TP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Réseau d'accès radio TP\n",
    "Lucas Hocquette - Quentin Goulas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1\n",
    "def sample_users(K,R):\n",
    "    v = np.random.uniform(low=0,high=R**2,size=K)\n",
    "    theta = np.random.uniform(low=0,high=2*np.pi,size=K)\n",
    "    r = np.sqrt(v)\n",
    "    x,y = r*np.cos(theta), r*np.sin(theta)\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The percentage of users for which the decoding condition is satisified is : 95.0%\n"
     ]
    }
   ],
   "source": [
    "# 2\n",
    "r = 1\n",
    "W = 3.84*10**6\n",
    "theta = 0.4\n",
    "sigma2 = 10**(-104/10)*1e-3\n",
    "P = 10**(40/10)*1e-3\n",
    "\n",
    "def measure_achievement_ratio(K,R,gamma,n_avg=1):\n",
    "    x,y = sample_users(K,r)\n",
    "    d = np.sqrt(x**2+y**2)\n",
    "    L = -128.1 - 37.6*np.log10(d)\n",
    "    l = 10**(L/10)\n",
    "    history = np.zeros(n_avg)\n",
    "    for i in range(n_avg):\n",
    "        h = np.random.exponential(0.5,K)\n",
    "        g = l*h\n",
    "        p = P/K\n",
    "        SINR = W/R*p*g/(theta*(K-1)*p*g+sigma2)\n",
    "        history[i] = np.mean(SINR>=gamma)\n",
    "\n",
    "    return history\n",
    "\n",
    "print(f'The percentage of users for which the decoding condition is satisified is : {measure_achievement_ratio(20,32*1e3,10**(7/10))[0]*100}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta = 98.1%\n"
     ]
    }
   ],
   "source": [
    "# 3 and 4\n",
    "\n",
    "achievement_ratio = measure_achievement_ratio(20,32*1e3,10**(7/10),100)\n",
    "print(f'delta = {np.mean(achievement_ratio)*100}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.         1.         0.99666667 0.9975     0.998      0.99166667\n",
      " 0.99285714 0.99125    0.99333333 0.987      0.99181818 0.99333333\n",
      " 0.99076923 0.98571429 0.98       0.991875   0.98235294 0.98166667\n",
      " 0.98263158 0.9825     0.98238095 0.975      0.98217391 0.96333333\n",
