An Adaptive Compressed Spectrum Sensing Method Based on a Deterministic Evaluation Model

Abstract

This invention belongs to the field of cognitive radio technology based on compressed spectrum sensing, specifically relating to an adaptive compressed spectrum sensing method based on a deterministic evaluation model. Firstly, in each sensing interval of the adaptive compressed spectrum sensing, a novel signal reconstruction algorithm is proposed. This algorithm incorporates prior knowledge into the l-axis of the block-sparse signal. 2，1 The method involves norm minimization. Secondly, the CDF of the reconstructed signal error is derived and used as the stopping criterion for observation sample acquisition. Finally, the energy detection method is used to process the currently reconstructed spectral signal to obtain the corresponding spectral usage status. This method improves the accuracy of spectral sensing while providing deterministic assurance for the sensing results.

Description

Technical Field

[0001] This invention belongs to the field of cognitive radio technology based on compressed spectrum sensing, and specifically relates to an adaptive compressed spectrum sensing method based on a deterministic evaluation model. Background Technology

[0002] Cognitive radio (CR) is a flexible and intelligent wireless communication technology designed to improve the efficiency of wireless spectrum utilization and address the problems of scarce and unbalanced spectrum allocation. Traditional wireless communication systems rely on fixed spectrum allocation, which becomes inefficient in the context of ever-increasing spectrum demand. Cognitive radio enables wireless devices to dynamically sense, identify, and utilize idle spectrum resources, providing higher spectrum utilization without interfering with existing users.

[0003] Compressed spectrum sensing, a crucial component of cognitive radio technology, aims to rapidly and efficiently detect and identify available spectrum using compressed sensing (CS) methods. Traditional spectrum sensing methods typically require long sampling times and high signal-to-noise ratios, leading to lower accuracy and real-time performance in dynamic environments and under high interference conditions. Compressed sensing-based spectrum sensing, however, can recover spectrum information through sparse representation at low sampling rates, significantly improving the speed and efficiency of the sensing process, particularly demonstrating significant advantages in resource-constrained scenarios and those with high real-time requirements.

[0004] With the continuous development of wireless communication technology, cognitive radio technology, which combines intelligent algorithms and compressed sensing, is becoming one of the key technologies for improving spectrum sensing efficiency and addressing challenges in complex environments. It can not only achieve spectrum sensing in traditional static environments, but also provide more accurate and timely spectrum information in dynamic and complex communication environments, such as high-speed mobile communication scenarios, providing theoretical basis and technical support for the design and optimization of next-generation wireless communication systems.

[0005] Adaptive compressed spectrum sensing (ACSS) plays a crucial role in cognitive radio networks because it reduces sampling rates and power consumption. Most existing ACSS schemes focus primarily on improving spectrum sensing performance but do not provide deterministic guarantees of sensing results. Summary of the Invention

[0006] To address the problems of existing technologies, this invention designs an adaptive compressed spectrum sensing (ACSS) method based on a deterministic estimation model. By deriving a closed-form expression for the cumulative distribution function (CDF) of the reconstruction error, it provides the confidence level of the reconstructed signal. Specifically, firstly, in each sensing interval of ACSS, this invention proposes a novel signal reconstruction algorithm that incorporates prior knowledge into the l-axis of the block sparse signal. 2,1 Norm minimization is performed. Secondly, the CDF of the reconstruction error is derived and used as a stopping criterion for collecting observation samples. Finally, the energy detection method is used to process the reconstructed spectral signal at the current time to obtain the corresponding binary spectral occupancy state.

[0007] Technical solution of the present invention:

[0008] An adaptive compressed spectrum sensing method based on a deterministic estimation model includes the following steps:

[0009] Step 1. Based on l 2，1 A signal reconstruction model combining norm minimization and prior knowledge mining reconstructs the spectral signal: The secondary user (SU) compresses and samples the frequency domain signal, then uses l... 2，1 Norm minimization is used to solve for a broadband signal, which serves as prior knowledge and l. 2，1 Norm minimization combined with solving the spectral signal of the current time slot is the reconstructed signal.

[0010] Step 2. Derive the CDF of the reconstructed signal error and use it as the stopping criterion for observation sample acquisition to achieve adaptive stopping of the sensing process: if the CDF is less than the preset error tolerance and greater than the preset probability value, stop sampling and obtain the reconstructed spectrum signal; otherwise, continue the next sampling process.

