STBC识别中不完全Gamma函数逆的近似解析求解算法

An analytical approximation algorithm for inverse incomplete Gamma function in STBC recognition

在雷达、通信信号的检测或识别等算法中通常会涉及到下不完全Gamma函数逆的求解.为了便于该类算法在DSP/FPGA等硬件平台上的实现,增强结果的可解释性,将求逆问题转化为对中心卡方随机变量最大值极限分布归一化常数的计算,利用极值分布的尾部等价性质,提出一种下不完全Gamma函数逆的近似解析求解算法,并将其应用于多输入输出空时分组码识别的阈值计算.仿真结果表明,当虚警概率小于0.001,天线个数小于8且样本量大于256时,该算法的相对误差小于10%,单次运算时间小于13μs,可满足实际工程应用需要.

Computing the inverse of lower incomplete gamma function is involved in signal detection and classification algorithm for radar and communication systems.In order to facilitate its implementation on DSP/FPGA and other hardware platforms and enhance the interpretability of the results,a new approximate analytical solution is proposed in this paper,in which the inverse of incomplete gamma function is transformed to the calculation of the normalized constant of limit distribution of the maximum value of central chi square random variables.By using the tail equivalence theory,the approximate analytical solution of the inverse of lower incomplete gamma function is derived and can be applied to the threshold selection for space-time block code recognition in multiple input multiple output systems.Simulation results show that when the false alarm probability is less than 0.001,the number of antennas is less than 8 and the sample size is greater than 256,the relative error of the proposed algorithm is less than 10%and its computational time is less than 13 microseconds,which can meet the requirements of the practical engineering applications.