KR101990077B1 - Digital signal processing method - Google Patents

Abstract

The present invention proposes a method for processing a digital signal comprising the processes of: converting an analog signal into a digital signal; converting the digital signal from time-based to frequency-based; arranging the frequency-based signal into one matrix signal; detecting a compressed signal from the matrix signal; and restoring the detected compressed signal into an original signal.

Description

[0001] Digital signal processing method [0002]

The present invention relates to a signal processing method, and more particularly, to a digital signal processing method for detecting and restoring a radar and a communication signal in a receiver to which a compressive sensing theory is applied.

Eldar, professor at the Technion Institute of Technology in Israel, says that the frequency-limited signal should be sampled at twice the bandwidth of the original signal to reconstruct the original signal. An innovative approach to overthrowing the Nyquist sampling theory Announced the Xampling receiver. The receiver, which uses the compression sense theory, can reconstruct the original signal through digital signal processing even if the original signals are sampled lower than the Nyquist rate, so that the signals over a wide frequency band can be converted to analog to digital ADC without the need for a low-speed ADC.

A receiver using a compression sensing theory such as a jam-flipping receiver can be roughly classified into an analog stage for compressing a signal by mixing a high-frequency signal with a pseudo-random pattern and a digital stage for converting an analog signal into a digital signal to restore the original signal. A signal processing method applied to a digital stage includes a preprocessing part for removing noise added to a compression signal or adjusting a signal intensity and two parts for detecting and restoring a compression signal based on an orthogonal matching pursuit . On the other hand, there is a research that implements the OMP algorithm on a field programmable gate array (FPGA) rather than an application-specific semiconductor (ASIC).

B. Knoop utilized Vivado high level synthesis (VLS), a register transfer logic (RTL) logic design tool based on Xilinx's C / C ++ language. The modified Gram - Schmidt QR matrix decomposition is applied to recover the compressed signal, and the block inverse matrix method is applied to the inverse matrix calculation required.

And, P. Blache and H. Rabah applied the modified Cholesky decomposition to calculate the inverse matrix without root computation. In addition, P. Blache and H. Rabah designed the logic in a graphical interface environment using the Xilinx System Generator based on Matlab Simulink.

However, the RTL logic implementing the conventional OMP algorithm is a method of storing the compressed signal input through the sensor and processing it, and thus it is difficult to apply to a system requiring real-time processing. In addition, when designing OMP as logic by utilizing hardware description language (HDL), there is a problem that it takes much time and cost.

Korean Patent No. 10-1727088 Korean Patent Publication No. 2018-0049035

Yonina C. Eldar, "Xampling: Signal Acquisition and Processing in Union of Subspaces ", IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL.59, NO.10, OCTOBER 2011. B. Knoop, J. Rust, S. Schmale, D. Peters-Drolshagen, and S. Paul, "Rapid Digital Architecture Design of Orthogonal Matching Pursuit", 24th European Signal Processing Conference (EUSIPCO), pp. 1857-861, 2016. P. Blache, H. Rabah, and A. Amira, "High-Level Prototyping and FPGA Implementation of the Orthogonal Matching Pursuit Algorithm", 11th International Conference on Information Science, ISSPA, pp.1336-1340 , July, 2012.

The present invention provides a digital signal processing method for converting an analog signal into a digital signal and restoring the original signal.

The present invention provides a digital signal processing method implemented in a Xilinx FPGA to process signals in real time.

The present invention provides a digital signal processing method capable of processing a compressed signal in real time in a frequency domain by applying an RTL logic structure considering data flow and input data in parallel.

According to an aspect of the present invention, there is provided a digital signal processing method comprising: converting an analog signal to a digital signal; Converting the digital signal from time based to frequency based; Arranging the frequency-based signals into one matrix signal; And detecting a compressed signal from the matrix signal and recovering the original signal.

The digital signal is output on a plurality of channels, converts a plurality of channels of digital signals into frequency-based signals, and arranges the plurality of frequency-based signals into one matrix (Y).

The start period of the process of restoring the original signal is determined according to the start period of the process of converting into the frequency-based signal.

The process of detecting and restoring the compressed signal is divided into at least two.

And the remaining compressed signal after the component of the compressed signal detected and restored at the previous stage is removed is detected and restored at the latter stage.

The process of detecting and recovering the compressed signal includes a process of detecting a compressed signal, a process of recovering the detected compressed signal, and a process of generating a residual compressed signal from which the recovered compressed signal is removed.

)의 상관 행렬을 구하고, 상관 행렬에서 가장 큰 에너지를 포함한 주파수 구간을 탐지한다. 즉, 값이 가장 큰 행의 번호인 서포트 벡터를 구한다.A matrix (Y) formed by dividing a compressed signal by a predetermined frequency interval and a measurement matrix

), And detects a frequency interval including the largest energy in the correlation matrix. That is, a support vector which is the number of the row having the largest value is obtained.

