CN114696931B - Low-complexity non-sparse broadband spectrum sensing method - Google Patents
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Abstract
The invention relates to a low-complexity non-sparse broadband spectrum sensing method. Most existing sub-nyquist sampling wideband spectrum sensing (widebandspectrum sensing, WSS) methods default to sparse spectrum. However, research data suggests that in the near future, the broadband spectrum will not be sparse anymore. The WSS algorithm for sub-Nyquist sampling provided by the invention can be well adapted to scenes with non-sparse spectrums. The key of the algorithm improvement of the invention is that a folding time-frequency spectrum model is established, and the special structure is the same as the folding frequency spectrum model in the NoR algorithm. Therefore, the invention designs a comprehensive sampling technology which comprises multipath uniform sampling, digital fractional delay and time-frequency conversion. The ador algorithm obtains more excellent perceptual performance with low computational complexity in non-sparse scenarios compared to two representative algorithms in the sub-nyquist WSS method.
Description
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a low-complexity non-sparse broadband spectrum sensing method.
Background
Since compressed sensing (compressed sensing, CS) was first applied to wideband spectrum sensing (wideband spectrum sensing, WSS), WSS methods based on sub-nyquist sampling have received extensive attention from experts and have been overwhelming. Some rather classical CS-based sensing methods, such as those based on non-convex optimization and greedy tracking, although they solve the problem of high nyquist sampling rate of WSS well, they require signal reconstruction, which places a significant computational burden. In order to overcome the disadvantage of high computational complexity of CS-based methods, some later studies have proposed reconstructing the power spectrum or covariance matrix of the wideband signal based on samples obtained by a multi-sampling scheme. Such methods are referred to as compression covariance aware-based methods. Then, based on the idea of the compressed covariance aware method, we propose a series of methods based on a multi-path sampling scheme, including a method of partial reconstruction of the power spectrum, and a non-reconstruction method. Clearly, we have chosen the direction of research as a prospective since later expert comparison studies concluded that the compressed covariance-based approach is more competitive than the CS-based approach.
Recent studies on WSS methods have taken into more practical applicability into account, that is, the design of algorithms has been more emphasized in combination with practical application scenarios. For example, in some papers that study WSS methods, there are scenarios that consider severe wireless channel drop, scenarios of discontinuous broadband spectrum, and most interesting, scenarios of electronic countermeasure applications. However, there is a class of WSS application scenarios that are rarely involved, i.e. non-sparse broadband spectrum. In the next decade, mobile data traffic will increase by a factor of about 1000, and in future networks, it is expected that the capacity and spectral efficiency of wireless systems will increase substantially by a factor of at least 10 to 1000. The above predictions mean that in the near future the wideband spectrum will not be sparse anymore. In fact, even now, due to the increase in the number of electronic monitoring, radar and communication devices and the presence of a large number of broadband non-stationary signals such as gaussian pulses, step signals and chirp signals, the received signal at a certain sensing time is not sparse any more, so that most of the sub-nyquist WSS methods which need to satisfy the sparse priors cannot be applied.
Although research on WSS methods in non-sparse scenes is urgent, few experts are involved. The learner has considered "do it if the spectrum is not sparse? And then, a cooperative protection mechanism capable of effectively identifying spectrum sensing failure in a non-sparse scene is provided. Still other experts propose another method for detecting whether the signal reconstruction process is unsuccessful due to non-sparse spectrum in WSS methods based on modulated wideband converter sampling. The authors in one study claim that they have provided a first solution to the WSS problem in the non-sparse case, whereas the wideband spectrum to be detected in the simulation verification experiments of the scheme contains only 16 sub-channels. In addition, experts propose a sub-Nyquist WSS method without sparse prior on the white space of the real-time television. But have some disadvantages: first, a priori information about the number of subchannels and input spectrum utilization is required; secondly, the process is complex: the method comprises three main modules, namely signal replacement and filtering, spectrum estimation and multi-subchannel joint detection, wherein the first module is exaggeratedly divided into three additional steps; third, the real computational complexity is not reflected because the simulation experiment run-time calculation is incomplete.
