation results Passed to the second multiplier Second multiplier Receive input data and calculate and the calculation results Passed to the first exponent First exponent Calculate based on input data and the calculation results Passed to the third multiplier The third multiplication instrument Receive input data and the first subtractor Output results and the second subtractor Output results ,calculate and the calculation results Passed to the first adder First adder only This input, the first adder Will Pass it on to the next unit.

[0016] Furthermore, the second arithmetic unit includes a third subtractor. Fourth subtractor The fourth multiplication instrument The Fifth Multiplication Instrument The sixth multiplication instrument Second exponent and the second adder ; Among them, the third subtractor Fourth subtractor The fourth multiplication instrument The Fifth Multiplication Instrument The sixth multiplication instrument Second exponent The additive term in the formula for cooperating with the Gaussian nuclear detector Complete calculation; second adder It additionally receives an intermediate accumulation result from the previous processing unit, which compares the locally calculated addend with the input result. By accumulating the sums, a double summation formula can be achieved. The iterative accumulation step in the calculation; the new accumulated sum obtained after the operation. Along with all the raw input data, it is passed to the next level of computing unit to keep the entire array's computing pipeline running continuously.

[0017] Furthermore, the third arithmetic unit includes a fifth subtractor. The sixth subtractor The seventh multiplication instrument The Eighth Multiplication Device The Ninth Multiplication Instrument Third exponent and the third adder ; Among them, the fifth subtractor The sixth subtractor The seventh multiplication instrument The Eighth Multiplication Device The Ninth Multiplication Instrument Third exponent The additive term in the formula for cooperating with the Gaussian nuclear detector Complete calculation; third adder It receives the locally calculated addend result, the accumulated result output by the upper cell, and the horizontal intermediate result of the left cell, and then merges and accumulates them.

[0018] Furthermore, the off-array arithmetic unit includes a multiplier. and used to provide constant values The register; the multiplier Receive the final accumulated result of the pulse array output, and... The output value of the Gaussian kernel detector is obtained after multiplication. and based on that The value is used to make a judgment.

[0019] Furthermore, the pulse array employs a pipelined processing mode for lengths of... The signal sequence, after 2 The first output is given after one clock cycle. One output per subsequent clock cycle This reduces the time complexity of the double summation operation from O( ) decreased to O( This enables real-time detection of BPSK signals under Laplace noise conditions.

[0020] Compared with existing technologies, the principles and advantages of this technical solution are as follows: 1. By introducing a Gaussian kernel function and utilizing its suppression effect on large-amplitude data, the impact of impulse interference on the decision detector can be effectively suppressed. It has excellent robustness against non-Gaussian noise and can provide bit error rate performance superior to traditional methods, making it possible to achieve reliable data transmission in noise-dominated communication environments.

[0021] 2. A pulsating array architecture is designed to decompose the complex decision algorithm into modular, pipelined hardware units. Parallel computation is employed, avoiding the drawbacks of traditional robust algorithms such as high computational load and difficulty in real-time implementation. This reduces the time complexity of the double summation operation from O(n log n). ) decreased to O( This meets the stringent real-time processing requirements of high data rate communication systems.

[0022] 3. By combining hardware and software, the detection problem of BPSK signals under Laplace noise can be effectively solved, providing a new, efficient and robust technical solution for digital communication under non-Gaussian channels. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the services required in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating the principle of a binary phase shift keying signal detection method based on a Gaussian kernel function according to an embodiment of the present invention (Input represents input; Row vector represents row vector; Column vector represents column vector; Threshold represents threshold). Figure 2 This is a framework diagram of a binary phase shift keying signal detection system based on a Gaussian kernel function according to an embodiment of the present invention; Figure 3 This is a structural diagram of a pulsating array in a binary phase-shift keying signal detection system based on a Gaussian kernel function according to an embodiment of the present invention (Date Information represents date information; DataBus represents data bus; ComputationResult Information represents calculation result information). Figure 4 This is a diagram showing the internal structure of the first arithmetic unit in the pulsating array; Figure 5 This is a diagram showing the internal structure of the second operational unit in the pulsating array; Figure 6 This is a diagram showing the internal structure of the third arithmetic unit in a pulsating array. Figure 7 This is a diagram showing the internal structure of an external arithmetic unit in a binary phase shift keying signal detection system based on a Gaussian kernel function, according to an embodiment of the present invention. Figure 8 for The timing diagram of the data of the pulsating array (acceleration array); Figure 9 A schematic diagram illustrating the error probability of binary signal detection; Figure 10 This diagram illustrates the impact of signal-to-noise ratio and kernel parameters on detection performance. Detailed Implementation