과 나머지 행렬(R_k, k=0 인 경우 R_k는 Y와 같다)을 곱하여 [수학식 1]의 상관 행렬(Z)을 구하는 과정과, 상관 행렬(Z)의 각 원소의 크기를 구하고 열 방향으로 더한 뒤 [수학식 2]의 값이 가장 큰 행의 번호 i_max를 구하는 과정과, 행 번호 i_max와 0㎐(DC)를 기준으로 대칭되는 번호를 구하여 [수학식 3]의 서포트 벡터(S_k)를 압축 신로호 구하는 과정을 포함한다.The process of detecting the compressed signal is performed by normalizing the measurement matrix A and taking 1 to 48 rows of the matrix obtained by taking the conjugate transpose when k ∈ {0, 1}

And the rest of the matrix (R _k, if k = 0 R _k are the same as Y) for multiplying to obtain the size of each element of the process of calculating a correlation matrix (Z) of Equation 1 and a correlation matrix (Z) column and it adds the direction equation (2) values are obtained for the process of calculating the number i _max of greater rows and row number i _max and the number to be symmetrical relative to the 0㎐ (DC) of [equation 3] on the Support Vector (S _k ) as a compressed signal.

[Equation 1]

&Quot; (2) "

&Quot; (3) "

Where A _c is the column size of the measurement matrix (A).

을 이용하여 [수학식 5]의 C 행렬을 생성하는 과정과, C 행렬의 역행렬을 구하는 과정과, 역행렬과 행렬

로부터 [수학식 6]의 사영 행렬(G)을 구하는 과정과, 사영 행렬(G)와 행렬(Y)를 이용하여 [수학식 7]의 복원 신호의 스펙트럼

을 계산하는 과정을 포함한다.The restoring process includes the steps of generating a matrix A _s of [Equation 4] by selecting only a column corresponding to a support vector in the measurement matrix A, and a matrix A _s ,

, Generating a C matrix of Equation (5) using an inverse matrix and a matrix, obtaining an inverse matrix of a C matrix,

(G) of the restored signal of Equation (6) using the projection matrix (G) and the matrix (Y)

.

&Quot; (4) "

&Quot; (5) "

&Quot; (6) "

&Quot; (7) "

를 이용하여 [수학식 8]의 압축 신호

를 추정하는 과정과, 수신된 행렬(Y)에서 추정한 압축 신호

을 제거한 [수학식 9]의 나머지 신호(R)을 구하는 과정을 포함한다.The step of generating the rest of the compressed signal is a matrix of the spectrum (A _s) and the reconstructed signal

The compression signal of the equation (8)

Estimating a received compression matrix Y,

(R) of Equation (9) by removing the residual signal (R).

&Quot; (8) "

&Quot; (9) "

The digital signal processing method according to embodiments of the present invention can process the process of detecting and restoring the compressed signal in real time. That is, since the processing speed of the digital signal is lower than the input speed of the signal, the compressed signal is stored and then the stored compressed signal is read and processed. However, since the present invention processes the compressed signal in a high-speed FPGA implemented with an orthogonal matching seek (OMP) algorithm, it can detect and restore in real time. In addition, the present invention provides a pipeline structure in which a reconstructing unit for detecting and restoring a compressed signal is composed of a plurality of reconstructing units, and the restored original signal excluding the original signal restored from the input compressed signal by the reconstructing unit at the previous stage is detected and restored . Accordingly, the present invention can detect and restore a compressed signal in a pipeline structure, and real-time detection and restoration are possible, so that a receiver capable of monitoring and intercepting a radar and a communication signal over a wide frequency band in real time can be developed.

1 is a block diagram illustrating a configuration of a digital signal processing apparatus according to an embodiment of the present invention.
2 is an HLS source code used for matrix multiplication.
3 is a block diagram illustrating a configuration and a processing flow of a reconstruction unit of a digital signal processing apparatus according to an embodiment of the present invention.
4 is a diagram for explaining an operation example of a matching module of a restoration unit;
5 and 6 are timing diagrams of input and output data of a reconstruction unit of a digital signal processing apparatus according to an embodiment of the present invention, respectively.
7 is a diagram for explaining major options applied in the synthesis of Vibado HLS.
8 is a diagram summarizing synthesis results of a restoration section of a signal processing apparatus;
FIG. 9 is a view showing a comparison between a processing time and a resource use amount for each module of the restoration unit; FIG.
10 is a diagram showing a result of C / RTL nose simulation.
11 shows the real part and the imaginary part spectrum of a signal restored by Vibado HLS and Matlab for a simulated compression signal.
12 is a diagram comparing performance of RTL logic developed by B. Knoop with a digital signal processing apparatus according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood, however, that the invention is not limited to the disclosed embodiments, but is capable of other various forms of implementation, and that these embodiments are provided so that this disclosure will be thorough and complete, It is provided to let you know completely.

1. Digital signal processing device

1 is a block diagram for explaining a digital signal processing apparatus according to an embodiment of the present invention.

