Graph_Signal_Processing/functions.py at master · mazyaniv/Graph_Signal_Processing · GitHub

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import math
import numpy as np
from numpy import linalg as LA
from matplotlib import pyplot as plt
from classes import prameters_class, Matrix_class
from methods import root_music, music, esprit
import scipy.signal as ss
from scipy.ndimage import gaussian_filter

# def get_key_by_value(dictionary, target_value):
#     for key, value in dictionary.items():
#         if value == target_value:
#             return key

# def angles_generate(pram):
#     while True:
#         range_array = np.arange(pram.teta_range[0], pram.teta_range[1], pram.Res)
#         teta = np.random.choice(range_array[1:-1], size=pram.D, replace=False)
#         if abs(teta[0] - teta[1]) > pram.delta:
#             break
#     return np.sort(teta)[::-1]

def angles_generate(pram):
    while True:
        range2 = [-30, 30] #TODO - note that the range is limited to [-30,30] for the sake of the simulation
        range_array = np.arange(range2[0], range2[1], pram.Res)
        teta = np.random.choice(range_array[1:-1], size=pram.D, replace=False)
        if pram.D >1 and abs(teta[0] - teta[1]) > pram.delta:
            break
        elif pram.D == 1:
            break
    return np.sort(teta)[::-1]
def generate_qpsk_symbols(K,D):
    random_symbols = np.random.randint(0, 4, (K,D))
    qpsk_constellation = np.array([1+1j, -1+1j, -1-1j, 1-1j]) / np.sqrt(2)
    qpsk_symbols = qpsk_constellation[random_symbols]
    return qpsk_symbols.T
def observ(SNR, K, A): #k=snapshots
    N = A.shape[0]
    D = A.shape[1]

    f_tone =1e9
    f_tone_vec = f_tone*np.ones(D)
    sample_rate = f_tone # nayquist rate
    t = np.arange(K)/sample_rate  # time vector
    s = np.exp(1j*2*np.pi*f_tone_vec.reshape(D,1)*t.reshape(1,K))

    # real_s = np.random.normal(0, 1 / math.sqrt(2), (D, K))
    # im_s = np.random.normal(0, 1 / math.sqrt(2), (D, K))
    # s = real_s + 1j * im_s

    # s = generate_qpsk_symbols(K,D)

    s_samp = s.reshape(D, K)
    real_n = np.random.normal(0, math.sqrt((10 ** (-SNR / 20))) / math.sqrt(2), (N, K))
    im_n = np.random.normal(0, math.sqrt((10 ** (-SNR / 20))) / math.sqrt(2), (N, K))
    n = real_n + 1j * im_n
    n_samp = n.reshape(N, K)
    x_a_samp = (A@s_samp) + n_samp
    return x_a_samp

def GFT(S, x):
    eigenvalues, eigenvectors = np.linalg.eig(S)
    # print(np.sort(np.real(eigenvalues)))
    sorted_eigenvectors = eigenvectors[:, np.argsort(np.real(eigenvalues))] #sorted in case of negative eigenvalues
    # print(sorted_eigenvectors.T.conjugate())
    x_tag = sorted_eigenvectors.T.conjugate()@x
    vector = np.zeros(len(x_tag), dtype=int)
    vector[:] = 1
    B = np.diag(vector)
    x_tag = B@x_tag #TODO just for checking filters
    return x_tag#np.average(x_tag,1)

def quantize(A, P, thresh_real=0, thresh_im=0):
    mask = np.zeros(np.shape(A), dtype=complex)
    mask[:P, :] = (1 / math.sqrt(2)) * (np.sign(A[:P, :].real - (thresh_real)) + (1j * (np.sign(A[:P, :].imag - ((thresh_im))))))
    mask[P:, :] = A[P:, :]
    return mask

