sumrate-cvxpy.py

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)