[0011] Step 3: Use energy detection method to make spectrum determination to obtain the spectrum occupancy and vacancy status.

[0012] The beneficial effects of this invention are as follows:

[0013] This invention provides a deterministic approach to compressed spectrum sensing results, enabling broadband spectrum sensing with adaptive adjustment of the sampling rate and reliable confidence of the sensing results. While improving the accuracy of spectrum sensing, it also ensures the determinism of the sensing results, thereby enhancing the spectrum supply capability of cognitive radio networks. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method of the present invention;

[0015] Figure 2 A schematic diagram of communication time frame division;

[0016] Figure 3 This is a schematic diagram of a block sparse signal.

[0017] Figure 4 This paper compares the spectrum sensing performance of the ACSS-DEM method of this invention with that of other algorithms.

[0018] Figure 5 The CDF curves for different numbers of sparse blocks in the embodiments of the present invention (number of sparse blocks: (a) 4, (b) 5, (3) 6, (4) 7);

[0019] Figure 6 Comparison of NMSE of reconstructed signals under different numbers of sparse blocks in embodiments of the present invention (number of sparse blocks: (a) 4, (b) 5, (c) 6, (d) 7). Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0021] Example

[0022] This invention is an adaptive compressed spectrum sensing method based on a deterministic evaluation model, and the specific steps are as follows: (e.g.) Figure 1 )

[0023] Step 1. Based on l 2，1 A method combining norm minimization and prior knowledge mining reconstructs the spectral signal: The secondary user (SU) compresses and samples the frequency domain signal, then... 2，1 Norm minimization is used to solve for a broadband signal, which serves as prior knowledge and l. 2，1 Norm minimization combined with solving the spectral signal of the current time slot is the reconstructed signal.

[0024] The prior knowledge is only used by l 2，1 Broadband spectral signals solved by norm minimization.

[0025] Step (11) as follows Figure 2 The system employs periodic compressed spectrum sensing. Each communication time frame T is divided into sensing time slots (duration: Ts), followed by a data transmission time slot Td (i.e., T = Ts + Td). During the sensing phase, the total interval Ts is divided into J time slots, each with a length τ = Ts / J. In each time slot τ, the secondary user samples the time-domain signal x(t) at the same sampling rate and obtains ΔM compressed measurements, where ΔM is the number of samples taken in each time slot. After j sensing cycles (j represents the number of sampling cycles), the signal is reconstructed using jΔM observation samples.

[0026] Specifically, secondary users have access to N×1 frequency domain signals. Compressed sampling is performed, and the compressed observations can be expressed as follows:

[0027]

[0028] Where Φ represents the observation matrix jΔM×N, n~N(0,σ) 2 I jΔM ) indicates observation noise.

[0029] Using l 2，1 Norm minimization model for signals Reconstruction is performed, and the reconstructed spectral signal is obtained. It can be represented as:

[0030]

[0031] Where δ represents the noise margin.

[0032] Reconstructed spectral signal This is provided as prior knowledge to step (12).

[0033] Step (12) combines the signal l 2，1 The inner product of norm minimization and the prior knowledge obtained in step (11) is used to solve for the wideband signal, as follows:

[0034] Using l 2，1 The inner product of the norm minimization model and prior knowledge on the signal Reconstruction is performed, and the reconstructed spectral signal is obtained. It can be represented as:

[0035]

[0036] Here, β is a balancing factor used to control the relative influence of the two parts before and after the minus sign, and its value ranges from (0,1).

[0037] Step 2. Derive the CDF of the reconstructed signal error and use it as the stopping criterion for observation sample acquisition to achieve adaptive stopping of the sensing process: if the CDF is less than the preset error tolerance and greater than the preset probability value, stop sampling and obtain the reconstructed spectrum signal; otherwise, continue the next sampling process.

[0038] Step (21) To represent a true spectral signal, if the number of samples M = jΔM satisfies the following inequality

[0039]

[0040] Then at least 1-2exp(-γ2(Γ) ξ ∩S N-1 The probability of )) makes satisfy

[0041]

[0042] in, Representation function exist The cone at point S N-1 express A unit sphere in space. γ(Γ) ξ ∩S N-1 ) represents the set Γ ξ ∩S N-1 The complexity is Gaussian. ρ and C represent constants.

