CN111525930A - Mixing matrix generation method of modulation broadband converter based on random impact sequence - Google Patents
Mixing matrix generation method of modulation broadband converter based on random impact sequence Download PDFInfo
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Abstract
The invention provides a mixing matrix generation method of a modulation broadband converter based on a random impact sequence. The method comprises the steps of 1, determining the range length d which can be selected by the non-0 position of a sequence which can be generated by each channel for a modulation broadband converter system with the number of channels being M and the length of a mixing sequence being M, and 2, distributing the range; and 3, determining the position of the non-0 element of the sequence. The invention is generated by a basic sequence delay, so that the amplitude error of each channel can be ensured to be equal for the amplitude error of the sequence caused by non-ideal hardware characteristics and the like, and the amplitude error of the sequence can be only converted into the linear error of an observation matrix without influencing the reconstruction probability of a support set.
Description
Technical Field
The invention belongs to the technical field of signal undersampling and wireless communication, and particularly relates to a mixing matrix generation method of a modulation broadband converter based on a random impulse sequence.
Background
In recent years, a compressed sensing theory is continuously developed, and the theory proves that on the premise that signals have sparsity, synchronous compression and sampling of the signals can be achieved, and then the original signals are restored through a proper reconstruction algorithm. The under-sampling method based on the compressed sensing theory can greatly reduce the sampling rate and the required storage and transmission data, breaks through the limit of the Nyquist sampling theorem, and can be widely applied to the fields of image processing, signal acquisition and the like.
A Modulated Wideband Converter (MWC) is a novel under-sampling system for multi-band signals based on the compressive sensing theory. A typical modulated wideband converter system is shown in figure 1. The modulation broadband converter system is composed of a plurality of groups of same channels, and the main elements of each channel comprise the following parts: multiplier, low pass filter and uniform sampling module, the sampled data of multiunit passageway act on signal reconstruction module jointly, and the processing procedure of signal does in proper order: mixing, low-pass filtering, uniform sampling and signal reconstruction.
The principle of modulating a wideband converter is as follows: the multi-band signal enters a modulation broadband converter system and is received by m channels in parallel, wherein m is a positive integer; each channel is modulated by a periodic sequence with the same period but different values, the purpose of the modulation is to shift the frequency spectrum, and the modulated signal is low-pass filtered to filter out the high-frequency part and leave the low-frequency part. Due to the low cut-off frequency of the low-pass filter, the bandwidth of the filtered signal is narrowed, so that the signal can be sampled at a low rate to obtain a series of global observation data of the signal. Then, low-speed sampling is carried out, and the sampling rate only needs to be larger than the width of the maximum low-pass filter frequency band, so that the sampling rate can be lower than the Nyquist frequency of the signal. And finally, recovering the original signal and the frequency spectrum thereof from the acquired data by utilizing the system sensing matrix obtained by calculation and a related signal reconstruction algorithm and through the mathematical relationship between the sensing matrix and the sampling information.
Because of the gaussian random matrix, it has been shown to satisfy the irrelevancy required in compressed sensing as most orthogonal basis matrices. Therefore, in a modulated wideband converter system, the matrix formed by the periodic mixing sequences of each channel is a gaussian random matrix. The individual elements in each channel sequence take randomly values +1 or-1 with equal probability. However, this option presents significant challenges for both hardware implementation and storage. Firstly, the random concept is contrary to the design, and only a deterministic sequence can be generated for storage and work when the hardware is implemented; secondly, for the mixed sequence of the MWC, the length is usually very long, if each element of the sequence needs to generate a level and there is no correlation between the sequences, the error is large, and the design is difficult to implement and store; and the sequence can cause various non-ideal errors when being generated, wherein the amplitude error is very difficult to control, and for a random +/-1 sequence, the amplitude error of the sequence can be converted into a non-linear error of an observation matrix due to numerous elements in the sequence, and the reconstruction accuracy of the sampling data is seriously influenced. A sequence which is simple in structure and can minimize the influence of the sequence amplitude error is urgently needed to be proposed.
Disclosure of Invention
The invention aims to solve the problems that a mixing sequence in the existing modulation broadband converter system is complex in structure and uncertain, and amplitude errors can be converted into a sensing matrix, and provides a mixing matrix generation method of a modulation broadband converter based on a random impulse sequence. The method designs a mixing matrix similar to a diagonal matrix, each channel of a mixing sequence generated by the matrix has only one element value of 1, and the rest positions are 0. The sequence is generated by delaying a base sequence, the delay time being determined by a function.