1, an apparatus for processing a digital signal according to an exemplary embodiment of the present invention includes an analog-to-digital converter (ADC) 100 for converting an analog signal into a digital signal, A plurality of Fast Fourier Transforms (FFTs) 200, an arranging unit 300 for arranging signals of a plurality of channels input from a plurality of FFTs 200 into a matrix, And at least one decompression unit (400, 500) for detecting and restoring the compressed signal. Such a digital signal processing device can design the entire signal processing RTL logic into a pipeline structure in order to process the ADC data in real time. That is, since the OMP is a feedback structure in which the current output is used as the next input, the same operation must be repeated a predetermined number of times until the input data is output through the internal process. The ADC 100, the FFT 200, and the sorting unit 300 are pre-processing units for pre-processing the compressed signal, and at least one of the restoring units 400 and 500 includes a part for detecting and restoring the compressed signal using the OMP, to be.

가 입력되고, 제 1 복원부(400)는 OMP 과정을 통해 압축 신호에서 추정한 압축 신호 성분을 제거한 나머지 신호 R(residue), 그리고 서포트 벡터(support vector; SV)를 구한다. 제 2 복원부(500)는 제 1 복원부(400)로부터 복원되고 남은 압축 신호 Y'와, 측정 행렬 A, 그리고

를 입력하고, 제 1 복원부(400)로부터 나머지 신호 R 및 서포트 벡터(SV)를 입력하여 OMP 과정을 통해 복원 신호의 스펙트럼 X와 서포트 벡터 SV를 출력한다.A driving method of such a digital signal processing apparatus will be described below. An analog signal is converted into a digital signal through the ADC 100, and a time-based signal is converted into a frequency-based signal through four FFTs 200, for example, a digital signal of four channels. In addition, the outputs of the four FFTs 200 are aligned by the alignment unit 300, and the alignment unit 300 outputs the compressed signal Y. FIG. That is, the arranging unit 300 arranges a plurality of signals output from the four FFTs 200 and outputs one compressed signal, that is, a matrix Y. Meanwhile, when the time-based signal is converted into a frequency-based signal by the FFT 200, energy is provided for each frequency unit, and the compressed signal can be detected by checking the energy of each frequency unit in the restoration units 400 and 500. At least one restoration unit (400, 500) detects a compressed signal, solves it, restores it, and outputs the original signal. That is, the restoration units 400 and 500 can detect a signal having the maximum energy as a compressed signal. At this time, the first decompression unit 400 detects and restores the first compressed signal, and the second decompression unit 500 detects and restores the second compressed signal from the signal received from the first decompression unit 400. That is, each of the restoring units 400 and 500 detects and restores one compressed signal every time the OMP is repeated. The first restoring unit 400 detects and restores one compressed signal, and the second restoring unit 400 Detects and compresses the compressed signal other than the compressed signal detected by the first decompression unit 400. [ The plurality of decompression units 400 and 500 may be provided to sequentially detect and recover the compressed signal. At this time, the size of the matrix is increased by repeating the OMP by the plurality of restoring units 400 and 500. That is, the size of the matrix computed by the second decompression unit 500 is larger than the size of the matrix computed by the first decompression unit 400. Meanwhile, the first reconstructing unit 400 normalizes the compressed signal Y output from the aligning unit 300, the measurement matrix A, and the measurement matrix A, and takes 1 to 48 rows of the matrix obtained by taking conjugate transparency

And the first decompression unit 400 obtains a residual signal R (residue) obtained by removing the compressed signal component estimated in the compressed signal through the OMP process, and a support vector (SV). The second reconstructing unit 500 reconstructs the compressed signal Y 'restored from the first reconstructing unit 400, the measurement matrix A, and

And inputs the remaining signal R and the support vector SV from the first reconstructing unit 400 and outputs the spectral X of the reconstructed signal and the support vector SV through the OMP process.

The OMP process performed through the first and second restoration units 400 and 500 is as follows. Here, the OMP stages 1 to 3 are a process of detecting a compressed signal, and the OMP stage 4 to the OMP stage 7 is a process of restoring a compressed signal, and the OMP stage 8 and the OMP stage 9 are stages of restoring the compressed signal And then generating the compressed signal. In the matching process for detecting a compressed signal, a correlation matrix between a matrix (Y) formed by dividing a compressed signal by a constant frequency interval and a measurement matrix is obtained, and a support vector (SV) Signal). For example, when a radio signal existing over a frequency range of 2 GHz is multiplied by a pseudo-random pattern signal, the entire 2 GHz is divided into small portions of 31 MHz units, and each portion is divided into low frequency bands (base band) Gathered. At this time, a number is assigned to each part, and a search is made for a support vector having the largest energy, that is, the number of the part having the largest data value, in order to find the number of the part where the signal exists. The restoration process of the OMP 4 stage to the OMP 7 stage selects only the column corresponding to the support vector in the measurement matrix A and restores the detected compressed signal through a plurality of least squares processes. The OMP 1 stage through the OMP 9 stage are performed to select and restore the compressed signal, and the remaining compressed signals except for the recovered compressed signal are generated.

