import numpy as np
import matplotlib.pyplot as plt
from bessel import ric_besselh,ric_besselh_derivative
import pandas as pd

# This file computes the monostatic RCS of a PEC sphere
# It uses the MIE series to provide an analytical solution for the monostatic RCS
# RCS = (j / (kr)) sum_n=1toinf [  -1**n  (2n+1)  (kr * j(n-1) - n * jn) / (kr * H(1)(n-1) - n * H(1)n)  - jn/H(1)n  ]  
#
# H(2)(n) = jn - 1.0j yn)
# jn --> Spherical-Bessel Function of the 1st kind of order n
# yn --> Spherical-Bessel Function of the 2nd kind of order n
# H(1)(n) = jn + 1.0j yn)
# jn --> Spherical-Bessel Function of the 1st kind of order n
# yn --> Spherical-Bessel Function of the 2nd kind of order n

frequency = np.linspace(0.05e9,5e9,1000)
wavelength = 3e8 / frequency


# Radius of circle in meters
Radius = 0.1
OrderN = 100

AreaOfCircle = np.pi * Radius**2

RCS = np.zeros(len(wavelength),dtype=complex)
RCS_NORM = np.zeros(len(wavelength))

for index,w in enumerate(wavelength):
    
    k = 2*np.pi/w
    kr = k * Radius
    sum_ = 0.0 + 0.0j
    
    kr_vec = kr * np.ones(1)
    Order = np.transpose(np.linspace(0,OrderN,OrderN+1))
    H = ric_besselh(Order,kr_vec,2)
    Hp = ric_besselh_derivative(Order,kr_vec,2)
    
    for n_ in range(OrderN):

        n = n_ + 1         

        # Sum up the series
        sum_ = (-1.0)**n * (2.0*n+1.0) / ( H[n] * Hp[n] )
        RCS[index] = RCS[index] + sum_
        
    RCS[index] =  abs(RCS[index])**2 * w**2 / (4 * np.pi)
    RCS_NORM[index] = RCS[index] / AreaOfCircle
    
Normalized_circumference = 2*np.pi * Radius / wavelength

plt.figure()
plt.plot(Normalized_circumference,RCS_NORM)   
plt.grid()
plt.xticks(np.linspace(0,10,11))
plt.xlabel("Circumference of Circle")
plt.ylabel("Normalized RCS by Area of Circle") 
plt.show()

plt.figure()
plt.plot(frequency/1e9,10*np.log10(RCS))   
plt.grid()
plt.xticks(np.linspace(0,10,21))
plt.xlim([min(frequency/1e9),max(frequency/1e9)])
plt.xlabel("Frequency (GHz)")
plt.ylabel("RCS (dBsm)") 
plt.show()

output_df = pd.DataFrame({'Frequency':frequency/1e9, 'coRCS':np.real(10*np.log10(RCS))})
output_df.to_csv("RCS_ANALYTIC.xlsx", index=False)