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I am trying to generate BER-SNR curve in Rayleigh channel using BPSK modulation. Can anyone help me to find what is wrong with the python code? The theoretical BER differs from the simulated BER. The red dotted line is theoretical and the blue one is simulated.

import math as mt
import numpy as np
import matplotlib.pyplot as plt
import numpy.random as nr
from scipy.linalg import toeplitz

# ------------Simulation parameters------------------------
N = 500 #No.of symbols
H_n = 10 #No.of channel elements
h_ray = np.zeros((H_n, 1), dtype = complex)

# ---------------------------------------------------------
EbN0dB = np.array(range(0, 11))
itr = len(EbN0dB)
ber = [None] * itr
theoreticalBER = [None] * itr

# -----------------------------Transmitter----------------------------
s = 2 * (nr.rand(N, 1) >= 0.5) - 1 # BPSK

# ------------------------------Channel-------------------------------
h_ray = (1/mt.sqrt(2)) * (nr.randn(H_n, 1) + 1j * nr.randn(H_n, 1)) 
 # Rayleigh fading channel
z = np.zeros((N-1,1))
c = np.concatenate((h_ray, z), axis=0)
r = np.concatenate(([h_ray[0]], np.zeros((1, N-1))), axis=1)
h_ray_y=toeplitz(c, r) # Toeplitz matrix instead of convolution

y_ray = np.dot(h_ray_y, s)

for n in range(itr):
 EbN0dB_n = EbN0dB[n]
 EbN0 = 10.0 ** (-EbN0dB_n/ 20.0)
 noise = 1/mt.sqrt(2) * (nr.randn(N+H_n-1) + 1j * nr.randn(N+H_n-1))
 r_ray = y_ray + EbN0 * noise
 # --------------------------Receiver------------------------------
 r_t = np.dot(np.dot(np.linalg.pinv(np.dot(h_ray_y.T, h_ray_y)), h_ray_y.T), r_ray) # (H.T * H)^(-1)*H.T*received 
 r_d = 2 * (np.real(r_t) >= 0) - 1
 errors = (s != r_d).sum()
 ber[n] = 1.0 * errors / N

 EbN0_th = 10.0 ** (EbN0dB_n / 10.0)
 theoreticalBER[n] = 0.5 *(1 - mt.sqrt(EbN0_th/ (1 + EbN0_th)))
ber=np.asanyarray(ber)
#-------------------------------------------------------------------------
plt.plot(EbN0dB, np.log10(ber), '--bo')
plt.plot(EbN0dB, np.log10(theoreticalBER), 'ro')
plt.xlabel('EbN0(dB)')
plt.ylabel('BER')
plt.grid(True)
plt.title('BPSK - Rayleigh')
plt.show()