[0025] The present invention will be further described below with reference to specific embodiments: like Figure 1 As shown in this embodiment, a binary phase shift keying signal detection method based on a Gaussian kernel function includes: S1. Establish a mathematical model for the BPSK signal under Laplace noise: The digital signal modulated by BPSK is represented as the following binary hypothesis detection:

[0026] and These are two forms of BPSK signals. The amplitude of the carrier signal. The frequency of the carrier signal. The signal length; The signal model received by the receiver is: ; in, The signal received by the receiver. The modulation signal to be detected. For signal amplitude, It is Laplace noise, and follows a mean of 1 / 2. variance is The probability density function of the noise sample follows a Laplace distribution and is independent and identically distributed, satisfying the following condition: That is, it is symmetric about the mean 0; Because Laplace noise has sharp peaks and heavy tails, traditional linear correlators are highly susceptible to noise spikes, leading to degraded detection performance. To address this issue in Laplace noise-based decision-making, a dual-summing Gaussian kernel detector is proposed. S2. Constructing a Gaussian kernel detector (GKD): ; in," "Indicates that it is defined as; and They are respectively The first in the signal sequence and the One sampling point; using Used as a matching signal to determine the received signal middle The type, of which and To match the first in the signal sequence and the One sampling point; The Gaussian kernel parameter has a value range of [0, 10], and the optimal value range is [2, 3]. Within this range, the Gaussian kernel detector has the lowest bit error rate. Its value determines the smoothness of noise and the sensitivity of the signal of the Gaussian kernel detector. S3. Based on the symmetry of the BPSK signal, a decision is made by combining the output value of the Gaussian kernel detector: when When >0, the decision is a digital signal 1; when When <0, the decision is a digital signal 0.

[0027] This invention utilizes the inherent symmetry of the BPSK signal to simplify the decision-making process. Under Laplace noise, the BPSK signal has two forms. and It is statistically symmetric about zero. The proof is as follows: (1) Proof of expectation Laplace noise They are independent and identically distributed, and their probability density function is... It is symmetric about the mean of 0, that is Therefore, the difference between two independent noise samples probability density function It must also be symmetrical about 0.

[0028] First, let's prove a key lemma. Lemma: Suppose... probability density function Let it be an even function. It is an odd function (i.e.) For any constant c, we have: ; Proof: According to the definition of expectation: Now calculate the terms on the right. ]: .because It is an odd function, therefore Substituting, we get: Perform variable substitution, let ,but , Reversing the upper and lower limits of integration yields: .because It is symmetrical, so = Therefore, we can obtain... The lemma is now complete.

[0029] Based on the linearity of expectation, we have: ; definition (This is an odd function) and Further, we can obtain ,in ， Therefore, the expected term is... .

[0030] when The signal to be detected in is (Matching situation). The expected value at this point is: ; when The signal to be detected in is (Mismatch scenario). The expected value at this point is: ; By the lemma, ; The sign is determined by the summation term. The sign is determined by this. .

[0031] According to the lemma, we can conclude that... The sign of is the same as the sign of 'c'. Therefore, symbols and The symbols are the same.

[0032] Therefore, the sign of the summation term is: ; because And the squared term Therefore, the sign of this term is non-negative. The sum of all non-negative terms must be positive (unless all terms are 0). Therefore, Therefore, we can obtain... .

[0033] (2) Proof of variance The definition of variance is: ; ; according to The definition is that when the matching signal is hour, When the matching signal is hour, .

[0034] From (1), we can see that ;

[0035] Therefore, it can be obtained Their variances are equal.

