A Fast-Converging Double Rotation Modulo Method

Abstract

The present invention discloses a double-rotation modulus calculation method with fast convergence, belonging to the technical field of wireless communication, and comprising the following steps: performing Fourier transform on the radar received signal to obtain a vector to be modulus-calculated; performing vector partitioning based on the accuracy requirement to obtain a plurality of vector regions; performing double rotation on the vector to be modulus-calculated, each vector region and the state machine to obtain the vector angle and the vector modulus value; in the present invention, by using the state machine to correspond to the vector region, after each double rotation of the vector, the absolute value of the ordinate of the rotated vector is re-compared to determine the current vector region of the vector, and the state machine is jumped to the corresponding state, thereby probabilistically skipping some states, reducing unnecessary rotations, and accelerating convergence. In this solution, the vector rotates two angles each time and is preferentially saved, which is equivalent to rotating at the optimal angle, can accelerate the convergence speed, and has higher accuracy when the input bit number is higher. The present invention solves the problem of excessive time consumption in the modulus calculation process of the LFMCW radar system.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a double-rotation modulus calculation method with fast convergence. Background Art

[0002] In an LFMCW radar system, it is usually necessary to perform a Fourier transform on the received signal to obtain relevant frequency information. However, the result of the Fourier transform is a complex number, which contains both amplitude and phase information. It is necessary to perform modulus calculation and angle calculation on it to obtain useful information. At this time, the CORDIC algorithm is often used for solution.

[0003] CORDIC is the abbreviation of Coordinate Rotation Digital Computer. This algorithm is widely used in various fields such as numerical processors, radar signal processing, scientific calculators, modulation schemes, wireless communication, software-defined radio, image and video processing algorithms, etc. The traditional CORDIC algorithm is ingeniously designed, and simplifies the hardware implementation process of modulus calculation into a combination of simple modules such as shifting and addition and subtraction. However, it requires multiple iterations to achieve high precision, and the amount of data processed each time is very large, making the modulus calculation time for a single Fourier transform even much longer than the time spent on the Fourier transform itself.

[0004] If a large amount of time is consumed in the modulus calculation process within the single sweep time range of the LFMCW radar system, it will extend the entire radar sweep period, reduce the data throughput, and it is difficult to meet the requirement of the LFMCW radar system for fast real-time response. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, the present invention provides a double-rotation modulus calculation method with fast convergence, which uses a state machine and double rotation to accelerate the convergence speed, and solves the problem of excessive time consumption in the modulus calculation process of the LFMCW radar system.

[0006] In order to achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0007] The present invention provides a double-rotation modulus calculation method with fast convergence, including the following steps:

[0008] S1. Perform a Fourier transform on the radar received signal to obtain a vector to be modulus calculated;

[0009] S2. Perform vector partitioning based on the accuracy requirement to obtain a number of vector regions;

[0010] S3. Perform double rotation based on the vector to be modulus calculated, each vector region and the state machine to obtain a vector angle and a vector modulus value.

[0011] Further, the step S2 includes the following steps:

[0012] S21. According to the angle division criterion, divide the range of 0° to 45° in the first quadrant of the coordinate system to obtain several divided regions. Among them, each of the said vector regions corresponds to an upper boundary angle θ ubi and a lower boundary angle θ dbi ;

[0013] S22. Determine whether the angle of the smallest region among the divided regions is less than the accuracy requirement. If so, obtain several vector regions; otherwise, return to step S21.

[0014] Furthermore, the calculation expression of the angle division criterion in step S21 is as follows:

[0015]

[0016] where y represents the dependent variable of the angle division proportional function, x represents the independent variable of the angle division proportional function, represents the proportional coefficient of the angle division proportional function, i represents the i-th angle division, and n represents the total number of angle divisions.

[0017] Furthermore, the states of the state machine include state 0, state 1, state 2,..., state n', where n' is a finite positive integer.

