CN103974284B - A kind of broader frequency spectrum cognitive method based on partial reconfiguration - Google Patents

Abstract

The invention provides a wideband spectrum sensing method based on partial reconstruction, which applies the idea of partial reconstruction to the minimum Interior point method for norm solution. According to the sampling value, the present invention gradually adjusts through multiple iterative calculations, which is different from the traditional reconstruction method without adjustment. The number of iterations used is not fixed and varies with the energy of the reconstructed subchannels. If the energy is large, reduce the number of iterations; if the energy is small, increase the number of iterations. The present invention can be applied in the broadband spectrum scene where the degree of sparsity is unknown, or even the degree of sparsity changes, and reduces the calculation time while ensuring the detection accuracy, and improves the real-time performance of detection.

Description

A Wideband Spectrum Sensing Method Based on Partial Reconstruction

technical field

The invention relates to the field of wireless communication, in particular to a wideband spectrum sensing method based on partial reconstruction.

Background technique

In cognitive radio (CR, Cognitive Radio), the two goals of providing reliable communication and efficient use of radio spectrum determine the importance of fast and accurate spectrum sensing. However, when sensing wideband spectrum, the required high sampling rate and massive sampling data processing capability pose severe challenges to the spectrum sensing hardware. In reality, the number of sub-bands occupied by primary users on the broadband spectrum is far less than the total number, which satisfies sparsity. So people naturally think of Compressed Sampling (CS, Compressed Sampling, also known as Compressed Sensing, Compressive Sensing). It shows that as long as the signal is compressible or sparse in a certain transformation domain, an observation matrix unrelated to the transformation base can be used to project the transformed high-dimensional signal onto a low-dimensional space, and then optimize the The original signal can be reconstructed with a high probability from these small number of projections, and finally processed according to the reconstructed signal to make a detection decision. Compressed sampling technology can greatly reduce the sampling rate requirements of equipment. Reconstruction is a key step in the research of compressed sampling. If the original signal cannot be reconstructed quickly and effectively according to the sampling value, then compressed sampling theory is very important for Nyquist. The superiority of the sampling law is also not highlighted.

At present, the research focus of compressed sampling is on the acquisition of low-speed observation sequences and the high-probability and high-precision reconstruction of signal waveforms. Among them, the commonly used reconstruction algorithms are mainly divided into three categories: the convex optimization algorithm based on the minimum l ₁ norm, the minimum greedy algorithm based on the l ₀ norm, and the combination algorithm. Some of these methods have high reconstruction accuracy, and some are suitable for occasions with a large amount of data, but they have two common shortcomings: the calculation is huge and the compression ratio is affected by the sparsity of the original signal. In addition, the existing broadband spectrum sensing technologies based on compressed sampling for cognitive radio all assume that the wideband spectrum sparsity is known. However, in the CR scenario, since the primary user (PU, Primary User) and the cognitive user (or secondary user, SU, Second User) cannot directly communicate or exchange information, and the spectrum occupancy of the primary user is dynamically changing , so the prior information of the sparsity of the broadband spectrum is not easy to obtain. Algorithms for sparsity estimation have been proposed in the literature: first use a small number of sampling values to quickly estimate the actual sparsity, and then adjust the total number of samples according to the estimated value before performing the operation. The method does not require prior knowledge of sparsity, but additional sampling is required. Another conservative method is to obtain the upper bound of sparsity based on the long-term statistical observation of cognitive users, so as to determine the compression ratio. However, this often results in an excessive number of samples, which further increases the amount of computation for subsequent signal reconstruction.