Disclosure of Invention
In view of this, the present invention aims to provide a low-complexity non-sparse wideband spectrum sensing method, so as to be suitable for application scenarios of non-sparse wideband spectrum sensing.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows:
a low-complexity non-sparse broadband spectrum sensing method comprises the following steps:
step 1: establishing a folding time spectrum model with an ADFS structure through a comprehensive sampling technology;
step 2: and realizing spectrum sensing based on the folding time spectrum model.
Furthermore, the spectrum sensing method expands the sensing domain from the frequency domain to the time-frequency domain, avoids spectrum reconstruction, and is not limited by sparse conditions.
Further, the step 1 specifically includes the following steps:
step a: comprehensively sampling;
step b: detecting a superimposed sub-band;
step c: and (5) classifying time-frequency subchannels.
Further, the integrated sampling in the step a includes multi-path sampling, digital fractional delay and time-frequency conversion.
Further, in the step a,
firstly, a multi-path sampling mechanism is used for sampling signals; the sampling mechanism uses M groups of parallel analog-to-digital converters, and each group of ADC uniformly samples signals at the sub-Nyquist rate of 1/NT, wherein N is a sampling rate reduction multiple; when M<N satisfies both sub-Nyquist sampling; setting the time offset of the ith sampling end as c i T is 0.ltoreq.c 0 ＜c 1 ＜…＜c M-1 N-1 is not more than; then the sub-nyquist sampling signal sequence at the i-th sampling end is obtained as follows:
second, after multiple sampling, a Digital Fractional Delay (DFD) is introduced before time-frequency transformation, forGo-c i DFD of T yields y i [n]；
Finally, obtaining y through time-frequency conversion i [n]Time-frequency transformed representation (coefficient):
wherein ,representing the sub-Nyquist sampling signal y obtained at the ith sampling end i [n]Time-frequency transform representation (coefficient) s at time p and frequency point k p,k+Fn N=0, 1, …, N-1 represents the time-frequency transformed representation (coefficient) of the signal x (t) at the instant p and the frequency point k+fn;
from the formula (2) obtained in the first step, a folded spectrum with a special structure of "almost disjoint subchannels (ADFS)" can be obtained.
Further, the step b includes setting the test statistic of the overlapped sub-band detection to beAssuming that the signals in the active time-frequency sub-channels are independent of each other, zero-mean, and that the noise is of power spectral density sigma 2 From equation (2), then for each free superimposed sub-band there is a distribution: />I.e. < ->Because the frequency spectrum has an ADFS structure when being folded, the superimposed sub-frequency bands obtained by each sampling end have similar amplitude, each superimposed sub-frequency band can be obtained, and the test statistics of the superimposed sub-frequency bands have the following distribution:
wherein ,Η0,(p,k) Representing that no active time-frequency sub-channel exists in the (p, k) th overlapped sub-frequency band; conversely, H 1,(p,k) Representing that the (p, k) th superimposed sub-band is occupied; and gamma is the signal to noise ratio;
according to the formula (3), the false alarm rate of the superposition sub-band detection problem can be obtained to satisfy:
wherein θp,k Is the detection threshold and Γ (a, x) is the incomplete gamma equationFurther Γ (n) = (n-1) +.! The method comprises the steps of carrying out a first treatment on the surface of the
After the false alarm rate is set, the detection threshold can be calculated according to equation (4), so that it can detect every overlapped sub-frequency band, when Eq p,k ]>θ p,k We store the corresponding occupied superimposed sub-band location labels (p, k) into the set Ω, and this set will be used for next discrimination of active sub-channel locations.
Further, in the step c, under the ADFS structure of the folded spectrum, when one overlapped sub-band is detected as active, it is necessary to identify which one of the time-frequency sub-channels overlapped in the sub-band is occupied;
white gaussian noise falseLet the optimal classification result be based on q p,k And phase vectorThe absolute value of the maximum inner product between:
then the firstThe time-frequency sub-channel is the occupied sub-channel in the corresponding active superposition sub-frequency band (p, k) epsilon omega, at this time, due to the +.>The time-frequency sub-channels are judged to be active, and the frequency domain can be obtainedThe subchannels are active (occupied).
The invention also provides a low-complexity non-sparse broadband spectrum sensing device, which comprises,
the model building device is used for building a folding time spectrum model with an ADFS structure through a comprehensive sampling technology;
and the spectrum sensing device is used for realizing spectrum sensing based on the folding time spectrum model.
