Foundations of User-Centric Cell-Free Massive MIMO.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e2d3858e",
   "metadata": {},
   "source": [
    "# Foundations of User-Centric Cell-Free Massive MIMO.\n",
    "\n",
    "In this notebook I will organize and filter my and Emil Björnson's code about SINR statics in a cell-free model of communication for 5G networks.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "067190e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# all my libs to this code:\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from numpy import matlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "411f4921",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some constants for Monte-Carlo simulation:\n",
    "\n",
    "L = 400 # Lenght of square (the universe of our simulation)\n",
    "n_antennas = 64 # Total number of APs in simulation.\n",
    "c = 299792458   # Light Speed\n",
    "freq = 5000000000   # 5 * 10^{9}. Hz\n",
    "loop = 1000 # number of realization of simulation\n",
    "nUe = 8     # Number of users in square\n",
    "APperdim = np.sqrt(n_antennas) # the number of antennas are normalized distributed in lines.\n",
    "\n",
    "# Generating the space of AP and UE for every repetition on simulation.\n",
    "APindex = np.linspace(L/APperdim, L, int(APperdim)) - (L/APperdim) / 2\n",
    "APcellfree = matlib.repmat(APindex, int(APperdim), 1) + 1j * (matlib.repmat(APindex, int(APperdim), 1)).T\n",
    "UEloc = (np.random.rand(loop, nUe) + 1j * np.random.rand(loop, nUe)) * L\n",
    "\n",
    "#   Main containers:\n",
    "SINR_cellfree = np.array([])\n",
    "SNR_total = np.array([])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "877b5802",
   "metadata": {},
   "source": [
    "The next cell contains all functions that I made or get with [Emil's Code](https://github.com/BPalhano/cell-free-book/blob/main/code/section1_figure11.m), I will optimizate some functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "876b755d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pow2db(x, size):\n",
    "\n",
    "    db = x.copy()\n",
    "    for i in range(size):\n",
    "        db[i] = 10 * np.log10(db[i] / 10)\n",
    "\n",
    "    return db\n",
    "\n",
    "def SNR(dist):\n",
    "    Sig = 10 + 96 - 30.5 - 37.7 * np.log10(np.sqrt(np.square(dist) + 100))\n",
    "\n",
    "    return Sig\n",
    "\n",
    "def db2pot(x):\n",
    "    pot = np.array([])\n",
    "    for i in range(len(x)):\n",
    "        pot = np.hstack((pot, 10**(x[i] / 10)))\n",
    "\n",
    "    return pot\n",
    "\n",
    "# The most important function here:\n",
    "def computeSINRs_MMSE(channel):\n",
    "    \n",
    "    vector = channel.copy()\n",
    "    r = channel.shape[0]\n",
    "    c = channel.shape[1]\n",
    "\n",
    "    SINRs = np.array([])\n",
    "\n",
    "    vectimesT = vector @ vector.T\n",
    "    vector = vector.T\n",
    "\n",
    "    for k in range(c):\n",
    "\n",
    "        desiredChannel = vector[k]\n",
    "        desiredtimesT = desiredChannel @ desiredChannel.T\n",
    "        solved = np.linalg.lstsq((vectimesT - desiredtimesT + \n",
    "                                  np.eye(r, dtype=float)), desiredChannel , rcond=-1)[0]\n",
    "        temp = desiredChannel @ solved\n",
    "        SINRs = np.hstack((SINRs, temp.reshape(-1)))\n",
    "\n",
    "\n",
    "    return SINRs\n",
    "\n",
    "def SINR_estimator(channel):\n",
    "    \n",
    "    noise_pwr = 1\n",
    "    transmited_pwr = np.linalg.norm(channel) ** 2\n",
    "    cdl = channel.copy()\n",
    "    r = channel.shape[0]\n",
    "    c = channel.shape[1]\n",
    "    SINR = np.array([])\n",
    "    \n",
    "    cdl = np.transpose(cdl @ cdl.T)\n",
    "    for k in range(c):\n",
    "        \n",
    "        channel_actual = cdl[k]\n",
    "        channel_actual_2 = channel_actual @ channel_actual.T\n",
    "        v_k = transmited_pwr*channel_actual_2 + (noise_pwr*noise_pwr*np.eye(r, dtype=float))\n",
    "        v_k_h = np.linalg.pinv(v_k) @ channel_actual\n",
    "        v_k_h_H = np.transpose(v_k_h.conj)\n",
    "        \n",
    "        actual_solve = (np.linalg.norm(v_k_h_H @ channel_actual) ** 2 ) * transmited_pwr\n",
    "        actual_solve = actual_solve * np.linalg.pinv(v_k_h_H @ v_k @ v_k_h)\n",
    "        SINRs = np.hstack((SINRs, actual_solve.reshape(-1)))\n",
    "\n",
    "    return SINRs\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1b9c120",
   "metadata": {},
   "source": [
    "The main loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "49472ad0",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_3168/829072230.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0mchannelCellfree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mchannelCellfree\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_antennas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnUe\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m     \u001b[0mSINR_cellfree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSINR_cellfree\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mSINR_estimator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchannelCellfree\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/tmp/ipykernel_3168/913947105.py\u001b[0m in \u001b[0;36mSINR_estimator\u001b[0;34m(channel)\u001b[0m\n\u001b[1;32m     61\u001b[0m         \u001b[0mv_k_h_H\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv_k_h\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         \u001b[0mactual_solve\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv_k_h_H\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mchannel_actual\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mtransmited_pwr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     64\u001b[0m         \u001b[0mactual_solve\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mactual_solve\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpinv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv_k_h_H\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mv_k\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mv_k_h\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m         \u001b[0mSINRs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSINRs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactual_solve\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: matmul: Input operand 0 does not have enough dimensions (has 0, gufunc core with signature (n?,k),(k,m?)->(n?,m?) requires 1)"
     ]
    }
   ],
   "source": [
    "#   Main loop:\n",
    "for i in range(loop):\n",
    "\n",
    "    channelCellfree = np.array([])\n",
    "\n",
    "    for j in range(nUe):\n",
    "\n",
    "        distanceCellfree = np.absolute(APcellfree.reshape(-1) - UEloc[i][j])\n",
    "        channelEvaluate = np.sqrt(np.multiply\n",
    "                                  (np.exp(1j * 2 * np.pi * np.random.rand(n_antennas, 1)),\n",
    "                                   SNR(distanceCellfree)))\n",
    "        \n",
    "        channelEvaluate = np.diagonal(channelEvaluate)\n",
    "        channelCellfree = np.hstack((channelCellfree, channelEvaluate.T))\n",
    "\n",
    "    channelCellfree = channelCellfree.reshape(n_antennas, nUe)\n",
    "    SINR_cellfree = np.hstack((SINR_cellfree,SINR_estimator(channelCellfree)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e81338a1",
   "metadata": {},
   "source": [
    "And here, the plot of eCDF of SINR in this simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bc902a39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'eCDF of Cell-free Massive MIMO model.')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.plot(pow2db(sorted(SINR_cellfree),(nUe*loop) ), np.linspace(0,1, (nUe*loop)), color='red', linestyle='dashed')\n",
    "plt.xlabel('SINR [dB]')\n",
    "plt.ylabel('CDF')\n",
    "plt.title('eCDF of Cell-free Massive MIMO model.')\n"
   ]
  }
 ],
 "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}