FPGA-based MUSIC spatial spectrum calculation method and device

Abstract

The invention discloses a MUSIC spatial spectrum calculation method and device based on an FPGA, and relates to the technical field of signal process.The method comprises the steps that firstly, a subspace formed by signal steering vectors in a two-dimensional search spectrum function in a MUSIC algorithm is converted into a steering vector calculation formula, the steering vector calculation formula is divided into four operation formulas according to mathematical operation, and the four operation formulas are used for calculating the spatial spectrum of the MUSIC; calculating the four operation formulas to obtain values of A, B, C and D, obtaining a subspace spanned by a signal steering vector based on the values of A, B, C and D, deforming a two-dimensional search spectrum function in the MUSIC algorithm based on the subspace spanned by the signal steering vector to obtain sum operation for solving an absolute value, and calculating the sum of the absolute value. And accumulating numerical calculation results based on sum operation of absolute values to obtain a spatial spectrum value under the current search angle. The operation speed of the MUSIC algorithm is improved by redesigning a calculation process suitable for FPGA architecture characteristics, the change can be responded more quickly by adopting the FPGA, and an instant and accurate direction estimation result is provided.

Description

Technical Field

[0001] The present application relates to the field of signal processing technology, and in particular to a method and device for calculating MUSIC spatial spectrum based on FPGA. Background Art

[0002] As a high-performance, low-power hardware acceleration platform, field programmable gate array (FPGA) has been widely used in the field of signal processing in recent years. FPGA has the advantages of strong parallel computing capability, high programmability and low power consumption, and is very suitable for implementing complex algorithms, such as spatial spectrum calculation of the Multiple Signal Classification (MUSIC) algorithm. Implementing the MUSIC algorithm through FPGA can not only significantly improve the calculation speed and meet the real-time requirements, but also effectively reduce the system power consumption and cost.

[0003] Overview of Traditional MUSIC Algorithm The traditional MUSIC algorithm is based on array signal processing theory and estimates the direction of the signal source by analyzing the signals received by the array. The algorithm first calculates the covariance matrix of the received signal, and then divides the feature space into signal subspace and noise subspace by eigenvalue decomposition of the covariance matrix. The direction of the signal source can be determined by searching for spectral peaks in the noise subspace. This subspace-based approach enables the MUSIC algorithm to achieve high-precision direction estimation in complex environments.

[0004] Limitations of Traditional Processors Although the MUSIC algorithm has high resolution and accuracy in theory, its implementation usually relies on high-performance general-purpose processors such as CPUs or GPUs. These processors perform well in processing complex mathematical operations, but in some application scenarios with extremely high real-time requirements, such as fast-moving radar systems or real-time wireless communication networks, the computing speed of traditional processors may not meet the needs. Specifically: The MUSIC algorithm involves a large number of matrix operations, including the calculation of the covariance matrix, eigenvalue decomposition, and spectrum peak search, which have high requirements on computing resources. In a high-speed moving radar system or a real-time wireless communication network, the position of the signal source may change rapidly, and multiple direction estimates need to be completed in a short time. Traditional processors may not provide sufficient computing speed to support such real-time processing. High-performance processors are often accompanied by high power consumption, which is unacceptable in some low-power application scenarios (such as portable devices or long-running monitoring systems).

[0005] Existing solutions and their shortcomings In order to solve the above problems, researchers have proposed some improvement methods, such as using FPGA (field programmable gate array) or ASIC (application-specific integrated circuit) to accelerate the implementation of the MUSIC algorithm. These hardware acceleration solutions can improve computing efficiency and reduce power consumption to a certain extent, but there are still the following shortcomings: First, limited flexibility. The design cycle of FPGA and ASIC is long, and once the design is completed, it is difficult to change and lacks flexibility. Second, the cost is high. The development of FPGA or ASIC requires a dedicated technical team and high R&D costs, which increases the overall cost. Third, the algorithm has poor adaptability. Existing hardware acceleration solutions are often optimized for specific MUSIC algorithm versions and have poor adaptability to newly emerging improved algorithms or variant algorithms. Summary of the invention

[0006] The purpose of this application is to provide a MUSIC spatial spectrum calculation method and device based on FPGA in order to overcome the existing technical defects, improve the running speed of the MUSIC algorithm by redesigning the calculation process suitable for the characteristics of FPGA architecture, and use FPGA to respond to changes more quickly and provide instant and accurate direction estimation results.