The invention is realized by the following technical scheme, and provides a mixing matrix generation method of a modulation broadband converter based on a random impact sequence, which comprises the following steps:
step one, for a modulation broadband converter system with M channels and M mixing sequence length, determining a range length d which can be selected by a non-0 position of a sequence which can be generated by each channel, and selecting a maximum integer which is not more than M/M as a maximum range which can be selected by the non-0 position of each sequence in order to ensure that the range of d is long enough and each channel has non-0 elements;
step two, distribution range: for a modulated broadband converter with m channels, a sequence of … m channels from the (i-1) × d +1 st position to the (i × d) th position of the modulated broadband converter may randomly select one position to take a value of 1 and the other positions to take a value of 0;
step three, determining the position of the non-0 element of the sequence: in order to make the position of the non-0 element of the sequence independent of the ordinal number of the channel and to be defined by the elementary function, the channel ordinal number i in the ith, i-1, … m channel sequence of the modulation broadband converter is first operated exponentially to obtain the distance eiAnd a rounding operation is performed followed by a remainder on d for the result obtained, i.e. the sequence of i, i-1, … m channels of the modulated wideband converter is at the th
The value of each position is 1, the value of the other positions is 0, wherein,
representing the largest integer no greater than a, mod (a, b) represents the remainder of dividing a by b.
Further, only one positive level impulse is generated in each channel.
Further, the amplitude error of each channel is equal.
The invention has the beneficial effects that:
1. the invention only needs to generate a positive level impact in each channel, compared with the traditional method that random positive and negative pulses with the same length as the sequence need to be generated in the sequence, the invention greatly reduces the pressure of hardware realization and storage, and improves the frequency mixing speed and the algorithm speed.
2. The invention expresses the correlation coefficient of the orthogonal basic matrix in the modulation broadband converter as 1, and can more easily obtain good reconstruction effect.
3. The invention is generated by a basic sequence delay, so that the amplitude error of each channel can be ensured to be equal for the amplitude error of the sequence caused by non-ideal hardware characteristics and the like, and the amplitude error of the sequence can be only converted into the linear error of an observation matrix without influencing the reconstruction probability of a support set.
Drawings
FIG. 1 is a schematic diagram of a typical modulated wideband converter system of the background art;
FIG. 2 is a graph showing the results of the present invention with a channel number of 50 and a sequence length of 195;
FIG. 3 is a schematic diagram showing the comparison of the reconstruction probabilities of two sequence support sets when SNR is 10 dB;
FIG. 4 is a schematic diagram showing the comparison of reconstruction probabilities of two sequence support sets with fixed channel number and varying signal-to-noise ratio;
FIG. 5 is a schematic diagram showing the comparison of the reconstruction probability of the support set when amplitude errors are added to different sequences.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
With reference to fig. 2, the present invention provides a mixing matrix generation method for a modulated wideband converter based on random impulse sequences, where the method includes the following steps:
step one, for a modulation broadband converter system with M channels and M mixing sequence length, determining a range length d which can be selected by a non-0 position of a sequence which can be generated by each channel, and selecting a maximum integer which is not more than M/M as a maximum range which can be selected by the non-0 position of each sequence in order to ensure that the range of d is long enough and each channel has non-0 elements;
step two, distribution range: for a modulated broadband converter with m channels, a sequence of … m channels from the (i-1) × d +1 st position to the (i × d) th position of the modulated broadband converter may randomly select one position to take a value of 1 and the other positions to take a value of 0;
step three, determining the position of the non-0 element of the sequence: to correlate non-0 element positions of a sequence with channel ordinalsIndependently, it can be defined as a simple elementary function, and the distance e is obtained by first performing an exponential operation on the channel number i in the sequence of i, i being 1, … m channels of the modulated wideband converteriAnd a rounding operation is performed followed by a remainder on d for the result obtained, i.e. the sequence of i, i-1, … m channels of the modulated wideband converter is at the th
The value of each position is 1, the value of the other positions is 0, wherein,
representing the largest integer no greater than a, mod (a, b) represents the remainder of dividing a by b.
The invention only needs to generate a positive level impact in each channel, compared with the traditional method that random positive and negative pulses with the same length as the sequence need to be generated in the sequence, the invention greatly reduces the pressure of hardware realization and storage, and improves the frequency mixing speed and the algorithm speed.
The invention is generated by a basic sequence delay, so that the amplitude error of each channel can be ensured to be equal for the amplitude error of the sequence caused by non-ideal hardware characteristics and the like, and the amplitude error of the sequence can be only converted into the linear error of an observation matrix without influencing the reconstruction probability of a support set.