The invention also provides a terminal comprising one or more processors; a storage means for storing one or more programs; the one or more programs, when executed by the one or more processors, cause the one or more processors to implement a low complexity non-sparse, wideband spectrum sensing method as described above.
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor implements a low complexity non-sparse wideband spectrum sensing method as described above.
Compared with the prior art, the low-complexity non-sparse broadband spectrum sensing method has the following advantages:
(1) In a scene that the broadband spectrum is not sparse, the method is very suitable for realizing broadband spectrum sensing at the sub-Nyquist sampling rate;
(2) In the scene of non-sparse broadband spectrum, the invention can omit the spectrum reconstruction process, thus greatly reducing the calculation complexity;
(3) In the scene of non-sparse broadband spectrum, the method and the device can still ensure excellent detection performance while reducing the calculation complexity.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a system design diagram of a low complexity non-sparse wideband spectrum sensing method of the present invention;
FIG. 2 is a diagram illustrating the structure of the spectrum obtained by the integrated sampling in the folding process of the present invention;
FIG. 3 is a graph showing the comparison of the detection performance of the present invention with other algorithms for different numbers of active subchannels of the present invention;
FIG. 4 is a graph showing the analysis of detection performance at various sample rate reduction multiples in accordance with the present invention;
fig. 5 is a graph comparing the computational complexity of the present invention with other algorithms at different numbers of active subchannels.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first", "a second", etc. may explicitly or implicitly include one or more such feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art in a specific case.
The invention will be described in detail below with reference to the drawings in connection with embodiments.
I. Folding time spectrum model
Let us assume a wideband signal x (T) to be detected, whose nyquist rate is 1/T. It comprises U consecutive non-overlapping sub-channels.
A. Multiple sampling and digital fractional delay
As shown in fig. 1, we use a multi-sampling mechanism to sample the signal x (t). The sampling mechanism uses M sets of parallel analog-to-digital converters (ADCs), each set of ADCs, i.e., each sampling end, to uniformly sample the signal at a sub-nyquist rate of 1/NT, where N is the sample rate reduction multiple. Thus, when M<N satisfies both sub-nyquist sampling. Setting the time offset of the ith sampling end as c i T is 0.ltoreq.c 0 ＜c 1 ＜…＜c M-1 N-1 is not more than. ThenThe sub-Nyquist sampling signal sequence of the ith sampling end is obtained as follows:
let us assume that X (ω) is the Fourier transform of X (T) and its bandwidth is [0,2 pi/T ]]. Thus, the first and second substrates are bonded together,the Discrete Time Fourier Transform (DTFT) of (a) is:
after the multisampling, we introduce a Digital Fractional Delay (DFD) before the time-frequency transformation. For a pair ofGo-c i DFD of T yields y i [n]Then y i [n]The DTFT of (2) is:
B. time-frequency conversion
1) Time-frequency conversion representation of signals
We use Gabor time-frequency transformation, whose time-frequency transformation atoms are:
where g (t) represents the window function, is assumed to be normalized, i.e., g 2 =1 and the bandwidth is ω∈ [0,2 pi/NT), the time domain support set is t∈ [0, nlt). Parameter τ 0 and ξ0 Representing the discrete time-frequency grid step size of the time-frequency transform. For simplicity of analysis we let τ 0 ＝PNT,ξ 0 =1/FNT, where P is some integer and f=u/N. Then signal xThe time-frequency transformed representation (or coefficient) of (t) is:
wherein the last line is derived from the Plancherel formula. Based on the band-limited assumption of g (t), the above formula can be approximated as:
2) Time-frequency transform representation of sub-nyquist sampled signals
Now consider a path of the sub-nyquist sampling signal y i [n]Is a time-frequency representation of (c). We sample atom g using discrete time p，k [n]＝g(n-pP)e j2πkn/F To do y i [n]Operation of time-frequency transformation coefficients:
let G d (e jωNT ) Represents g [ n ]]The DTFT of (c) is:
according to equation (8), equation (7) can be written as:
from equation (3), we can also derive:
substituting (10) into (9), we obtain:
from equation (12), the time-frequency transformed representation (coefficient) of the sub-nyquist sampling signal can be written as:
/>
C. model display
Fig. 2 is a virtual model demonstration of equation (12), namely a folded time-frequency spectrum model.