[0018] Furthermore, step S3 includes the following steps:

[0019] S31. When the state of the state machine is 0, place the vector to be modulus into the vector region divided between 0° and 45°, and jump to the next state;

[0020] S32. According to the number of vector regions, obtain the same number of rotation states;

[0021] S33. According to the vector rotation model, rotate the vector to be modulus clockwise by the upper boundary angle and the lower boundary angle of the vector region respectively to obtain a first rotated vector and a second rotated vector;

[0022] S34. Determine whether the absolute value of the ordinate of the first rotated vector is less than the absolute value of the ordinate of the second rotated vector. If so, use the first rotated vector as the vector to be partitioned; otherwise, use the second rotated vector as the vector to be partitioned;

[0023] S35. According to the angle division criterion and the ordinate of the vector to be partitioned, obtain the vector region where the vector to be partitioned is located, and jump to the corresponding state;

[0024] S36. When the state is less than the preset iteration number N, repeat steps S33 to S35; otherwise, enter step S37;

[0025] S37. Calculate the total rotation coefficient and the vector angle based on the positive and negative coefficients of the ordinate of the vector to be partitioned and the angle of the previous rotation corresponding to the vector to be partitioned.

[0026] S38. Calculate the vector modulus based on the total rotation coefficient and the abscissa of the vector to be partitioned, and return to state 0.

[0027] Furthermore, the calculation expression of the vector rotation model in step S33 is as follows:

[0028] x n″ = k(x n″-1 + y n″-1 tanθ n″-1 )

[0029] y n″ = k(y n″-1 + x n″-1 tanθ n″-1 )

[0030] where x n″ and y n″ represent the abscissa and ordinate of the rotated vector respectively, x n″-1 and y n″-1 represent the abscissa and ordinate of the vector before rotation respectively, and tanθ n″-1 represents the tangent value of the rotation angle.

[0031] Furthermore, the calculation expressions of the total rotation coefficient and the vector angle are as follows:

[0032] k = Π n″-1 cosθ i

[0033] α j = α j-1 + dθ j-1

[0034]

[0035] where k represents the total rotation coefficient, Π n″-1 cosθ i represents the cumulative rotation coefficient, cosθ i represents the cosine value of the angle of the i-th division, α j represents the angle of the rotated vector, α j-1 represents the angle of the vector before rotation, d represents the positive and negative coefficient, θ j-1 represents the angle of the previous rotation, quadrant1st indicates that the vector is in the first quadrant after rotation, and quadrant4th indicates that the vector is in the fourth quadrant after rotation.

[0036] Further, the calculation expression of the vector modulus value is as follows:

[0037] mod = k * x n

[0038] Where mod represents the vector modulus value.

[0039] The beneficial effects of the present invention are as follows: The present invention provides a double-rotation modulus calculation method with fast convergence. By using a state machine to correspond to vector regions, after each double-rotation of the vector, the absolute value of the ordinate of the rotated vector is re-compared to determine the current vector region where the vector is located, and the state machine is jumped to the corresponding state, thereby probabilistically skipping some states, reducing unnecessary rotations, and accelerating convergence. In this solution, the vector rotates two angles each time and is preferentially saved, which is equivalent to rotating at the optimal angle, can accelerate the convergence speed, and has higher precision when the input bits are higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flowchart of the steps of a double-rotation modulus calculation method with fast convergence in an embodiment of the present invention.

[0041] Figure 2 It is a vector partition diagram in an embodiment of the present invention.

[0042] Figure 3 It is a double-rotation schematic diagram in an embodiment of the present invention.

[0043] Figure 4 It is a double-rotation maximum difference schematic diagram in an embodiment of the present invention.

[0044] Figure 5 It is a state transition schematic diagram in an embodiment of the present invention.

[0045] Figure 6 It is a modulus value statistics and precision comparison diagram in an embodiment of the present invention.

[0046] Figure 7 It is a single modulus calculation timing diagram using the double-rotation modulus calculation method in an embodiment of the present invention.

[0047] Figure 8 It is a traditional single modulus calculation timing diagram in an embodiment of the present invention.

[0048] Figure 9 It is a schematic diagram of the radar system MCU structure in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0049] The following describes the specific embodiments of the present invention to facilitate the understanding of those skilled in the art of the present technology. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0050] CORDIC: Coordinate Rotation Digital Computer.