def G_DOA(pram):
    labels = np.zeros((pram.monte, pram.D))
    theta_vector = np.zeros((pram.monte, pram.D))
    # ind = 0
    for l in range(pram.monte):
        teta = angles_generate(pram)
        # print(teta)
        labels[l, :] = teta
        S = (Matrix_class(pram)).steering(teta)
        theta_range = np.arange(pram.teta_range[0], pram.teta_range[1], pram.Res)
        obs_a = observ(pram.SNR, pram.K, S)
        x_vec = quantize(obs_a, pram.N_q)
        x_vec_s = np.average(x_vec, 1)
        spectrum = np.zeros((len(theta_range)))
        for idx, theta in enumerate(theta_range):
            steering2 = np.exp(-1j * np.pi * np.arange(pram.M) * np.sin(np.radians(theta_range[idx]))).reshape(pram.M,1) #Matrix_class(my_parameters2).steering(theta_range[j])
            A_s = steering2 @ steering2.T.conjugate() - (1 / (pram.M - 1)) * np.eye(pram.M)  # Matrix_class(my_parameters2).Adjacency()
            x_tag_s = GFT(A_s, x_vec_s) #GFT(A_s_mat[:,:,idx], x_vec[:,i])
            sorted_indices = np.argsort(x_tag_s)[::-1]
            spectrum[idx]= 1/LA.norm(np.abs(np.delete(x_tag_s, sorted_indices[:1]))/np.max(np.abs(x_tag_s))) #TODO
        # plt.title(f"Piquancy function for {pram.D} source/s, SNR={pram.SNR}")
        # plt.ylabel(r"$\xi(\theta)$")
        # plt.xlabel(r"$\theta^\degree$")
        # plt.plot(theta_range, spectrum)#,marker=".")
        # plt.show()
        peaks, _ = ss.find_peaks(spectrum,distance=pram.delta/pram.Res)
        peaks = list(peaks)
        peaks.sort(key=lambda x: spectrum[x])
        pred = np.array(peaks[-pram.D:])
        pred = np.sort(pred)[::-1]
        theta_vector[l,:] = pred*pram.Res+pram.teta_range[0]
        # print(ind)
        # ind += 1
    # print("labels:",labels)
    # print(theta_vector)
    sub_vec = theta_vector - labels
    RMSE = ((np.sum(np.sum(np.power(sub_vec, 2), 1)) / (sub_vec.shape[0] * (theta_vector.shape[1]))) ** 0.5)
    return RMSE
def general(pram):
    rho = pram.D*(10**(pram.SNR / 10))+1#pram.D * (10 ** (-pram.SNR / 10)+1)
    labels = np.zeros((pram.monte, pram.D))
    teta_vector1 = np.zeros((pram.monte, pram.D))
    teta_vector2 = np.zeros((pram.monte, pram.D))
    for i in range(pram.monte):
        while True:
            teta = angles_generate(pram)
            labels[i, :] = teta
            # print(teta)
            A = Matrix_class(pram).steering(teta)
            my_vec = observ(pram.SNR, pram.K, A)
            my_vec = quantize(my_vec, pram.N_q)
            R = np.cov(my_vec) #covariance(my_vec, my_vec)

            # R1 = np.zeros(R.shape, dtype=complex)
            # R1[:pram.N_q, :pram.N_q] = rho*((math.pi / 2) *
            #                            (np.subtract(R[:pram.N_q, :pram.N_q],
            #                                         (1 - (2 / math.pi)) * np.identity(pram.N_q)))) # R_quantize_lin
            # R1[pram.N_q:, :pram.N_q] = ((math.pi*rho/2)**0.5)*R[pram.N_q:, :pram.N_q]  # R_mixed
            # R1[:pram.N_q, pram.N_q:] = ((math.pi*rho/2)**0.5)*R[:pram.N_q, pram.N_q:]  # R_mixed
            # R1[pram.N_q:, pram.N_q:] = R[pram.N_q:, pram.N_q:]  # R_analog
            #
            # R2 = np.zeros(R.shape, dtype=complex)
            # R2[:pram.N_q,:pram.N_q] = rho*(np.sin((math.pi / 2) * R[:pram.N_q,:pram.N_q].real)
            #                                 + 1j * np.sin((math.pi / 2) * R[:pram.N_q,:pram.N_q].imag)) #R_quantize_sin
            # R2[pram.N_q:,:pram.N_q] = ((math.pi*rho/2)**0.5)*R[pram.N_q:,:pram.N_q]#R_mixed
            # R2[:pram.N_q,pram.N_q:] = ((math.pi*rho/2)**0.5)*R[:pram.N_q,pram.N_q:]#R_mixed
            # R2[pram.N_q:,pram.N_q:] = R[pram.N_q:,pram.N_q:] #R_analog
            pred1 = music(pram, R)
            # pred2 = music(pram, R2)
            if pred1.shape == teta_vector1[i,:].shape:# and pred2.shape == teta_vector1[i,:].shape:
                break
        teta_vector1[i,:] = pred1
        # teta_vector2[i, :] = pred2
    sub_vec1 = teta_vector1 - labels
    # print("labels=",labels)
    # print("pred1=",teta_vector1)
    # sub_vec2 = teta_vector2 - labels
    RMSE1 = ((np.sum(np.sum(np.power(sub_vec1, 2), 1)) / (sub_vec1.shape[0] * (teta_vector1.shape[1]))) ** 0.5)
    # RMSE2 = ((np.sum(np.sum(np.power(sub_vec2, 2), 1)) / (sub_vec2.shape[0] * (teta_vector2.shape[1]))) ** 0.5)
    return RMSE1#, RMSE2 #TODO modulo

