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WMMSE_ADMM_Func.py
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WMMSE_ADMM_Func.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue May 5 11:20:11 2020
@author: Sucharita Chakraborty
"""
import numpy as np
#The functions in this script implement Algorithm 2 and Algorithm 1 using ADMM
#This function is for saving run time, its implementataion is the same as the last function in this script.
#The difference from the last function is that arrays except power coefficients are not saved for a fair comparison of run times.
def WMMSE_ADMM_timing(L,K, Pmax, a_MR, B_MR):
#Initialize the square roots of the power coefficients
mu_MR_WMMSE = 0.1*np.sqrt(Pmax/K)*np.ones((L,K))
#Solution accuracy (epsilon_wmmse)
delta = 0.01
#ADMM penalty parameter
penalty = 0.001
#Initialize the objective function as zero
objLower=0
#This is for computing the objective function and computing the other terms later
SINRnumerator = np.power( np.abs( np.sum(mu_MR_WMMSE * a_MR , axis = 0)), 2)
SINRdenominator = np.ones(K)
for k in range (0,K):
for i in range(0,K):
SINRdenominator[k] = SINRdenominator[k]+ mu_MR_WMMSE[:,i:i+1].T @ B_MR[:,:,k,i] @ mu_MR_WMMSE[:,i:i+1]
SINR = SINRnumerator/(SINRdenominator-SINRnumerator)
#Current objective function
objUpper = np.sum( np.log2(1 + SINR) )
#Continue iterations until stopping criterion in (52) is satisfied (prelogfactors are omitted)
while np.power(np.abs(objUpper - objLower), 2) > delta:
#Update the old objective by the current objective
objLower = objUpper
#Equation (53)
v = np.sqrt(SINRnumerator) / SINRdenominator
#Equation (56)
e = 1 - SINRnumerator/SINRdenominator
#Equation (55)
w = 1/e
#Make preparations for ADMM algorithm in Algorithm 1
Ainv = np.zeros((L,L,K), dtype = 'float')
c = np.zeros((L,K), dtype = 'float')
for k in range (0,K):
A = (penalty/2)*np.eye(L)
for i in range (0,K):
A = A + w[i] * v[i]**2 * B_MR[:,:,i,k]
Ainv[:,:,k] = np.linalg.inv(A)
c[:,k] = w[k] * v[k] * a_MR[:,k]
# Dual variable initialization for ADMM
g = np.zeros((L,K))
#Start the ADMM
#Initial large difference in (51) to start the algoritm
diff = 100
#Set the iteration counter for ADMM
inner_iteration = 0
#Perturbed random initialization mentioned in the paper
q = mu_MR_WMMSE*(1+np.random.rand(L,K))
#Run Algorithm 1 until the stopping criterion in (51) is satisfied
while diff>0.001:
inner_iteration += 1
#Update the first block of primal variables as in (48)
for k in range (0,K):
c2= c[:,k:k+1] + (penalty/2) * (q[:,k:k+1] + g[:,k:k+1])
mu_MR_WMMSE[:,k:k+1]= Ainv[:,:,k] @ c2
#Update the second block of primal variables as in (49)
q = mu_MR_WMMSE - g
q_norm = np.linalg.norm(q,axis=1)
for l in np.argwhere(q_norm>np.sqrt(Pmax)):
q[l,:] = q[l,:]*np.sqrt(Pmax)/q_norm[l]
#Update dual variable g as in (50)
g = q - mu_MR_WMMSE + g
#To prevent any misconvergence issues in the first iterations, we guarentee at least 5 ADMM iterations are run
if inner_iteration>5:
diff = np.linalg.norm(mu_MR_WMMSE-q,'fro')/np.linalg.norm(mu_MR_WMMSE,'fro')
# Update the variables and compute the new objective
SINRnumerator = np.power( np.abs( np.sum(mu_MR_WMMSE * a_MR , axis = 0)), 2)
SINRdenominator = np.ones(K)
for k in range (0,K):
for i in range(0,K):
SINRdenominator[k] = SINRdenominator[k]+mu_MR_WMMSE[:,i:i+1].T@ B_MR[:,:,k,i]@ mu_MR_WMMSE[:,i:i+1]