      " 0.9764     0.96961538 0.96444444 0.96892857 0.96241379 0.94666667\n",
      " 0.96548387 0.939375   0.94606061 0.95647059 0.95428571 0.93694444\n",
      " 0.94675676 0.925      0.92820513 0.91475    0.88170732 0.90666667\n",
      " 0.88116279 0.88159091 0.89644444 0.84934783 0.87574468 0.893125\n",
      " 0.8344898  0.8216     0.80588235 0.77134615 0.75811321 0.79\n",
      " 0.69036364 0.69446429 0.61912281 0.44827586 0.42101695 0.23133333\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.         0.         0.         0.\n",
      " 0.         0.         0.        ]\n",
      "The maximum number of users on the network is 42\n"
     ]
    },
    {
     "data": {
      "image/png": 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95i7fwMOvLubfby/noOG9ufTYPSnIDb7wzYxn5qzg9YXr2VxTx6aaoD6jR0EuPQpzKMzNpsGC+eobDAMazHh/1SYeeW0JdQ0N7D+4J699uA4Ddi8rYHnVFv567kQ+OqQXAKs2buWSh96ivCiXLxw4hL37l6XpnehYnghcpkspESQs/DxwXNi5NZJKgX+Y2cc7PNIIunsiiMuKqi3c8uJ7PDFrOYeN7sOXDh5CaX4un7ruRdZtruXRrx/Exq11fPmOGazauJUsic219RwwpBenTxjI4Xv2pUdBLhBUjL+1eD2ba+qZMLRX0qudXYUnApfp2psI5gBjzWxrOJwPvGlmaWnY3RNBx1qwciMnXfsivYrzWLFhK6UFOdx81kcZ1LuIB2Ys5I7/vc/CNZvJy87ikJEVlBbk8Py7q1izqQaAQb2KOHPiIE7dfyA9i/N2WPeitdXc9uL7XPiJEZQX5TW3+U7jicBlumSJIEpl8Z3ANEl/C4dPInhYzHUDwypLuO6M/Tn7tmns3a8HN541ftudSV8+ZBhfOmgory1cxz/fWso/Zy5jS209h46qZNLooH+Lv7z0Ib+c+g7XPD2Pu86ZwLiB5QBs2FLLObfPYM7yDVTX1PF/nx6brl10zrUiUp/FYfMPh4SDz5vZa7FGlYRfEcRj0dpq+pQWkJfT9ofNZy+p4vy7Z7Cuupa/fHkCe/Ur49w7Z/Dc3JUcOLw3L8xbxcNfPZB9B/XcadlXP1zLzx6bzZbaBob0LmJw72JO2rcfe+zWoyN2axu/InCZLtkVQYufekm9Gv+A94G7wr8PwnGuGxnQsyilJAAwpl8P7jl3ImWFuZxx88t8677XefqdFVx+4l5cf+b+9CnN58ePzqK+YfuPji219fxy6tuccv1/Wb5+C7uXFTBn+QZueWEBp/35f8xdvqGjds0514pkRUOvAAY0VxNowLBYInJd0oCeRdx73kQ+e+NLTHljCWd/bDCfnzgYgB8eN4Zv3PMa90z7kE/t25+HX13EzS+8xwerq/nchEFceswelIYV0QvXVHPy9f/lrFum8dDXDqR/eSELVm7kJ1NmUVPXwJ3nHEB+jj+R7VxHilQ0tCvxoqFd25J1m3nq7eWcfsAgcsKH3syMz930Mm8tXo+ADVvr2Lt/Dy45ek8OHlmx0zreXlrFaTf8jz6l+Ry7z+7c8NwC8nKy2Li1jnMOHsqPjh/T5ri8aMhlupSKhpqs4ERJvw3/ju/Y8Fx30q+8