[0007] The purpose of this application is achieved through the following technical solutions:

[0008] In a first aspect, the present application proposes a MUSIC spatial spectrum calculation method based on FPGA, the method is applied to FPGA, and the method includes:

[0009] The subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm is converted into the steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, x i and i are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength;

[0010] The steering vector calculation formula is divided into four calculation formulas according to mathematical operations, which are: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters;

[0011] The four operation formulas are calculated to obtain the values ​​of A, B, C, and D, and based on the values ​​of A, B, C, and D, the subspace spanned by the signal-guided vector is obtained;

[0012] Based on the subspace spanned by the signal-guided vector, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the sum operation of the absolute value.

[0013] The numerical calculation results are accumulated based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

[0014] In one possible embodiment, The steps for calculation include:

[0015] Pre-set search range, step and antenna array configuration;

[0016] Based on the search range and step and antenna array configuration, calculate the search range and step and antenna array configuration in the preset All values ​​are amplified and stored in ROM.

[0017] In one possible embodiment, for B = 2π / λ i The steps for calculation include:

[0018] Using the wavelength calculation formula, B = 2π / λ i Transformed into Get the value of B, where f is the signal frequency measured in real time and c is the speed of light.

[0019] In a possible embodiment, the step of calculating C=A*B includes:

[0020] The value of C is obtained by calculating C=A*B using the multiplier of the FPGA.

[0021] In a possible embodiment, the step of calculating D=exp(-j*C) includes:

[0022] The CORDIC IP core is used to perform complex multiplication and trigonometric function operations on D=exp(-j*C) to obtain the value of D.

[0023] In a possible embodiment, based on the subspace spanned by the signal-guided vector, the step of deforming the two-dimensional search spectrum function in the MUSIC algorithm to obtain the absolute value and sum operation includes:

[0024] The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product;

[0025] Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

[0026] In a possible embodiment, the two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector.

[0027] In a second aspect, the present application proposes a MUSIC spatial spectrum calculation device based on FPGA, the device comprising:

[0028] The first conversion module is used to convert the subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm into a steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, x i and i are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength;

[0029] The splitting module is used to split the steering vector calculation formula into four operation formulas according to mathematical operations, namely: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters;

[0030] A calculation module, used for calculating the four operation formulas to obtain the values ​​of A, B, C, and D, and obtaining the subspace spanned by the signal steering vector based on the values ​​of A, B, C, and D;

[0031] The second conversion module is used to transform the two-dimensional search spectrum function in the MUSIC algorithm based on the subspace spanned by the signal-guided vector to obtain a sum operation for obtaining an absolute value;

[0032] The accumulation module is used to accumulate the numerical calculation results based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

[0033] In a possible embodiment, the second conversion module is further used for:

[0034] The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product;

[0035] Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

[0036] In a possible embodiment, the two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector.

[0037] The above-mentioned main scheme of the present application and its further options can be freely combined to form multiple schemes, all of which are schemes that can be adopted and claimed for protection in the present application; and in the present application, (non-conflicting options) options and other options can also be freely combined. After understanding the scheme of the present application, those skilled in the art can understand that there are multiple combinations based on the prior art and common knowledge, all of which are technical schemes to be protected by the present application, and they are not exhaustively listed here.

[0038] The present application discloses a MUSIC spatial spectrum calculation method and device based on FPGA, which relates to the field of signal processing technology. First, the subspace formed by the signal-guided vector in the two-dimensional search spectrum function in the MUSIC algorithm is converted into a guide vector calculation formula, and the guide vector calculation formula is split into four operation formulas according to mathematical operations. The four operation formulas are calculated to obtain the values ​​of A, B, C, and D. Based on the values ​​of A, B, C, and D, the subspace formed by the signal-guided vector is obtained. Based on the subspace formed by the signal-guided vector, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the sum operation of the absolute value, and the numerical calculation results are accumulated based on the sum operation of the absolute value to obtain the spatial spectrum value under the current search angle. The operation speed of the MUSIC algorithm is improved by redesigning the calculation process suitable for the characteristics of the FPGA architecture, and the use of FPGA enables faster response to changes and provides instant and accurate direction estimation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1A schematic flow chart of a MUSIC spatial spectrum calculation method based on FPGA proposed in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0041] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0042] Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative work shall fall within the scope of protection of this application.

