CN108989255B - Multichannel compression sampling method based on random demodulation principle - Google Patents
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Abstract
The invention provides a multichannel compression sampling method based on a random demodulation principle, which belongs to the field of signal processing and aims to reduce the symbol conversion rate of a pseudorandom sequence used as a modulation signal to be lower than the Nyquist rate of an input signal, and the method comprises the following implementation steps: c sampling channels are established; c sampling channels asynchronously generate low-rate modulation signals; c sampling channels randomly modulate an input signal x (t); c sampling channels carry out low-pass filtering on the modulated signals; c sampling channels perform synchronous low-speed uniform sampling on the C filtered signals; the compressed signal y (n) is reconstructed. The invention reduces the symbol conversion rate of the pseudo-random sequence in a single sampling channel by a method of asynchronously generating a plurality of pseudo-random sequences by a plurality of sampling channels under the condition of ensuring that the reconstruction effect after compression sampling is not reduced, so as to enhance the physical realizability of a compression sampling structure suitable for high-frequency signals.
Description
Technical Field
The invention belongs to the technical field of signal processing, relates to a multichannel compression sampling method, and particularly relates to a multichannel compression sampling method based on a random demodulation principle, which can be applied to the fields of multimedia information systems, medical imaging, remote sensing imaging, communication systems, sensor networks and the like.
Background
Sampling refers to the process of converting a continuous quantity in the time or space domain into a discrete quantity. A signal sampling method guided by the nyquist sampling theorem requires that the sampling rate of the signal is not less than twice the highest frequency of the signal, which is called the nyquist rate. Because the higher the sampling rate is, the greater the engineering difficulty of the analog-to-digital converter is, but with the development of electronic information technology, the data volume that people need to process is also growing at a high speed, the existing analog-to-digital converter is difficult to meet the requirement of the nyquist sampling theorem on the sampling rate, and the sampling becomes a bottleneck of the development of a digital signal processing system. Compressive sampling techniques are a revolution in signal processing and are widely used in many areas related to signal processing.
The compressive sampling method is a method for sampling signals at a sampling rate far lower than the nyquist rate, and currently, the compression sampling techniques studied at home and abroad mainly have 4 types: time interleaving, random filtering, random demodulation, and modulation of the wideband converter. However, except for the random demodulation and modulation broadband converter, the other two types of compression sampling technologies have the defect that the hardware implementation is difficult to overcome, wherein the sampling rate used by the time-interleaved sampling scheme during sampling is time-varying, the randomness of the sampling rate has certain difficulty in engineering practice, and is particularly prominent during high-frequency signal acquisition; in the random filtering sampling scheme, when sampling, direct down-sampling after random convolution can cause an aliasing problem, low sampling is realized at the rear end in a digital down-sampling mode, and acquisition of a perception matrix during reconstruction is very difficult.
Random demodulation is a compressive sampling method proposed by Jason.Laska et al of Rice university based on compressive sensing theory, the sampling method is a single-channel compressive sampling method, which modulates a signal by using a high-speed aperiodic pseudorandom sequence, disperses the frequency spectrum of the signal in a full-spectrum space, the symbol transformation rate of the aperiodic pseudorandom sequence is not lower than the Nyquist rate of the input signal, then performs low-pass filtering on the signal, acquires the spectral characteristics of the signal in a low-frequency band, and performs low-speed sampling at the sub-Nyquist rate.
The modulation broadband converter is a compression sampling structure which is provided by Mishali in combination with a Fourier analysis idea and a compression sensing theory aiming at a sparse broadband signal with a continuous frequency spectrum, the method is a multi-channel compression sampling method, each channel utilizes a periodic pseudo-random sequence to carry out frequency mixing on an input signal, the frequency spectrum of the input signal can be shifted to a low frequency domain, then sampling it in the low frequency domain, the sampled signal containing the full spectral information of the input signal, therefore, the spectral information of the input signal can be accurately reconstructed by using the compressively sampled signal, but this method has a disadvantage that, when each channel mixes an input signal with a periodic pseudo-random sequence, the symbol transition rate of the periodic pseudo-random sequence is required to be not lower than the nyquist rate of the signal, for high frequency signals, higher rate pseudo-random sequence generators are still not easy to engineer.
