Micro Doppler Sim

• N_R = number of rotors (4 for quadcopter)
• N_B = number of blades per rotor (2)
• σ_{j,k} = RCS of blade k on rotor j (set to 1.0 for uniform)
• λ = wavelength = c / fc
• R_j(t) = distance from rotor j to radar
• φ_k(t) = phase function (Equation 2)

Equation (2): Phase Function

φ_k(t) = (4π/λ) · L₂ · cos(β) · cos(Ω_j·t + φ_j + k·2π/N_B)

• L₂ = blade length (0.07 m)
• β = elevation angle
• Ω_j = rotation rate of rotor j (sign indicates CW/CCW)
• φ_j = initial random phase of rotor j
• k = blade index, N_B = blades per rotor

Default Parameters

Read the full parameter table from docs/instruction.md (Section 3). Key values:

Implementation Checklist

1. Define all parameters in a config structure/dict at the top
2. Compute β = arctan(z / sqrt(x² + y²))
3. Compute R_j for each rotor (Euclidean distance)
4. Generate random initial phases with fixed seed
5. Loop over rotors (j) and blades (k), accumulate complex signal
6. Compute blade-tip trajectories for 3D plot
7. Generate four output plots: power spectrum, range profiles, trajectories, spectrogram

Spectrogram Parameters

Verification Targets

• β ≈ 0.3805 rad (21.8°)
• Range ≈ 53.85 m
• f_d_max ≈ ±2700 Hz
• Power spectrum: symmetric peaks within ±3000 Hz
• Range profile: constant horizontal line at ~53.85 m
• Trajectories: 8 circles in horizontal plane
• Spectrogram: periodic sinusoidal modulations at period 6.25 ms