[0043] In the existing technology, researchers have proposed some improvement methods, such as using FPGA (field programmable gate array) or ASIC (application-specific integrated circuit) to accelerate the implementation of the MUSIC algorithm. These hardware acceleration solutions can improve computing efficiency and reduce power consumption to a certain extent, but there are still the following shortcomings: First, limited flexibility. The design cycle of FPGA and ASIC is long, and once the design is completed, it is difficult to change and lacks flexibility. Second, the cost is high. The development of FPGA or ASIC requires a dedicated technical team and high R&D costs, which increases the overall cost. Third, the algorithm has poor adaptability. Existing hardware acceleration solutions are often optimized for specific versions of the MUSIC algorithm, and have poor adaptability to newly emerging improved algorithms or variant algorithms.

[0044] Therefore, in order to solve the above technical problems, the embodiment of the present application proposes a MUSIC spatial spectrum calculation method and device based on FPGA, which optimizes the implementation process of the MUSIC algorithm by utilizing the parallel processing capability of FPGA, and emphasizes the acceleration of the key part of the MUSIC algorithm - the steering vector correlation calculation, which is described in detail below.

[0045] Please refer to Figure 1 , Figure 1 A schematic flow chart of a MUSIC spatial spectrum calculation method based on FPGA proposed in an embodiment of the present application is shown. The method is applied to FPGA and includes:

[0046] Step S1, converting the subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm into a steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, xi and i are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength.

[0047] The two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector. Noise subspace E N is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues ​​after the eigenvalue decomposition of the signal covariance matrix, and E N =[e N+1 ,e N+2 ,...,e M ], N is the number of targets, M is the number of array elements, is the subspace spanned by the signal-oriented vector, which is the same as the N-dimensional signal subspace spanned by the eigenvector corresponding to the large eigenvalue after eigenvalue decomposition of the covariance matrix, and is a complex matrix of dimension M×N,

[0048] Step S2: split the steering vector calculation formula into four calculation formulas according to mathematical operations, which are: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters.

[0049] The calculation of the steering vector mainly involves a variety of complex operations such as sine, cosine, multiplication, division, and exponentiation. In order to use FPGA to implement it, the steering vector calculation formula is split into four calculation formulas according to the operation: B=2π / λ i ,i=1,2,...,N、C=A*B、D=exp(-j*C), then solve each calculation formula separately, and finally get the subspace spanned by the signal-guided vector.

[0050] right The steps for calculation include:

[0051] Pre-set search range, step and antenna array configuration;

[0052] Based on the search range and step and antenna array configuration, calculate the search range and step and antenna array configuration in the preset All values ​​are amplified and stored in ROM.

[0053] The result of calculating the steering vector A depends on the known antenna array coordinates and the preset horizontal and vertical search angles. The angle range is -30° to +30°, with a step of 1°, which means that there are 61 different angle values ​​in each dimension (from -30° to +30°). For an antenna array containing 8 array elements, for each pair of horizontal and vertical angle combinations, a set of steering vector components specific to the angle needs to be calculated.

[0054] Since the horizontal and vertical angles are fixed and the position of the antenna array is known, the corresponding steering vector parts under all possible angle combinations are calculated. Because the result of A is usually in decimal form, in order to facilitate storage and reduce hardware resource consumption, this result will be multiplied by the amplification factor (2 15 ), so that the amplified result can accurately use a 16-bit integer to represent the information of each array element.

[0055] Based on the above preprocessing steps, there are a total of (61*61=3721) different combinations, and for each combination, 8 16-bit data need to be stored to represent the situation of 8 array elements. Therefore, the entire ROM needs to support a data width of (16*8=128bit) bits and a depth of at least 3721 to cover all possible angle pairs.

[0056] For B = 2π / λ i The steps for calculation include:

[0057] Using the wavelength calculation formula, B = 2π / λ i Transformed into Get the value of B, where f is the signal frequency measured in real time and c is the speed of light.

