Compressed sensing spectrum detecting method under blind sparse condition
A technology of compressed sensing and spectrum detection, which is applied to electrical components, transmission monitoring, transmission systems, etc., can solve problems such as slow convergence speed of detection algorithms, missing spectrum detection, and increased algorithm complexity, and achieve convergence and complexity. Low degree, good real-time effect
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[0029] Specific implementation manner 1: The spectrum detection method of compressed sensing under blind sparse conditions in this implementation manner is specifically prepared according to the following steps:
[0030] Step 1. A mathematical model established based on the compressed sensing theory for the antenna received signal x of length N Perform optimization iterative solution; where the measurement matrix is Θ, the signal after compression sampling is y, f is the sparse basis coefficient to be sought, Ψ is the transformation basis matrix, and Φ is the Gaussian random matrix;
[0031] Step 2: Under the premise that the measurement matrix Θ satisfies the RIP property of the matrix, simplify the mathematical model obtained in Step 1 to obtain the convex optimization problem of the signal;
[0032] Step 3. Use the greedy tracking algorithm to perform correlation detection on the convex optimization problem of the signal, and obtain the most relevant element, and merge it with t...
Example Embodiment
[0042] Specific embodiment two: this embodiment is different from specific embodiment one in that: in step one, the mathematical model established on the antenna received signal x of length N according to the compressed sensing theory The specific problem of the optimization iterative solution is described as follows:
[0043] (1) The length of the signal received by the antenna is N, and the compressed sampling rate is K sub-bands are randomly selected from N frequency bands as frequency bands occupied by authorized users, and M is the number of compressed sampling points;
[0044] (2) N×1 dimensional noise-free signal x_o obtained by inverse Fourier transformation of the frequency band occupied by authorized users; x_o∈R N , The inverse Fourier transform method is x_o=Ψf, f is the sparse base coefficient to be sought;
[0045] (3) If there are only K elements in f that are non-zero, then the signal x_o is said to be sparse under the transformation basis of Ψ, and the original sign...
Example Embodiment
[0053] Specific embodiment three: this embodiment is different from specific embodiment one or two in that in step two, under the premise that the measurement matrix is Θ and satisfies the RIP property of the matrix, the mathematical model obtained in step one is simplified to obtain the convex optimization problem of the signal The specific process is:
[0054] Although the 0-norm algorithm of compressed sensing is optimal, it is an NP-hard problem. In order to find the sparsest solution, an exhaustive list is required This possibility is that the algorithm complexity is extremely high; relevant data show that under the premise that the measurement matrix Θ satisfies the RIP property of the matrix, MATLAB software is used as the simulation software, input: sampling vector y, compressed sensing measurement matrix Θ=ΦΨ, iteration Termination threshold s, the purpose of the algorithm in the invention is to output the spectrum sensing result under the premise that the above variab...
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