Disclosure of Invention
The present invention aims to provide a multi-channel compressive sampling method based on the random demodulation principle, which aims to ensure the same reconstruction effect after compressive sampling, and simultaneously realize that the symbol transformation rate of a random sequence in a single sampling channel is far less than the nyquist rate of an input signal, so as to enhance the physical realizability of the compressive sampling structure suitable for high-frequency signals.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) c sampling channels are established:
c parallel sampling channels are established, C is more than or equal to 2 and less than or equal to N/2, N represents the input signal x (t) at the Nyquist rate FsThe number of the lower corresponding sampling points, the ith sampling channel comprises a pseudo-random sequence generator, a modulator, a low-pass filter and an analog-to-digital converter, wherein t represents the time used by the sampling structure, i is more than or equal to 1 and less than or equal to C, and the pseudo-random sequence generator and the analog-to-digital converter are controlled by the same clock;
(2) the C sampling channels asynchronously generate low rate modulated signals:
the starting time of the pseudo-random sequence generator in each sampling channel i is delayed by 1/F relative to the starting time of the pseudo-random sequence generator in the (i-1) th sampling channelsAfter the time length is long, the random amplitude is +/-1, and the time length is C/FsPseudo-random sequence composed of N/C chips
And the random sequence is applied
As a modulation signal pi(t) obtaining C low rate modulated signals, where Δ t represents a delay time duration, and Δ t is 1/Fs；
(3) The C sampling channels randomly modulate the input signal x (t):
multiplying the input signal x (t) by the low-rate modulation signal of each channel in the time domain by each channel in the C sampling channels to obtain C modulated signals, wherein the modulated signal in the channel i is xi1(t)，xi1(t)＝x(t)pi(t)；
(4) The C sampling channels low-pass filter the modulated signal:
each channel i in the C sampling channels uses the low-pass filter of the channel to carry out x on the signal modulated in the channel ii1(t) low-pass filtering to obtain C filtered signals, wherein the filtered signal in the channel i is xi2(t)；
(5) C sampling channels perform synchronous low-speed uniform sampling on the C filtered signals:
the analog-to-digital converters in the C sampling channels adopt a synchronous low-speed uniform sampling mode to perform low-speed uniform sampling on the filtered signals in each sampling channel to obtain C sampling signals, and the C sampling signals are spliced according to the sequence of the channel serial numbers from small to large or from large to small to obtain compressed signals y (n);
(6) reconstructing the compressed signal y (n):
(6a) obtaining a measurement matrix AM,N：
The sparse basis function ψ (t) of the input signal x (t) is compared with the modulation signal p for each sampling channel ii(t) and the impulse response function h of the low-pass filteri(t) performing convolution and sampling to obtain C measurement matrixes, and splicing the C measurement matrixes according to the splicing sequence of the sampling signals in the compressed signals y (n) to obtain a measurement matrix AM,N；
(6b) Using measurement matrix AM,NThe compressed signal y (n) is reconstructed to obtain a reconstructed signal x (n).