[0058] Since the wavelength in calculation formula B cannot be predicted and calculated in advance, its parameters can only be given by the frequency measurement function module in real-time operation, so calculation formula B needs to be calculated in real time in FPGA. i Deformation can be Where f is the real-time measured signal frequency, c = 3*10 8 is the speed of light. Multiply the signal frequency f by the coefficient By calculation, the coefficient Converting it to binary is: 0.00000000000000000000000001011001111101000001111000100000011011101100011110011.

[0059] To avoid large-bit-width decimal multiplication operations in FPGA, complex decimal multiplication can be converted into truncated addition operations, that is, the original data is truncated from the highest bit to the "1" bit in the binary decimal and added. In the decimal, the bits that are "1" are the 26th, 28th, 29th, 32nd to 36th, 38th, 44th to 47th, ... bits, etc. In certain applications, there is an upper limit to the operating frequency, such as 18GHz. In this case, the frequency f is represented in binary and can be represented as a maximum of 36 bits wide: that is, f[35:0]. Then: B = f[35:26] + f[35:28] + f[35:29] + f[35:32] + f[35:33] + f[35:34] + f[35:35]

[0060] Since the highest bit of the frequency is bit35, the calculation accuracy above 35 bits in the binary decimal will be discarded, and the frequency data f[25:0] is not involved in the calculation and is directly discarded, which affects the calculation accuracy to a certain extent. Therefore, in order to improve the calculation accuracy, the above operation is changed to: the coefficient is first expanded by 2 25 After the addition operation is completed, the lower 25 bits are truncated, that is, the coefficient first becomes 0.1011001111101000001111000100000011011101100011110011, then B'=f[35:1]+f[35:3]+f[35:4]+f[35:7]+…+f[35:34]. After that, the lower 25 bits are truncated to obtain B=B'[35:25]+B'

[24] , where adding B'

[24] is a rounding operation, and the final width is 11 bits.

[0061] The steps of calculating C=A*B include:

[0062] The value of C is obtained by calculating C=A*B using the multiplier of the FPGA.

[0063] C=A*B can be calculated using the multiplier resources of FPGA. The number of multipliers is 8 array elements, and the input bit width is 16*11. After the calculation of formula B is completed, a 128-bit data is read from the ROM every clock, and it is decomposed into 8 16-bit data to the a input port of each multiplier; the b input port of the multiplier is the result of calculation B. The result of calculation C is 27 bits.

[0064] The steps of calculating D=exp(-j*C) include:

[0065] The CORDIC IP core is used to perform complex multiplication and trigonometric function operations on D=exp(-j*C) to obtain the value of D.

[0066] D = exp(-j*C) is expressed as D = cos(C)-jsin(C), which is divided into two parts, the real part and the imaginary part, for calculation respectively. The FPGA CORDIC IP core can be used to calculate the sine and cosine values.

[0067] However, since the result of A is expanded by 2 in the process of storing A in the first step, 15 times, that is, the value actually obtained by the above calculation is: C'=A*B*2 15 , that is, C = C' / 2 15 . If the lower 15 bits of C' are directly cut off at this time, the CORDIC calculation accuracy of FPGA will be greatly affected. Therefore, it is necessary to re-derive the calculation formula on this basis. Since the exponential function has a period of 2π, the calculation formula D is transformed into: D = exp(-jmod(C, 2π)), D = exp(-jmod(C', 2π*2 15 ) / 2 15 ) where mod(·) represents the modulo operation.

[0068] After calculation, 2π*2 15 =205857, so the modulo operation in FPGA can be realized by adding the calculated result of C' to π*2 15 (102943) performs a circular comparison. If C'>102943, then C'=C'-205857; and if C'<-102943, then C'=C'+205857, until the condition is not satisfied.

[0069] Then divide the modulo result by 2 15 Then input the CORDIC port to calculate the sine and cosine values. Since the result of C' is 27 bits, the bit width remains unchanged after modulo, which is still 27 bits. The result of modulo is divided by 2 15 This is equivalent to using the lower 15 bits (bit14 to bit0) of the 27-bit data as decimal places and the upper 12 bits (bit27 to bit15) as integer places. At the same time, the absolute value of a number modulo 2π must be less than π, so bits 27 to 17 of the integer part are all integer signs, and only bits 16 to 15 are integer values. If the input bit width of the CORDIC is configured to be 16 bits, according to its input interface rules, bit 15 is the sign bit, bit 14 to bit 13 are integer bits, and bit 12 to bit 0 are decimal places, then the modulo data bits 17 to bit 2 can be directly input into the input port of the CORDIC.