과 행렬 R_k을 곱하여 상관행렬 Z를 구한다. OMP 1 step (matching): normalizing the measurement matrix A and taking 1 to 48 rows of the matrix taking the conjugate transposse

And the matrix R _k to obtain a correlation matrix Z.

Here, R _k is a complex matrix representing the residue, and R ₀ = Y when the number of repetitions is k = 0. Since k = 0 is the output of the first decompression unit 400, the matrix R ₀ generated by the first decompression unit 400 becomes the matrix Y. [

OMP Step 2 (Matching): Find the size of each element of the correlation matrix Z, add it in the column direction, and find the number i _max of the row with the largest value.

Step 3 (Matching) of OMP: Obtain a support vector (SV) by finding the symmetric number based on the number i _max and 0 Hz (DC) of the largest row obtained in the previous step.

Here, A _c is the column size of the measurement matrix A, and the number of elements of the support vector increases by 2 (k + 1) every repetition.

OMP Step 4 (optional): Create a new matrix A _s by selecting only the column corresponding to the support vector in the measurement matrix A.

Here, the column of the matrix A _s increases by 2 (k + 1) every repetition. That is, the first case of applying the OMP, i.e. of the case to 1, and when through the restoration unit 400, the column of the matrix A _s is 2, applying a second OMP, that is, if through the second decompression unit (500) A _s The heat is 4.

을 활용하여 C 행렬을 구한다.OMP 5th step (least squares): matrix with matrix A _s and conjugate transpose

To obtain a C matrix.

OMP Step 6 (least squares): Obtain the inverse matrix of the matrix obtained in the previous step and obtain the projection matrix G.

를 계산한다. 즉, 압축 신호를 복원하여 복원 신호를 생성한다.OMP Step 7 (Least squares): Spectra of reconstructed signal using projection matrix G and matrix Y

. That is, the restored signal is generated by restoring the compressed signal.

행렬의 행은 매 반복마다 2(k+1)씩 증가한다. 즉, 첫번째 OMP를 적용할 경우, 즉 제 1 복원부(400)를 통하면 행렬

의 행은 2이고, 두번째 OMP를 적용할 경우, 즉 제 2 복원부(500)를 통하면

의 행은 4이다. here,

The row of the matrix increases by 2 (k + 1) every repetition. That is, when the first OMP is applied, that is, through the first restoring unit 400,

Is 2, and when the second OMP is applied, that is, through the second restoration unit 500

Is 4.

를 이용하여 압축 신호

를 추정한다. 즉, OMP 4 단계에서 생성된 행렬 A_s와 복원 신호의 스펙트럼

를 이용하여 압축 신호

를추정한다.OMP Step 8 (least squares):

Lt; RTI ID = 0.0 >

. That is, the matrix A _s generated in step 4 of the OMP and the spectrum of the restored signal

Lt; RTI ID = 0.0 >

.

을 제거한 나머지 신호 R(residue)을 구한다. OMP step 9 (remainder): Compressed signal component estimated from received compressed signal Y

And the remaining signal R (residue).

와 서포트 벡터를 구한다Repeating the steps from the first step while increasing k by the number of repetitions set by the user,

And a support vector

2. Constraints

Meanwhile, the digital signal processing apparatus of the present invention can be designed based on Xilinx Vivado HLS which automatically converts C / C ++ language into HDL optimized for Xilinx FPGA. That is, the first and second restoring units 400 for performing the OMP process can be designed based on the Xilinx Vibado HLS. The performance measure of RTL logic using Vivado HLS is latency which is the time until input data is output and initial interval which is the time interval when data is input. In order to design a device that processes input data in real time, it is desirable to satisfy a start cycle condition rather than a processing time. To this end, the start period of the signal processing unit, that is, the restoration unit, may be determined according to the FFT 200 used in the preprocessing step, that is, the Xilinx FFT IP. The length is 256, and the start period of the Xilinx FFT IP having the streaming structure is 1 clock, but the processing time is 256 clocks. If the operation clock of the signal processing apparatus is set to 248 MHz in accordance with the speed of the ADC 100, since the clock is 1/248 MHz = 4 ns, the processing time of the FFT 200 is 256 x 4 ns = 1,024 ns. Accordingly, the first reconstruction unit 400 receiving the output of the FFT 200 should be able to process data every 1,024 ns, which is 256 clocks. However, considering that the RTL logic implementation process is easier as the operation clock is lower, the operating frequency of the OMP can be set to 124 MHz. At this time, every clock is 1 / 124MHz = 8ns and the start period should be 1,024ns / 8ns = 128 clocks.