[0043] Based on Gaussian complexity γ(Γ) ξ ∩S N-1 ) and Gaussian width w(Γ) ξ ∩S N-1 The relationship between the sample size M and the number of samples M satisfies the following inequality.

[0044]

[0045] Step (22) Gaussian width w(Γ) ξ ∩S N-1 The upper bound of ) can be represented as

[0046] w(Γ ξ ∩S N-1 )≤E[dist(g,N ξ )]

[0047] in, Represents ξ(x) f ) in x f The normal cone at the location, g ~ N(0,I) N () is a random Gaussian vector. According to Jensen's inequality,

[0048] w 2 (Γ ξ ∩S N-1 )

[0049]

[0050] For μ≥0, fix any g, and choose any... available

[0051]

[0052] Define parameters:

[0053]

[0054] It can be deduced that:

[0055]

[0056] therefore:

[0057]

[0058] Define parameters:

[0059]

[0060] According to convex geometry theory, it can be deduced that:

[0061]

[0062]

[0063] Where, μ k Represents χ k The mean of the distribution, l represents the number of non-adjacent blocks into which the sparse signal is divided, and s represents the number of blocks with signal.

[0064] This leads to the derivation of the cumulative distribution function (CDF) of the reconstruction error:

[0065]

[0066] in, σ represents the standard deviation of the observation noise.

[0067] Criteria for stopping the perception process: e represents the preset error tolerance, p set This represents the preset probability value.

[0068] When the stopping criterion is met, sampling stops, and the reconstructed spectral signal is obtained.

[0069] Otherwise, continue with the next sampling process.

[0070] Step 3. Spectrum State Decision

[0071] Obtain the reconstructed spectral signal Then, the corresponding binary spectrum state is obtained through an energy detection method. Specifically, the energy detection method involves: first, the receiving device samples within the target frequency band to acquire the received signal. This signal can be represented by two assumptions: when the frequency band is idle, only noise is received; when the frequency band is occupied, a superposition of noise and the primary user signal is received. After sampling the signal, its energy value is calculated by summing the squares of the sampled signal amplitudes. Subsequently, this energy value is compared with a preset threshold, which is typically designed based on noise power statistics or detection probability and false alarm probability. If the energy value is below the threshold, the frequency band is determined to be idle; otherwise, it is determined to be occupied, thus generating the binary state of the target frequency band (e.g., 0 indicates idle, 1 indicates occupied).

[0072] The method of the present invention is applicable to, for example, Figure 3 Compressed spectral sensing of the block sparse signal is shown.

[0073] A simulation environment was set up to compare and verify the performance of the proposed method (ACSS-DEM) with typical methods. The methods compared include: ①ACSS-JL, an adaptive compressed spectrum sensing method based on Johnson-Lindenstrauss; ②ACSS-SOC, an adaptive compressed spectrum sensing method based on sparsity estimation; ③ACSS-CV, an adaptive compressed spectrum sensing method based on cross-validation.

[0074] The results are shown in the attached figure, where:

[0075] Figure 4 To compare the spectrum sensing performance with the comparative methods, where the horizontal axis represents the false alarm probability and the vertical axis represents the correct detection probability, it can be seen that, under the same false alarm probability, the method of the present invention has the highest correct detection probability.

[0076] Figure 5 The CDF curves are shown for different numbers of sparse blocks (number of sparse blocks: (a) 4, (b) 5, (3) 6, (4) 7); it can be seen that the theoretical CDF value and the experimental value obtained by this method are in good agreement.

[0077] Figure 6 To compare the NMSE (normalized mean square error) of the reconstructed signals with different numbers of sparse blocks (number of sparse blocks: (a) 4, (b) 5, (c) 6, (d) 7) with the comparison method, the method of the present invention has the smallest normalized mean square error.

[0078] In summary, compared with the comparative methods, the method of the present invention has the best spectrum sensing performance.

[0079] The above description is merely a preferred embodiment of the present invention, and the scope of the claims made by the present invention is not limited thereto. The present invention has many other embodiments, and those skilled in the art can make various corresponding changes and modifications based on the present invention without departing from its spirit and essence; however, all such changes and modifications should fall within the protection scope of the appended claims.