On the other hand, complete reconstruction of the original signal is not necessary in many processing applications. Many times, we just want to extract useful information from observation sequences or filter out uninteresting information in subsequent processing. At this time, it is obviously not the best choice to solve the signal extraction and filtering problems after trying to reconstruct all the signals through the observation sequence. For example, in a cognitive radio system, cognitive users only care about whether the channel is occupied or not, but not the specific conditions of the channel. Therefore, it is not always necessary to reconstruct the original signal accurately. Whether it is the reconstruction algorithm that minimizes the l ₁ norm or the greedy algorithm, they all go through multiple iterations and gradually adjust to finally get the optimal solution, which is an approximation process. Basis Pursuit De-noising (BPDN, BasisPursuit De-noising) is a classic algorithm based on the minimum l ₁ norm to reconstruct the signal contaminated by noise. Scholars have improved this method, but focused on improving the accuracy of the BPDN algorithm or expanding its performance in other sparse noise (such as impulse noise) environments. How to reduce the amount of calculation under the premise of meeting the accuracy requirements requires further research.

Contents of the invention

In order to solve the problem that the calculation amount is huge and the compression ratio is affected by the sparsity of the original signal in the existing wideband spectrum sensing technology, the present invention provides a wideband spectrum sensing method based on partial reconstruction, which can be used when the sparsity is unknown or even sparse In the wide-band spectrum scene with varying degrees, and while ensuring the detection accuracy, the calculation time is reduced and the real-time performance of the detection is improved.

The present invention comprises the following steps:

1) The cognitive user samples the spectrum and transmits the low-speed sampling sequence to the fusion center;

2) The fusion center uses the interior point method to completely reconstruct the original signal, the number of recording iterations is T, and the number of updating iterations is T=T-1;

3) Calculate the energy of each sub-channel, the maximum value is recorded as J _max , the minimum value is recorded as J _min , and the threshold value is defined

_Gmma =0.5(Jmax- _Jmin );

4) Use interior point method for partial reconstruction;

5) Calculate the energy value of each channel after reconstruction, record the number of channels greater than the threshold Gmma and the serial number of the sub-signal, and feed it back to the cognitive user;

6) Update the number of iterations according to the energy of the sub-channel, if the energy of the sub-channel is greater than 2Gmma, or the difference between the energy values of the two sub-channels is less than 1.5Gmma, then in the next detection cycle, T=T+1, otherwise T=T -1;

7) Repeat step 4) to step 6);

The complete reconstruction of the original signal using the interior point method includes the following steps:

1) Input error tolerance ε and maximum number of iterations T _max ;

2) According to the target frequency band spectrum compression detection model y=Φx, initialize the data, set the current iteration number T=0, x=0, u=1∈R ^N , define a relatively large number, denoted as λ, and require λ≥| |2Φ ^T y|| _∞ , where Φ is the M×N dimensional observation matrix, y is the observed sequence, and u is the convergence error;

3) Let T=T+1, pass Calculate the search direction (Δx, Δu), where H is the Hessian matrix, and g is the gradient of the current (x,u);

4) Calculation step s, s is the smallest element in the vector {λ/|2Φ ^T (Φx-y)|};

5) Update (x, u) = (x, u) + s(Δx, Δu);

6) Calculate the convergence error u;

7) Repeat step 3) to step 6) until the error tolerance ε is satisfied, that is, min||x|| ₁ st||y-Φx||<ε or stop when the maximum iteration number T _max is reached.

The partial reconstruction using the interior point method includes the following steps:

1) Let T=T+1, pass Calculate the search direction (Δx, Δu), where H is the Hessian matrix, and g is the gradient of the current (x,u);

2) Calculation step size s, s is the smallest element in the vector {λ/|2Φ ^T (Φ _x -y)|};

3) Update (x, u) = (x, u) + s(Δx, Δu);

4) Calculate the convergence error u;

5) Repeat step 1) to step 4), and iteratively stops when it reaches the updated number of iterations T.

The beneficial effect of the invention is that: the idea of partial reconstruction is applied to the interior point method based on the minimum l ₁ norm solution, and a spectrum sensing method based on partial reconstruction is proposed. According to the sampling value, the present invention gradually adjusts through multiple iterative calculations, which is different from the traditional reconstruction method without adjustment. The number of iterations used is not fixed and varies with the energy of the reconstructed subchannels. If the energy is large, reduce the number of iterations; if the energy is small, increase the number of iterations. The present invention can be applied in the broadband spectrum scene where the degree of sparsity is unknown, or even the degree of sparsity changes, and reduces the calculation time while ensuring the detection accuracy, and improves the real-time performance of detection.

