CN111896820A - Method for acquiring sensing matrix of pulse sequence random demodulation hardware system - Google Patents

Abstract

The present invention is a method for obtaining the sensing matrix of a random demodulation hardware system of a pulse sequence. The invention belongs to the field of signal processing. The invention determines the input signal of the random demodulation hardware system of the pulse sequence, and sets the initial time shift parameter value; the output signal of the random demodulation hardware system of the pulse sequence is uniformly sampled, and the sampling rate and the sampling time are the same. It is the same as the random demodulation hardware system of the pulse sequence to obtain the sampled value; perform FFT transformation on the obtained sampled value to obtain the frequency domain value of the sampled value; remove the influence of the actual filter from the frequency domain value of the sampled value, and obtain the removal of the actual filter value. The frequency domain of the sampled values affected by the sensor; change the count variable and the time shift parameter to obtain the perception matrix. The present invention reduces the deviation in the theoretical calculation, and is more in line with the characteristics of the actual system. Therefore, the calculation content and influencing factors are greatly reduced.

Description

A Method for Obtaining Perception Matrix of Pulse Sequence Random Demodulation Hardware System

technical field

The invention relates to the technical field of signal processing, and relates to a method for obtaining a perceptual matrix of a random demodulation hardware system of a pulse sequence.

Background technique

Richard Baraniuk of Rice University and his research team proposed the Random Demodulation (RD) system in 2006, which is a technology and method that extends the theory of compressed sensing to the analog domain, mainly for compressed sampling of multi-frequency signals. , its structure is shown in Figure 1, which mainly includes four parts: mixing, low-pass filtering, uniform sampling, and signal reconstruction. The signal processing flow is as follows: the analog signal is first multiplied by a pseudo-random sequence in an analog multiplier to achieve frequency mixing, then filtered by an analog low-pass filter, and finally sampled by a traditional low-speed ADC to obtain a series of observations data, and finally use the correlation algorithm of compressed sensing to obtain the original measured signal. The hardware structure of the RD system is simple and easy to implement physically. And with the further improvement of the structure, some scholars have applied it to the sampling of pulse sequences in recent years, and achieved good results.

It can be seen from the above analysis that in order to perfectly reconstruct the pulse sequence, the key is to obtain the sensing matrix of the random demodulation system. The sensing matrix of the system can be obtained only by obtaining the mixing sequence, the basis function of the pulse sequence and the sparse basis. . However, the parameters used by this method to obtain the system perception matrix are ideal, and it is inevitable that there are some deviations from the actual system, which cannot well represent the compressed observation process of the actual system, which affects the reconstruction effect of the signal.

SUMMARY OF THE INVENTION

In order to solve the problem that the parameters used in the existing method for obtaining the sensing matrix of the random demodulation hardware system for the pulse sequence are ideal, resulting in a deviation from the actual system, the invention provides a method for obtaining random pulse sequences. For a method for demodulating a hardware system perception matrix, the present invention provides the following technical solutions:

A method for obtaining a random demodulation hardware system perception matrix of a pulse sequence, comprising the following steps:

Step 1: Determine the input signal of the random demodulation hardware system of the pulse sequence, and set the initial time shift parameter value;

Step 2: Set the initial value of the pseudo-random sequence signal and keep it unchanged;

Step 3: uniformly sample the output signal of the pulse sequence random demodulation hardware system, the sampling rate and sampling time are the same as those of the pulse sequence random demodulation hardware system, and obtain the sampling value;

Step 4: Perform FFT transformation on the obtained sample value to obtain the frequency domain value of the sample value;

Step 5: remove the influence of the actual filter from the frequency domain value of the sampled value, and obtain the frequency domain of the sampled value from which the influence of the actual filter is removed;

Step 6: Add the frequency domain of the sampled values affected by the actual filter to the i-th column of the perception matrix to obtain the value of the i-th column of the perception matrix of the actual system;

Step 7: Change the counting variable and time-shift parameter, and repeat steps 1 to 6 to get the perception matrix.

Preferably, the step 1 is specifically: determine the input signal of the pulse sequence random demodulation hardware system, and express the input signal s _i (t) of the pulse sequence random demodulation hardware system by the following formula:

s _i (t)=g(t _i )

Among them, t is the time shift parameter value, g(t) is a single pulse signal, and i is the initialization count variable;

Set the initial time-shift parameter value, the time-shift parameter step value is Δt, the amplitude value is 1, and the number of time-shift calculations is N.