In the figure, we represent itself with the transform coefficients of each subchannel. In fig. 2, there are NFP time-frequency subchannels in total, each of which is represented by a small box. For example, one of the cassettes s p,nF+k Is the (p, nf+k) th time-frequency subchannel in the grid of signal time-frequency transform coefficients. In addition, the folded spectrum includes FP superimposed sub-bands, each represented by a cubic cylinder. As shown in the figure, a solid line is used to draw a cubic columnRepresenting the (p, k) th superimposed sub-band in the Nyquist time-frequency transform coefficient grid obtained by the ith sampling end.
Furthermore, the small box centered with the "active" word represents that this time-frequency subchannel subband is occupied (active). And we define that the superimposed sub-band containing any active time-frequency sub-channel is active and vice versa.
Introduction to AdNoR Algorithm
In this section we introduce a special folded time-frequency spectrum structure, named almost disjoint subchannels (Approximate Disjoint Folded Subband, ADFS). Based on the ADFS structure, we first determine active superimposed sub-bands and then find the active sub-channels in each active superimposed sub-band.
ADFS structure
Definition: almost disjoint subchannels (ADFS)
When each active superimposed sub-band in the folded time spectrum contains only one active time-frequency sub-channel, the fold is said to be
The time spectrum has an ADFS structure. In mathematical language can be described as:
this structure is reflected in fig. 2, i.e. there are no two or more small boxes marked with an "active" word in one cube.
B. Superposition sub-band detection
Based on the ADFS structure, the superimposed sub-frequency bands obtained by each sampling end have similar amplitude, namely:
the test statistic of the superposition sub-band detection is set asAssuming that the signals in the active time-frequency sub-channels are independent of each other, zero-mean, and that the noise is of power spectral density sigma 2 Additive white gaussian noise of (c). It can be seen from equation (12) that for each free (unoccupied) superimposed sub-band there is a distribution: />I.e.For each superimposed sub-band, it is examined
The test statistics have the following distribution:
wherein ,Η0,(p,k) Representing that no active time-frequency sub-channel exists in the (p, k) th overlapped sub-frequency band; conversely, H 1,(p,k) Representing that the (p, k) th superimposed sub-band is occupied; and gamma is the signal to noise ratio.
From equation (15), it can be obtainedProbability density function of (c):
wherein Γ (·) is a gamma function; i v (. Cndot.) is a v-th order modified Bessel function.
In the binary hypothesis testing problem, the test probability and the false alarm rate can be obtained by the following two formulas:
P d ＝Pr(E[q p,k ]>θ p,k |H 1,(p,k) ), (17)
P fa ＝Pr(E[q p,k ]>θ p,k |H 0,(p,k) ), (18)
wherein θp,k Is the detection threshold. According to formulas (16) and (18), the false alarm rate of the superposition sub-band detection problem can be known to satisfy:
wherein Γ (a, x) is the incomplete gamma equationFurther Γ (n) = (n-1) +.! .
When deficiency occursAfter the alarm rate is set, the detection threshold can be calculated according to the formula (19), so that each superimposed sub-frequency band can be detected. When E [ q ] p,k ]>θ p,k We store the corresponding occupied superimposed sub-band location labels (p, k) into the set Ω, and this set will be used for the next discrimination of sub-channel locations.
C. Time-frequency sub-channel classification
Under the ADFS structure, when an overlapping sub-band is detected as active, it is necessary to identify which one of the time-frequency sub-channels overlapping the sub-band is occupied. This is essentially a classification problem. Under Gaussian white noise assumption, the optimal classification result can be based on q p,k And phase vectorThe absolute value of the maximum inner product between:
then the firstThe time-frequency sub-channel is the occupied sub-channel in the corresponding active superposition sub-frequency band (p, k) epsilon omega.
AdNoR algorithm flow
1): for each superimposed sub-band do
2): calculation ofAs test statistics for superposition of sub-band detection.
3)：if E[q p,k ]>θ p,k then
4): the (p, k) th superimposed sub-band is occupied;
5): for time-frequency subchannels do each superimposed on a sub-band (p, k)
6): calculation of
7)：end for
8): selection of
9): first, theThe individual time-frequency subchannels are occupied.
