doa-using-just-eigenvectors

Author: 777arc

figure-generating-scripts/doa_trying_phase_of_eigenvectors.py

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+# TLDR- works fine for 1 signal, but if there are more then the signals need to be at different amplitudes
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+sample_rate = 1e6
+d = 0.5 # half wavelength spacing
+N = 10000 # number of samples to simulate
+t = np.arange(N)/sample_rate # time vector
+
+Nr = 8 # elements
+theta1 =  15 / 180 * np.pi
+theta2 =  60 / 180 * np.pi
+theta3 = -50 / 180 * np.pi
+
+tone1 = 1.0 * np.exp(2j*np.pi*0.0173e6*t).reshape(1,-1)
+tone2 = 0.5 * np.exp(2j*np.pi*0.0257e6*t).reshape(1,-1)
+tone3 = 0.25 * np.exp(2j*np.pi*0.0312e6*t).reshape(1,-1)
+
+s1 = np.exp(-2j * np.pi * d * np.arange(Nr) * np.sin(theta1)).reshape(-1,1) # 8x1
+s2 = np.exp(-2j * np.pi * d * np.arange(Nr) * np.sin(theta2)).reshape(-1,1)
+s3 = np.exp(-2j * np.pi * d * np.arange(Nr) * np.sin(theta3)).reshape(-1,1)
+
+# Simulate received signal
+r = s1 @ tone1 + s2 @ tone2 + s3 @ tone3
+n = np.random.randn(Nr, N) + 1j*np.random.randn(Nr, N)
+r = r + 0.00001*n # 8xN
+
+# Compute covariance matrix
+R = r @ r.conj().T / N
+
+# Eigenvalue decomposition
+w, V = np.linalg.eig(R)
+idx = np.argsort(np.abs(w))[::-1]
+w = w[idx]
+V = V[:, idx]
+
+if False:
+    # Plot eigenvalues
+    plt.figure()
+    plt.plot(np.sort(np.abs(w))[::-1], 'k*')
+    plt.xlabel('Index')
+    plt.ylabel('Eigenvalue')
+    plt.show()
+
+for i in range(3):
+    phases = np.angle(V[:, i])
+    # find phase between adjacent elements
+    phase_diffs = []
+    for i in range(len(phases)-1):
+        phase_diffs.append(phases[i+1] - phases[i])
+    phase_diffs = np.array(phase_diffs)
+    phase_diffs = np.mod(phase_diffs + np.pi, 2*np.pi) - np.pi # make them all between -np.pi and np.pi
+    print(phase_diffs)
+    phase_diff = np.mean(phase_diffs)
+
+    # Convert to AoA
+    result = np.arcsin(phase_diff / (-2*np.pi*d))
+    print(np.rad2deg(result))