[0051] LFMCW: Linear Frequency Modulated Continuous Wave.

[0052] MCU: Microcontroller Unit.

[0053] CORDIC plays an important role in the calculation of hyperbolic functions and trigonometric functions. The CORDIC algorithm is applicable to the evolution of a variety of elementary functions. At the same time, the design that takes into account the accuracy, number of iterations, and speed of CORDIC has become a challenging problem. However, implementing it in hardware requires a significant increase in cycle time.

[0054] State: The state of the state machine.

[0055] Since not all input data needs to start rotating from 45°, as long as it is judged whether to continue iteration after each rotation, and once the accuracy requirement is met, the result is output. For (n is a natural number) near the vector, a small number of rotation times can achieve the required modulus accuracy, so that the total calculation time after multiple calculations is greatly reduced, realizing high-speed and high-precision modulus calculation.

[0056] Embodiment 1

[0057] As Figure 1 shown, in an embodiment of the present invention, the present invention provides a fast-converging double-rotation modulus calculation method, including the following steps:

[0058] S1. Perform Fourier transform on the radar received signal to obtain the vector to be calculated for modulus.

[0059] In order to minimize the distribution interval of the vector to reduce the number of rotation iterations, the vector can be rotated to the first quadrant by symmetric rotation (changing the signs of x and y), and then compare the magnitudes of the abscissa and ordinate of the rotated vector to rotate the vector between 0° and 45° in the first quadrant (if the abscissa is greater than the ordinate, keep the values of the abscissa and ordinate, otherwise exchange the values of the abscissa and ordinate), and store the region information where the original vector is located to restore the true angle value.

[0060] S2. Perform vector partitioning based on the accuracy requirement to obtain several vector regions.

[0061] Step S2 includes the following steps:

[0062] S21. According to the angle division criterion, divide the range of 0° to 45° in the first quadrant of the coordinate system to obtain several divided regions. Among them, each of the vector regions corresponds to an upper boundary angle θ ubi and a lower boundary angle θ dbi ;

[0063] The calculation expression of the angle division criterion in step S21 is as follows:

[0064]

[0065] where y represents the dependent variable of the angle division proportional function, x represents the independent variable of the angle division proportional function, represents the proportional coefficient of the angle division proportional function, i represents the i-th angle division, and n represents the total number of angle divisions;

[0066] As Figure 2 shown, draw several lines in the range of 0° to 45° in the first quadrant. The modulus accuracy determines the number n of divided regions, so that the angle of the smallest region where is located is less than the accuracy requirement. For example, for the vector region state5 in Figure 2 , its angle accuracy is less than or equal to 3.57° (tanθ is less than or equal to 1 / 16). Dividing the vector region in this way is, on the one hand, to facilitate comparing the vector ordinate with the regions obtained by the angle division criterion to find the region corresponding to the vector, because dividing by 2 to the power of i is equivalent to shifting i bits to the right. On the other hand, it is consistent with the rotation angle to ensure the convergence of the result. The region between adjacent two lines corresponds to a state of the state machine. It is stipulated that the clockwise direction is the positive direction of the state machine. The goal is to jump to the last state as soon as possible. At this time, the vector meets the required accuracy requirement, the ordinate y≈0, and the abscissa x is the modulus value of the vector;

[0067] For example, after the vector is input, the state machine enters state 0. When in state 0, the vector is rotated to between 0° and 45°, and it is determined that the vector is in vector region 2. Then, in the next cycle, the state machine enters state 2; during state 2, the vector is rotated by the corresponding angle and it is determined that the vector is in region 5 at this time. Then, in the next cycle, the state machine enters state 5 and outputs the result; the entire calculation process only uses three states: state 0, state 2, and state 5, omitting unnecessary rotations, reducing a large amount of power consumption and waiting time;

[0068] S22. Judge whether the angle of the smallest region in each of the divided regions is less than the accuracy requirement. If so, obtain several vector regions; otherwise, return to step S21;