[0036] When the actual signal is In this matching scenario, the calculated detector The expected value is a positive number. Although a single calculation may fluctuate due to noise, its value has a high probability of falling to the right of zero. Therefore, when a value greater than zero is observed... When the value is 1, the most reasonable decision is the digital signal 1.

[0037] When the actual signal is At that time, based on the symmetry of the proof (the expected value is opposite), in this mismatch case, the detector The expected value will become an exact negative number. This means that the calculated value will be... The value has a high probability of falling to the left of zero. Therefore, when a value less than zero is observed... When the value is 0, the most reasonable decision is a digital signal of 0.

[0038] when = When, the sum of the two error probabilities (i.e. It reaches its minimum value when the threshold is 0.

[0039] Therefore, we can obtain: ; (3) Minimum error rate Error probability for: ; in It is given When true The conditional probability. Assuming the prior probabilities are equal, then ; From (1) and (2), it can be proven that, ; ; Under two assumptions The conditional probability density function is as follows Figure 9 As shown, it is clear that due to the inherent receiver symmetry, the errors are identical. Therefore, we can obtain:

[0040] Furthermore, this embodiment also includes, as follows: Figure 2The system shown is a binary phase shift keying signal detection system based on a Gaussian kernel function, used to implement the above-mentioned BPSK signal detection method based on a Gaussian kernel function. It includes a memory DDR, a pulsating array, and an off-array processing unit. The DDR memory is used to store the original data and the calculation results; Pulsating arrays are used for fast calculation This yields the final summation result; The off-array processing unit receives the final accumulated result from the pulsating array and makes a decision.

[0041] Specifically, such as Figure 3 As shown, the total size of the pulsating array is ,Depend on It consists of three processing units, including a first arithmetic unit, a second arithmetic unit, and a third arithmetic unit. The functions and configurations of each unit are as follows: First operational unit: quantity is One port, fixed in the first row of the pulse array, has no accumulated result input port and receives raw input data. and Calculate the first intermediate result and pass it to the subsequent calculation unit; Second operational unit: quantity is 1, distributed in the second row to the 2nd row of the pulsating array. All lines Units and The unit is equipped with an accumulation input port and an output port; it receives input data and the accumulation result above, and after completing the calculation, it transmits the input data to the right and lower units and the accumulation result to the lower unit. Third operational unit: quantity is One, located in the last row of the pulsating array, except for Units outside the unit, that is, from arrive All units; two accumulation results and two input data input ports: two input ports from above, receiving the accumulation results and input data from above respectively; two horizontal input ports from the previous column, receiving the accumulation results and input data from the left respectively, merging intermediate results from different paths and performing accumulation operation.

[0042] Specifically, such as Figure 4 As shown, the first arithmetic unit includes a first subtractor. Second subtractor First multiplication device Second multiplication device Third multiplication instrument First indexer and the first adder ; Among them, the second subtractor Receive input data and ,calculate The calculation result is then passed to the first multiplier. First multiplier Calculate based on input data and the calculation results Passed to the second multiplier Second multiplier Receive input data and calculate and the calculation results Passed to the first exponent First exponent Calculate based on input data and the calculation results Passed to the third multiplier The third multiplication instrument Receive input data and the first subtractor Output results and the second subtractor Output results ,calculate and the calculation results Passed to the first adder First adder only This input, the first adder Will Pass it on to the next unit.

[0043] Specifically, such as Figure 5 As shown, the second arithmetic unit includes a third subtractor. Fourth subtractor The fourth multiplication instrument The Fifth Multiplication Instrument The sixth multiplication instrument Second exponent and the second adder ; Among them, the third subtractor Fourth subtractor The fourth multiplication instrument The Fifth Multiplication Instrument The sixth multiplication instrument Second exponent The additive term in the formula for cooperating with the Gaussian nuclear detector Complete calculation; second adder It additionally receives an intermediate accumulation result from the previous processing unit, which compares the locally calculated addend with the input result. By accumulating the sums, a double summation formula can be achieved. The iterative accumulation step in the calculation; the new accumulated sum obtained after the operation. Along with all the raw input data, it is passed to the next level of computing unit to keep the entire array's computing pipeline running continuously.

