基于数值分析理论的低复杂度MED算法

经典的最大特征值检测（MED）算法在检测相关信号时具有优异的性能.然而，随着信号维度的不断增大，MED算法面临着严重的感知判决量和判决门限计算的效率和实现问题，从而极大地限制了该算法在现代认知通信系统中的进一步应用.为此，提出了一种基于数值分析理论框架的低复杂度MED频谱感知算法.所提算法利用Rayleigh商加速幂法迭代地计算感知判决量，与经典的幂法相比，在检测高维信号时具有更快的收敛速度；此外，不同于经典的查表法，新算法基于三次样条插值法快速、准确地确定任意给定目标虚警概率所对应的感知判决门限.所提MED算法在保持原有算法检测性能的同时，有效提升了计算效率，降低了算法实现复杂度；其对于高维条件下的频谱感知问题尤其具有吸引力.最后，仿真结果证明了所提算法的有效性.

Low Complexity MED Algorithm Based on Numerical Analysis Theories

The classical Maximum Eigenvalue Detection (MED) algorithm has an excellent performance in detecting correlated signals. However, with the increasing signal dimensionality, the MED algorithm faces serious problems in the calculation efficiency and implementation of the test statistic and decision threshold, which greatly limits the further application of the algorithm in modern cognitive communication systems. To this end, a low-implementation complexity MED algorithm based on a numerical analysis theoretical framework is proposed. The new algorithm uses the Rayleigh quotient accelerated power method to iteratively compute the test statistic, which has a fast convergence rate in detecting high-dimensional signals compared with the classical power method. Meanwhile, different from the classical look-up table method, the new threshold calculation method based on the cubic spline interpolation method is proposed, which can quickly determine the decision threshold corresponding to any given target false-alarm probability. The proposed MED algorithm effectively improves the computational efficiency and reduces the complexity of algorithm implementation while maintaining the detection performance of the original algorithm, which is particularly attractive for spectrum sensing problems in high-dimensional conditions. Finally, the simulation results demonstrate the effectiveness of the proposed algorithm.