Compared with the prior art, the invention has the following advantages:
the invention applies the random demodulation principle to a plurality of sampling channels, breaks through the limit of the random demodulation principle to the symbol conversion rate of the modulation signals, and reduces the symbol conversion rate of the modulation signals used by each sampling channel along with the increase of the number of the sampling channels, so that the symbol conversion rate is far less than the Nyquist rate of the input signals; then when generating pseudo-random sequence as modulation signal, delaying the start time of pseudo-random sequence generated by each channel in turn to make the start and stop times of the chips of pseudo-random sequence generated by each channel mutually staggered, and using analog-to-digital converter to make synchronous sampling to implement staggered modulation of pseudo-random sequence to input signal so as to ensure that the reconstruction effect after compression sampling is not reduced.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a simulation comparison graph of reconstruction effects after compressive sampling of signals using the present invention and a prior modulated broadband converter architecture;
detailed description of the invention
The invention is described in detail below with reference to the following figures and specific examples:
referring to fig. 1, a multichannel compressive sampling method based on a random demodulation principle includes the following steps:
step 1) establishing C sampling channels:
c parallel sampling channels are established, C is more than or equal to 2 and less than or equal to N/2, N represents the input signal x (t) at the Nyquist rate FsThe number of the sampling points is corresponding to the number of the sampling points, the ith sampling channel comprises a pseudo-random sequence generator, a modulator, a low-pass filter and an analog-to-digital converter, the pseudo-random sequence generator in each sampling channel is realized by a linear feedback shift register, wherein t represents the time used by the sampling structure, i is more than or equal to 1 and less than or equal to C, and the C pseudo-random sequence generators and the C analog-to-digital converters are controlled by the same clock;
in this example, since the number of sampling channels is too small, the effect of reducing the symbol conversion rate of the modulation signal is not obvious, when the number of sampling channels is too large, more physical devices are required, the volume of the whole sampling structure is larger, and the physical implementation difficulty of the sampling structure is increased, in comprehensive consideration, the number of channels C is 10, even if the physical implementation is facilitated, the symbol conversion rate of the modulation signal can be reduced by one order of magnitude, in addition, the parallel structure enables each channel to simultaneously perform compression processing, the real-time performance of signal processing can be ensured, and the input signal x (t) is a frequency hopping signal with a frequency set of {0.8,1.4,2.1,2.4,2.7,3.0,3.3} MHz, and the nyquist rate F (t) } of x (t)s＝107Hz, and the number of sampling points is 1000.
The method for constructing the pseudorandom sequence comprises two major methods, one is the method for constructing the pseudorandom sequence based on the number theory, and the other is the method for constructing the pseudorandom sequence based on the linear feedback shift register.
Step 2)10 sampling channels asynchronously generate low-rate modulation signals:
after the starting time of the pseudo-random sequence generator in each sampling channel i is delayed by 0.1ms relative to the starting time of the pseudo-random sequence generator in the i-1 th sampling channel, a pseudo-random sequence consisting of 100 chips with the amplitude of +/-1 and the time length of 1ms is generated
And the random sequence is applied
As a modulation signal pi(t) obtaining 10 low-rate modulation signals, wherein, Δ t represents delay time length, and Δ t is 1/FsPseudo random sequence
Is a piecewise constant function constructed by using a shift register based on linear feedback
As a function of the time delay of (a),
the expression of (a) is:
wherein t represents the time used by the sampling structure, and k represents the piecewise constant function
Section number of (1), 2, …,100, alpha)kRepresenting piecewise constant functions
Value in the k-th paragraph, αkE { +1, -1} and αkThe probabilities of values +1 and-1 are equal.
Because the starting time of the pseudo-random sequence generator in each sampling channel is delayed by 0.1ms in sequence and the time length of the pseudo-random sequence chip is 1ms, the starting time and the ending time of the modulation signal code element generated by each channel are mutually staggered, although the symbol conversion rate of the modulation signal code element in a single sampling channel is 106Hz, much less than the Nyquist rate 10 of the input signal7Hz, but overall, the symbol conversion rate of the 10 pseudorandom sequences is the nyquist rate of the input signal x (t).
Step 3), randomly modulating an input signal x (t) by 10 sampling channels:
taking an input signal x (t) as an input signal of 10 sampling channels respectively, multiplying the input signal x (t) by a low-rate modulation signal of each channel in the 10 sampling channels in a time domain to obtain 10 modulated signals, wherein the modulated signal in the channel i is xi1(t)，xi1(t)＝x(t)pi(t)；
Due to the modulation signal p in the sampling channel ii(t) is a pseudo-random sequence, the frequency spectrum of which is a full-band signal, the modulated signal multiplies the input signal in the time domain, i.e. the input signal x (t) is convolved in the frequency domain, according to the principle of spectrum modulation, the frequency of the input signal is shifted and added in the full-band due to the full-band characteristic of the modulated signal, so that the modulated signal xi1(t) contains the spectral information of the input signal x (t) over the full frequency band.