10)：end if
11)：end for
E. Computational complexity analysis
The computational complexity of the three algorithms OMP, nar and adnar is next analyzed. The computational complexity is measured in terms of the number of real floating point operations. To ensure comparative fairness, we choose appropriate parameters to ensure that the three algorithms have the same number of subchannels, compression, and number of samples sampled.
The computational complexity of OMP algorithm is:
the computational complexity of the NoR algorithm is:
CC NoR ＝O(4FM)+O(8DNM+4DN). (22)
the first part O (4 FM) of the above equation is the computational complexity of the superimposed subband detection step of the algorithm, while the second part O (8dnm+4dn) is the computational complexity of the subchannel classification step.
For the ador algorithm, an additional amount of computation is in the superimposed sub-band detection section compared to the NoR algorithm. It needs to detect more than (P-1) F superimposed subbands than NoR. As for the subchannel classifying section, the computational complexity thereof is related to the number D of active subchannels, the number M of sampling ends, and the sampling rate reduction multiple N, and these three parameters are set identically in both algorithms.
Therefore, the computational complexity of the ador algorithm is:
CC AdNoR ＝O(4PFM)+O(8DNM+4DN). (23)
because of the uncertainty of D in a non-sparse broadband spectrum scene, the calculation complexity of three algorithms cannot be accurately compared in theory, and therefore simulation analysis is adopted for comparison.
III simulation
In order to verify the excellent performance of AdNoR, the invention establishes a non-sparse broadband spectrum sensing experiment and compares the performance of OMP, noR and AdNoR algorithms. Our wideband spectrum to be detected is divided into u=fn=360 subchannels, each of width 4MHz. At most only one user transmits data at the same time on each sub-channel, and the signal adopts QPSK modulation mode. In the ador algorithm, the Gabor transform selects a gaussian window with a window length P, which is also the time coefficient of Gabor.
Comparison of detection performance under different number of active subchannels
In the first experiment, we set d= 5,20,40,70,110,160,220, the sampling rate drop multiple n=8, the compression degree N/m=2, the time coefficient p=180 of gabor transformation, and the false alarm rate P fa Signal to noise ratio snr=10 db=0.01. The OMP algorithm uses a measurement matrix to obtain sub-nyquist sampling points, the matrix size being related to the number of sub-channels in the wideband U and the sampling compression ratio N/M, but not directly related to N, F. Fig. 3 shows the perceptual performance of three classes of algorithms. We can see that the perceptual performance of ador is much better than the other two without sparseness of the spectrum, since both OMP and NoR algorithms require the spectrum to meet the sparseness condition.
Detection performance comparison at different sample rate reduction multiples
In a second experiment we set n=8, 12,18, N/m=2, d=50, p=180, p fa =0.01. In this experiment, we only discuss the effect of N on the performance of ador, since it can be seen from the previous experiment that when d=40, the detection probability of the other two algorithms has reached below 80%, and it is obvious that the requirements of spectrum sensing performance cannot be met; thus, the other two algorithms are not involved in the discussion. In fig. 4, we can see that the ador algorithm is greatly affected by N,its performance decreases with increasing N. The reasons are as follows: n, i.e. the sample rate decreases by a multiple and is also a fold of the spectrum, it will be appreciated that as the fold increases, the probability that the ADFS structure is satisfied decreases, which will directly affect the accuracy of the sub-channel classification.
Comparison of computational complexity
Fig. 5 shows a comparison of the computational complexity of the three algorithms derived from the parameters of the first experiment and formulas (21) (22) (23). We can see that under reasonable parameter settings, there is a CC present NoR <CC AdNoR <CC OMP . And with the increase of D, the computational complexity of AdNoR is more and more similar to that of NoR algorithm, and the ratio of the complexity of OMP and other two algorithms is more and more large.