SINR = SINRnumerator/(SINRdenominator-SINRnumerator)
objUpper = np.sum(np.log2(1+SINR))
#Square roots of the power coefficients
return mu_MR_WMMSE.T
def WMMSE_ADMM_iteration(L,K, Pmax, prelogFactor, a_MR, B_MR):
mu_MR_WMMSE = 0.1*np.sqrt(Pmax/K)*np.ones((L,K))
delta = 0.01
penalty = 0.001
objLower=0
SINRnumerator = np.power( np.abs( np.sum(mu_MR_WMMSE * a_MR , axis = 0)), 2)
SINRdenominator = np.ones(K)
for k in range (0,K):
for i in range(0,K):
SINRdenominator[k] = SINRdenominator[k]+ mu_MR_WMMSE[:,i:i+1].T @ B_MR[:,:,k,i] @ mu_MR_WMMSE[:,i:i+1]
SINR = SINRnumerator/(SINRdenominator-SINRnumerator)
objUpper = np.sum( np.log2(1 + SINR) )
SE_WMMSE_ADMM = np.zeros((200), dtype = 'float')
objval = np.zeros((200))
iteration = 0
objval_1blk = np.zeros((1000))
objval_2blk = np.zeros((1000))
while np.power(np.abs(objUpper - objLower), 2) > delta:
SE_WMMSE_ADMM[iteration] = prelogFactor * np.sum( np.log2(1 + SINR) )
objLower=objUpper
v = np.sqrt(SINRnumerator) / SINRdenominator
e = 1 - SINRnumerator/SINRdenominator
w = 1/e
A2 = np.zeros((L,L,K), dtype = 'float')
Ainv = np.zeros((L,L,K), dtype = 'float')
c2 = np.zeros((L,K), dtype = 'float')
for k in range (0,K):
for i in range (0,K):
A2[:,:,k] = A2[:,:,k] + w[i] * v[i]**2 * B_MR[:,:,i,k]
Ainv[:,:,k] = np.linalg.inv(A2[:,:,k]+(penalty/2)*np.eye(L))
c2[:,k] = w[k] * v[k] * a_MR[:,k]
# Variable initialization for ADMM
g = np.zeros((L,K))
#Start the ADMM
diff = 100
inner_iteration = 0
q = mu_MR_WMMSE*(1+np.random.rand(L,K))
while diff>0.001:
for k in range (0,K):
c= c2[:,k:k+1] + (penalty/2) * (q[:,k:k+1] + g[:,k:k+1])
mu_MR_WMMSE[:,k:k+1]= Ainv[:,:,k] @ c
if iteration==0:
objvalk = np.zeros((K))
for k in range(0, K):
objvalk[k] = mu_MR_WMMSE[:,k:k+1].T @ A2[:,:,k] @ mu_MR_WMMSE[:,k:k+1] - 2 * c2[:,k:k+1].T @ mu_MR_WMMSE[:,k:k+1]
objval_1blk[inner_iteration] = np.sum (objvalk)
q = mu_MR_WMMSE - g
q_norm=np.linalg.norm(q,axis=1)
for l in np.argwhere(q_norm>np.sqrt(Pmax)):
q[l,:]=q[l,:]*np.sqrt(Pmax)/q_norm[l]
if iteration==0:
objvalk = np.zeros((K))
for k in range(0, K):
objvalk[k] = q[:,k:k+1].T @ A2[:,:,k] @ q[:,k:k+1] - 2 * c2[:,k:k+1].T @ q[:,k:k+1]
objval_2blk[inner_iteration] = np.sum (objvalk)
inner_iteration += 1
#Update dual variable g
g = q - mu_MR_WMMSE + g
#
if inner_iteration>5:
diff = np.linalg.norm(mu_MR_WMMSE-q,'fro')/np.linalg.norm(mu_MR_WMMSE,'fro')
if iteration==0:
inner_iteration2 = inner_iteration
SINRnumerator = np.power( np.abs( np.sum(mu_MR_WMMSE * a_MR , axis = 0)), 2)
SINRdenominator = np.ones(K)
for k in range (0,K):
for i in range(0,K):
SINRdenominator[k] = SINRdenominator[k]+mu_MR_WMMSE[:,i:i+1].T@ B_MR[:,:,k,i]@ mu_MR_WMMSE[:,i:i+1]
SINR = SINRnumerator/(SINRdenominator-SINRnumerator)
objUpper = np.sum(np.log2(1+SINR))
A1 = np.zeros((L,L,K), dtype = 'float')
c1 = np.zeros((L,K), dtype = 'float')
for k in range (0,K):
for i in range (0,K):
A1[:,:,k] = A1[:,:,k] + w[i] * v[i]**2 * B_MR[:,:,i,k]
c1[:,k] = w[k] * v[k]* a_MR[:,k]
objvalk = np.zeros((K))
for k in range(0, K):
objvalk[k] = mu_MR_WMMSE[:,k:k+1].T @ A1[:,:,k] @ mu_MR_WMMSE[:,k:k+1] - 2 * c1[:,k:k+1].T @ mu_MR_WMMSE[:,k:k+1]
objval[iteration] = np.sum (objvalk)
iteration += 1
return (mu_MR_WMMSE.T, SE_WMMSE_ADMM, objval, iteration, objval_1blk, objval_2blk, inner_iteration2)