能量检测中的BPSK信号最优检测门限

在认知无线电中,授权用户对主用户进行频谱感知时,会存在使得虚警与漏检概率之和最小的最优检测门限。以研究高斯白噪声环境下BPSK信号的有效检测问题为目的。通过对能量检测统计量的数学分布进行理论推导,将最优检测门限问题转化为和值最小的求解问题,给出了由采样点数、噪声方差、信噪比所决定的最优检测门限计算公式,并给出证明。在不同信噪比下对和值曲线变化规律的仿真说明了最优检测门限的存在性。通过对文中门限和恒虚警概率门限下的检测概率性能分析、文中门限和恒检测概率门限下的虚警概率性能分析、以及不同指标变化时其他2种门限向文中门限收敛的性能分析,说明了最优检测门限下的检测性能较优。此外,蒙特卡洛实验验证了理论分析的正确性。

The Best Detection Threshold for BPSK Signals Based on Energy Detection Method

Effective detection problem for BPSK (binary phase shift keying) signals under condition of Gaussian white noise environments is studied. In cognitive radio, when second user senses spectrum from first user, this makes the best detection threshold with the minimum of sum of false alarm and missed detection rate in existence. By theoretical derivation for distribution character of energy detection static, the best detection threshold problem is converted to solution of the minimum of the sum, computation expression is determined by sampling length, noise variance and signal to noise ratio (SNR) are given. The simulation of sum value curve variety in different SNR shows that the best detection threshold is in existence. The performance of the best threshold is even better than before by analysis for detection ratio performance between the threshold and the one in constant false alarm ratio (CFAR), false alarm ratio performance between the threshold and the one in constant detection ratio (CDR), other two thresholds'' convergence to the threshold performance. Besides, Monte Carlo experiment shows that the mathematic analysis is correct.