基于隨機(jī)矩陣非漸近譜理論的協(xié)作頻譜感知算法研究

許煒陽; 李有均; 徐宏乾; 謝匯強(qiáng)

doi:10.11999/JEIT170309

基于隨機(jī)矩陣非漸近譜理論的協(xié)作頻譜感知算法研究

doi: 10.11999/JEIT170309

基金項(xiàng)目:

國(guó)家自然科學(xué)基金(61201177)

計(jì)量
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2017-04-07
- 修回日期: 2017-09-01
- 刊出日期: 2018-01-19

Study on Cooperative Spectrum Sensing Algorithm Based on Random Matrix Non-asymptotic Spectral Theory

Funds:

The National Natural Science Foundation of China (61201177)

摘要

摘要: 將隨機(jī)矩陣的非漸近譜理論應(yīng)用到協(xié)作頻譜感知中，對(duì)接收信號(hào)樣本協(xié)方差矩陣的最大特征值和最小特征值進(jìn)行分析，該文提出一種精確的最大最小特征值差(Exact Maximum Minimum Eigenvalue Difference, EMMED)的協(xié)作感知算法。對(duì)于任意給定的協(xié)作用戶個(gè)數(shù)K和采樣點(diǎn)數(shù)N，首先推導(dǎo)了最大最小特征值之差的精確概率密度函數(shù)(Probability Density Function, PDF)和累積分布函數(shù)(Cumulative Distribution Function, CDF)，然后利用該分布函數(shù)設(shè)計(jì)了所提算法的判決閾值。理論分析表明，EMMED算法的判決閾值較已有的漸進(jìn)最大最小特征值差(Asymptotic Maximum Minimum Eigenvalue Difference, AMMED)檢測(cè)更為精確，算法無需主用戶信號(hào)特征并且能夠?qū)乖肼暡淮_定度影響。仿真結(jié)果表明，存在噪聲不確定度的感知環(huán)境下，EMMED算法較已有的精確最大特征值(Exact Maximum Eigenvalue, EME)和EMMER等頻譜感知算法具有更好的檢測(cè)性能。
- 頻譜感知 /
- 隨機(jī)矩陣 /
- 非漸近譜理論 /
- 最大最小特征值
Abstract: The non-asymptotic spectral theory of random matrix is applied to cooperative spectrum sensing, the maximum eigenvalue and the minimum eigenvalue of the sampled signal covariance matrix are analyzed and an Exact Maximum Minimum Eigenvalues Difference (EMMED) algorithm is proposed. For any given numbers of cooperative users K and sampling points N, the exact Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of the difference between the maximum and minimum eigenvalues are derived. Then, an accurate decision threshold is designed by using the distribution function. Theoretical analysis shows, the EMMED algorithm has the characteristics that the decision threshold is more accurate than the existing Asymptotic Maximum Minimum Eigenvalue Difference (AMMED) algorithm, without the characteristics of the main user signal and not affected by noise uncertainty. In addition, the simulation results show that the EMMED algorithm has better detection performance than the existing Exact Maximum Eigenvalue (EME) and EMMER algorithms in the real sensing environment with noisy uncertainty.
- Spectrum sensing /
- Random matrix /
- Non-asymptotic spectral theory /
- Maximum minimum eigenvalue

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參考文獻(xiàn)(21)

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