Step 4), performing low-pass filtering on the modulated signals by 10 sampling channels:
each channel i in the 10 sampling channels uses the low-pass filter of the channel to perform x on the signal modulated in the channel ii1(t) low-pass filtering to obtain 10 filtered signals, wherein the filtered signal in the channel i is xi2(t), the expression of which is:
xi2(t)＝(x(t)pi(t))*hi(t)
wherein x (t) represents an input signal, pi(t) is the modulation signal in sampling channel i, hi(t) is the impulse response of the filter in the sampling channel i, which represents the convolution operation.
After the input signal x (t) has been modulated in each sampling channel i, xi1(t) all frequency bands contain frequency information of input signals, the signals are subjected to low-pass, band-pass or high-pass filtering to obtain frequency spectrum information of the input signals x (t), and in order to enable a following analog-to-digital converter to work at a low speed, the low-pass filter is adopted to carry out low-pass filtering on the signals to obtain the frequency spectrum information of the input signals x (t)i1(t) performing anti-aliasing filtering.
Step 5), 10 sampling channels perform synchronous low-speed uniform sampling on the 10 filtered signals:
the analog-to-digital converter in 10 sampling channels adopts a synchronous low-speed uniform sampling mode to perform low-speed uniform sampling on the filtered signals in each sampling channel to obtain 10 sampling signals, and the 10 sampling signals are spliced according to the sequence of the channel serial numbers from small to large or from large to small to obtain a compressed signal y (n), wherein the expression is as follows:
y(n)＝{y1(n),…,yi(n),…,yC(n)}
wherein { } denotes a set, yi(n) denotes the sampled signal in sampling channel i, yiThe expression of (n) is:
yi(n)＝(x(t)pi(t))*hi(t)|t＝nΔt'
wherein x (t) represents an input signal, pi(t) is the modulation signal in sampling channel i, hi(t) isImpulse response of filter in sampling channel i represents convolution operation, t represents time used by the sampling structure, and the branch patht＝nΔt'Denotes sampling at time t ═ n Δ t ', n denotes the sample number, n ═ 1,2, …,25, Δ t' denotes the sample interval, Δ t ═ 25ms, signal yi(n) has a length of 25.
Because the starting and stopping moments of the chips of the modulation signals used by each channel are mutually staggered, when the analog-to-digital converter carries out synchronous sampling, the staggered modulation of the pseudo-random sequence on the input signals can be realized, and the reconstruction effect after compression sampling can be ensured not to be reduced. Also, when synchronous uniform sampling is performed, the sampling interval Δ t' of the analog-to-digital converter in each channel is 25ms, and the sampling frequency is 4 × 104Hz, much lower than the Nyquist rate 10 of the input signal7Hz。
Step 6) reconstructing the compressed signal y (n):
step 6a) obtaining a measurement matrix AM,N：
The sparse basis function ψ (t) of the input signal x (t) is compared with the modulation signal p for each sampling channel ii(t) and the impulse response function h of the low-pass filteri(t) performing convolution and sampling to obtain 10 measurement matrixes, and splicing the 10 measurement matrixes according to the splicing sequence of the sampling signals in the compressed signals y (n) to obtain a measurement matrix AM,N；
Obtaining the measurement matrix A as described in step (6a)M,NThe expression is as follows:
AM,N＝{A1,…,Ai,…AC}
wherein { } denotes a set, AiAnd (3) representing a measurement matrix in the sampling channel i, wherein the calculation formula is as follows:
Ai＝(ψ(t)pi(t))*hi(t)|t＝nΔt'
where ψ (t) represents a sparse basis function of the input signal x (t), pi(t) is the modulation signal in sampling channel i, hi(t) is the impulse response of the filter in the sampling channel i, representing the convolution operation, t representing the time used by the sampling structure, the calculation of the Yt＝nΔt'This indicates that sampling is performed at time t ═ n Δ t ', where n indicates the sample number, n ═ 1,2, …,25, Δ t ' indicates the sampling interval, and Δ t ' indicates 25 ms.
