File:MIMO Capacity.png
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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:
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:07, 15 February 2019 | | 3,000 × 1,500 (160 KB) | wikimediacommons>Kirlf | User created page with UploadWizard |
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