The simulation experiment is carried out according to the following steps:
firstly, assume the sampling signal function is:
wherein K represents the number of carrier frequencies (including negative frequencies); tau isiRepresents a delay constant;
the simulation parameters are set as follows: the Nyquist frequency of the artificial input signal being fNYQThe maximum bandwidth B is 50MHz at 10 GHz. The sampling frequency satisfies fs＝fp. And the repetition frequency f of the random wave functionpTaking the value as 51.282MHz, and calculating to obtain the randomThe minimum value M of the number of changes in the amplitude of the signal within a single period of the wave function is 195. The number N of non-zero bands will be set to different values for different purposes of the simulation experiment. Amplitude E of the frequency bandiCarrier frequency f set according to experimental conditions without affecting experimental resultsiRandomly selecting time delay parameter delta t of different frequency bandsiTaking a random value. The discrete signal length of the original signal under the condition of Nyquist frequency sampling is 19695. The number of sampling points per channel is d 101. If each observation is independently carried out, the number d of sampling points of each channel satisfies d ≧ 2KjointI.e. an accurate recovery of the signal is guaranteed, where KjointJoint sparsity after modeling for simulating multi-band signals. Here, in order to ensure accurate recovery of the signal, the number of sampling points of each channel is set to be far larger than the joint sparsity. The reconstruction algorithm used in the simulation experiment is a classical SOMP algorithm.
And secondly, verifying the reliability of the system formed by the method. The results are shown in two different cases, both as an average of 500 experiments, where first the signals of different values are evaluated when the SNR is 10dB, in particular when N is 4,6,8, and the success rate of the two systems from m 20 to m 80 is recorded, each time with an increase of 2 channels. Then for the signal with N-6, when m-50 and m-24 (m-2K), the experimental results from SNR-5 dB to SNR-30 dB were recorded, with 1dB increase in SNR each time. The results of the experiment are shown in fig. 3 and 4. The signal-to-noise ratio of the original signal is defined as:
wherein the SNRORIRepresenting the signal-to-noise ratio, x, of the original signalORIRepresenting the original signal, nORIRepresenting the original noise.
And thirdly, amplitude errors are added to the sequence, the maximum amplitude of the errors is from 0 to 1, the amplitude is increased by 0.05 each time, the symbol errors are randomly generated between 0 and the maximum errors, N is 6, m is 50, and the experimental result is shown in fig. 5.
As can be seen from fig. 3 to fig. 5, the new sequence has better reconstruction performance than the random ± 1 sequence, the reconstruction performance of the support set of the mixing sequence generated by the new matrix is not affected by the amplitude error, while the reconstruction efficiency of the support set of the mixing sequence generated by the gaussian random matrix is greatly affected by the amplitude error of the sequence.
The mixing matrix generation method of the modulation broadband converter based on the random impulse sequence provided by the invention is described in detail above, a specific example is applied in the text to explain the principle and the implementation of the invention, and the description of the above embodiment is only used to help understanding the method of the invention and the core idea thereof; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
Claims (3)
1. A mixing matrix generation method of a modulation broadband converter based on random impact sequences is characterized in that: the method comprises the following steps:
step one, for a modulation broadband converter system with M channels and M mixing sequence length, determining a range length d which can be selected by a non-0 position of a sequence which can be generated by each channel, and selecting a maximum integer which is not more than M/M as a maximum range which can be selected by the non-0 position of each sequence in order to ensure that the range of d is long enough and each channel has non-0 elements;
step two, distribution range: for a modulated broadband converter with m channels, a sequence of … m channels from the (i-1) × d +1 st position to the (i × d) th position of the modulated broadband converter may randomly select one position to take a value of 1 and the other positions to take a value of 0;
step three, determining the position of the non-0 element of the sequence: in order to make the position of the non-0 element of the sequence independent of the ordinal number of the channel and to be defined by the elementary function, the channel ordinal number i in the ith, i-1, … m channel sequence of the modulation broadband converter is first operated exponentially to obtain the distance eiAnd a rounding operation is performed, and then the result obtained is subjected to a remainder on d, that is to sayThe ith, i-1, … m channel sequence of the modulation broadband converter is at the ith
The value of each position is 1, the value of the other positions is 0, wherein,
representing the largest integer no greater than a, mod (a, b) represents the remainder of dividing a by b.
2. The method of claim 1, wherein: only one positive level impulse is generated in each channel.
3. The method of claim 2, wherein: the amplitude error of each channel is equal.
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| CN114928414A (en) * | 2022-04-07 | 2022-08-19 | 北京遥测技术研究所 | Method for measuring and calibrating sensing matrix coefficient of modulation broadband converter |
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