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uwmmse.py
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import pdb
import tensorflow as tf
import tensorflow_addons as tfa
from activations import *
# UWMMSE
class UWMMSE(object):
# Initialize
def __init__( self, Pmax=1., tx_antennas=1, rx_antennas=1, signal_dim=1, var=7e-10, feature_dim=1, batch_size=64, layers=4, learning_rate=1e-3, max_gradient_norm=5.0, exp='uwmmse' ):
self.Pmax = tf.cast( Pmax, tf.float64 )
self.variance = var
self.feature_dim = feature_dim
self.batch_size = batch_size
self.layers = layers
self.learning_rate = learning_rate
self.max_gradient_norm = max_gradient_norm
self.exp = exp
self.global_step = tf.Variable(0, trainable=False, name='global_step')
self.T = tx_antennas
self.R = rx_antennas
self.d = signal_dim
self.build_model()
# Build Model
def build_model(self):
self.init_placeholders()
self.build_network()
self.build_objective()
def init_placeholders(self):
# CSI [Batch_size X Nodes X Nodes]
self.H = tf.compat.v1.placeholder(tf.complex128, shape=[None, None, None, self.R, self.T], name="H")
# Normlize input to gcn
def inp_norm(self):
mu = tf.reduce_mean( self.H_gcn, axis=[-1], keepdims=True )
sig = tf.cast( tf.math.reduce_std( self.H_gcn, axis=[-1], keepdims=True ), tf.complex128 )
H = tf.math.divide( ( self.H_gcn - mu ), sig )
return(H)
# Declare complex trainable variables (omega)
def dec_com_var(self, use_bias=True, name='_', shape=(1,1)):
w_r = tf.compat.v1.get_variable( name=name+'w_r', shape=shape, initializer=tf.initializers.glorot_uniform(), dtype=tf.float64)
w_i = tf.compat.v1.get_variable( name=name+'w_i', shape=shape, initializer=tf.initializers.glorot_uniform(), dtype=tf.float64)
w = tf.complex(w_r,w_i)
if use_bias:
b_r = tf.compat.v1.get_variable( name=name+'b_r', shape=(shape[-1],), initializer=tf.initializers.glorot_uniform(), dtype=tf.float64)
b_i = tf.compat.v1.get_variable( name=name+'b_i', shape=(shape[-1],), initializer=tf.initializers.glorot_uniform(), dtype=tf.float64)
b = tf.complex(b_r,b_i)
return(w,b)
return(w)
# Building network
def build_network(self):
# Retrieve number of nodes for initializing V
self.nNodes = tf.shape( self.H )[1]
# Extract diagonals
self.dia = tf.transpose( tf.compat.v1.matrix_diag_part(tf.transpose(self.H,(0,3,4,1,2))), (0,3,1,2) )
# Variance tensor
self.var = tf.cast( self.variance * tf.eye( self.R, batch_shape=[self.nNodes], dtype=tf.float64 ), tf.complex128 )
self.var = tf.tile( tf.expand_dims( self.var, axis=0 ), tf.constant( [self.batch_size,1,1,1] ) )
if self.exp == 'uwmmse':
# Learn GCN i/p
w, b = self.dec_com_var(name='1x1_conv', shape=(self.R * self.T,1))
if self.T < self.R:
self.H_gcn = tf.reshape( tf.transpose( self.H, (0,1,2,4,3) ), [ self.batch_size, self.nNodes, self.nNodes, self.R * self.T ] )
else:
self.H_gcn = tf.reshape( self.H, [ self.batch_size, self.nNodes, self.nNodes, self.R * self.T ] )
self.H_gcn = tf.add( tf.matmul( self.H_gcn, w ), b )
self.H_gcn = tf.squeeze(tf.squeeze( self.H_gcn ))
self.H_gcn = self.inp_norm()
# Diagonal for GCN i/p
self.dH_gcn = tf.linalg.diag_part( self.H_gcn )
self.dH_gcn = tf.compat.v1.matrix_diag( self.dH_gcn )
# Maximum V = sqrt(Pmax)
Vmax = tf.math.sqrt(self.Pmax/(2 * self.T * self.d))
