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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "57a55a8c",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "dc4b9dfd",
"metadata": {},
"source": [
"# Digital Frame Synchronization\n"
]
},
{
"cell_type": "markdown",
"id": "fc118de2-937b-4157-a5a1-9b7f152bf59b",
"metadata": {},
"source": [
"First we need to create the access code, a barker sequence which has a very good autocorrelation."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "20dcd173-2889-4e21-9746-3d0a0ab060e8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Access code: 13 bit pattern [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1] = left padded bytes [31, 53]\n"
]
}
],
"source": [
"ac = [ 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, ]\n",
"\n",
"ac_pad = [0] * int(8 * np.ceil(len(ac) / 8) - len(ac)) + ac\n",
"ac_bytes = list(np.packbits(ac_pad))\n",
"\n",
"print(f\"Access code: {len(ac)} bit pattern {ac} = left padded bytes {ac_bytes}\")"
]
},
{
"cell_type": "markdown",
"id": "5cfd3c9a-d697-4462-bc26-26e82d25cbfd",
"metadata": {},
"source": [
"To correlate with the access code we need its symbols, thus the functions to modulate the access code."
]
},
{
"cell_type": "markdown",
"id": "d328e765-e977-4de9-9694-35012193a0aa",
"metadata": {},
"source": [
"### Symbols for QPSK"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "515891a9-dbd2-4088-9a41-b792d878f0fc",
"metadata": {},
"outputs": [],
"source": [
"def modulate_qpsk(m):\n",
" ampl = 1\n",
" sym = {\n",
" 0: ampl * (-1 -1j) / np.sqrt(2),\n",
" 1: ampl * ( 1 -1j) / np.sqrt(2),\n",
" 2: ampl * (-1 +1j) / np.sqrt(2),\n",
" 3: ampl * ( 1 +1j) / np.sqrt(2)\n",
" }\n",
"\n",
" return map(lambda k: sym[k], m)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "3a4c834f-7012-4e22-b9f3-865527d09c02",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Modulate chunks [0, 1, 3, 3, 0, 3, 1, 1] with QPSK into 8 symbols:\n",
"[(-0.7071067811865475-0.7071067811865475j), (0.7071067811865475-0.7071067811865475j), (0.7071067811865475+0.7071067811865475j), (0.7071067811865475+0.7071067811865475j), (-0.7071067811865475-0.7071067811865475j), (0.7071067811865475+0.7071067811865475j), (0.7071067811865475-0.7071067811865475j), (0.7071067811865475-0.7071067811865475j)]\n",
"\n",
"Reversed complex conjugate list for FIR filter:\n",
"[(0.7071067811865475+0.7071067811865475j), (0.7071067811865475+0.7071067811865475j), (0.7071067811865475-0.7071067811865475j), (-0.7071067811865475+0.7071067811865475j), (0.7071067811865475-0.7071067811865475j), (0.7071067811865475-0.7071067811865475j), (0.7071067811865475+0.7071067811865475j), (-0.7071067811865475+0.7071067811865475j)]\n"
]
}
],
"source": [
"# convert into chunks of 2 bits for QPSK\n",
"chunks = list(np.matmul(np.array(ac_pad).reshape((-1,2)), np.array([2, 1])))\n",
"syms = list(modulate_qpsk(chunks))\n",
"print(f\"Modulate chunks {chunks} with QPSK into {len(syms)} symbols:\\n{syms}\\n\")\n",
"\n",
"fir_syms = list(np.conj(syms[::-1]))\n",
"print(f\"Reversed complex conjugate list for FIR filter:\\n{fir_syms}\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d6155b2e-9405-4d20-8c05-72af45575a04",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1440x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, (left, right) = plt.subplots(1, 2, figsize = (20, 4))\n",
"\n",
"left.plot(np.real(syms), \".-\")\n",
"left.plot(np.imag(syms), \".-\")\n",
"left.set_title(\"Access Code\")\n",
"\n",
"right.plot(np.real(fir_syms), \".-\")\n",
"right.plot(np.imag(fir_syms), \".-\")\n",
"right.set_title(\"FIR Filter\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8163c2e0-0652-43c5-ad32-eaf0e94a638e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1440x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, (left, right) = plt.subplots(1, 2, figsize = (20, 4))\n",
"\n",
"left.plot(np.real(syms), np.imag(syms))\n",
"left.set_title(\"AC Constellation Diagram\")\n",
"\n",
"xc = np.convolve(fir_syms, syms)\n",
"right.plot(np.abs(xc))\n",
"right.set_title(\"AC Autocorrelation\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "bc633da5-61b7-4569-adaf-3d019e0f1b17",
"metadata": {},
"source": [
"## Symbols for 16-QAM"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b56d782d-fcea-4fb9-b0c1-9c3933d5ce6c",
"metadata": {},
"outputs": [],
"source": [
"def modulate_16qam(m):\n",
" sym = {\n",
" 0: 1 -1j,\n",
" 1: -1 -1j,\n",
" 2: 3 -3j,\n",
" 3: -3 -3j,\n",
" 4: -3 -1j,\n",
" 5: 3 -1j,\n",
" 6: -1 -3j,\n",
" 7: 1 -3j,\n",
" 8: -3 +3j,\n",
" 9: 3 +3j,\n",
" 10: -1 +1j,\n",
" 11: 1 +1j,\n",
" 12: 1 +3j,\n",
" 13: -1 +3j,\n",
" 14: 3 +1j,\n",
" 15: -3 +1j,\n",
" \n",
" }\n",
" return map(lambda k: sym[k]*np.sqrt(0.1), m)\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "2fb687aa-0061-4626-bf6b-3ec7d628d739",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1, 10, 3, 4]\n",
"[(-0.31622776601683794-0.31622776601683794j), (-0.31622776601683794+0.31622776601683794j), (-0.9486832980505138-0.9486832980505138j), (-0.9486832980505138-0.31622776601683794j)]\n"
]
}
],
"source": [
"# convert into chunks of 4 bits for QPSK\n",
"chunks = list(np.matmul(np.array(ac_pad).reshape((-1,4)), np.array([4, 3, 2, 1])))\n",
"syms = list(modulate_16qam(chunks))\n",
"\n",
"print(chunks)\n",
"print(syms)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5951be43",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
|