3. Fixed-point modeling

Prior to designing a digital signal processing apparatus according to an embodiment of the present invention, an algorithm is implemented in Matlab and the performance of OMP according to the number of bits is simulated. Experimental results show that more than 95% of signal restoration performance can be obtained when fixed-point variables of 14 bits or more are used. Table 1 shows the size and fixed-point format of input / output data determined according to the experimental results.

variable Matrix size form Number of bits / decimal division R, Y 20 x 32 Complex number 14/8 I / O

48 x 20 Complex number 14/8 input A 20 x 96 Complex number 14/8 input

2 (k + 1) x 32 Complex number 14/10 Print

4. I / O module design

Since the input / output data is a complex matrix having a large bit width, all the input / output ports can be designed using a block RAM (BRAM) interface. For example, in FIG. 1, data may be stored in the outputs of the arranging unit 300 and the first restoring unit 400, between the first and second restoring units 400 and 500, and in the output of the second restoring unit 500 Block RAM can be provided. That is, a first data storage unit may be provided between the output of the sorting unit 300 and the input of the first decompression unit 400, and the output of the first decompression unit 400 and the input of the second decompression unit 500 And a third data storage unit may be provided at the output of the second decompression unit 500. In this case, Meanwhile, although the block RAM is described as an example of a data storage unit, various storage units such as a DRAM and an SRAM may be used in addition to the block RAM.

In order to process the mathematical expressions (1) - (3) quickly, input matrix or matrix and matrix are divided into multiple vectors so that a large amount of data is simultaneously input. For example, if we divide the matrix by four submatrices of size 20 × 8 in the column direction and divide each submatrix by 20 vectors of size 18 in the row direction, 20 × 4 = 80 samples per clock At the same time, the module can receive input. Then, the elements of the matrix, which is the result of the operation of Equation (1), can be computed every four clocks, so that matrix multiplication can be processed at high speed.

The Vibado HLS directive source code for dividing the input matrix into multiple vectors is as follows. If the dim indicated by parentheses is 1, the port indicated by variable in the row direction and 2 by the column direction are divided into separate vectors.

#pragma HLS ARRAY_RESHAPE variable = () complete dim = ()

K = 1, that is, the size of the X matrix, which is the output of the second decompression unit 500, is also 4 × 32. The X matrix is divided into four sub-matrices each having a size of 4 x 8 in the column direction, and an output port is formed by the number of rows, so that data is output smoothly.

5. Matrix multiplication module design

All OMP submodules contain matrix multiplication operations. The matrix multiplication operation can be implemented using three for loop statements as shown in FIG. 2, which shows the matrix product HLS source code. For example, when multiplying a matrix of size r × m by a matrix of m × c, the outer loop should be r, the intermediate loop c times, and the inner loop m times. When implementing the matrix multiplication with Vivado HLS, the most efficient hardware structure is that all operations are performed on the m-loop.

The matrix multiplication requires a total of r × c × m repetitions. As the matrix size increases, the total number of iterations increases by a factor of several. In this case, applying the pipeline structure to the c loop, the m loops are automatically unrolled, and the total number of iterations is reduced by r × c, so the processing speed can be significantly improved. Instead, the resources used in the m-loop increase by m times.

If such high-speed processing is required, the processing speed can be increased by increasing the resource usage in the loop. However, the area of the RTL logic increases, and timing violations may occur in the register-to-register connection stage. Therefore, it is necessary to balance the resource usage with the matrix multiplication rate to meet the constraints.

6. Rescue structure

The overall signal flow of the digital signal processing apparatus is shown in FIG. That is, the structure and signal flow of the first and second restoration units 400 and 500 are shown in FIG. As shown in FIG. 3, the decompression unit is composed of seven modules, and the module-based pipeline design (dataflow) is performed so that the input data sequentially passes through the module. That is, the matching module 110 for performing the OMP 1 stage to the OMP 3 stage, the selection module 120 for performing the OMP 4 stage, the C matrix module 130 for performing the OMP 5 stage, to obtain the inverse matrix C ^-1 module 140 and the G matrix module 150 to perform the OMP step 6, and X matrix module 160 to perform the OMP step 7, OMP performing step 8 and step 9 OMP R matrix module 170 as shown in FIG. Here, the matching module 110 detects the compressed signal, the selection module 120 to the X matrix module 160 restore the compressed signal, and the R matrix module 170 restores the remaining compressed signals except for the recovered compressed signal . That is, the matching module 110 is a detection module for detecting a compressed signal, and the selection module 120 to the X matrix module 160 are reconstruction modules for reconstructing the compressed signal. The R matrix module 170 reconstructs the reconstructed compressed signal And generates the remaining compressed signals.

There are three for loops in the matching module 110, and when the numbers of each loop are r, c, and m in order from the outside, all operations are performed in the m loop. FIG. 4 shows an operation example of the matching module. FIG. 4 shows the order in which elements of the Z matrix of the OMP 1 stage are generated according to the r and c loop numbers. As shown in FIG. 4, each time the value of c increases, four elements from the 0th row to the 3th row of the matrix are calculated. c Store the value of the maximum value of the vector and the number of r corresponding to it, if s is the value obtained by accumulating this value in the direction of the arrow until the number of the loop is 31. At this time, the tournament method is utilized to find the maximum value. Then, s vector which accumulates the elements of the 4th to 7th rows of the Z matrix is sought and the maximum value is found and compared with the previous maximum value. In this way, the maximum value is searched, and the r value corresponding to the value is designated as a support vector.