[0069] S3. Perform double rotation based on the vector to be modulus-calculated, each vector region, and the state machine to obtain the vector angle and the vector modulus value;

[0070] As Figure 3 shown, by rotating clockwise according to the vector rotation model and iterating a preset number of times, the vector modulus value can be obtained. It should be noted that if the rotated vector is in the fourth quadrant, it needs to be flipped to the first quadrant; if the rotated vector is in the first quadrant, the vector remains unchanged. Figure 3 In [reference], in order to make any vector in the 35.56° - 45° region, after rotating by an angle, the vector region it is in is as close as possible to the last vector region, the optimal rotation angle required is 35.78° (and the central angle of this vector region). In this way, all vectors in the region can be rotated into the -9.22° - 9.22° region. Then, for the next state at state 3 or a state after state 3, at least state 2 is skipped, but tan35.78°≠(1 / 2) i , i ∈ n, which means that hardware implementation requires a multiplier and the hardware overhead is very large;

[0071] As Figure 4 shown, if we find θ that is closest to 35.78° and tanθ=(1 / 2) i , i ∈ n for rotation. If the vector is close to 45°, rotate by 26.6°, then the next state is state 2; if it rotates by 45°, then the next state is state 5 and the calculation ends directly; if the vector is close to 26.6°, rotate by 26.6°, then the next state is state 5 and the calculation ends directly; if it rotates by 45°, then the next state is state 2; Through Figure 4 it can be found that rotating any vector in a region by the upper boundary angle and the lower boundary angle of this region simultaneously can achieve the same effect as rotating by the central angle of this region. However, this method does not add a multiplier and only uses resources that are nearly twice the original to achieve a convergence speed more than twice that of the original. After rotating using this method, new vector coordinates are obtained, the vector is repartitioned, the region where the new vector is located is judged, and the next state is jumped to;

[0072] The step S3 includes the following steps:

[0073] S31. When the state of the state machine is 0, place the vector to be modulus-calculated into the vector region divided between 0° and 45°, and jump to the next state;

[0074] S32. Obtain the same number of rotation states according to the number of vector regions;

[0075] As Figure 5As shown, in state 0, if the input is valid (valid = 1), then according to the angle division criterion, the input vector is assigned to a fixed interval between 0° and 45°, and jumps to the corresponding next state. Figure 5 There are five rotation states corresponding to five intervals, each interval has an upper boundary and a lower boundary, and in these five rotation states, the vector will be rotated by the upper boundary angle θ. ubi and the lower boundary angle θ. dbi Compare the y - coordinate of the rotated vector, and store the vector coordinates closer to the x - axis; the jump between rotation states is at least separated by one state, as described by the double rotation mentioned above. This can achieve rapid convergence and enter the modulus - finding state as soon as possible.

[0076] S33. According to the vector rotation model, rotate the vector to be modulus - found clockwise by the upper boundary angle and the lower boundary angle of the vector region respectively to obtain a first rotated vector and a second rotated vector.

[0077] The calculation expression of the vector rotation model in step S33 is as follows:

[0078] x n″ = k(x n″-1 + y n″-1 tanθ n″-1 )

[0079] y n″ = k(y n″-1 + x n″-1 tanθ n″-1 )

[0080] where x n″ and y n″ respectively represent the abscissa and ordinate of the rotated vector, k represents the total rotation coefficient, x n″-1 and y n″-1 respectively represent the abscissa and ordinate of the vector before rotation, tanθ n″-1 represents the tangent value of the rotation angle, Π n″-1 cosθ i represents the cumulative rotation coefficient, and cosθ i represents the cosine value of the angle of the i - th division.

[0081] S34. Judge whether the absolute value of the ordinate of the first rotated vector is less than the absolute value of the ordinate of the second rotated vector. If so, take the first rotated vector as the vector to be partitioned, otherwise take the second rotated vector as the vector to be partitioned.

[0082] S35. According to the angle division criterion and the ordinate of the vector to be partitioned, obtain the vector region where the vector to be partitioned is located, and jump to the corresponding state.

[0083] S36. If the state is less than the preset number of iterations N, repeat steps S33 to S35; otherwise, proceed to step S37.