[0044] Specifically, such as Figure 6 As shown, the third arithmetic unit includes a fifth subtractor. The sixth subtractor The seventh multiplication instrument The Eighth Multiplication Device The Ninth Multiplication Instrument Third exponent and the third adder ; Among them, the fifth subtractor The sixth subtractor The seventh multiplication instrument The Eighth Multiplication Device The Ninth Multiplication Instrument Third exponent The additive term in the formula for cooperating with the Gaussian nuclear detector Complete calculation; third adder It receives the locally calculated addend result, the accumulated result output by the upper cell, and the horizontal intermediate result of the left cell, and then merges and accumulates them.

[0045] like Figure 7 As shown, the off-array arithmetic unit includes a multiplier. and used to provide constant values The register; the multiplier Receive the final accumulated result of the pulse array output, and... The output value of the Gaussian kernel detector is obtained after multiplication. and based on that The value is used to make a judgment.

[0046] To verify the performance of the BPSK signal detection method based on Gaussian kernel function proposed in this invention under Laplace noise, Monte Carlo simulation experiments were conducted using MATLAB: Signal Model: Using BPSK signals, its mathematical model is as follows: and Number of signal sampling points Let's set it to 100. According to the linear model, the signal-to-noise ratio (SNR) can be defined as... .

[0047] Noise model: Laplace noise with a mean of 0 was used, and its signal-to-noise ratio (SNR) was set to 0dB, 5dB and 10dB respectively to simulate non-Gaussian channel environments of different intensities.

[0048] Detectors: such as Figure 10 As shown, the detector of this invention (GKD) employs the proposed detector based on the Gaussian kernel function, whose kernel parameters are... A scan is performed within the range [0,10] to find the optimal value.

[0049] Contrast detectors: Matched filter (MF), Kendall correlation coefficient detector (KT).

[0050] Number of simulations: The number of Monte Carlo simulations for each group of experiments is [number missing]. This is done twice to ensure the reliability of the statistical results.

[0051] Simulation variables: The experiment was conducted in two parts to investigate the effects of signal-to-noise ratio and kernel parameters on detection performance. SNR analysis: Under fixed kernel parameters With a signal-to-noise ratio (SNR) of 2, the scanning signal-to-noise ratio (SNR) ranges from 0 dB to 10 dB.

[0052] Kernel parameter analysis: Kernel parameters were scanned under signal-to-noise ratio (SNR) conditions of 0dB, 5dB, and 10dB, respectively. From 0 to 10.

[0053] The simulation results are shown in the figure. Figure 10 This demonstrates the variance of Laplace noise. The bit error rate performance of the detector of the present invention when the signal-to-noise ratio (SNR) is 0dB, 5dB and 10dB, respectively, and the bit error rate performance curves of the detector with a fixed kernel parameter of 2, compared with those of the other two detectors.

[0054] 1. Analysis of the variation of bit error rate with kernel parameters (left side of the figure) Figure 10 The left side shows the bit error rate of the GKD detector as a function of kernel parameters under signal-to-noise ratios (SNR) of 0 dB, 5 dB, and 10 dB. The curve showing the change.

[0055] Importance of nuclear parameters: For the detector (GKD) of this invention, its performance improves with increasing signal-to-noise ratio, and... The optimal value is found between approximately 2 and 3, after which it tends to plateau. This indicates that the selection of kernel parameters is crucial to the performance of this invention, and that the optimal value can be found through a simple parameter scan, providing clear guidance for practical applications.

[0056] 2. Analysis of the variation of bit error rate with signal-to-noise ratio (right side of the figure) Figure 10 The right side shows the results with fixed kernel parameters. The curves showing the change of bit error rate as a function of signal-to-noise ratio (SNR) for the three detectors under the condition that = 2.

[0057] Superior performance: As the signal-to-noise ratio increases from 0 dB to 10 dB, the bit error rate of the detector (GKD) of this invention is consistently lower than that of the matched filter (MF) and the Kendall correlation coefficient detector (KT). This strongly demonstrates that the nonlinear processing of the Gaussian kernel function has a significant suppression effect on Laplace noise, and its decision performance is far superior to the other two detection methods.

