def test_calc_whitening_matrix(self):
A = misc.randn_c(3, 3)
# B is symmetric and positive semi-definite
B = np.dot(A, A.conjugate().T)
Wd = misc.calc_whitening_matrix(B)
D = np.dot(np.dot(Wd.conjugate().T, B), Wd)
# D must be an identity matrix
np.testing.assert_array_almost_equal(D, np.eye(3))
def test_calc_whitening_matrix(self):
A = misc.randn_c(3, 3)
# B is symmetric and positive semi-definite
B = np.dot(A, A.conjugate().T)
Wd = misc.calc_whitening_matrix(B)
D = np.dot(np.dot(Wd.conjugate().T, B), Wd)
# D must be an identity matrix
np.testing.assert_array_almost_equal(D, np.eye(3))
def test_calc_whitening_matrices(self):
Nr = np.array([2, 2])
Nt = np.array([2, 2])
K = Nt.size
Nti = 1
iPu = 1e-1 # Power for each user (linear scale)
pe = 1e-3 # External interference power (in linear scale)
noise_var = 1e-4
# Generate the multi-user channel
mu_channel = multiuser.MultiUserChannelMatrixExtInt()
mu_channel.randomize(Nr, Nt, K, Nti)
mu_channel.noise_var = noise_var
bd_obj = blockdiagonalization.BDWithExtIntBase(K, iPu, noise_var, pe)
W_all_k = bd_obj.calc_whitening_matrices(mu_channel)
R_all_k = mu_channel.calc_cov_matrix_extint_plus_noise(pe)
for W, R in zip(W_all_k, R_all_k):
np.testing.assert_array_almost_equal(
W,
calc_whitening_matrix(R).conjugate().T)
def test_calc_whitening_matrices(self):
Nr = np.array([2, 2])
Nt = np.array([2, 2])
K = Nt.size
Nti = 1
iPu = 1e-1 # Power for each user (linear scale)
pe = 1e-3 # External interference power (in linear scale)
noise_var = 1e-4
# Generate the multi-user channel
mu_channel = multiuser.MultiUserChannelMatrixExtInt()
mu_channel.randomize(Nr, Nt, K, Nti)
mu_channel.noise_var = noise_var
bd_obj = blockdiagonalization.BDWithExtIntBase(K, iPu, noise_var, pe)
W_all_k = bd_obj.calc_whitening_matrices(mu_channel)
R_all_k = mu_channel.calc_cov_matrix_extint_plus_noise(pe)
for W, R in zip(W_all_k, R_all_k):
np.testing.assert_array_almost_equal(
W,
calc_whitening_matrix(R).conjugate().T)