# Initialize V
V = Vmax * tf.ones([self.batch_size, self.nNodes, self.T, self.d], dtype=tf.float64)
V = tf.complex(V,V)
self.V = V
# Iterate over layers k
for l in range(self.layers):
with tf.compat.v1.variable_scope('Layer{}'.format(1), reuse=tf.compat.v1.AUTO_REUSE):
# Compute U^k
U = self.U_block( V )
self.U = U
# Compute W_wmmse^k
W_wmmse = self.W_block( U, V )
if self.exp == 'wmmse':
# Compute V^k
V = self.V_block( U, W_wmmse, tf.complex(tf.cast(0.0, tf.float64),tf.cast(0.0, tf.float64)) )
else:
# Learn xi^k
a = self.gcn('a')
# Expand xi^k across MLP layers
aw1 = tf.expand_dims(a[:,:,:5],-2)
ab1 = tf.expand_dims(a[:,:,5:10],-2)
aw2 = tf.expand_dims(a[:,:,10:15],-1)
ab2 = tf.expand_dims(a[:,:,15:],-1)
# Phi_xi^k
phi = cart_relu( tf.add( tf.matmul( cart_leaky_relu( tf.add( tf.matmul(W_wmmse, aw1), ab1 ) ), aw2 ), ab2 ) )
# Compute W^k = W_wmmse + f_lin(W_wmmse;theta)
W = W_wmmse + phi
# mu
mu = self.dec_com_var(use_bias=False, name='mu',shape=[1])
# Compute V^k
V = self.V_block( U, W, mu )
## Saturation non-linearity -> V if Tr(V'V) < Pmax ; V * sqrt(P)/Vfrobenius if Tr(V'V) > Pmax
norm = tf.math.real(tf.linalg.norm(V, ord='fro',axis=[-2,-1]))
mask = tf.math.divide( tf.math.multiply(norm, ( 0.5 + 0.5 * tf.math.sign( tf.math.square(norm) - self.Pmax ) ) ), tf.math.sqrt(self.Pmax) ) + ( 0.5 + 0.5 * tf.math.sign( self.Pmax - tf.math.square(norm) ) )
mask = tf.cast( tf.expand_dims( tf.expand_dims(mask,axis=-1), axis=-1 ), tf.complex128 )
V = tf.math.divide( V, mask )
self.V = V
# Final V
self.pow_alloc = tf.math.real(tf.linalg.norm(V, ord='fro',axis=[-2,-1]))
def U_block(self, V):
# Identity
I = tf.cast(tf.eye(self.R, dtype=tf.float64),tf.complex128)
# H_ii'V_i
num = tf.compat.v1.matmul( self.dia, V )
# sigma^2*I + sum_j( (H_ji V_jV_j' H_ji' )
den = tf.reduce_sum( tf.matmul( self.H, tf.matmul( tf.expand_dims( tf.matmul( V, tf.linalg.adjoint( V ) ), axis=1 ), tf.linalg.adjoint( self.H ) ) ), axis=2 ) + self.var
# U = den^-1 num
return( tf.compat.v1.matmul( tf.compat.v1.matrix_inverse( den + 1e-4*I ), num ) )
# Sum-rate = z
def W_block(self, U, V):
# Identity
I = tf.cast(tf.eye( self.d, batch_shape=[self.nNodes], dtype=tf.float64 ),tf.complex128)
I = tf.tile( tf.expand_dims( I, axis=0 ), tf.constant( [self.batch_size,1,1,1] ) )
# 1 - U_i' H_ii V_i
den = I - tf.matmul( tf.linalg.adjoint( U ), tf.matmul( self.dia, V ) )
#pdb.set_trace()
# W = den^-1
return( tf.compat.v1.matrix_inverse( den ) )
def V_block(self, U, W, mu):
# Identity
I = tf.cast(tf.eye(self.T, dtype=tf.float64),tf.complex128)
# H_ii U_i W_i
num = tf.matmul( tf.linalg.adjoint(self.dia), tf.matmul( U, W ) )
# expand mu
mu = tf.reshape( mu, shape=[1,1,1,1,1] )
# sum_j( (H_ij' U_j W _j U_j' H_ij )
den = tf.reduce_sum( tf.math.add( tf.matmul( tf.linalg.adjoint( self.H ), tf.matmul( tf.expand_dims( tf.matmul( tf.matmul( U, W ), tf.linalg.adjoint( U ) ), axis=2 ), self.H ) ), mu ), axis=1 )
# V = den^-1 num
return( tf.compat.v1.matmul( tf.compat.v1.matrix_inverse( den + 1e-4*I ), num ) )
def gcn(self, name):
# 2 Layers
L = 2
# Dims
inp_dim = self.R+self.T
input_dim = [inp_dim,32]
output_dim = [32,16]