[0058] In summary, the simulation results fully verify that the Gaussian kernel function-based detector proposed in this invention significantly outperforms the matched filter and Kendall correlation coefficient detectors under Laplace noise environments of varying intensities. This invention not only solves the challenge of signal detection in non-Gaussian channels but also demonstrates its high efficiency and robustness in practical applications, providing a novel solution for achieving highly reliable data communication and signal processing in complex non-Gaussian channel environments.

[0059] Figure 8 It is a precise timing diagram used to depict a The specific operations and data flow of each processing unit (PE) in the pulsating array during continuous clock cycles (t=0 to t=3). , ， ， ， ， ， ， ， ， The diagram clearly illustrates the start-up process of the production line, where at t=0, only... The pipeline begins operation, while other units are gradually activated along the cycle due to pipeline delays. The key information in the diagram lies in the data dependencies; for example, at t=1, and Activated The calculation results ( This indicates that it successfully received and accumulated the output calculated in the previous cycle. This demonstrates the vertical transmission of results. The most crucial feature of this diagram is shown in... In terms of behavior: at t=2, When activated, its computational content ( This proves that it is a data fusion node, not only receiving data from above. The calculation result also received from its left side. The cumulative result, so at t=2, at The result of the double summation is obtained. At t=3, the result of the next double summation is obtained, and so on for each subsequent cycle. Therefore, this figure not only illustrates the standard pulsating pipeline operation, but also reveals a complex two-dimensional accumulation mode, in which some processing units can aggregate the computation results from both the horizontal and vertical dimensions to execute more advanced algorithms.

[0060] Through this systolic array architecture, this invention transforms the complex double summation operation into a highly parallel and pipelined hardware operation. For an n-dimensional matrix, the systolic array operation unit, after... After one cycle, the first double summation result will be obtained. In each subsequent cycle, a double summation result will be obtained. Therefore, this systolic array architecture reduces the computational time complexity from... It dropped to This significantly reduces time complexity and enables real-time, rapid detection of BPSK signals in Laplace noise.

[0061] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for detecting a binary phase shift keying signal based on a Gaussian kernel function, characterized by, Comprise: S1, establish BPSK signal mathematical model under Laplace noise: The digital signal modulated by BPSK is expressed as the following binary hypothesis detection: ， ； and A is the amplitude of the carrier signal for BPSK signals, is the frequency of the carrier signal, is the signal length; The signal model received by the receiver is as follows: ； wherein S is the signal received by the receiver, S is the modulated signal to be detected, S is the signal amplitude, S is the Laplace noise; S2, construct Gaussian kernel detector: ； wherein, represents is defined as; and are respectively the first and the second sampling points in the signal sequence; using as a matching signal to judge the type of the received signal in , wherein and are the first and the second sampling points in the matching signal sequence; is a Gaussian kernel parameter; S3, based on the symmetry of BPSK signal, combined with the output value of Gaussian kernel detector to make decision: When > 0, the decision is for digital signal 1; when < 0, the decision is for digital signal 0.

2. The method according to claim 1, wherein, Laplace noise Follow the mean variance is The probability density function of the noise sample follows a Laplace distribution and is independent and identically distributed, satisfying the following condition: That is, it is symmetric about the mean 0.

3. The method of claim 1, wherein the method is characterized by: Gaussian kernel parameter The value range of is [0, 10], and the optimal value interval is [2, 3], in which the bit error rate of the Gaussian kernel detector is the lowest.

4. A system for detecting a binary phase shift keying (BPSK) signal based on a Gaussian kernel function, for implementing the method for detecting a BPSK signal based on a Gaussian kernel function according to any one of claims 1-3, characterized in that, Including memory DDR, pulsatile array and array operation unit outside the array; Among them, the memory DDR is used to store raw data and operation results; The systolic array is used to quickly compute , to obtain a final accumulated result. The array operation unit outside the array receives the final accumulation result from the pulsatile array and makes a decision.