kM9/bMi2JAAgiZ+dtBc9CnI4bI8+PPTVA/n7BQc3mwQA9ty9BzefNZ6Fazdz9dPzOHrv3Xj6O4dy1scGc8sL7/HsnBWdtTvOZYQot49eSfBA2V/CUacD083sBzHH1iy/Isgcr364lpq6BiaGzYBsqa1n8jUvsnrTVv75zY/TqziP+Ss3UlPX0OqDb35F4DJde28fPRb4iJk1hCu7A3gNSEsicJljvyZ3GRXkZnP15/blhKtf4ISrX6BqSy3V4dPV5x86jO9/co8u8XCbc7uaqI3OlQNrwtfdo80B1yWN6lvKlSfvwz0vL2RMvx6MHVDGKx+s5YbnFvDh6mquOu0j3ry3c20UJRH8H/CapGcI7iD6OHBJrFE5l8Sn9h3Ap/YdkDDcn6EVxfxi6tssuekl7j13oicD59qg1cpiM7sHmAg8DDwEfMzM7os7MOeiksSXDxnGNafvxxsL1/HXaR+mOyTnupSoTxBlAauAdcAoSWlpcM65ZI4buzsTh/XipucXsLVue09z7y7fwCsfrGXVxq1pjM65XVerRUOSfgV8BpgFNDZ6b8DzMcbVojlz5my7A8S5ptZvruXtpVXs+1AJfcIuQ2ctqWLT0nm8vVQcdMjHd+jUxzkXrY7gJGB0Y+ujzu3KygpzKc7PYcm6zVSW5rOyaisbttSSn5PN1roGPlxTzfDKkp2Wq61vYM6yDRTn5zC0orjF9dc1GFtr6ynO7xK9vDoXSZSzeQFBhzK7RCIYPXq03wvukvrXzKV85e5XOfv4Mfz+33M5qV8Plv31Uj5cU03DsT/hyvMmbns2AYJmLc685WVKVldTmJvN1B8dQVHezh+Nqi21fOaGl1i6fAP/+sHh9C7J78zdcq5dgr7Ampes0bmrJf2JoPew1yXdIOlPjX8xxOlchzhqzG4Mryzmisdms7WugV9+ah8ABvQsZEDPQi57ZCZVW2pZV13DzMXrOe2G/7F2Uw3fP3oPNtfW88w7K3da55baes67cwZvL62ivsF4cf7qzt4t52KTrLB0BkHDc1OAnwH/DYcb/5zbJWVlia9NGgHABYeNYFhYFJQlccXkvZi3YiNjL3+Cj1zxJMdf/QK19Q3cd/7HOO/jw6goyWPqW0t3WF99g3Hx/a/z0oI1XHXaOEoLcnjx3VWdvl/OxaXFoiEzu6PpOEk9gYFm9masUTnXTp/erz+Dexft1AfCJ/boy3Vn7McHq6vJy8kiPyeLw/boQ//yQgCO3ns3HnxlEdU1dduKh37/5FymvrWMy47bk0/vN4DHZy3jhXmrMLOkl9vOdRVR7hp6FjgxnPcVYIWkF83s4phjcy5lkhg/pPluM47dZ/cWlzt2n925+6UPeeadlRw3dnfmrdjIn5+bz6f368+XDwlaXj94ZCWPz1rO+6urk1YsO9dVRLmPrszMqoBPA3ea2QTgiHjDci49JgztTUVJHv94awlmxuVTZlGYl80Pjt1z2zyHjAhaTX3h3Z3rEpzriqIkghxJuwOnAY/FHI9zaZWdpaDZ63dW8LfXFvPCvFV8+8hRVCTcITS4dxH9ywt5YZ7XE7juIUoiuAJ4HJhvZtMlDQPejTcs59LnuH36saW2ge8/9CZ77FbKmWFPa40kccjICv47fzV19Q0trMW5riNKW0MPmNlYM/tqOLzAzE6OPzTn0uOAob2oKMmntt64YvLeO3Sy0+igERVs2FLHm4vXpyFC5zpWq4lA0ihJT0maGQ6PlXRZ/KE5lx7ZWeLbR43iW0eM4oChzVc4HzSiAgm/jdR1C1GKhm4CLgVqAcJbRz8bZ1DOpdvpBwzim0eMbHF6r+I89urXg/94PYHrBqIkgiIzm9ZkXF0cwTjXlRw0ooLXPlzLgpUb0x2Kc+0SJRGskjScoMVRJJ0CLE2+iHPd32njB1JakMvka1/k+bl+K6nruqIkgq8DNwB7SFoMXAR8Jc6gnOsKhleW8OjXD6J/eSFfuG0aN/9nAWaW7rCca7OkiUBSNvA1MzsCqAT2MLODzeyDTonOuV3cwF5FPPTVAzlqzG78/B9v85vH53gycF1O0kRgZvXAweHrTWa2oVOicq4LKc7P4boz9uNzEwZx3bPzPRm4LidKfwSvSZoCPABsahxpZg+3tqCko4E/AtnAzWZ2ZZPpg4A7gPJwnkvMbGrk6J3bRWRliZ9P3huA656dD8B3PznaG6VzXUKURFAArAY+kTDOCDqzb1FYrHQtcCSwCJguaYqZzU6Y7TLgfjO7XtIYYCowJHr4zu06miaDPXfvwQnj+qU5Kuda12oiMLMvprjuA4B5ZrYAQNK9wGQgMREY0CN8XQYsSXFbzu0SGpPBywtW8+fn5nP82N39qsDt8qI0Q10JnEvwS33b/Gb2pVYW7Q8sTBheBExoMs/lwBOSLgSKaaFVU0nnAecBDBo0qLWQnUurrCxx7iHDuOTht/jv/NUcFLZW6tyuKsrto48S/Fr/N/CPhL+OcDpwu5kNAI4F7pK0U0xmdqOZjTez8ZWVlR20aefic9K+/akoyefG5xc0O93MOPPml/nDv+d2cmTO7SxKHUGRmX0/hXUvBgYmDA8IxyU6BzgawMz+J6kAqABWpLA953YZBbnZfOHAwfz2ibm8s6yKPXbrscP0J2cv54V5q9hUU8dFR4xKU5TOBaJcETwm6dgU1j0dGClpqKQ8gvaJpjSZ50PgcABJexJUTPsjmq5bOHPiYApzs3e6KjAz/vR00JL7/BUb/VZTl3YtJgJJGyRVAd8kSAabJVUljE/KzOqACwj6Mnib4O6gWZKukHRiONu3gXMlvQHcA3zB/FPhuonyojw+89GBTHl9CUvXb942/pk5K5i5uIp9+pdRtaWOVRtr0hilc0kSgZmVmlmP8H+WmRUmDPdoabkm65hqZqPMbLiZ/SIc92MzmxK+nm1mB5nZODP7iJk90TG75dyu4ZyDhyLBl26fwZJ1mzEz/vjUPAb0LORbRwatm85b4Y3WufSK0h/BU1HGOed2NrBXETedNZ5Fa6qZfO2LXP/cfN5YuI6vHzZiW73BfG+91KVZsqKhAkm9gQpJPSX1Cv+GENwa6pyLYNLoPjz0tQPJz8ni1/+aQ7+yAk7ebwC79SigKC/bE4FLu2R3DZ1P0NJoP+AVoPGpmCrgmnjDcq57GdW3lEe+fhA//ftsThzXj7yc4DfYsMpiLxpyaddiIjCzPwJ/lHShmV3diTE51y1VlORz9en77jBuRGUJ099fm6aInAtE6bzek4BzMRleWcLidZuprvFO/1z6RHmOwDkXk+F9SgBYsHJTK3M6Fx9PBM6l0YgwEXiFsUunNicCSaMk3RRHMM5lmsG9i8iSP0vg0ivZ7aNjJT0haaakn0vaXdJDwNPs2JS0cy5F+TnZDOpV5FcELq2SXRHcBPwVOJmg/Z/XgfnACDP7ffyhOZcZRvQpYf4KryNw6ZMsEeSb2e1mNie8lXSTmX3PzLZ0VnDOZYLhlSW8t2oTdfUN6Q7FZahkD5QVSNqX7Q+SbU0cNrNX4w7OuUwwvLKEmvoGFq3dzJCK4nSH4zJQskSwDLiqhWFjxz6MnXMpGp5w55AnApcOyZ4sntSJcTiXsYZXBl/+81Zs5PA9+1JT14AEudl+d7frHC0mAkkfT7Kcmdl/YojHuYxTXpRHRUkeU95YwovzVzP9vTWM6lvCoxccnO7QXIZIVjT03WbGGTCWoAvK7Fgici4DjR1QztPvrGBEnxJG7VbKGwvXsX5zLWWFuekOzWWAZEVDJyQOSzoIuIygruDCmONyLqNcffq+VNfUU1maz/NzV3LWrdOYuXg9B42oSHdoLgO02nm9pMOBHxFcDfzSzJ6MPSrnMkxxfg7F+cHHceyAMgBeX7jOE4HrFMnqCI4DfgisBy4zsxc6LSrnMlh5UR5Dehfx5qJ16Q7FZYhkVwR/BxYBq4HvSfpe4kQzO7HZpZxz7TZ2QDnT31+T7jBchkiWCA7rtCicczsYN7CcKW8sYUXVFvr0KEh3OK6bS1ZZ/FxnBuKc225cWE/wxqL1HDnGE4GLV7I6grcIKoh3mkTwHMHY2KJyLsPt1a+M7CzxxsJ1HDmmb7rDcd1csqKh4zstCufcDgrzshnVt5Q3vMLYdYIWn2E3sw8S/4CNwH5ARTjsnIvRuAFlvLloPWbNXZg713GSdUzzmKS9w9e7AzOBLwF3Sbqoc8JzLnONG1jO+s21fLC6Ot2huG4uWatWQ81sZvj6i8CT4dPGEwgSgnMuRmO3VRivS28grttLlghqE14fDkwFMLMNgPeg4VzMRvUtpSA3izcXrU93KK6bS1ZZvFDShQQPle0H/AtAUiHgLWE5F7Pc7Cz26lfGGwvXpTsU180luyI4B9gL+ALwGTNbF46fCNwWb1jOOYB9+pcxe2mVVxi7WCW7a2iFmX3FzCab2RMJ458xs99GWbmkoyXNkTRP0iUtzHOapNmSZkn6a9t3wbnuq195AdU19WzcWpfuUFw31mrro6mSlA1cCxxJULw0XdIUM5udMM9I4FLgIDNbK6lPXPE41xVVluYDsHLDVkoLvETWxSPOvvAOAOaZ2QIzqwHuBSY3medc4FozWwvBVUiM8TjX5VSUBIlg1caaNEfiurOkiUBStqRvpbju/sDChOFF4bhEo4BRkl6U9JKko1uI4zxJMyTNWLlyZYrhONf1JF4ROBeXpInAzOqB02Pcfg4wEpgUbucmSeXNxHGjmY03s/GVlZUxhuPcrqVy2xWBJwIXnyh1BC9Kuga4D9jUONLMXm1lucUEfRs3GhCOS7QIeNnMaoH3JM0lSAzTI8TlXLfXsyiP7Cz5FYGLVZRE8JHw/xUJ4wz4RCvLTQdGShpKkAA+C3yuyTyPEFwJ3CapgqCoaEGEmJzLCFlZondxnicCF6tWE4GZpdRBjZnVSboAeBzIBm41s1mSrgBmmNmUcNpRkmYD9cB3zWx1KttzrruqKMn3oiEXqyid1/cFfgn0M7NjJI0BPmZmt7S2rJlNJWyaImHcjxNeG3Bx+Oeca0ZlaT4rPRG4GEW5ffR2gl/u/cLhucBFMcXjnGuioiSfVV405GIUJRFUmNn9hA3NmVkdQTGOc64TVJbms2pjjTcz4WITJRFsktSbsNtKSRMBbw7RuU5SUZJHTX0DVZu9mQkXjyh3DX0bmAIMl/QiUAmcEmtUzrlttj1UtnELZUXezITreFHuGnpF0qHAaIKO6+eE9/075zpB40NlKzfUMMJb43IxaLVoSNKbwPeALWY205OAc51r+xWBVxi7eESpIzgBqAPulzRd0nckDYo5LudcyNsbcnFrNRGY2Qdm9msz25/gyeCxwHuxR+acA6CsMJfcbPlDZS42kfojkDQY+Ez4V09QVOSc6wSSqCjJ9ysCF5soTxa/TNBH8QPAqWbmbQE518m8mQkXpyhXBGeZ2ZzYI3HOtaiyNJ/lVVvSHYbrpqJUFi+TdFVjxzCSfiepLPbInHPbVJTk+RWBi02URHArsAE4LfyrAm6LMyjn3I4am5loaPBmJlzHi1I0NNzMTk4Y/qmk12OKxznXjIqSfOobjLXVNfQOHzBzrqNEuSLYLOngxgFJBwGb4wvJOddU47ME3om9i0OUK4KvAHcm1AusBc6OLyTnXFMVJdsfKhu9W2mao3HdTZS2ht4AxknqEQ5XxR6Vc24H268IvMLYdbxID5SBJwDn0inxisC5jhaljsA5l2Y9CnLIy8nyKwIXC08EznUBkqj0ZiZcTKI0Q32qpNLw9WWSHpa0X/yhOecSVXgn9i4mUa4IfmRmG8JbSI8AbgGujzcs51xTfkXg4hIlETR2VH8ccKOZ/QPIiy8k51xzKku9mQkXjyiJYLGkGwiaoJ4qKT/ics65DlRZks+aTTXUezMTroNF+UI/DXgc+KSZrQN6Ad+NMyjn3M6GVhbTYPD0OyvSHYrrZpImAknZwKtm9rCZvQtgZkvN7IlOic45t83xY/sxvLKYX/xjNlvr6ltfwLmIkiYCM6sH5ngfxc6lX252Fj86fgzvr67mjv++n+5wXDcS5cninsAsSdOATY0jzezE2KJyzjVr0ug+HDa