极坐标方法产生高斯白噪声

产生N（0,1）高斯白噪声序列，最常见的方法是极坐标法，其计算步骤如下所示：

（1）　　产生两个独立同分布的随机序列（0,1），U1，U2；

（2）　　令V1=2U1-1；V2=2U2-1；并计算S=V1^2+V2^2

（3）　　若S>1,则返回第一步；否则计算Y=sqrt（-2*ln（S）/S）

（4）　　令实部I=V1*Y，虚部Q=V2*Y，再求Output=I+Q*i，即可得到随机复数高斯白噪声序列。

理论上，可证明上述产生的I、Q两路序列为相互独立的高斯白噪声序列。由于第（3）部，序列以一定的概率被去掉了,为了产生长度为N的高斯白噪声序列，U1、U2长度应为1.27N。上述算法，适用于长生长度较长的高斯白噪声序列，不适用于产生短的高斯白噪声序列。

-Polar method for generating Gaussian white noise N (0,1) Gaussian white noise sequence, the most common approach is the polar coordinate method, the calculation steps are as follows: (1) generate two independent and identically distributed random sequence (0, 1), U1, U2　(2) so that V1 = 2U1-1　V2 = 2U2-1　and calculate S = V1 ^ 2+V2 ^ 2　(3) If S>　1, then return to the first step　otherwise calculate Y = sqrt (-2* ln (S)/S)　(4) so ​ ​ that the real part of I = V1* Y, the imaginary part of Q = V2* Y, then seek Output = I+Q* i, you can get a random complex white Gaussian noise sequence. Theoretically, these can be produced to prove I, Q two independent sequence of Gaussian white noise sequence. Since the first (3) of the sequence with a certain probability of being removed, in order to produce a length N of Gaussian white noise sequence, U1, U2 length should 1.27N. The above algorithm for a longer length of Gaussian white noise sequence longevity, not to produce a short wh