Step 6b) Using the measurement matrix AM,NAnd reconstructing the compressed signal y (n) by adopting a compressed sensing reconstruction algorithm to obtain a reconstructed signal x (n).
The principle of reconstructing signals by using a compressed sensing theory is that an observation equation y is described as Ax in a compressed observation process of sparse signals, wherein A is an observation equation, and the observation equation is a set of underdetermined linear equations because the row number of A is less than the column number, but the original signals can be recovered at a high probability by using the sparsity of the signals as a priori condition.
The technical effects of the present invention will be described below with reference to simulation experiments.
1. Simulation conditions and contents:
the simulation parameters are set as follows: using a frequency hopping signal with a frequency set of {0.8,1.4,2.1,2.4,2.7,3.0,3.3} MHz and a hopping rate of 2000 hops/second as an input signal, using white Gaussian noise as noise, a signal-to-noise ratio of 25dB, and a sampling frequency of Fs＝107Hz, the length of the input signal is 35000, the compression ratio is 4, the length of the compressed and sampled signal is 8750, the number of sampling channels is 10, and the cut-off frequency of the low-pass filter is 106Hz, the sparse basis adopts a Fourier transform basis. Matlab is used for simulating and comparing the reconstruction effect of the signal which is compressed and sampled by adopting the invention and the existing modulation broadband converter structure, and the result is shown in figure 2;
2. and (3) simulation result analysis:
referring to fig. 2, the top graph shows a spectrogram of a reconstructed signal obtained by compression sampling an input signal by using the prior art, and the bottom graph shows a spectrogram of a reconstructed signal obtained by compression sampling an input signal by using the present invention, it can be seen from the graphs that both the position of a main lobe of a spectrum and the amplitude of the spectrum are consistent, and both have the same reconstruction effect, but compared with the prior art, the present invention reduces the symbol transformation rate of a pseudorandom sequence, which is a modulation signal, by 10 times. In summary, the method of the present invention can achieve the purpose of reducing the symbol transformation rate of the modulation signal while ensuring the same reconstruction effect after the compression sampling.
Claims (7)
1. A multichannel compression sampling method based on random demodulation principle is characterized by comprising the following steps:
(1) c sampling channels are established:
c parallel sampling channels are established, C is more than or equal to 2 and less than or equal to N/2, N represents the input signal x (t) at the Nyquist rate FsThe number of the lower corresponding sampling points, the ith sampling channel comprises a pseudo-random sequence generator, a modulator, a low-pass filter and an analog-to-digital converter, wherein t represents the time used in the sampling process, i is more than or equal to 1 and less than or equal to C, and the pseudo-random sequence generator and the analog-to-digital converter are controlled by the same clock;
(2) the C sampling channels asynchronously generate low rate modulated signals:
the starting time of the pseudo-random sequence generator in each sampling channel i is delayed by 1/F relative to the starting time of the pseudo-random sequence generator in the (i-1) th sampling channelsAfter the time length is long, the random amplitude is +/-1, and the time length is C/FsPseudo-random sequence composed of N/C chips
And using the random sequence as a modulation signal pi(t) obtaining C low rate modulated signals, where Δ t represents a delay time duration, and Δ t is 1/Fs；
(3) The C sampling channels randomly modulate the input signal x (t):
multiplying the input signal x (t) by the low-rate modulation signal of each channel in the time domain by each channel in the C sampling channels to obtain C modulated signals, wherein the modulated signal in the channel i is xi1(t)，xi1(t)＝x(t)pi(t)；
(4) The C sampling channels low-pass filter the modulated signal:
each channel i in the C sampling channels uses the low-pass filter of the channel to carry out x on the signal modulated in the channel ii1(t) performing a low-pass filtering,obtaining C filtered signals, wherein the filtered signal in the channel i is xi2(t)；
(5) C sampling channels perform synchronous low-speed uniform sampling on the C filtered signals:
the analog-to-digital converters in the C sampling channels adopt a synchronous low-speed uniform sampling mode to perform low-speed uniform sampling on the filtered signals in each sampling channel to obtain C sampling signals, and the C sampling signals are spliced according to the sequence of the channel serial numbers from small to large or from large to small to obtain compressed signals y (n);
(6) reconstructing the compressed signal y (n):
(6a) obtaining a measurement matrix AM,N：
The sparse basis function ψ (t) of the input signal x (t) is compared with the modulation signal p for each sampling channel ii(t) and the impulse response function h of the low-pass filteri(t) performing convolution and sampling to obtain C measurement matrixes, and splicing the C measurement matrixes according to the splicing sequence of the sampling signals in the compressed signals y (n) to obtain a measurement matrix AM,N；
(6b) Using measurement matrix AM,NThe compressed signal y (n) is reconstructed to obtain a reconstructed signal x (n).
