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I'm trying to calculate Ricean Fading PDF using following equation. RIcean Fading PDF. where 'y' is normalized envelope and 'gamma' is SNR

if the K value is large, then 

math.exp(-((1.+_gamma)*pow(_y,2.) + _gamma))

exp results in big floating point (e.q. 1.01e-5088). in python it will shows '0.0' as value

mpmath.besseli(0,2. * _y * np.sqrt(_gamma * (1. + _gamma)))

the value of Bessel Function shows big int value (e.q. 7.78e+5092). in python it will shows '**inf**' value

How can i store big integer and floating point value in python and calculate the pdf?

def rice_pdf(self, _y, _gamma):
   return 2. * _y * (1. + _gamma) * math.exp(-((1.+_gamma)*pow(_y,2.) + _gamma)) * special.i0(2. * _y * np.sqrt(_gamma * (1. + _gamma)))

Thanks.

LO_py
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1 Answers1

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If you have a way to compute the logarithm of the bessel function, you can avoid the multiplication of very large and very small numbers by transforming into a summation with subsequent exonentiation, which should solve the numerical problems (exploit the fact that exp(a) * exp(b) == exp(a + b)).

def rice_pdf(_y, _gamma):
    a = np.log(2. * _y * (1. + _gamma))
    b = -((1.+_gamma)*pow(_y,2.) + _gamma)
    c = lni(2. * _y * np.sqrt(_gamma * (1. + _gamma))) 
    return np.exp(a + b + c)

This function assumes there exist an implementation of lni that computes log(i0(z)). However, I am aware of no existing implementation of such a function. You can work around this by using mpmath for intermediate results:

def lni(z):
    i0 = mpmath.besseli(0, z)  # may become a big number
    logi0 = mpmath.log(i0)  # logarithm brings big number into sensible range
    return float(logi0)  # convert back to normal floating point
MB-F
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  • Wow. exactly it is, it didn't comes to mind to use exponential solution. Thank you so much. it was great help. – LO_py Apr 10 '17 at 01:32