The input Y matrix, on the other hand, is also used in the module to compute the X and R matrices after the matching module 110. The Vivado HLS manual recommends that the output of one module should not be passed over to the next module for inter-module pipeline behavior. Therefore, it is designed so that the signal including the Y matrix passes through the inside of the module and is transmitted to the next module.

과

를 생성한다. 이러한 연산은 대수 연산이 필요하지 않다. The selection module 120 takes only the column corresponding to the support vector in the measurement matrix A and generates a new matrix

and

. These operations do not require logarithmic operations.

The C matrix module 130 multiplies the output of the selection module 120 to generate a C matrix. Like the matching module 110, the pipeline directive is applied to the second loop so that the innermost loop is released.

The inverse matrix module 140 obtains the inverse matrix of the C matrix. In this case, the C matrix is a square matrix, the diagonal elements are always real numbers, and the elements symmetric with respect to the diagonal elements are complex conjugate values. The inverse matrix of the C matrix also has the same property. Using these characteristics can reduce the computation and RTL logic resources required for inverse operations. The C matrix increases in size by a factor of 2 according to the number of repetitions k. When K = 0, that is, the size of the matrix in the first decompression unit 400 is 2 × 2, and the following inverse matrix formula can be applied.

If K = 1, that is, the size of the matrix in the second decompression unit 500 is 4 × 4, and the applicable inverse matrix formula is as follows.

At this time, detC is a real value depending on the characteristics of the C matrix. The inverse operation of the fixed-point detC is implemented using a floating-point operator.

을 계산한다. 이때, G 행렬 모듈(160)은

와 역행렬 C^-1를 이용하여 사행 행렬 G를 구한다. 즉,

은 C 행렬 모듈(130) 및 G 행렬 모듈(150)에 입력된다.The G and X matrix modules 150 and 160 are all complex matrix multiplications and are implemented similar to the matching module 110. That is, the G and X matrix modules 150 and 160 perform OMP steps 6 and 7, respectively. The G matrix module 160 obtains a meander matrix G from the inverse matrix, and the X matrix module 160 obtains the spectrum

. At this time, the G matrix module 160

And the inverse matrix C ^-1 . In other words,

Are input to the C matrix module 130 and the G matrix module 150. [

를 이용하여 압축 신호

를 생성하고, 수신된 압축 신호에서 추정한 압축 신호 성분을 제거한 나머지 신호 R(residue)을 구한다. 이때, R 행렬 모듈(170)은 정합 모듈(110)과 마찬가지로 4개의 표본이 동시에 계산되도록 한다.In the R matrix module 170, OMPs 8 and 9 are performed simultaneously. That is, the R matrix module 170

Lt; RTI ID = 0.0 >

And obtains a residual signal R (residue) by removing the compressed signal component estimated from the received compressed signal. At this time, the R matrix module 170 allows four samples to be calculated simultaneously as in the case of the matching module 110.

7. RTL logic optimization

Optimization is performed to reduce unnecessary FPGA resource consumption and to smoothly route the gates. That is, for example, a multiplier, a memory, a lookup table, a register, and the like are disposed in predetermined positions in the FPGA, and the paths between them are programmed and operated. At this time, it is possible to reduce the number of multipliers so that FPGA resources can be connected smoothly. That is, for the general complex multiplication operation, four multipliers are required to multiply A and B as in the third term of the following equation. However, if the complex multiplication operation is changed to P ₀ , P ₁ , and P ₂ as shown in the following equation, it is possible to operate with three multipliers, thereby saving the multiplier resources. The Vivado HLS DSP library has a hls :: cmpy function that is a complex multiplier that uses three multipliers.

Where _{a, P 0 = (A r +} A i) B i, P 1 = (B r + B i) A r, P 2 = (A i -A r) B r

Even if the processing time and the start period of the designed RTL logic satisfy the given constraints, the FPGA resources may not be connected smoothly in the implementation process, resulting in excessive timing violation. In this case, the logic in the FPGA does not work properly. To solve this problem, we can increase the start period in the matrix multiplication loop. Thus, the Vivado also has the effect of reducing the critical path by adjusting the operation of the HLS in the iterative operation so that it can be carried out freely for a plurality of clocks. Instead, the processing time of the iteration may increase, which may be against the start cycle constraint. However, it can be solved by increasing the amount of logic involved in the loop.

The following is the Vivado HLS directive source code to mitigate the critical path. Increasing the start cycle from 1 to 2 increases the processing time by a factor of two, but by using the UNROLL factor directive, the number of iterations of the loop is reduced by factor times, thereby doubling the resource usage and maintaining the processing time of the module.

#pragma HLS PIPELINE II = 2

#pragma HLS UNROLL factor = 2

The operation of the digital signal processing apparatus according to an embodiment of the present invention as described above will be described with reference to the timing diagrams of FIGS. 5 and 6. FIG.