Preferably, the step 4 is specifically: performing FFT transformation on the obtained sample value to obtain the frequency domain value Y _i [l] of the sample value, first expressing the frequency domain value S[m] of the original signal by the following formula (m= -M,1-M,…,M):

By quantizing the analog time amount in the frequency domain value S[m] of the original signal into N uniform grids, the quantized frequency domain value S[m] of the original signal is expressed by the following formula:

S[m]≈G[m]e ^-j2πmniδ/T

Among them, G[m] is the frequency domain form of the pulse signal g(t), T is the observation time length, and δ is the size of the quantization grid.

Preferably, the step 5 is specifically:

Step 5.1: Mix and filter the original signal, and express the frequency domain form Y _i [l] (l=-L,1-L,...,L) of the sampled value after mixing and filtering by the following formula:

Among them, P is the frequency domain form of the mixing function, L is the length of obtaining the sampling value Y _i [l], and H [l] is the frequency response characteristic of the actual filter;

Step 5.2: Remove the influence of the actual filter from the frequency domain value of the sampled value to obtain the frequency domain of the sampled value with the influence of the actual filter removed, and express the frequency domain of the sampled value with the influence of the actual filter removed by the following formula Y _i [l ]′:

Among them, H[l] represents the frequency response characteristic at the frequency domain sampling value Y _i [l] corresponding to the actual filter.

Preferably, the step 6 is specifically as follows: adding the frequency domain form Y _i [l]' of the sampling value with the influence of the actual filter removed into the i-th column of the perception matrix, to obtain the actual system's perception matrix of the i-th column. value, the value Φ _i of the i-th column of the perception matrix of the actual system is represented by the following formula:

Preferably, step 7 is specifically: changing the count variable to i plus 1, and the time shift parameter to t _i +Δt, repeating steps 1 to 6 to obtain a perception matrix, which is represented by the following formula: The perception matrix Φ:

The present invention has the following beneficial effects:

The present invention realizes the method of obtaining the perception matrix without knowing the real situation of the random demodulation hardware system for the pulse sequence. Experiments with this method only need to ensure that the pseudo-random sequence used for mixing with the measured signal is the same as the pseudo-random sequence used to construct the perception matrix, and it is not necessary to know the value of the specific pseudo-random sequence. That is, as long as the pseudo-random sequence generated each time is guaranteed to be the same. Such requirements are easy to meet, and the perception matrix is directly obtained from the actual system, which reduces the deviation in theoretical calculation and is more in line with the characteristics of the actual system. Therefore, the calculation content and influencing factors are greatly reduced.

Description of drawings

Fig. 1 is the structure diagram of random demodulation system;

Fig. 2 is a perceptual matrix effect diagram obtained by theoretical calculation;

Fig. 3 is the perception matrix effect diagram obtained by the calculation of the present invention;

Fig. 4 is the error comparison diagram between the perception matrix obtained by theoretical calculation and the perception matrix obtained by the present invention;

Fig. 5 is the reconstruction effect diagram that the perceptual matrix obtained by theoretical calculation is reconstructed;

FIG. 6 is a reconstruction effect diagram of the perceptual matrix obtained by the present invention for reconstruction.

Detailed ways

The present invention is described in detail below with reference to specific embodiments.

Specific embodiment one:

As shown in FIG. 1 , the present invention provides a method for obtaining a sensing matrix of a random demodulation hardware system of a pulse sequence, comprising the following steps:

A method for obtaining a random demodulation hardware system perception matrix of a pulse sequence, comprising the following steps:

Step 1: Determine the input signal of the random demodulation hardware system of the pulse sequence, and set the initial time shift parameter value;

The step 1 is specifically: determine the input signal of the pulse sequence random demodulation hardware system, and express the input signal s _i (t) of the pulse sequence random demodulation hardware system by the following formula:

s _i (t)=g(t _i )

Among them, t is the time shift parameter value, g(t) is a single pulse signal, and i is the initialization count variable;

Set the initial time-shift parameter value, the time-shift parameter step value is Δt, the amplitude value is 1, and the number of time-shift calculations is N.

Step 2: Set the initial value of the pseudo-random sequence signal and keep it unchanged;

Step 3: uniformly sample the output signal of the pulse sequence random demodulation hardware system, the sampling rate and sampling time are the same as those of the pulse sequence random demodulation hardware system, and obtain the sampling value;

Step 4: Perform FFT transformation on the obtained sample value to obtain the frequency domain value of the sample value;

The step 4 is specifically: performing FFT transformation on the obtained sampled value to obtain the frequency domain value of the sampled value, Y _i [l], first expressing the frequency domain value S[m] of the original signal by the following formula (m=-M ,1-M,…,M):

By quantizing the analog time amount in the frequency domain value S[m] of the original signal into N uniform grids, the quantized frequency domain value S[m] of the original signal is expressed by the following formula:

Among them, G[m] is the frequency domain form of the pulse signal g(t), T is the observation time length, and δ is the size of the quantization grid.