Description of drawings

Figure 1(a) is a graph of the original observation sequence of a CR broadband spectrum sensing scene.

Figure 1(b) is a fully reconstructed sequence graph of a CR broadband spectrum sensing scene using the interior point method for 25 iterations.

Figure 1(c) is a partially reconstructed graph of a CR wideband spectrum sensing scene iterated 12 times.

Figure 1(d) is a partially reconstructed graph of a CR wideband spectrum sensing scene iterated 6 times.

Fig. 2 is the change of the number of iterations with the detection cycle when the present invention is applied to the scene in Fig. 1 .

Figure 3 is a comparison of the time taken by the present invention and a fully reconstructed retest over 100 test cycles.

detailed description

The present invention will be further described below in conjunction with accompanying drawing.

The core idea of the present invention is to combine the compressed sampling technology with the perception of wideband spectrum in cognitive radio. The interior point method based on the minimum l ₁ norm solution is improved by partial reconstruction. Let the number of iterations change with the energy of the reconstructed sub-channel. The present invention can not only be applied in the broadband spectrum environment with constant sparsity, but also can achieve good detection effect in the case of time-varying sparsity. On the premise of ensuring the precision, the invention can reduce the operation time and improve the real-time performance of detection.

In cognitive wireless networks, the task of spectrum sensing is to realize dynamic spectrum access under the premise of protecting the primary user. Cognitive users need to detect in each sampling period to determine whether there is a primary user in the frequency band. In order to reduce the data acquisition and storage of sensing nodes, each cognitive user uses an analog/information converter to directly obtain information from broadband analog signals. The present invention discusses that in the case of not completely reconstructing the original signal, the energy of the partially reconstructed sub-channel is compared with the threshold value, thereby testing two hypotheses and making a decision. The spectrum compression detection model of the target frequency band can be expressed as: y=Φx.

Corresponding to the two cases where the primary user does not exist and exists, the two assumptions are as follows:

H ₀ :x=ω

H ₁ : x=ω+s

Where s=[s(0),...,s(N-1)] ^T and ω=[ω(0),...,ω(N-1)] ^T are random sparse The sequence of sampled values of signal and noise, and s and ω are independent of each other. M is the number of sampling points, and Φ is an M×N-dimensional observation matrix.

When Φ satisfies the finite isometric constraints, s can be reconstructed. The model it solves is:

min||x|| ₁ st||y-Φx||＜ε

or write the unconstrained problem:

min||y-Φx||+λ||x|| ₁

The methods for solving the above two expressions are collectively called basis pursuit denoising method (BPDN). The role of the parameter ε or λ is to control the balance between sparsity and allowable error, and strive to ensure that the signal error is minimized while making the signal representation as sparse as possible. Compared with other reconstruction algorithms, BPDN algorithm has a better denoising effect on Gaussian white noise. However, the complexity of the BPDN method is very high. It requires the number of samples M to satisfy M>cK, c≈log ₂ (N/K+1), the time complexity is O(N ³ ), and K is the degree of sparsity. The present invention is applied to the scene where the sparsity is unknown, and M takes the upper bound.

It can be seen from the above description that BPDN is essentially an optimization principle. Note that it is also an optimization problem with constraints. The standard form of linear programming (LP, Linear Program) is:

minc ^T x stAx = b

Among them, the variable x∈R ^m , c ^T x is the objective function, and Ax=b is the equality constraint. Obviously, the expression min||x ₁ st||y-Φx||<ε and the expression minc ^T x stAx=b can be transformed into each other. Therefore, the method of solving linear programming can be used to solve the BPDN problem.

