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Created August 3, 2021 13:11
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import cvxpy as cp
import numpy as np
# Number of channels
N = 10
N0 = 1 # Normalized noise level
SNR_dB = 10 # The signal to noise ratio in dB
P = 10**(SNR_dB/10) # Sum power budget defined via the SNR
# The channel specific gains drawn from Gaussian distribution
g = np.abs(np.random.randn(N, 1))
G = np.diag(g[0:,0]) # Make gains a diagonal matrix
# Problem construction
# The individual power allocations as variables (N x 1 real vector)
p = cp.Variable(N)
objective = cp.Maximize(cp.sum(cp.log(1 + (G @ p) / N0)))
constraints = []
constraints.append(p >= 0) # Positive powers constraint
constraints.append(cp.sum(p) <= P) # Total power budget
problem = cp.Problem(objective, constraints)
# Solve the problem
result = problem.solve()
# Print the optimal sum rate
# This has now natural log basis making the unit nats
print('Sum-rate (capacity) in nats', result)
# Show the power allocation
print('Power allocation', p.value)
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