{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Complex Ambiguity Function (CAF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pylab\n",
    "from matplotlib.pyplot import plot, ylim, xlabel, ylabel, grid, savefig, imshow, contour\n",
    "import numpy as np\n",
    "from matplotlib.pyplot import psd\n",
    "pylab.rcParams['savefig.dpi'] = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from caf_verilog import sim_helper as sh\n",
    "from caf_verilog.caf import simple_caf\n",
    "from gps_helper.prn import PRN\n",
    "from sk_dsp_comm import sigsys as ss\n",
    "from sk_dsp_comm import digitalcom as dc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prn = PRN(10)\n",
    "prn2 = PRN(20)\n",
    "fs = 625e3\n",
    "Ns = fs / 200e3\n",
    "prn_seq = prn.prn_seq()\n",
    "prn_seq = [*prn_seq, *prn_seq]\n",
    "prn_seq2 = prn2.prn_seq()\n",
    "prn_seq,b = ss.nrz_bits2(np.array(prn_seq), Ns)\n",
    "prn_seq2,b2 = ss.nrz_bits2(np.array(prn_seq2), Ns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Px,f = psd(prn_seq, 2**12, Fs=fs)\n",
    "plot(f, 10*np.log10(Px))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_size = 100\n",
    "foas = np.arange(-f_size, f_size + 1) * 1000\n",
    "foas, len(foas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CAF Module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from caf_verilog.caf import CAF\n",
    "from caf_verilog.sim_helper import sim_shift\n",
    "from caf_verilog.xcorr import dot_xcorr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "len(prn_seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "center = 3000\n",
    "corr_length = len(foas) - 1\n",
    "shift = 15\n",
    "ncorr = np.arange(0, corr_length * 2)\n",
    "foa_offset = 16\n",
    "theta_shift = np.exp(1j*2*np.pi*ncorr*(foas[foa_offset])/float(fs))\n",
    "ref, rec = sim_shift(prn_seq, center, corr_length, shift=shift)\n",
    "caf = CAF(ref, rec * theta_shift, foas, fs=fs, n_bits=8, ref_i_bits=8, rec_i_bits=8)\n",
    "caf.gen_tb()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ref = np.array(ref)\n",
    "rec = np.array(rec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xcorr_res_shift = dot_xcorr(ref, rec * theta_shift)\n",
    "xcorr_res = dot_xcorr(ref, rec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(rec.real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(np.abs(np.array(xcorr_res_shift)))\n",
    "ylim([0, corr_length])\n",
    "grid();\n",
    "xlabel(\"Inverse Center Offset (Samples)\")\n",
    "savefig('caf_test_shift.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "am_pos = np.argmax(abs(np.array(xcorr_res_shift)))\n",
    "am_pos, abs(np.array(xcorr_res))[am_pos]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(abs(np.array(xcorr_res)))\n",
    "ylim([0, corr_length])\n",
    "grid();\n",
    "am_pos = np.argmax(abs(np.array(xcorr_res)))\n",
    "am_pos, abs(np.array(xcorr_res))[am_pos]\n",
    "xlabel(\"Inverse Center Offset (Samples)\")\n",
    "savefig('caf_test_signal.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CAF Surface Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from caf_verilog.caf import simple_caf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ref, rec = sim_shift(prn_seq, center, corr_length, shift=shift, freq_shift=foas[105], fs=fs, padding=True)\n",
    "ref = np.array(ref)\n",
    "rec = np.array(rec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res, dt = simple_caf(ref, rec, foas=foas, fs=fs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res_np = np.array(caf_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "imshow(caf_res_np, interpolation='none', extent=[-corr_length, corr_length, corr_length, -corr_length])\n",
    "xlabel(\"N-th Sample\")\n",
    "ylabel(\"N-th Frequency Offset\")\n",
    "grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "contour(dt, foas / fs, caf_res_np, levels=int(np.ceil(np.log10(corr_length))))\n",
    "ylabel(\"Offset in Hz\")\n",
    "xlabel(\"Offset in Time (s)\")\n",
    "grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quanztization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from caf_verilog.quantizer import quantize\n",
    "from caf_verilog.caf import dot_caf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ref_dot, rec_dot = sim_shift(prn_seq, center, corr_length, shift=shift, freq_shift=foas[105], fs=fs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ref_quant = quantize(ref_dot, n_bits=8)\n",
    "rec_quant = quantize(rec_dot, n_bits=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res_dot = dot_caf(ref_dot, rec_dot, foas=foas, fs=fs, n_bits=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res_dot_np = np.array(caf_res_dot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.shape(caf_res_dot_np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "imshow(np.abs(caf_res_dot_np), interpolation='none', extent=[corr_length, -corr_length, corr_length, -corr_length])\n",
    "xlabel(\"N-th Sample\")\n",
    "ylabel(\"N-th Frequency Offset\")\n",
    "grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res_dot_quant = dot_caf(ref_quant, rec_quant, foas=foas, fs=fs, n_bits=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "caf_res_dot_quant_np = np.array(caf_res_dot_quant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.shape(caf_res_dot_quant_np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "imshow(np.abs(caf_res_dot_quant_np), interpolation='none', extent=[corr_length, -corr_length, corr_length, -corr_length])\n",
    "xlabel(\"N-th Sample\")\n",
    "ylabel(\"N-th Frequency Offset\")\n",
    "grid();"
   ]
  }
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