2. The method of multi-channel compressive sampling based on random demodulation principle as claimed in claim 1, wherein said step (1) of establishing C sampling channels, wherein the pseudo random sequence generator in each sampling channel is implemented by a linear feedback shift register.
3. The multi-channel compressive sampling method based on the random demodulation principle as claimed in claim 1, wherein the pseudo-random sequence generated in the sampling channel i in step (2) is a time delay function using a piecewise constant function constructed based on a linear feedback shift register, and the expression of the time delay function is:
where t represents the time taken for this sampling process, FsDenotes the Nyquist rate of the input signal x (t), C denotes the number of sampling channels, k denotes the segment sequence of the piecewise constant function, k is 1,2, …, N/C, alphakRepresents the value of the piecewise constant function in the k section, alphakE { +1, -1} and αkThe probabilities of values +1 and-1 are equal.
4. Method for multichannel compressive sampling based on the principle of random demodulation as claimed in claim 1, characterized in that the filtered signal x in sampling channel i in step (4)i2(t), the expression of which is:
xi2(t)＝(x(t)pi(t))*hi(t)
wherein x (t) represents an input signal, pi(t) is the modulation signal in sampling channel i, hi(t) is the impulse response of the filter in the sampling channel i, which represents the convolution operation.
5. The method for multichannel compressive sampling based on random demodulation principle as claimed in claim 1, wherein the compressed signal y (n) in step (5) is expressed as:
y(n)＝{y1(n),…,yi(n),…,yC(n)}
wherein { } denotes a set, yi(n) denotes the sampled signal in sampling channel i, yiThe expression of (n) is:
yi(n)＝(x(t)pi(t))*hi(t)|t＝nΔt'
wherein x (t) represents an input signal, pi(t) is the modulation signal in sampling channel i, hi(t) is the impulse response of the filter in the sampling channel i, representing the convolution operation, t representing the time used for this sampling procedure, the calculation of the Yt＝nΔt'Denotes that sampling is performed at time t ═ n Δ t ', n denotes a sampling point number, n ═ 1,2, …, M, Δ t' denotes a sampling interval, Δ t ═ CM/FsM is the sampling signal yi(n) length.
6. Multichannel compressive sampling method based on the random demodulation principle as claimed in claim 1, characterized in that said acquisition of the measurement matrix A in step (6a)M,NThe expression is as follows:
AM,N＝{A1,…,Ai,…AC}
wherein { } denotes a set, AiAnd (3) representing a measurement matrix in the sampling channel i, wherein the calculation formula is as follows:
Ai＝(ψ(t)pi(t))*hi(t)|t＝nΔt'
where ψ (t) represents a sparse basis function of the input signal x (t), pi(t) is the modulation signal in sampling channel i, hi(t) is the impulse response of the filter in the sampling channel i, representing the convolution operation, t representing the time used for this sampling procedure, the calculation of the Yt=nΔt'Denotes sampling at time t ═ n Δ t ', n denotes the sample number, n ═ 1,2, …, M, Δ t' denotes the sampling interval, Δ t ═ CM/FsM is the sampling signal y in the sampling channel ii(n) length.
7. The method for multichannel compressive sampling based on random demodulation principle as claimed in claim 1, wherein the step (6b) reconstructs the compressed signal y (n) by using a compressed sensing reconstruction algorithm.
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