Comprehensive evaluation of AdNoR algorithm
Considering fig. 5 and 3 together, when d=220, the computational complexity of the ador algorithm is almost an order of magnitude different from that of NoR, and the detection probability is far higher than that of the other two algorithms. It can be seen that when D is large, i.e. the spectrum is not sparse, the ador algorithm not only has much higher detection performance than the other two algorithms, but also has a low computational complexity comparable to the NoR algorithm. While the feature of greater impact of N on the ador algorithm, reflected in fig. 4, does not constitute a problem. Since the larger N means that the larger the number M of sampling ends is, i.e. the higher the hardware cost and the higher the energy consumption, this has a rule against practical application. Therefore, for the AdNoR algorithm, excellent detection performance can be obtained by selecting the N value according with the actual application scene. In summary, our ador algorithm is very suitable for application scenarios of non-sparse wideband spectrum sensing.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (4)
1. A low-complexity non-sparse broadband spectrum sensing method is characterized in that: the spectrum sensing method expands the sensing domain from the frequency domain to the time-frequency domain, avoids spectrum reconstruction and is not limited by sparse conditions, and comprises the following steps:
step 1: establishing a folding time spectrum model with an ADFS structure through a comprehensive sampling technology; the method specifically comprises the following steps:
step a: comprehensively sampling; the comprehensive sampling comprises multipath sampling, digital fractional delay and time-frequency conversion;
firstly, a multi-path sampling mechanism is used for sampling signals; the sampling mechanism uses M groups of parallel analog-to-digital converters, and each group of ADC uniformly samples signals at the sub-Nyquist rate of 1/NT, wherein N is a sampling rate reduction multiple; when M<N satisfies both sub-Nyquist sampling; setting the time offset of the ith sampling end as c i T is 0.ltoreq.c 0 ＜c 1 ＜…c M-1 N-1 is not more than; then the sub-nyquist sampling signal sequence at the i-th sampling end is obtained as follows:
second, after multiplexing, a digital fractional delay DFD is introduced before time-frequency conversion, forGo-c i DFD of T yields y i [n]；
Finally, obtaining y through time-frequency conversion i [n]Time-frequency transform of (a) represents coefficients:
wherein ,representing the sub-Nyquist sampling signal y obtained at the ith sampling end i [n]Time-frequency transformation representing coefficient s at time p and frequency point k p,k+Fn N=0, 1, …, N-1 represents the time-frequency transform representation coefficient of the signal x (t) at the time p and the frequency point k+fn;
according to the formula (2) obtained in the first step, a folding time spectrum with a special structure of 'almost disjoint sub-channels ADFS' can be obtained;
step b: detecting a superimposed sub-band;
the test statistic of the superposition sub-band detection is set asWhen the signals in the active time-frequency sub-channels are mutually independent, zero-mean, and the noise is the power spectral density sigma 2 From equation (2), then for each free superimposed sub-band there is a distribution: />I.e. < ->Because the frequency spectrum has an ADFS structure when being folded, the superimposed sub-frequency bands obtained by each sampling end have similar amplitude, each superimposed sub-frequency band can be obtained, and the test statistics of the superimposed sub-frequency bands have the following distribution:
H 0,(p,k) :
wherein ,H0,(p,k) Representing that no active time-frequency sub-channel exists in the (p, k) th overlapped sub-frequency band; conversely, H 1,(p,k) Representing that the (p, k) th superimposed sub-band is occupied; and gamma is the signal to noise ratio;
according to the formula (3), the false alarm rate of the superposition sub-band detection problem can be obtained to satisfy:
wherein θp,k Is the detection threshold and Γ (a, x) is the incomplete gamma equationFurther Γ (n) = (n-1) +.! The method comprises the steps of carrying out a first treatment on the surface of the
After the false alarm rate is set, the detection threshold can be calculated according to equation (4), so that it can detect every overlapped sub-frequency band, when Eq p,k ]>θ p,k We store the corresponding occupied superimposed sub-band location labels (p, k) into the set Ω, and this set will be used for next discrimination of active sub-channel locations;
step c: classifying time-frequency sub-channels;
under the ADFS structure of the folded spectrum, when one overlapped sub-frequency band is detected as active, the occupied sub-channel needs to be distinguished in the time-frequency sub-channels overlapped in the sub-frequency band;
when Gaussian white noise is used, the optimal classification result can be based on q p,k And phase vectorThe absolute value of the maximum inner product between:
then the firstThe time-frequency sub-channel is the occupied sub-channel in the corresponding active superposition sub-frequency band (p, k) epsilon omega, at this time, due to the +.>The time-frequency sub-channels are judged to be active, and the +.>The subchannels are active;
step 2: and realizing spectrum sensing based on the folding time spectrum model.