5 is a timing diagram of input data of a restoration unit of a digital signal processing apparatus according to an embodiment of the present invention. As shown in FIG. 5, the control signal of the restoration unit includes ap_done to notify completion of operation, ap_start as a start signal, ap_idle to indicate RTL logic wait state, ap_ready to inform that it is ready to receive input, and ap_clk as a clock input. When ap_start becomes high, the restoration section starts to operate. Before the ap_done signal becomes high, the ap_ready signal becomes high and new data is input. This means that the module-based pipeline structure is operating properly as shown in FIG. The start period corresponds to the difference between the times T1 and T2 when the ap_ready signal becomes high and the processing time is the difference between L1 and L2 which is the time when the ap_start and ap_done signals become high.

Data Y is input in parallel through a total of four ports, but only a single port is shown in FIG. Since the data Y is a complex number, it is divided into a real number and an imaginary number port. The addresses [2: 0] and ce (chip enable), which are addresses for controlling the block RAM to read data, are simultaneously high and the actual signals are inputted one clock after one clock. Through the data port q0 [279: 0], we can see that 20 samples of 14 bits per sample are input simultaneously at 280 bits.

역시 4개의 AeH 포트를 통해 병렬로 입력되며, 각 포트 마다 실수와 허수 값을 입력 받는다. 타이밍 완화 기법이 적용되어, 신호 Y와는 달리 ce 신호가 띄엄띄엄 하이(high)가 되는 것을 확인할 수 있다. data

It is also input in parallel through four AeH ports, and real and imaginary values are input to each port. As the timing relaxation technique is applied, it can be confirmed that the ce signal is spatially high, unlike the signal Y. [

Data A is sequentially input 280 bits through q0 [279: 0] port one clock after address [6: 0] of block RAM storing matrix A when ce is high have. Since the column size of A is 96, the address of the block RAM is assigned 7 bits.

6 is a timing diagram of output data of a reconstruction unit of a digital signal processing apparatus according to an embodiment of the present invention. As shown in Fig. 6, the support vector value which is the result of the matching module at approximately 900 ns time point is outputted through the sv [31: 0] port together with the valid signal. Then, the data Y is output through the d [279: 0] port, and the data R is output successively. It can be confirmed that the address signal [2: 0] is output together with the ce signal which is the input of the block RAM for storing the output data. Both matrix Y and matrix R are output at four ports, but only one port is shown in FIG. When all outputs are complete, you can see that the ap_done signal goes high. After that, the support vector value of the data input at about 900 ns starts to be output at about 1700 ns.

The verification result of the digital signal processing apparatus according to an embodiment of the present invention will now be described.

1) synthesis results

The main options applied in the Vibado HLS synthesis are shown in FIG. We have set three options: bind, schedule, and uncertainty to minimize the timing violation that occurs in Vivado implementation. Binding is the step of mapping operators such as addition and multiplication to specific RTL logic gates. When this option is set to 'High', the synthesis time is long but the RTL logic is optimized. Scheduling is a step of determining an operation to be performed for each clock. If 'High', it takes a long time to synthesize but the operation is performed in the minimum clock. As shown in FIG. 7, the bind and schedule are set to be performed at maximum (effort = high), and the clock cycle is 7.142 ns.

The synthesis result of the restoration unit of the signal processing apparatus is summarized in FIG. In Fig. 8, the clock Clock is the target clock, and the Estimated (Est.) Value indicates the clock that can be set to the maximum. When K = 0, that is, the first reconstruction unit has a clock of 7.14 ns and an estimated value of 4.98 ns. That is, the first decompression unit can operate fast at a clock of 7.14 ns and a clock speed of 4.98 ns. In other words, the first decompression unit has a period of 131 clocks until a signal is input and output, that is, the processing time (latency) is 131 clocks, and a time from input of the first signal until input of the next signal, 106 clocks. Also, when K = 1, that is, the second reconstruction unit has a clock of 7.14 ns and an estimated value of 5.61 ns. That is, the second reconstruction unit has no problem even if the clock is 7.14 ns and the clock is rapidly operated to 5.61 ns. The second restoration unit has a latency of 124 clocks and an interval of 104 clocks. Therefore, it can be seen that the restoration unit according to the present invention has a period of 128 clock or less, which is a constraint, and the inter-module pipeline scheme is applied.

