Ring Law simulation for a large random matrix with gaussain variates

ringLaw.py

#!/usr/bin/env python

import numpy as np
import matplotlib.pyplot as plt

C = 1
for N in range(20,300,70):

	tit = 'N = ' + str(N)
	
	m = np.random.randn(N,N)/np.sqrt(N)
	w,v = np.linalg.eig(m)



	fig = plt.figure()
	fig.subplot(2,2,C)
	fig.plot(np.real(w), np.imag(w), '.')
	fig.title(tit)
	ax = fig.gca()
	ax.set_xlim([-2,2])
	ax.set_ylim([-2,2])
	ax.set_aspect('equal')
	ax.grid()

	# ax = fig.add_subplot(2,2,C)
	# ax.imshow(np.abs(w))

	C+=1

plt.show()

# Massive MIMO as a Big Data System

# Large random matrices are used models for the massive data
# arising from the monitoring of the massive MIMO system.

# A standard random matrix is systematically formed to map the system.

# A kind of high-dimensional analysis is then performed to compare experimental 
# findings with Random Matrix  theoretical predictions (such as Marchenko-Pastur Law, 
# Ring Law) in order to differentiate the signal from white noise