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Summary
| Description |
English: The source code is also available in our GitHub repository. |
| Date | |
| Source | Own work |
| Author | Kirlf |
| PNG development |  This plot was created with Matplotlib. |
| Source code | Python codeimport numpy as np
from numpy import linalg as LA
import warnings
warnings.filterwarnings('ignore')
import matplotlib.pyplot as plt
def waterpouring(Mt, SNR_dB, H_chan):
SNR = 10**(SNR_dB/10)
r = LA.matrix_rank(H_chan)
H_sq = np.dot(H_chan,np.matrix(H_chan, dtype=complex).H)
lambdas = LA.eigvals(H_sq)
lambdas = np.sort(lambdas)[::-1]
p = 1;
gammas = np.zeros((r,1))
flag = True
while flag == True:
lambdas_r_p_1 = lambdas[0:(r-p+1)]
inv_lambdas_sum = np.sum(1/lambdas_r_p_1)
mu = ( Mt / (r - p + 1) ) * ( 1 + (1/SNR) * inv_lambdas_sum)
for idx, item in enumerate(lambdas_r_p_1):
gammas[idx] = mu - (Mt/(SNR*item))
if gammas[r-p] < 0: #due to Python starts from 0
gammas[r-p] = 0 #due to Python starts from 0
p = p + 1
else:
flag = False
res = []
for gamma in gammas:
res.append(float(gamma))
return np.array(res)
def openloop_capacity(H_chan, SNR_dB):
SNR = 10**(SNR_dB/10)
Mt = np.shape(H_chan)[1]
H_sq = np.dot(H_chan,np.matrix(H_chan, dtype=complex).H)
lambdas = LA.eigvals(H_sq)
lambdas = np.sort(lambdas)[::-1]
c = 0
for eig in lambdas:
c = c + np.log2(1 + SNR*eig/Mt)
return np.real(c)
def closedloop_capacity(H_chan, SNR_dB):
SNR = 10**(SNR_dB/10)
Mt = np.shape(H_chan)[1]
H_sq = np.dot(H_chan,np.matrix(H_chan, dtype=complex).H)
lambdas = LA.eigvals(H_sq)
lambdas = np.real(np.sort(lambdas))[::-1]
c = 0
gammas = waterpouring(Mt, SNR_dB, H_chan)
for idx, item in enumerate(lambdas):
c = c + np.log2(1+ SNR*item*gammas[idx]/Mt)
return np.real(c)
Mr = 4
Mt = 4
counter = 1000
SNR_dBs = [i for i in range(1, 21)]
C_open = np.empty((len(SNR_dBs), counter))
C_closed = np.empty((len(SNR_dBs), counter))
for c in range(counter):
H_chan = (np.random.randn(Mr,Mt) + 1j*np.random.randn(Mr, Mt))/np.sqrt(2)
for idx, SNR_dB in enumerate(SNR_dBs):
C_open[idx, c] = openloop_capacity(H_chan, SNR_dB)
C_closed[idx, c] = closedloop_capacity(H_chan, SNR_dB)
C_open_erg = np.mean(C_open, axis=1)
C_closed_erg = np.mean(C_closed, axis=1)
fig = plt.figure(figsize=(10, 5), dpi=300)
plt.plot(SNR_dBs, C_open_erg, label='Channel Unknown (CU)')
plt.plot(SNR_dBs, C_closed_erg, label='Channel Known (CK)')
plt.title("Ergodic Capacity")
plt.xlabel('SNR (dB)')
plt.ylabel('Capacity (bps/Hz)')
plt.legend()
plt.grid()
plt.savefig('MIMO_Capacity.png')
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:07, 15 February 2019 | | 3,000 × 1,500 (160 KB) | Kirlf | User created page with UploadWizard |
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