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    "# Optimizing chirp parameters for accuracy\n",
    "\n",
    "[![](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/matt-chv/mmWrt/blob/main/docs/Chirp_Solver.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f05d45",
   "metadata": {},
   "source": [
    "## The problem\n",
    "\n",
    "Range range, resolution and accuracy is a function of the chirp definition.\n",
    "\n",
    "While defining optimal chirp bandwidth, slope, sampling frequency and maximum ADC buffer size is a fairly simple problem to solve for a single target.\n",
    "\n",
    "Optimizing chirp definition to minimise measurement error over multiple targets can be a more daunting task.\n",
    "\n",
    "## The solution\n",
    "\n",
    "This workbook shows a simple non-optimised solution for this multi-target error minimisation.\n",
    "\n",
    "A likely improvement would be to leverage `scipy.optimize.minimize`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee64b92f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install a pip package in the current Jupyter kernel\n",
    "import sys\n",
    "!{sys.executable} -m pip install mmWrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c74d5114",
   "metadata": {},
   "outputs": [],
   "source": [
    "from os.path import abspath, join, pardir\n",
    "import sys\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from matplotlib import colors\n",
    "from numpy import arange, where, expand_dims\n",
    "\n",
    "# uncomment below if the notebook is launched from project's root folder\n",
    "dp = abspath(join(\".\",pardir))\n",
    "sys.path.insert(0, dp)\n",
    "\n",
    "\n",
    "from mmWrt.Raytracing import rt_points  # noqa: E402\n",
    "from mmWrt.Scene import Radar, Transmitter, Receiver, Target  # noqa: E402\n",
    "from mmWrt import RadarSignalProcessing as rsp  # noqa: E402\n",
    "\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8a440f7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████████████████████████████████| 2249991/2249991 [00:05<00:00, 424840.61it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal config: {'bw': 3000000000.0, 'fs': 100.0, 'slope': 600000000.0, 'error': 0.0}, yields error: 0.0\n",
      "CPU times: total: 2.81 s\n",
      "Wall time: 5.31 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "c = 3e8\n",
    "\n",
    "# Define targets, by default non set values are 0\n",
    "# so below is a target at x0=1.5 and y0=0, z0=0 with no speed vector\n",
    "target1 = Target(1.5)\n",
    "target2 = Target(2)\n",
    "\n",
    "# initialize the error to the error when no targets are identified\n",
    "min_error = target1.distance() + target2.distance()  # we start at 2.5\n",
    "\n",
    "# initialize chirp config with text values\n",
    "config = {\"bw\": \"?\", \"fs\": \"?\", \"error\": \"?\"}\n",
    "\n",
    "# this scan will take minutes\n",
    "bws = [0.1e9, 0.2e9, 0.3e9, 0.5e9, 1e9, 2e9, 3e9, 4e9]\n",
    "slopes = range(1, 100)\n",
    "fss = arange(100, 25e6, 100)\n",
    "\n",
    "# this scan takes seconds to verify that min_error is 0 with those settings\n",
    "bws = [2.9e9, 3e9, 3.1e9]\n",
    "slopes = [5, 6, 7]\n",
    "fs = range(50, 200)\n",
    "\n",
    "debug_ON = False\n",
    "\n",
    "with tqdm(total=len(bws) * len(slopes) * len(fss)) as pbar:\n",
    "    for bw in bws:\n",
    "        for slope_m in slopes:\n",
    "            slope = slope_m * 1e8\n",
    "            for fs in fss:\n",
    "                pbar.update(1)\n",
    "                try:\n",
    "\n",
    "                    radar = Radar(transmitter=Transmitter(bw=bw, slope=slope),\n",
    "                                  receiver=Receiver(fs=fs,\n",
    "                                                    max_adc_buffer_size=512,\n",
    "                                                    debug=debug_ON),\n",
    "                                  debug=debug_ON)\n",
    "\n",
    "                    bb = rt_points(radar, [target1, target2], debug=debug_ON)\n",
    "                    # data_matrix = bb['adc_cube'][0][0][0]\n",
    "                    Distances, range_profile = rsp.range_fft(bb)\n",
    "                    ca_cfar = rsp.cfar_ca_1d(range_profile)\n",
    "\n",
    "                    range_profile = range_profile\n",
    "                    ca_cfar = ca_cfar\n",
    "                    mag_r = abs(range_profile)\n",
    "                    mag_c = abs(ca_cfar)\n",
    "                    # little hack to remove small FFT ripples : mag_r> 5\n",
    "                    target_filter = ((mag_r > mag_c) & (mag_r > 5))\n",
    "\n",
    "                    index_peaks = where(target_filter)[0]\n",
    "                    grouped_peaks = rsp.peak_grouping_1d(index_peaks)\n",
    "\n",
    "                    found_targets = [Target(Distances[i])\n",
    "                                     for i in grouped_peaks]\n",
    "                    error = rsp.error([target1, target2], found_targets)\n",
    "                    # print(\"error\", error)\n",
    "                    if error < min_error:\n",
    "                        min_error = error\n",
    "                        config = {\"bw\": bw, \"fs\": fs,\n",
    "                                  \"slope\": slope,\n",
    "                                  \"error\": error}\n",
    "                except Exception:\n",
    "                    pass\n",
    "                    # print(str(ex))\n",
    "                    # raise\n",
    "\n",
    "# yields 0 error for bw=3e9, fs=100, slope=6e8\n",
    "print(f\"optimal config: {config}, yields error: {min_error}\")"
   ]
  }
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