[0084] S37. Calculate the total rotation coefficient and the vector angle based on the positive and negative coefficients of the ordinate of the vector to be partitioned and the angle of the previous rotation corresponding to the vector to be partitioned.

[0085] The calculation expressions for the total rotation coefficient and the vector angle are as follows:

[0086] k = Π n″-1 cosθ i

[0087] α j = α j-1 + dθ j-1

[0088]

[0089] where k represents the total rotation coefficient, Π n″-1 cosθ i represents the cumulative rotation coefficient, cosθ i represents the cosine value of the angle of the i-th division, α j represents the angle of the rotated vector, α j-1 represents the angle of the vector before rotation, d represents the positive and negative coefficient, θ j-1 represents the angle of the previous rotation, quadrant1st represents that the vector is in the first quadrant after rotation, and quadrant4th represents that the vector is in the fourth quadrant after rotation;

[0090] S38. Calculate the vector modulus based on the total rotation coefficient and the abscissa of the vector to be partitioned, and return to state 0.

[0091] Embodiment 2

[0092] In the above embodiment, a simple principle introduction was given using an example with only 5 rotation states. In the practical example of the present invention, a circuit with 13 rotation states for modulo operation on 32-bit radar signals is implemented to verify whether the average number of calculation cycles is significantly reduced and whether the accuracy is improved;

[0093] Import the obtained data into matlab for plotting and compare the accuracy with the original CORDIC algorithm iterated 13 times.

[0094] As Figure 6 shown, under the condition of randomly generating real and imaginary parts, compared with the relative error of the traditional calculation method on the right, overall, under the condition of modulo operation on 32-bit data, the relative error of the present invention is within 8×10 -9 or less, while the traditional method is at 2.5×10-8 The following can be obtained that the modulo accuracy of the present invention is better;

[0095] As Figure 7 and Figure 8 shown, in the comparison of the single modulo timing between the present invention and the traditional modulo algorithm, the state machine (state_crt) of the present invention skips states such as 2, 4, 5, 6, 8, 10, 11, 12, etc. This also indicates that the rotated vector is not in the area corresponding to this state, but enters an area with higher accuracy. While the traditional single modulo requires modulo operation for each vector area and state one by one. The present invention uses double rotation to improve the convergence speed, raise the lower limit of this modulo algorithm, and realizes skipping at least one state for each rotation. The modulo value (mod) is obtained at state 14, and the modulo value is output and the output valid (valid_out = 1) vector modulo value and vector angle are displayed at state 15. (mem_x, mem_y) stores the vector coordinates after each rotation.

[0096] In summary, the present invention consumes a small amount of additional resources, realizes fast convergence, and the accuracy is slightly better than the traditional method.

[0097] Embodiment 3

[0098] As Figure 9 shown, in order to verify that this algorithm indeed significantly reduces the solution time of the distance speed by one time, it is applied to an MCU for processing radar signals. 64 points are sampled for Fourier transform to obtain the results of 64 complex numbers, and the modulo operation is performed using the method of the present invention;

[0099] The system in this embodiment uses a cotex-m3 core, an advanced high-performance bus matrix and an advanced peripheral bus, various transmission protocol interfaces such as a universal asynchronous serial interface, direct memory access, an analog-to-digital converter for sampling data, a Fourier transform module and a modulo module.

[0100] The CORDIC algorithm module of the present invention is mounted as a peripheral on the advanced peripheral bus, and DMA is used to control the data transmission process:

[0101] After the ADC samples 64 frames of data, it sends a transmission request to the DMA. After the DMA asks the FFT module and finds it idle, it sends the sampled data to the FFT for Fourier transform; after the FFT completes the Fourier transform and sends a transmission request to the DMA, the DMA sends the sampled data to the CORDIC for modulo operation after asking the CORDIC module and finding it idle;

[0102] Using the modelsim software for simulation verification, it can be seen that at a 50Mhz clock frequency, the total consumption time is 8800ns; while replacing the modulo algorithm module of the present invention with a traditional algorithm, at the same 50Mhz clock frequency, the total consumption time is 19200ns;

[0103] It can be seen that the present invention has a significant effect in reducing the modulo operation time, and the consumed time is less than half of the traditional one.