The simplex method is a general method for solving linear programming. The theoretical basis is that if the feasible region of the linear programming problem exists (there is no contradiction between the constraints), then the feasible region is a convex set in the vector space R ^N. The feasible solution corresponding to the vertex becomes the basic feasible solution. If the optimal value of the linear programming problem exists, the optimal solution must be reached at a vertex of the convex set. The idea of the simplex method is: first find a basic feasible solution, calculate the objective function value at the vertex to see if it is the optimal solution; if not, compare the objective function values of the surrounding adjacent vertices, and switch to the smaller one vertex, and repeat the process. In the simplex method, only adjacent vertices are searched, and the calculation amount of each iteration is small, but many vertices need to be visited to find the optimal solution. In the worst case all non-optimal vertices may need to be visited. In order to reduce the number of iteration steps, many scholars have proposed the interior point method. The alternative method is to move along the "shortest path" inside the feasible region, that is, to move along the fastest direction that minimizes the objective function value in the next iteration.

According to the method of the present invention, the interior point method is first used to completely reconstruct the signal of the original channel according to the sampling sequence, and the specific implementation steps include:

Input: error tolerance ε, maximum number of iterations T _max ;

Initialization: the current number of iterations T=0, x=0, u=1∈R ^N , define a relatively large number, denoted as λ, and require λ≥||2Φ ^T y|| _∞ ;

Refactoring operation:

Let T=T+1;

pass

Calculate the search direction (Δx, Δu), where H is the Hessian matrix, and g is the gradient of the current (x,u);

Calculate the step size s, s is the smallest element in the vector {λ/|2Φ ^T (Φx-y)|};

Update: (x,u)=(x,u)+s(Δx,Δu);

Compute the convergence error u,

Repeat the reconstruction operation until the error requirement is met or the maximum number of iterations is reached, then stop and output the result, and record the number of iterations T used.

The interior point method usually needs to consider all feasible directions in order to find the best moving direction at each iteration. In other words, compared with the simplex method, the interior point method trades a larger amount of computation in each iteration for a reduction in the number of iterations. In practice, in spectrum sensing, the existence of the primary user can be correctly detected through the feasible solution obtained in the iterative process. Figure 1 of the manual simply assumes a CR wideband spectrum sensing scenario, including 50 non-overlapping sub-channels, each channel is represented by 10 numbers, and 3 sub-channels are selected to be occupied and the spectrum amplitude balance is 1. The signal-to-noise ratio is 10dB. Figure 1(a) is the original observation sequence, that is, y, Figure 1(b) is the completely reconstructed sequence using the interior point method, and the number of iterations is 25, Figure 1(c) and Figure 1(d) are partial reconstructions result of the structure. The number of iterations in Figure 1(c) is 12, and that in Figure 1(d) is 6. Obviously, the reconstruction signal obtained after full iteration is more accurate, and the reconstruction effect becomes worse and worse as the number of iterations decreases. But this does not mean that the accuracy of the test results will be affected. In fact, in the last two pictures, it is still possible to tell which channels are occupied by the naked eye. Even with partial reconstruction, the energy of the sub-channel occupied by the primary user is far greater than that of the empty channel.

Update T=T-1, and calculate the energy of each sub-channel, select the largest one as J _max , and the smallest one as J _min . A threshold value Gmma=0.5(J _max -J _min ) is defined, and this threshold value will be used in subsequent detections. Record the number of channels and sub-signal numbers greater than the threshold value Gmma, and feed back to cognitive users; think that there are primary users in these channels, and cognitive users cannot occupy them;

In the second detection cycle, the cognitive user detects the spectrum again and transmits the projected result to the fusion center. The center uses the interior point method for partial reconstruction but is forced to stop when the number of iterations reaches the updated T. Calculate the energy value of each channel after reconstruction, compare it with Gmma and make a judgment;

Still in this period, the energy of the sub-channels is analyzed. If there is a sub-channel whose energy is greater than 2Gmma, update T=T+1; if there is a difference between two sub-channel energy values less than 1.5Gmma, also T=T+1; otherwise, T=T-1.