Step 5: remove the influence of the actual filter from the frequency domain value of the sampled value, and obtain the frequency domain of the sampled value from which the influence of the actual filter is removed;

The step 5 is specifically:

Step 5.1: Mix and filter the original signal, and express the frequency domain form Y _i [l] (l=-L,1-L,...,L) of the sampled value after mixing and filtering by the following formula:

Among them, P is the frequency domain form of the mixing function, L is the length of obtaining the sampling value Y _i [l], and H [l] is the frequency response characteristic of the actual filter;

Step 5.2: Remove the influence of the actual filter from the frequency domain value of the sampled value to obtain the frequency domain of the sampled value with the influence of the actual filter removed, and express the frequency domain of the sampled value with the influence of the actual filter removed by the following formula Y _i [l ]′:

Among them, H[l] represents the frequency response characteristic at the frequency domain sampling value Y _i [l] corresponding to the actual filter.

Step 6: Add the frequency domain of the sampled values affected by the actual filter to the i-th column of the perception matrix to obtain the value of the i-th column of the perception matrix of the actual system;

The step 6 is specifically as follows: adding the frequency domain Y _i [l]' of the sampling value affected by the actual filter to the i-th column of the perception matrix, to obtain the value of the i-th column of the perception matrix of the actual system, and by the following steps: The formula represents the value Φ _i of the i-th column of the perception matrix of the actual system:

Step 7: Change the counting variable and time-shift parameter, and repeat steps 1 to 6 to get the perception matrix.

Step 7 is as follows: changing the count variable to i plus 1, the time shift parameter to t _i +Δt, repeating steps 1 to 6 to obtain a perception matrix, which is represented by the following formula Φ:

The invention solves the problem that the parameters used in the existing method for acquiring the perception matrix in the random demodulation hardware system of the pulse sequence are ideal, resulting in deviation from the actual system. The method of the present invention only needs to ensure that the pseudo-random sequence used when mixing with the measured signal is the same as the pseudo-random sequence used when constructing the perception matrix, and does not need to know the value of the specific pseudo-random sequence, that is, it only needs to ensure that each time The resulting pseudorandom sequences are all the same. Such requirements are easy to meet, and the perception matrix is directly obtained from the actual system, which reduces the deviation in theoretical calculation and is more in line with the characteristics of the actual system. Therefore, the calculation content and influencing factors are greatly reduced.

Specific embodiment two:

In order to verify the effectiveness of this method, the following experiments are carried out to verify.

The measured signal is set as a pulse sequence composed of four Gaussian pulses, and a method for obtaining the sensing matrix of the random demodulation hardware system of the pulse sequence is characterized in that it includes the following steps:

Step 1: Set the input signal of the system as s _i (t)=g(t _i ), the initial time shift parameter value is t=t ₁ (the initial time shift parameter value t ₁ needs to ensure a single pulse signal g(t ) is completely within the valid sampling time), the time-shift parameter step is Δt, the amplitude is 1, the number of time-shift calculations is N, the initialization count variable is i, and the perception matrix is Φ;

Step 2: Set the initial value of the pseudo-random sequence signal and keep it unchanged;

Step 3: uniformly sample the system output signal, keep the sampling rate and sampling time consistent with the sampling rate and sampling time in the actual sampling process, and obtain the sampling value y _i [l];

Step 4: Perform FFT transformation on the obtained sample values to obtain the frequency domain value Y _i [l] of the sample values, l=-L,-L+1,...,L;

The analog time in the frequency domain value S[m] of the original signal is quantized into N uniform grids by t=nδ, then t _i =n _i δ expresses the quantized frequency domain value of the original signal by the following formula S[m]:

为量化网格的大小。Among them, G[m] is the frequency domain form of the pulse signal g(t), T is the observation time length,

is the size of the quantization grid.

Step 5: Remove the influence of the actual filter h(t) from the obtained sampling, and obtain the frequency domain form Y _i [l]' of the sampling value with the influence of the actual filter removed, l=-L,-L+1, ...,L, as follows:

Among them, H[l] represents the frequency response characteristic at the frequency domain sampling value Y _i [l] corresponding to the actual filter.

Step 6: Add the frequency domain form Y _i [l]' of the sampled values that remove the influence of the actual filter, l=-L,-L+1,...,L into the i-th column of the perception matrix, as follows shown:

Step 7: The counting variable i is incremented by 1, the time shift parameter t _i+1 =t _i +Δt, and the operations from steps 1 to 6 are repeated to obtain the perception matrix Φ.

