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   "source": [
    "# Exercise on Fundamentals\n",
    "This notebook reproduces several textbook radar problems, solved with functions from `radarx.fundamentals`.\n",
    "These probelms are taken from \n",
    " - Rahman, H. (2019). Fundamental principles of radar. CRC Press."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from radarx.fundamentals import constants, doppler, principles, timing, power, system"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2",
   "metadata": {},
   "source": [
    "### Example 2.8 — S‑Band Pulsed Radar\n",
    "\n",
    "> **Problem**  \n",
    "> Consider an **S‑band** pulsed radar transmitting **250 kW** of peak power with a pulse width of **1.5 µs** and a PRF of **500 pps**.  \n",
    "> The radar operates at a frequency of **3000 MHz**.  \n",
    "> 1. **(a)** Determine the maximum *unambiguous range*, *range resolution*, and *duty factor*.  \n",
    "> 2. **(b)** Compute the *average transmitted power* and the *energy radiated in the first 10 ms*.  \n",
    "> 3. **(c)** Calculate the *Doppler shift* for a target approaching with a radial velocity of **30 m s⁻¹**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Given values\n",
    "P_peak = 250e3  # W\n",
    "PRF = 500  # Hz\n",
    "tau = 1.5e-6  # s\n",
    "f0 = 3.0e9  # Hz\n",
    "lam = constants.C / f0\n",
    "v_r = 30  # m/s\n",
    "t_interval = 10e-3  # 10 ms\n",
    "\n",
    "# (a)\n",
    "R_unamb = doppler.unambiguous_range(PRF)\n",
    "R_res = principles.compute_range_resolution(tau)\n",
    "duty = timing.compute_duty_cycle(tau, PRF)\n",
    "duty_factor = tau * PRF\n",
    "\n",
    "# (b)\n",
    "P_avg = power.compute_average_power(P_peak, duty)\n",
    "E_10ms = P_avg * t_interval\n",
    "\n",
    "# (c)\n",
    "f_d = doppler.doppler_frequency_shift(f0, v_r)\n",
    "\n",
    "print(f\"Unambiguous range      : {R_unamb:,.0f} m\")\n",
    "print(f\"Range resolution       : {R_res:,.2f} m\")\n",
    "print(f\"Duty cycle             : {duty:.4f}  (fraction)\")\n",
    "print(f\"Duty factor (τ·PRF)    : {duty_factor:.4f}\")\n",
    "print(f\"Average power          : {P_avg:,.1f} W\")\n",
    "print(f\"Energy in first 10 ms  : {E_10ms:.4f} J\")\n",
    "print(f\"Doppler shift (30 m/s) : {f_d:.2f} Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4",
   "metadata": {},
   "source": [
    "### Example 3.1 — X‑Band Antenna Gain\n",
    "\n",
    "> **Problem**  \n",
    "> Calculate the maximum gain of an **X‑band** antenna operating at **8 GHz** with a diameter of **1 m**.  \n",
    "> Repeat for diameters **1.5 m** and **2.0 m**.  \n",
    "> Assume aperture efficiency ρₐ = 1 so Aₑ = A.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x = 8e9\n",
    "lam_x = constants.C / f_x\n",
    "for D in [1.0, 1.5, 2.0]:\n",
    "    Ae = np.pi * (D / 2) ** 2\n",
    "    G = 4 * np.pi * Ae / lam_x**2  # linear\n",
    "    G_dB = 10 * np.log10(G)\n",
    "    print(f\"Diameter {D:>3.1f} m → Gain = {G_dB:.2f} dB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6",
   "metadata": {},
   "source": [
    "### Example 3.9 — Required Peak Power\n",
    "\n",
    "> **Problem**  \n",
    "> An X‑band radar uses the same 3 m circular antenna (efficiency **0.8**) for Tx/Rx at **8 GHz**.  \n",
    "> The system should yield an average received power of **3 × 10⁻¹⁴ W** from a **1 m²** target at **100 km**.  \n",
    "> Total system loss is **3 dB**.  Determine the required **transmitter peak power**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = 8e9\n",
    "lam = constants.C / f\n",
    "D = 3.0\n",
    "rho = 0.8\n",
    "R = 100e3\n",
    "sigma = 1.0\n",
    "P_rx = 3e-14\n",
    "L_lin = 10 ** (3 / 10)  # 3 dB loss\n",
    "\n",
    "Ae = rho * np.pi * (D / 2) ** 2\n",
    "G = 4 * np.pi * Ae / lam**2\n",
    "\n",
    "P_tx = system.solve_peak_power(P_rx, G, lam, sigma, R, L_lin)\n",
    "P_tx\n",
    "# print(f\"Required peak power ≈ {P_tx/1e6:.2f} MW\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8",
   "metadata": {},
   "source": [
    "### Multipath Propagation Example\n",
    "\n",
    "> **Problem**  \n",
    "> A radar at **30 m** height tracks a target at **50 m**, range **40 km**, RCS **4 m²**.  \n",
    "> Antenna gain **34.77 dB**, peak power **1 MW**, frequency **5.4 GHz**.  \n",
    "> Above a smooth plane, estimate:  \n",
    "> 1. **(a)** Multipath propagation factor (two‑ray).  \n",
    "> 2. **(b)** Received signal power.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9",
   "metadata": {},
   "outputs": [],
   "source": [
    "ht, hr, R = 30.0, 50.0, 40e3\n",
    "sigma = 4.0\n",
    "P_t = 1e6\n",
    "f_c = 5.4e9\n",
    "lam_c = constants.C / f_c\n",
    "G_lin = 10 ** (34.77 / 10)\n",
    "\n",
    "delta_r = 2 * ht * hr / R\n",
    "delta_phi = 4 * np.pi * delta_r / lam_c\n",
    "F = 2 * np.abs(np.cos(delta_phi / 2))\n",
    "print(f\"Propagation factor |F| ≈ {F:.2f}\")\n",
    "\n",
    "P_r = system.radar_equation(P_t, G_lin, lam_c, sigma, R, 1.0) * F**2\n",
    "print(f\"Received power ≈ {P_r:.2e} W\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10",
   "metadata": {},
   "source": [
    "### Missile Doppler Shift\n",
    "\n",
    "> **Problem**  \n",
    "> A missile closing at **300 m s⁻¹** is illuminated by a **12 GHz** radar.  \n",
    "> 1. Compute the **exact** Doppler frequency.  \n",
    "> 2. Compute the **approximate** Doppler frequency (v ≪ c).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11",
   "metadata": {},
   "outputs": [],
   "source": [
    "f0 = 12e9\n",
    "v = 300\n",
    "f_d_exact = doppler.doppler_frequency_shift(f0, v, exact=True)\n",
    "f_d_approx = doppler.doppler_frequency_shift(f0, v, exact=False)\n",
    "print(f\"Exact Doppler  : {f_d_exact:.2f} Hz\")\n",
    "print(f\"Approx Doppler : {f_d_approx:.2f} Hz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12",
   "metadata": {},
   "outputs": [],
   "source": []
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