def G_DOA2(pram,q): #TODO reduce complexity and sace performance
    labels = np.zeros((pram.monte, pram.D))
    theta_vector = np.zeros((pram.monte, pram.D))
    ind = 0
    for l in range(pram.monte):
        teta = angles_generate(pram)
        labels[l, :] = teta
        S = Matrix_class(pram).steering(teta)
        theta_range = np.arange(pram.teta_range[0], pram.teta_range[1], pram.Res)
        # A_s_mat = np.zeros((pram.M, pram.M,len(theta_range)), dtype=complex)
        # for j in range(len(theta_range)):
        #     steering2 = np.exp(-1j * np.pi * np.arange(pram.M) * np.sin(np.radians(theta_range[j]))).reshape(pram.M,1)#Matrix_class(my_parameters2).steering(theta_range[j])
        #     A_s = steering2 @ steering2.T.conjugate() - (1 / (pram.M - 1)) * np.eye(pram.M)  # Matrix_class(my_parameters2).Adjacency()
        #     A_s_mat[:,:,j] = A_s
        # spectrum_vec = np.zeros((pram.K,len(theta_range)))
        obs_a = observ(pram.SNR, pram.K, S)
        x_vec = quantize(obs_a, q)
        # for i in range(pram.K):
        spectrum = np.zeros(len(theta_range))
        for idx, theta in enumerate(theta_range):
            steering2 = np.exp(-1j * np.pi * np.arange(pram.M) * np.sin(np.radians(theta_range[idx]))).reshape(pram.M,1) #Matrix_class(my_parameters2).steering(theta_range[j])
            A_s = steering2 @ steering2.T.conjugate() - (1 / (pram.M - 1)) * np.eye(pram.M)  # Matrix_class(my_parameters2).Adjacency()
            x_tag_s = GFT(A_s, x_vec) #GFT(A_s_mat[:,:,idx], x_vec[:,i])
            sorted_indices = np.argsort(x_tag_s)[::-1]
            spectrum[idx]= 1/LA.norm(np.abs(x_tag_s[:-pram.D])/np.max(np.abs(x_tag_s)))
            # spectrum[idx]= 1/LA.norm(np.abs(np.delete(x_tag_s, sorted_indices[:1]))/np.max(np.abs(x_tag_s)))
        # spectrum_vec[i,:]=spectrum
        # spectrum = np.average(spectrum_vec,0)
        # plt.plot(theta_range, spectrum,marker="*")
        # plt.show()
        peaks, _ = ss.find_peaks(spectrum,distance=pram.delta/pram.Res)
        peaks = list(peaks)
        peaks.sort(key=lambda x: spectrum[x])
        pred = np.array(peaks[-pram.D:])
        pred = np.sort(pred)[::-1]
        theta_vector[l,:] = pred*pram.Res+pram.teta_range[0]
        # print(ind)
        ind += 1
    # print(labels)
    # print(theta_vector)
    sub_vec = theta_vector - labels
    RMSE = ((np.sum(np.sum(np.power(sub_vec, 2), 1)) / (sub_vec.shape[0] * (theta_vector.shape[1]))) ** 0.5)
    return RMSE