[0070] Step S3, calculate the four operation formulas to obtain the values ​​of A, B, C, and D, and obtain the subspace spanned by the signal-guided vector based on the values ​​of A, B, C, and D.

[0071] After obtaining the values ​​of A, B, C, and D, four calculation formulas are used: B=2π / λ i , C = A*B, D = exp(-j*C) can get the exact value in the steering vector calculation formula, that is, get the subspace spanned by the signal steering vector in the spectrum function calculation formula of the two-dimensional search

[0072] Step S4: Based on the subspace spanned by the signal-guided vector, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain a sum operation for obtaining the absolute value.

[0073] Step S4 includes:

[0074] The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product;

[0075] Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

[0076] Since the noise subspace and the steering vector are theoretically orthogonal, the denominator of the two-dimensional search spectrum function in the MUSIC algorithm is The value is 0, then the spatial spectrum within the target search range The value of is infinite. However, due to the existence of noise and other non-ideal conditions, the denominator will not be 0, but a minimum value will appear, and a maximum value will appear after taking the reciprocal. Since both the maximum value and the minimum value can achieve the purpose of target direction detection, in order to simplify the calculation, only the denominator is calculated.

[0077] At the same time, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain in, Representation calculation The square of the inner product can be further converted into an operation to find the sum of absolute values: in, is a 1×M row vector, It is an M×1 column vector. The result of multiplying two vectors is a scalar value.

[0078] Step S5: Accumulate the numerical calculation results based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

[0079] Then, the MN numerical calculation results are accumulated, and the accumulated result is the spatial spectrum value at the current search angle. In the FPGA implementation, M complex multipliers are required to multiply the real-time input and vector elements, and then perform pipeline addition to achieve real-time output of the spatial spectrum.

[0080] Therefore, the MUSIC spatial spectrum calculation method proposed in the embodiment of the present application mathematically decomposes and reorganizes the core formula used to calculate the two-dimensional spatial spectrum value in the MUSIC algorithm, making it more suitable for hardware implementation. By further decomposing the original formula, four simpler sub-formulas A, B, C and D are obtained, which can be directly mapped to the FPGA for execution. The obtained results A, B, C, and D are used to reconstruct the space formed by the signal-guided vector, and the two-dimensional search spectrum function form in the MUSIC algorithm is adjusted accordingly. Finally, through a process of finding the sum of absolute values, the calculation results are accumulated at different angles to find the optimal spatial spectrum peak position, which corresponds to the position estimation of the signal source.

[0081] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0082] First, by redesigning the calculation process to suit the characteristics of FPGA architecture, the running speed of the MUSIC algorithm can be significantly improved compared with traditional software implementation.

[0083] Second, it makes full use of the rich logic resources inside the FPGA and its powerful parallel processing capabilities, so that it can maintain high efficiency even when facing highly complex operations such as trigonometric functions, multiplication and division.

[0084] Third, because FPGAs can handle multiple tasks simultaneously with extremely low latency, this approach allows the system to respond to changes more quickly and provide more immediate and accurate direction estimates.

[0085] Fourth, compared with general-purpose processors or GPU solutions, FPGA-based designs often have lower energy consumption while completing the same functions.

[0086] A possible implementation of a MUSIC spatial spectrum calculation device based on FPGA is provided below, which is used to execute the various execution steps and corresponding technical effects of the MUSIC spatial spectrum calculation method shown in the above embodiments and possible implementations. The device includes:

[0087] The first conversion module is used to convert the subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm into a steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, x i andi are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength;

[0088] The splitting module is used to split the steering vector calculation formula into four operation formulas according to mathematical operations, namely: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters;

[0089] A calculation module, used for calculating the four operation formulas to obtain the values ​​of A, B, C, and D, and obtaining the subspace spanned by the signal steering vector based on the values ​​of A, B, C, and D;

[0090] The second conversion module is used to transform the two-dimensional search spectrum function in the MUSIC algorithm based on the subspace spanned by the signal-guided vector to obtain a sum operation for obtaining an absolute value;

[0091] The accumulation module is used to accumulate the numerical calculation results based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

[0092] In a possible implementation, the second conversion module is further used for:

[0093] The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product;

[0094] Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

[0095] In a possible implementation, the two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector.