The operation of the subsequent detection cycle is the same as that of the second detection cycle, and in summary, proceed according to the following steps.

1. Perform partial reconstruction according to the number of iterations updated in the previous detection cycle;

2. Calculate the energy of each sub-channel according to the partially reconstructed results;

3. Compare with the threshold value and make a judgment;

4. Update the number of iterations.

According to the description of the present invention and the accompanying drawings 2 and 3 of the description, those skilled in the art should not be difficult to see that the present invention can be applied to wideband spectrum detection of cognitive radio. Adaptively adjust the number of iterations according to the channel environment and accuracy requirements. The present invention can not only be applied in the broadband spectrum scene where the degree of sparsity is unknown or even changes, but also reduce the calculation time and improve the real-time performance of detection under the condition of ensuring the detection accuracy. Has a wide range of application.

There are many specific application approaches of the present invention, and the above description is only a preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, some improvements can also be made without departing from the principles of the present invention. Improvements should also be regarded as the protection scope of the present invention. The contents not described in detail in the application of the present invention belong to the prior art known to those skilled in the art.

Claims (3)

1. A wideband spectrum sensing method based on partial reconstruction, characterized in that it comprises the following steps: 1) The cognitive user samples the spectrum and transmits the low-speed sampling sequence to the fusion center; 2) The fusion center uses the interior point method to completely reconstruct the original signal, the number of recording iterations is T, and the number of updating iterations is T=T-1; 3) Calculating the energy of each sub-channel, the maximum value is recorded as J _max , the minimum value is recorded as J _min , and the threshold value Gmma=0.5(J _max -J _min ) is defined; 4) Use interior point method for partial reconstruction; 5) Calculate the energy value of each channel after reconstruction, record the number of channels greater than the threshold Gmma and the serial number of the sub-signal, and feed it back to the cognitive user; 6) Update the number of iterations according to the energy of the sub-channel, if the energy of the sub-channel is greater than 2Gmma, or the difference between the energy values of the two sub-channels is less than 1.5Gmma, then in the next detection cycle, T=T+1, otherwise T=T -1; 7) Repeat step 4) to step 6). 2. The broadband spectrum sensing method based on partial reconstruction according to claim 1, characterized in that the full reconstruction of the original signal using the interior point method comprises the following steps: 1) Input error tolerance ε and maximum number of iterations T _max ; 2) According to the target frequency band spectrum compression detection model y=Φx, initialize the data, set the current number of iterations T=0, x=0, Define a relatively large number, denoted as λ, requiring λ≥||2Φ ^T y|| _∞ , where Φ is the M×N dimensional observation matrix, y is the observed sequence, and u is the convergence error; 3) Let T=T+1, pass Calculate the search direction (Δx,Δu), where H is the Hessian matrix, and g is the gradient of the current (x,u); 4) Calculation step s, s is the smallest element in the vector {λ/|2Φ ^T (Φx-y)|}; 5) Update (x,u)=(x,u)+s(Δx,Δu); 6) Calculate the convergence error u; 7) Repeat step 3) to step 6) until the error tolerance ε is satisfied, that is, min||x|| ₁ st||y-Φx||<ε or stop when the maximum iteration number T _max is reached. 3. The broadband spectrum sensing method based on partial reconstruction according to claim 1, characterized in that: said use of interior point method to carry out partial reconstruction comprises the following steps: 1) Let T=T+1, pass Calculate the search direction (Δx,Δu), where H is the Hessian matrix, and g is the gradient of the current (x,u); 2) Calculation step s, s is the smallest element in the vector {λ/|2Φ ^T (Φx-y)|}; 3) Update (x,u)=(x,u)+s(Δx,Δu); 4) Calculate the convergence error u; 5) Repeat step 1) to step 4), and iteratively stops when it reaches the updated number of iterations T.