2. A low complexity non-sparse wideband spectrum sensing device, characterized by: the spectrum sensing device expands the sensing domain from the frequency domain to the time-frequency domain, avoids spectrum reconstruction, is not limited by sparse conditions, comprises,
the model building device is used for building a folding time spectrum model with an ADFS structure through a comprehensive sampling technology; the model building device comprises a comprehensive sampling device, a superposition sub-frequency band detection device and a time-frequency sub-channel classification device;
the comprehensive sampling device comprises a multipath sampling device, a digital fractional delay device and a time-frequency conversion device;
the comprehensive sampling device is used for sampling signals by using a multi-path sampling mechanism; the sampling mechanism uses M groups of parallel analog-to-digital converters, and each group of ADC uniformly samples signals at a sub-Nyquist rate of 1NT, wherein N is a sampling rate reduction multiple; when M<N satisfies both sub-Nyquist sampling; setting the time offset of the ith sampling end as c i T, and present; then the sub-nyquist sampling signal sequence at the i-th sampling end is obtained as follows:
second, after multiplexing, a digital fractional delay DFD is introduced before time-frequency conversion, forGo-c i DFD of T yields y i [n]；
Finally, obtaining the product through time-frequency conversiony i [n]Time-frequency transform of (a) represents coefficients:
wherein ,representing the sub-Nyquist sampling signal y obtained at the ith sampling end i [n]Time-frequency transformation representing coefficient s at time p and frequency point k p,k+Fn N=0, 1, …, N-1 represents the time-frequency transform representation coefficient of the signal x (t) at the time p and the frequency point k+fn;
according to the formula (2) obtained in the first step, a folding time spectrum with a special structure of 'almost disjoint sub-channels ADFS' can be obtained;
the overlapped sub-frequency band detection device is used for setting the test statistic of the overlapped sub-frequency band detection asWhen the signals in the active time-frequency sub-channels are mutually independent, zero-mean, and the noise is the power spectral density sigma 2 From equation (2), then for each free superimposed sub-band there is a distribution: />I.e. < ->Because the frequency spectrum has an ADFS structure when being folded, the superimposed sub-frequency bands obtained by each sampling end have similar amplitude, each superimposed sub-frequency band can be obtained, and the test statistics of the superimposed sub-frequency bands have the following distribution:
H 0,(p,k) :
wherein ,H0,(p,k) Representing that no active time-frequency sub-channel exists in the (p, k) th overlapped sub-frequency band; conversely, H 1,(p,k) Representing that the (p, k) th superimposed sub-band is occupied; and gamma is the signal to noise ratio;
according to the formula (3), the false alarm rate of the superposition sub-band detection problem can be obtained to satisfy:
wherein θp,k Is the detection threshold and Γ (a, x) is the incomplete gamma equationFurther Γ (n) = (n-1) +.! The method comprises the steps of carrying out a first treatment on the surface of the
After the false alarm rate is set, the detection threshold can be calculated according to equation (4), so that it can detect every overlapped sub-frequency band, when Eq p,k ]>θ p,k We store the corresponding occupied superimposed sub-band location labels (p, k) into the set Ω, and this set will be used for next discrimination of active sub-channel locations;
the time-frequency sub-channel classifying device is used for distinguishing which one of the time-frequency sub-channels overlapped in one overlapped sub-frequency band is occupied when the overlapped sub-frequency band is detected to be active under the ADFS structure of the folded time-frequency spectrum;
when Gaussian white noise is used, the optimal classification result can be based on q p,k And phase vectorThe absolute value of the maximum inner product between:
then the firstThe time-frequency sub-channel is the occupied sub-channel in the corresponding active superposition sub-frequency band (p, k) epsilon omega, at this time, due to the +.>The time-frequency sub-channels are judged to be active, and the +.>The subchannels are active;
and the spectrum sensing device is used for realizing spectrum sensing based on the folding time spectrum model.
3. A terminal, characterized by: the terminal includes one or more processors; a storage means for storing one or more programs; the one or more programs, when executed by the one or more processors, cause the one or more processors to implement a low complexity non-sparse, wideband spectrum sensing method as recited in claim 1.
4. A computer-readable storage medium having stored thereon a computer program, characterized by: the program, when executed by a processor, implements a low complexity non-sparse, wideband spectrum sensing method as claimed in claim 1.
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