Claims

1. An adaptive compressed spectrum sensing method based on a deterministic evaluation model, characterized in that, Includes the following steps: Step 1. Based on l 2，1 A signal reconstruction model combining norm minimization and prior knowledge mining reconstructs the spectral signal: The secondary user (SU) compresses and samples the frequency domain signal, then uses l... 2，1 Norm minimization is used to solve for a broadband signal, which serves as prior knowledge and l. 2，1 Norm minimization combined with solving for the spectral signal of the current time slot, i.e., the reconstructed signal; Step 1 includes the following steps: Step 11: Periodic compressed spectrum sensing is employed. Each communication time frame T is divided into sensing time slots of duration Ts, followed by a data transmission time slot Td. During the sensing phase, the total interval Ts is divided into J time slots, each with a length τ = Ts / J. In each time slot τ, the secondary user samples the time-domain signal x(t) at the same sampling rate and obtains ΔM compressed measurement values. After j sensing processes, the signal is reconstructed using jΔM observation samples. Specifically, the secondary user samples the N×1 frequency domain signal... Compressed sampling is performed, and the compressed observations are expressed as follows: Where Φ represents the observation matrix jΔM×N, n~N(0,σ) 2 I jΔM () indicates observation noise; Using l 2，1 Norm minimization model for signals Reconstruction is performed, and the reconstructed spectral signal is obtained. Represented as: Where δ represents the noise margin; Reconstructed spectral signal Provided as prior knowledge to step 12; Step 12: Combine the signal l 2，1 Solving for wideband signals by minimizing the norm and the inner product of prior knowledge is as follows: Using l 2，1 The inner product of the norm minimization model and prior knowledge on the signal Reconstruction is performed, and the reconstructed spectral signal is obtained. Represented as: Where β is a balancing factor used to control the relative influence of the two parts before and after the minus sign, and its value ranges from (0,1). Step 2. Derive the CDF of the reconstructed signal error and use it as the stopping criterion for observation sample acquisition to achieve adaptive stopping of the sensing process: if the CDF is less than a preset error tolerance and greater than a preset probability value, stop sampling and obtain the reconstructed spectrum signal; otherwise, continue the next sampling process; Step 2 includes the following steps: Step 21: Let To represent a true spectral signal, if the number of samples M = jΔM satisfies the following inequality Then at least 1-2exp(-γ) 2 (Γ ξ ∩S N-1 The probability of )) makes satisfy in, Representation function exist The cone at point S N-1 express The unit sphere in space; γ(Γ) ξ ∩S N-1 ) represents the set Γ ξ ∩S N-1 Gaussian complexity; ρ and C represent constants, Based on Gaussian complexity γ(Γ) ξ ∩S N-1 ) and Gaussian width w(Γ) ξ ∩S N-1 The relationship between the sample size M and the number of samples M satisfies the following inequality. v represents a constant; Step 22: Gaussian width w(Γ) ξ ∩S N-1 The upper bound of ) is represented as w(Γ ξ ∩S N-1 )≤E[dist(g,N ξ )] in, Represents ξ(x) f )exist The normal cone at the location, g ~ N(0,I) N () is a random Gaussian vector; according to Jensen's inequality, For μ≥0, fix any g, and choose any... get Define parameters: Derivation: therefore: Define parameters: Based on convex geometry theory, it is derived that: Where, μ k Represents χ k The mean of the distribution, l represents the number of non-adjacent blocks into which the sparse signal is divided, k represents the mean amount of sparse signal in each non-adjacent block, and s represents the number of blocks with signals. Thus, the cumulative distribution function (CDF) of the reconstruction error is derived: in, σ represents the standard deviation of the observation noise. The stopping criteria for the sensing process are as follows: e represents the preset error tolerance, p set This represents a preset probability value; If the stopping criterion is met, sampling stops, and the reconstructed spectrum signal is obtained. Otherwise, continue with the next sampling process; Step 3: Use energy detection method to make spectrum determination to obtain the spectrum occupancy and vacancy status.

2. The method according to claim 1, characterized in that, In step 3, the energy detection method is as follows: First, the receiving device samples within the target frequency band to obtain the received signal. This signal is represented by two assumptions: when the frequency band is idle, only noise is received; when the frequency band is occupied, the signal received is a superposition of noise and the main user signal. After sampling the signal, its energy value is calculated by accumulating the squares of the sampled signal amplitudes. Then, the energy value is compared with a preset threshold. If the energy value is lower than the threshold, the frequency band is determined to be idle; otherwise, it is determined to be occupied, thereby generating the binary state of the target frequency band.

Images