[0104] Since it is inconvenient to compare the accuracy of the modulo operation results through simulation, in this embodiment, the data is exported, plotted using Matlab and compared with the abs modulo function of Matlab to calculate the relative error. Compared with the traditional modulo calculation, the present invention has the same accuracy when performing modulo calculation on 16-bit data, but the consumed time is greatly reduced.

Claims

1. A double-rotation modulo method with fast convergence, characterized in that, It includes the following steps: S1. Perform Fourier transform on the radar received signal to obtain the vector to be modulus calculated; S2. Perform vector partitioning based on the accuracy requirement to obtain a number of vector regions; S3. Perform double rotation based on the vector to be modulus calculated, each vector region and the state machine to obtain the vector angle and the vector modulus value. Specifically: S31. When the state of the state machine is 0, place the vector to be modulus calculated into the vector region divided between 0° and 45°, and jump to the next state; S32. Obtain the same number of rotation states according to the number of vector regions; S33. According to the vector rotation model, rotate the vector to be modulus calculated clockwise by the upper boundary angle and the lower boundary angle of the vector region respectively to obtain the first rotated vector and the second rotated vector; S34. Judge whether the absolute value of the ordinate of the first rotated vector is less than the absolute value of the ordinate of the second rotated vector. If so, take the first rotated vector as the vector to be partitioned, otherwise take the second rotated vector as the vector to be partitioned; S35. According to the angle division criterion and the ordinate of the vector to be partitioned, obtain the vector region where the vector to be partitioned is located, and jump to the corresponding state; S36. When the status is less than the preset number of iterations N , repeat steps S33 to S35; otherwise, proceed to step S37. S37. Calculate the total rotation coefficient and the vector angle based on the positive and negative coefficients of the ordinate of the vector to be partitioned and the angle of the previous rotation corresponding to the vector to be partitioned; S38. Calculate the vector modulus value based on the total rotation coefficient and the abscissa of the vector to be partitioned, and return to state 0.

2. The fast-converging double-rotation modulo method according to claim 1, characterized in that The step S2 includes the following steps: S21. According to the angle division criterion, divide the range of 0° to 45° in the first quadrant of the coordinate system to obtain several divided regions, where each of the vector regions corresponds to an upper boundary angle and a lower boundary angle ; S22. Judge whether the angle of the smallest region among the divided regions is less than the accuracy requirement. If so, obtain a number of vector regions, otherwise return to step S21.

3. The fast-converging double-rotation modulo method according to claim 2, wherein The calculation expression of the angle division criterion in the step S21 is as follows: Among them, y represents the dependent variable of the proportional function for angle division, x represents the independent variable of the proportional function for angle division, represents the proportionality coefficient of the proportional function for angle division, i represents the i th angle division, n represents the total number of angle divisions.

4. The fast-converging double-rotation modular method according to claim 3, wherein, The states of the state machine include state 0, state 1, state 2, …, state , where is a finite positive integer.

5. The fast-converging double-rotation modulo method according to claim 1, wherein The calculation expression of the vector rotation model in the step S33 is as follows: Among them, and represent the abscissa and ordinate of the rotated vector respectively, and represent the abscissa and ordinate of the vector before rotation respectively, represents the tangent value of the rotation angle, k represents the total rotation coefficient.

6. The fast-converging double-rotation modulo method according to claim 1, characterized in that The calculation expressions of the total rotation coefficient and the vector angle are respectively as follows: Among them, k represents the total rotation coefficient, represents the cumulative rotation coefficient, represents the i cosine value of the angle of the th division, represents the vector angle after rotation, represents the vector angle before rotation, represents the positive / negative coefficient, represents the angle of the previous rotation, represents that the vector is in the first quadrant after rotation, represents that the vector is in the fourth quadrant after rotation.

7. The fast-converging double-rotation modulo method according to claim 1, characterized in that The calculation expression of the vector modulus value is as follows: Where, mod represents the vector modulus value.

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