2) Processing time and resource usage per module

FIG. 9 is a diagram showing the processing time and the resource use amount for each module of the restoration unit. FIG. That is, in FIG. 9, K = 0 and K = 1, that is, the first and second restoring units are BRAMs of the matching module, the selecting module, the C matrix module, the inverse matrix module, the G matrix module, the M matrix module, DSP, flip-flop (FF), and look-up table (LUT). As shown in FIG. 9, it is confirmed that more than 240 DSPs are consumed in the matching module in both the first and second restoration units, and a processing time of 100 clocks or more is required. In addition, it can be seen that the flip-flop and the look-up table are consumed much in comparison with other modules in the matching module. It should be noted that the amount of DSP usage required for inverse matrix computation is significantly increased in the second reconstruction unit than in the first reconstruction unit. This is due to the fact that the size of the C matrix is doubled, which means that many FPGA resources and processing time are consumed for matching and inverse matrix computation in OMP. Also, it can be confirmed that the sum of the processing times of the plurality of modules of the second restoring unit is larger than the sum of the processing times of the plurality of modules of the first restoring unit shown in FIG. 8 by applying the pipeline design

3) C / RTL nose simulation results

Vivado HLS has a C / RTL nasal cosimulation function capable of simultaneously simulating C and HDL, and the results are shown in Fig. It should be noted that the processing time and the input period value in Figs. 8 and 10 are different from each other. The start period value of the C / RTL nose simulation is mainly larger than the synthesis result value, and must be designed based on the C / RTL nose simulation result value.

11 shows the real part and the imaginary part spectrum of a signal restored by Vibado HLS and Matlab for a simulated compression signal. That is, Fig. 11 (a) is the spectrum of the real part and Fig. 11 (b) is the spectrum of the imaginary part. Also, the solid line is the result of Vivado HLS, and the dotted line is the result of MATLAB. The normalized mean square error (NMSE) of the two values was calculated to be about 1.8 × 10 ^-3 . As shown in the figure, the Vibado HLS result (solid line) and the MATLAB result (dotted line) according to the present invention are almost identical.

4) Performance comparison

FIG. 12 shows a comparison between the performance of the logic signal developed by B. Knoop and the digital signal processing apparatus according to an embodiment of the present invention. The logic parameters of the present invention were N = 48, M = 20, K = 2 and targeted to a Kintex Ultrascale FPGA (xcku115-flvb2104-2-i). B. Knoop used Virtex7 FPGAs for N = 128, M = 32, and K = 5. That is, the present invention performed two OMP processes for a 48 × 20 matrix and B. Knoop performed five OMP processes for a 128 × 32 matrix. As shown in FIG. 12, in the present invention, the block RAM (BRAM) is about 16 times, the DSP core is about 2.5 times, the flip flop (FF) is about 5.6 times, and the lookup table (LUT) is about 9.7 times It uses a lot of resources, but the processing time is about 10 times faster. This is because the digital signal processor is designed for real-time processing.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention.

100: ADC 200: FFT
300: matching portion 400: first restoration portion
500: second restoration unit

Claims (10)

Converting an analog signal into a digital signal;
Converting the digital signal from time based to frequency based;
Arranging the frequency-based signals into one matrix signal; And
Detecting a compressed signal from the matrix signal and restoring the original signal;
The process of detecting and restoring the compressed signal includes:
Detecting a compressed signal;
Recovering the detected compressed signal,
And generating a remaining compressed signal from which the restored compressed signal component is removed,
Wherein the step of detecting the compressed signal comprises:
The measurement matrix A is normalized and the first to 48 rows of the matrix taking the conjugate transpose are taken respectively

And multiplied by the rest of the matrix (R _k) a process of calculating a correlation matrix (Z) of Equation 1 and,
Calculating a size of each element of the correlation matrix Z and adding it to the column direction and obtaining the number i _max of the row having the largest value of the expression (2)
Calculating a symmetric number based on the row number i _max and 0 Hz (DC), and obtaining the support vector (S _k ) of Equation (3) using the compressed signal.
[Equation 1]

&Quot; (2) "

&Quot; (3) "

Where A _c is the column size of the measurement matrix (A).
The digital signal processing method according to claim 1, wherein the digital signal is output in a plurality of channels, and the plurality of channels are converted into frequency-based signals, and the plurality of frequency-based signals are arranged in a matrix (Y).
The digital signal processing method of claim 2, wherein the start period of the process of restoring the original signal is determined according to a start period of a process of converting into the frequency-based signal.
The method of claim 2, wherein the process of detecting and restoring the compressed signal is repeated at least twice.
5. The digital signal processing method according to claim 4, wherein the remaining compressed signal from which the component of the compressed signal detected and restored at the previous stage is removed is detected and restored at the latter stage.
delete delete delete The method of claim 1,
Selecting a column corresponding to a support vector in a measurement matrix A to generate a matrix A _s of Equation 4;
A matrix (A _s ) and a matrix taking the conjugate transpose

Generating a C matrix of Equation (5)
A process of obtaining an inverse matrix of a C matrix,
Inverse matrix and matrix

(G) of the equation (6)
The spectrum of the reconstructed signal of Equation (7) is calculated using the projective matrix (G) and the matrix (Y)

And calculating the digital signal.
&Quot; (4) "

&Quot; (5) "

&Quot; (6) "

&Quot; (7) "

The method according to claim 9, the step of generating the rest of the compressed signal is a matrix of the spectrum (A _s) and the reconstructed signal

The compression signal of the equation (8)

Estimating,
The compressed signal estimated from the received matrix Y

(R) of Equation (9) by removing the residual signal (R).
&Quot; (8) "

&Quot; (9) "

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