5. A Gaussian kernel function based binary phase shift keying signal detection system according to claim 4, characterized in that, The total size of the systolic array is , which is composed of processing units, including a first operation unit, a second operation unit, and a third operation unit, and the functions and configurations of each unit are as follows: The first operation unit: the number is fixed in the first row of the pulsating array, has no accumulated result input port, receives original input data and , calculates the first intermediate result and passes it to the subsequent operation unit; The second operation units are distributed in the whole of the second to the th rows of the systolic array, and the number of the second operation units is The second operation units are distributed in the whole of the second to the th rows of the systolic array, and the number of the second operation units is The second operation units are distributed in the whole of the second to the th rows of the systolic array, and the number of the second operation units is The second operation units are distributed in the whole of the second to the th rows of the systolic array, and the number of the second operation units is The second operation units are distributed in the whole of the second to the th rows of the systolic array, and the number of the second operation units is The third operation unit: the number is one, which is located in the last row of the systolic array except the unit, that is, all the units from to ; two accumulated results and two input data input ports: two input ports from above, which respectively receive the accumulated results and input data from above; Two are horizontal input ports from the previous column, respectively receiving the left side of the accumulation result and input data, fusing the intermediate results in different paths and performing accumulation operation.

6. The Gaussian kernel function based BPSK signal detection system according to claim 5, wherein, The first operation unit includes a first subtractor , a second subtractor , a first multiplier , a second multiplier , a third multiplier , a first exponentiator , and a first adder ​ Among them, the second subtractor Receive input data and ,calculate The calculation result is then passed to the first multiplier. First multiplier Calculate based on input data and the calculation results Passed to the second multiplier Second multiplier Receive input data and calculate and the calculation results Passed to the first exponent First exponent Calculate based on input data and the calculation results Passed to the third multiplier The third multiplication instrument Receive input data and the first subtractor Output results and the second subtractor Output results ,calculate and the calculation results Passed to the first adder First adder only This input, the first adder Will Pass it on to the next unit.

7. The Gaussian kernel function based BPSK signal detection system according to claim 5, wherein, The second operation unit includes a third subtracter , a fourth subtracter , a fourth multiplier , a fifth multiplier , a sixth multiplier , a second exponentiator , and a second adder ; wherein the third subtracter , the fourth subtracter , the fourth multiplier , the fifth multiplier , the sixth multiplier , the second exponentiator performs the complete calculation of the addend term in the Gaussian kernel detector formula ; the second adder further receives an intermediate accumulation result from the previous processing unit, which accumulates the locally calculated addend term result with the incoming to realize the iterative accumulation step in the double summation formula ; the new accumulated sum after the operation is passed to the next processing unit together with all the input raw data to maintain the entire array calculation pipeline continuously.

8. The Gaussian kernel function based BPSK signal detection system of claim 5, wherein, The third operation unit includes a fifth subtracter , a sixth subtracter , a seventh multiplier , an eighth multiplier , a ninth multiplier , a third exponentiator , and a third adder ; Among them, the fifth subtractor The sixth subtractor The seventh multiplication instrument The Eighth Multiplication Device The Ninth Multiplication Instrument Third exponent The additive term in the formula for cooperating with the Gaussian nuclear detector Complete calculation; third adder It receives the locally calculated addend result, the accumulated result output by the upper cell, and the horizontal intermediate result of the left cell, and then merges and accumulates them.

9. The Gaussian kernel function based BPSK signal detection system of claim 4, wherein, The off-array arithmetic unit includes a multiplier. MUL and used to provide constant values The register; the multiplier MUL Receive the final accumulated result of the pulse array output, and... The output value of the Gaussian kernel detector is obtained after multiplication. and based on that The value is used to make a judgment.

10. The Gaussian kernel function based BPSK signal detection system of claim 4, wherein, The pulsating array adopts a pipeline processing mode, and for a signal sequence with a length of , the first is output after 2 clock cycles, and one is output every clock cycle, so that the time complexity of double summation operation is reduced from O( ) to O( ), and real-time detection of BPSK signals in a Laplace noise environment is realized.

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