Figure 2 and Figure 3 are the perception matrix obtained by theoretical calculation and the perception matrix obtained by this method respectively, Figure 4 is the error between the perception matrix obtained by theoretical calculation and the perception matrix obtained by this method, the error is 10 Within ^-2 , it can be considered that the perceptual matrix obtained by this method is correct. Fig. 5 and Fig. 6 are the reconstruction effects of the perceptual matrix obtained by theoretical calculation and the perceptual matrix obtained by this method respectively. The results show that the original signal can be reconstructed by using the perceptual matrix obtained by this method. Achieve perfect reconstruction of the signal.

The above is only a preferred embodiment of a method for obtaining the sensing matrix of a hardware system of random demodulation of pulse sequence. The technical solutions under this idea all belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims (6)

1. A method for obtaining a sensing matrix of a pulse sequence random demodulation hardware system is characterized by comprising the following steps: the method comprises the following steps:

step 1: determining an input signal of a pulse sequence random demodulation hardware system, and setting an initial time shift parameter value;

step 2: setting an initial value of a pseudo-random sequence signal and keeping the initial value unchanged;

and step 3: uniformly sampling output signals of the pulse sequence random demodulation hardware system, wherein the sampling rate and the sampling time are the same as those of the pulse sequence random demodulation hardware system, and obtaining sampling values;

and 4, step 4: carrying out FFT (fast Fourier transform) on the obtained sampling value to obtain a frequency domain value of the sampling value;

and 5: removing the influence of the actual filter from the frequency domain value of the sampling value to obtain a frequency domain of the sampling value without the influence of the actual filter;

step 6: adding the frequency domain of the sampling value without the influence of the actual filter into the ith row of the sensing matrix to obtain the value of the ith row of the sensing matrix of the actual system;

and 7: changing the counting variable and the time shifting parameter, and repeating the steps 1 to 6 to obtain the perception matrix.

2. The method of claim 1, wherein the method comprises the following steps: the step 1 specifically comprises the following steps: determining an input signal of a pulse sequence random demodulation hardware system, and expressing the input signal s of the pulse sequence random demodulation hardware system by the following formula_i(t)：

s_i(t)＝g(t-t_i)

Wherein t is a time shift parameter value, g (t) is a single pulse signal, and i is an initialization counting variable;

setting an initial time shift parameter value, wherein the time shift parameter step value is delta t, the amplitude is 1, and the time shift frequency is calculated to be N.

3. The method of claim 1, wherein the method comprises the following steps: the step 4 specifically comprises the following steps: FFT conversion is carried out on the obtained sampling value to obtain the frequency domain value Y of the sampling value_i[l]First, the frequency domain value S [ m ] of the original signal is expressed by the following formula](m＝-M,1-M,…,M)：

By quantizing the amount of analog time in the frequency-domain values S [ m ] of the original signal to N uniform grids, the quantized frequency-domain values S [ m ] of the original signal are represented by:

wherein G [ m ] is the frequency domain form of the pulse signal G (T), T is the observation time length, and is the size of the quantization grid.

4. The method of claim 1, wherein the method comprises the following steps: the step 5 specifically comprises the following steps:

step 5.1: mixing and filtering the original signal, and expressing the frequency domain form Y of the sampling value after mixing and filtering by the following formula_i[l](l＝-L,1-L,…,L)：

Wherein, P is the frequency domain form of the mixing function, L is the acquisition sampling value Y_i[l]Length of (H1)]Representing the frequency response of the actual filter;

step 5.2: removing the influence of the actual filter from the frequency domain value of the sampling value to obtain the frequency domain of the sampling value without the influence of the actual filter, and expressing the frequency domain Y of the sampling value without the influence of the actual filter by the following formula_i[l]′:

Wherein, H [ l ]]Representing the frequency domain sample values Y corresponding to the actual filter_i[l]Frequency response characteristic of (c).

5. The method of claim 1, wherein the method comprises the following steps: the step 6 specifically comprises the following steps: frequency domain Y of sampling values from which the effect of the actual filter is to be removed_i[l]' adding the value phi to the ith column of the sensing matrix to obtain the value of the ith column of the sensing matrix of the actual system, and expressing the value phi of the ith column of the sensing matrix of the actual system by the following formula_i：

6. According to claim 1The method for acquiring the pulse sequence random demodulation hardware system sensing matrix is characterized by comprising the following steps: the step 7 specifically comprises the following steps: changing the count variable to i plus 1 and the time shift parameter to t_i+ Δ t, repeating steps 1 to 6 to obtain a sensing matrix, and expressing the sensing matrix Φ by the following formula:

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