feat: refactored music

Author: nmb735

src/music.py

@@ -0,0 +1,62 @@
+# =================================================================================================================================== #
+# ----------------------------------------------------------- DESCRIPTION ----------------------------------------------------------- #
+# This script contains the functions for analyzing Angle of Arrival (AoA) measurements from RFID systems, using the classical         #
+# antenna-array method "MUSIC Algorithm".                                                                                             #
+# =================================================================================================================================== #
+
+
+# =================================================================================================================================== #
+# --------------------------------------------------------- EXTERNAL IMPORTS -------------------------------------------------------- #
+import numpy as np  # Mathematical functions.                                                                                         #
+# =================================================================================================================================== #
+
+
+# =================================================================================================================================== #
+# ---------------------------------------------------------- MUSIC FUNCTION --------------------------------------------------------- #
+def music_algorithm(phasor1, phasor2, L, wavelength, aoa_scan):
+    """
+    Implement the MUSIC (MUltiple SIgnal Classification) algorithm for RFID AoA estimation.
+    
+    Parameters:
+        phasor1    [np.ndarray] : Complex phasors from antenna 1
+        phasor2    [np.ndarray] : Complex phasors from antenna 2
+        L          [float]      : Antenna separation distance (in meters)
+        wavelength [float]      : Signal wavelength (in meters)
+        aoa_scan   [np.ndarray] : Array of angles to scan (in degrees)
+        
+    Returns:
+        - tuple : (theta_music, P_music)
+            - theta_music : Estimated angle using MUSIC algorithm
+            - P_music     : MUSIC spectrum
+    """
+    # STEP 1: Form spatial covariance matrix
+    # Reshape phasors to column vectors and combine
+    x1 = phasor1.reshape(-1, 1)
+    x2 = phasor2.reshape(-1, 1)
+    X = np.hstack((x1, x2))  # Combine signals from both antennas
+    # Calculate spatial covariance matrix
+    R = X.conj().T @ X / X.shape[0]
+    # STEP 2: Eigendecomposition
+    eigenvalues, eigenvectors = np.linalg.eig(R)
+    # Sort eigenvectors by eigenvalues in descending order
+    idx = np.argsort(eigenvalues)[::-1]
+    eigenvectors = eigenvectors[:, idx]
+    # STEP 3: Noise subspace (assuming 1 signal, so 1 eigenvector for signal)
+    # Take all eigenvectors except the first one
+    En = eigenvectors[:, 1:]
+    # STEP 4: MUSIC spectrum calculation
+    k = 2 * np.pi / wavelength
+    P_music = np.zeros(len(aoa_scan))
+    for i in range(len(aoa_scan)):
+        # Array steering vector
+        a = np.array([1, np.exp(-1j * k * L * np.sin(np.deg2rad(aoa_scan[i])))])
+        a = a.reshape(-1, 1) 
+        # MUSIC pseudospectrum - FIX: Extract scalar value using .item()
+        denominator = a.conj().T @ (En @ En.conj().T) @ a
+        P_music[i] = 1 / np.abs(denominator.item())  # Use .item() to extract scalar value
+    # STEP 5: Normalize spectrum
+    P_music = P_music / np.max(P_music) if np.max(P_music) > 0 else P_music
+    # STEP 6: Find peak
+    theta_music = aoa_scan[np.argmax(P_music)]
+    
+    return theta_music, P_music