[0096] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A MUSIC spatial spectrum calculation method based on FPGA, characterized in that: The method is applied to FPGA, and the method comprises: The subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm is converted into the steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, x i and i are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength; The steering vector calculation formula is divided into four calculation formulas according to mathematical operations, which are: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters; The four operation formulas are calculated to obtain the values ​​of A, B, C, and D, and based on the values ​​of A, B, C, and D, the subspace spanned by the signal-guided vector is obtained; Based on the subspace spanned by the signal-guided vector, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the sum operation of the absolute value. The numerical calculation results are accumulated based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

2. The MUSIC spatial spectrum calculation method according to claim 1, characterized in that: right The steps for calculation include: Pre-set search range, step and antenna array configuration; Based on the search range and step and antenna array configuration, calculate the search range and step and antenna array configuration in the preset All values ​​are amplified and stored in ROM.

3. The MUSIC spatial spectrum calculation method according to claim 2, characterized in that: For B = 2π / λ i The steps for calculation include: Using the wavelength calculation formula, B = 2π / λ i Transformed into Get the value of B, where f is the signal frequency measured in real time and c is the speed of light.

4. The MUSIC spatial spectrum calculation method according to claim 3, characterized in that: The steps of calculating C=A*B include: The value of C is obtained by calculating C=A*B using the multiplier of the FPGA.

5. The MUSIC spatial spectrum calculation method according to claim 4, characterized in that: The steps of calculating D=exp(-j*C) include: The CORDIC IP core is used to perform complex multiplication and trigonometric function operations on D=exp(-j*C) to obtain the value of D.

6. The MUSIC spatial spectrum calculation method according to claim 2, characterized in that: Based on the subspace spanned by the signal-guided vector, the two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the step of obtaining the absolute value and operation, including: The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product; Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

7. The MUSIC spatial spectrum calculation method according to claim 1, characterized in that: The two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector.

8. A MUSIC spatial spectrum calculation device based on FPGA, characterized in that: The device comprises: The first conversion module is used to convert the subspace spanned by the signal steering vector in the two-dimensional search spectrum function in the MUSIC algorithm into a steering vector calculation formula: Where θ is the horizontal search direction, is the vertical search direction, x i and i are the horizontal and vertical coordinates of the positions of the M antenna array elements, λ i is the wavelength; The splitting module is used to split the steering vector calculation formula into four operation formulas according to mathematical operations, namely: B=2π / λ i , C=A*B, D=exp(-j*C), where A, B, C, and D are different parameters; A calculation module, used for calculating the four operation formulas to obtain the values ​​of A, B, C, and D, and obtaining the subspace spanned by the signal steering vector based on the values ​​of A, B, C, and D; The second conversion module is used to transform the two-dimensional search spectrum function in the MUSIC algorithm based on the subspace spanned by the signal-guided vector to obtain a sum operation for obtaining an absolute value; The accumulation module is used to accumulate the numerical calculation results based on the absolute value sum operation to obtain the spatial spectrum value at the current search angle.

9. The MUSIC spatial spectrum calculation device according to claim 8, characterized in that: The second conversion module is also used for: The two-dimensional search spectrum function in the MUSIC algorithm is deformed to obtain the deformation formula: in, Representation calculation The square of the inner product; Transform the transformation formula to obtain the sum operation of absolute value: in is a 1×M row vector, is an M×1 column vector, N is the number of targets, and M is the number of array elements.

10. The MUSIC spatial spectrum calculation device according to claim 8, characterized in that: The two-dimensional search spectrum function in the MUSIC algorithm is: in is the spatial spectrum within the target search range, E N is the noise subspace, is the conjugate transpose of the noise subspace, is the subspace spanned by the signal-directed vector, is the conjugate transpose of the subspace spanned by the signal-directed vector.

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