## NSI [Batch_size X Nodes X Features]
x = tf.concat([self.U,self.V], -2) #GV: the NSI is now the most recent U and V values at each node
with tf.compat.v1.variable_scope('gcn_'+name):
##Reduce the NSI x
w, b = self.dec_com_var(name='nsi', shape=(self.d, 1))
x = tf.squeeze( cart_leaky_relu(tf.add(tf.matmul(x, w),b) ) )
for l in range(L):
with tf.compat.v1.variable_scope('gc_l{}'.format(l+1)):
## Weights, biases
w0, b0 = self.dec_com_var(name='tr0', shape=(input_dim[l], output_dim[l]))
w1, b1 = self.dec_com_var(name='tr1', shape=(input_dim[l], output_dim[l]))
# XW
x1 = tf.matmul(x, w1)
x0 = tf.matmul(x, w0)
# diag(A)XW0 + AXW1
x1 = tf.matmul(self.H_gcn+.001, x1)
x0 = tf.matmul(self.dH_gcn, x0)
## AXW + B
x1 = tf.add(x1, b1)
x0 = tf.add(x0, b0)
# Combine
x = x1 + x0
# activation(AXW + B)
if l == L-1:
x = cart_leaky_relu(x)
else:
x = cart_leaky_relu(x)
# Output
output = x
return output
def build_objective(self):
# H_ii V_i V_i' H_ii'
num = tf.matmul( tf.matmul( tf.matmul( self.dia, self.V ), tf.linalg.adjoint( self.V ) ), tf.linalg.adjoint( self.dia ) )
# sigma^2 + sum_j j ~= i ( (H_ji)^2 * (v_j)^2 )
den = tf.reduce_sum( tf.matmul( self.H, tf.matmul( tf.expand_dims( tf.matmul( self.V, tf.linalg.adjoint( self.V ) ), axis=1 ), tf.linalg.adjoint( self.H ) ) ), axis=2 ) + self.var - num
# rate = log(1 + SINR)
self.rate = tf.math.log( tf.math.real( tf.compat.v1.matrix_determinant( tf.cast( tf.eye( self.R, batch_shape=[self.nNodes], dtype=tf.float64 ), tf.complex128 ) + tf.matmul( tf.compat.v1.matrix_inverse( den ), num ) ) ) ) / tf.cast( tf.math.log( 2.0 ), tf.float64 )
# Sum Rate = sum_i ( rate )
self.utility = tf.reduce_sum( self.rate, axis=1 )
self.util = tf.reduce_mean( self.rate, axis=1 )
# Minimization objective
self.obj = -tf.reduce_mean( self.util )
if self.exp == 'uwmmse':
self.init_optimizer()
def init_optimizer(self):
# Gradients and SGD update operation for training the model
self.trainable_params = tf.compat.v1.trainable_variables()
# Optimizer
self.opt = tfa.optimizers.NovoGrad(learning_rate=self.learning_rate)
# Compute gradients of loss w.r.t. all trainable variables
self.gradients = tf.gradients(self.obj, self.trainable_params)
# Clip gradients by a given maximum_gradient_norm
clip_gradients, _ = tf.clip_by_global_norm(self.gradients, self.max_gradient_norm)
# Update the model
self.updates = self.opt.apply_gradients(zip(clip_gradients, self.trainable_params))#, global_step=self.global_step)
def save(self, sess, path, var_list=None, global_step=None):
saver = tf.compat.v1.train.Saver(var_list)
save_path = saver.save(sess, save_path=path, global_step=global_step)
def restore(self, sess, path, var_list=None):
saver = tf.compat.v1.train.Saver(var_list)
saver.restore(sess, save_path=tf.train.latest_checkpoint(path))
def train(self, sess, inputs, inp_gcn=None):
input_feed = dict()
input_feed[self.H.name] = inputs
output_feed = [self.obj, self.utility, self.pow_alloc, self.updates]
outputs = sess.run(output_feed, input_feed)
return outputs[0], outputs[1], outputs[2]
def eval(self, sess, inputs, inp_gcn=None):
input_feed = dict()
input_feed[self.H.name] = inputs
output_feed = [self.obj, self.utility, self.pow_alloc]
outputs = sess.run(output_feed, input_feed)
return outputs[0], outputs[1], outputs[2]