6kj89NY9P7TtgW9MTzrVHlETwo9ijcM5FdtnxY/jk75/nd0/M4cqTx6Y7HNcNtFpZbGbPAe8DueHr6cCrMcflnGvB8MoSzj5wCPfNWMjidd4ivGu/KE8Wnws8CNwQjuoPPBJjTM65Vhw2ug9msHBNdbpDcd1AlNtHvw4cRNBFJeHdQ32irFzS0ZLmSJon6ZIk850sySSNj7Je5zJd75Lgmc41m7yjGtd+URLBVjPbdrZJygFafaIlvPX0WuAYYAxwuqQxzcxXCnwTeDlq0M5lut7FQSJY7U8auw4QJRE8J+kHQKGkI4EHgL9HWO4AYJ6ZLQgTyb3A5Gbm+xnwK2BLxJidy3g9GxOBXxG4DhAlEVwCrATeAs4HpgKXRViuP7AwYXhROG6bsBXTgWH7RS2SdJ6kGZJmrFy5MsKmnevecrOz6FGQ40VDrkNE6aqyAbgJuElSL2CAmbW7sRNJWcBVwBcixHAjcCPA+PHjvaEV54DeJfl+ReA6RJS7hp6V1CNMAq8QJITfR1j3YmBgwvCAcFyjUmBv4FlJ7wMTgSleYexcNL2L81iz0ROBa78oRUNlYX/FnwbuNLMJwOERlpsOjJQ0VFIe8FlgSuNEM1tvZhVmNsTMhgAvASea2Yw274VzGahXcR6rN3llsWu/KIkgR9LuBK2QPhZ1xWZWB1xA0HLp28D9ZjZL0hWSvHkK59qpd0me1xG4DhGliYkrCL7MXzCz6ZKGAe9GWbmZTSWoXE4c9+MW5p0UZZ3OuUCv4jzWVtfS0GBkZSnd4bguLEpl8QMEt4w2Di8ATo4zKOdc63oX51PfYKzfXLvtdlLnUtFqIpB0G808QGZmX4olIudcJI1PF6/eVOOJwLVLlKKhxHqBAuBTwJJ4wnHORdUr4eniEX1K0hyN68qiFA09lDgs6R7ghdgics5F0pgIvMLYtVcqndCPJGKjc865+PQuDjql8YfKXHtFqSPYwI51BMuA78cWkXMuEr8icB0lStFQaWcE4pxrm7ycLEq9vSHXAVIpGnLO7SJ6F+exypuidu3kicC5LqxXsT9d7NqvxUQgaWhnBuKca7veJfmeCFy7JbsieBBA0lOdFItzro16F+f5XUOu3ZJVFmeFPZONknRx04lmdlV8YTnnouhVnMfaTTXe3pBrl2RXBJ8F6gmSRWkzf865NOtVnEddg1G1pTbdobgurMUrAjObA/xK0ptm9s9OjMk5F1Fie0PlRd7ekEtNlLuG/ivpqsY+gyX9TlJZ7JE551rV+HSxVxi79oiSCG4FNhB0THMaUAXcFmdQzrlotjc854nApS5K66PDzSyx/4GfSno9pnicc23QWDTkVwSuPaJcEWyWdHDjgKSDgM3xheSciyqxKWrnUhXliuArwJ0J9QJrgbPjC8k5F1V+Tjal+Tn+LIFrlyiNzr0BjJPUIxyuij0q51xkvbwTe9dOUa4IAE8Azu2qvL0h117e6JxzXZw3M+HayxOBc11cr+I8ryx27RKpaEjSgcCQxPnN7M6YYnLOtUHvknzWVtdgZkje3pBruyhdVd4FDAdeJ2h7CIKuKz0ROLcL6F2cR229UbWljrLC3HSH47qgKFcE44ExZmatzumc63SJfRd7InCpiFJHMBPYLe5AnHOp2Z4IvJ7ApSbKFUEFMFvSNGDbmWZmJ8YWlXMussaG57y9IZeqKIng8riDcM6lrrE4aP1m75PApSbKk8XPSeoLfDQcNc3MVsQblnMuKk8Err1arSOQdBowDTiVoBnqlyWdEmXlko6WNEfSPEmXNDP9YkmzJb0p6SlJg9u6A85lutKCHCSo8kTgUhSlaOiHwEcbrwIkVQL/JuzcviWSsoFrgSOBRcB0SVPMbHbCbK8B482sWtJXgV8Dn2n7bjiXubKyRI+CXNZ5InApinLXUFaToqDVEZc7AJhnZgvMrAa4F5icOIOZPWNm1eHgS8CACOt1zjVRXpTrRUMuZVGuCP4l6XHgnnD4M8DUCMv1BxYmDC8CJiSZ/xyg2b6RJZ0HnAcwaNCgCJt2LrOUFeayrtoTgUtNlMri70o6GTgoHHWjmf2tI4OQdCbBg2uHthDDjcCNAOPHj/cH25xroqzQrwhc6iK1NWRmDwEPtXHdi4GBCcMDwnE7kHQEQT3EoWbmT8Q4l4KywlwWr/WOA11qWizrl/RC+H+DpKqEvw2SovRNMB0YKWmopDzgs8CUJtvYF7gBONFvSXUudWWFXlnsUtfiFYGZHRz+L01lxWZWJ+kC4HEgG7jVzGZJugKYYWZTgN8AJcADYauJH/oTy861XWPRkLdA6lIRqfVRM/t8a+OaY2ZTaVKxbGY/Tnh9RBtidc61oLwol/oGY1NNPSX5kTsedA6IdhvoXokDknKA/eMJxzmXisani9dVe3tDru2S1RFcKmkDMDaxfgBYDjzaaRE651pVVhi0QOp3DrlUtJgIzOz/gDLgTjPrEf6VmllvM7u080J0zrVmW3tD/iyBS0HSoiEza2B7Y3POuV2UNzzn2iNKHcGrkjwZOLcLKy/yROBSF+X2ggnAGZI+ADYBAszMxsYamXMusm2VxZ4IXAqiJIJPxh6Fc65divKyyc2WXxG4lLRaNGRmHwDlwAnhX3k4zjm3i5DkDc+5lEXpmOabwF+APuHf3ZIujDsw51zb9CjM9c5pXEqiFA2dA0wws00Akn4F/A+4Os7AnHNtU+4tkLoURblrSEB9wnB9OM45twsJGp7zJ4td20W5IriNoJ/ivxEkgMnALbFG5Zxrs/KiPOat3JjuMFwXFKVjmqskPQscDBjwRTN7Le7AnHNtU1aY608Wu5REKRpqpCb/nXO7kB6FuVRtqaO+wTvxc20T5a6hHwN3AD2BCuA2SZfFHZhzrm3Kw4fKNmzxqwLXNlHqCM4AxpnZFgBJVwKvAz+PMS7nXBttb4q6lvKivDRH47qSKEVDS4CChOF8mul72DmXXt7wnEtVlCuC9cAsSU8SVBYfCUyT9CcAM/tGjPE55yLyhudcqqIkgr+Ff42ejScU51x7eMNzLlVRbh+9Q1IeMCocNcfM/ExzbhdT5lcELkVROq+fRHDX0PsEt44OlHS2mT0fa2TOuTbZ3kuZP13s2iZK0dDvgKPMbA6ApFHAPXgH9s7tUvJzsinIzfIrAtdmUe4aym1MAgBmNhfIjS8k51yqygvzPBG4NotyRfCKpJuBu8PhM4AZ8YXknEuV90ngUhElEXwF+DrQeJvof4DrYovIOZeysiJvitq1XdJEICkbeMPM9gCu6pyQnHOpKivMZeGa6nSH4bqYpHUEZlYPzJE0qJPicc61Q5l3TuNSEKVoqCfBk8XTgE2NI83sxNiics6lxHspc6mIkgh+FHsUzrkOUVaYS3VNPTV1DeTltKWVeZfJWkwEkgoIKopHAG8Bt5hZXWcF5pxru8SniytL89Mcjesqkv1kuAMYT5AEjiF4sMw5twvzFkhdKpIlgjFmdqaZ3QCcAhzS1pVLOlrSHEnzJF3SzPR8SfeF01+WNKSt23DObbc9EXgzEy66ZIlg20+KVIqEwltPryW4mhgDnC5pTJPZzgHWmtkI4PfAr9q6Hefcdo0d0vgVgWuLZJXF4yRVha8FFIbDAszMerSy7gOAeWa2AEDSvcBkYHbCPJOBy8PXDwLXSJKZeaerzqWg8YrgBw/PpLTgnTRH4zraNw4fyQnj+nX4eltMBGaW3c519wcWJgwvAia0NI+Z1UlaD/QGViXOJOk84DyAQYP8kQbnWjKoVxFnfWwwqzZuTXcoLgaNib6jRbl9NO3M7EbgRoDx48f71YJzLcjOEldM3jvdYbguJs4bjRcDAxOGB7BzX8fb5pGUA5QBq2OMyTnnXBNxJoLpwEhJQ8Mezj4LTGkyzxTg7PD1KcDTXj/gnHOdK7aiobDM/wLgcSAbuNXMZkm6AphhZlOAW4C7JM0D1hAkC+ecc50o1joCM5sKTG0y7scJr7cAp8YZg3POueS8MRLnnMtwngiccy7DeSJwzrkM54nAOecynLra3ZqSVgIftGGRCpo8qZwhfL8zT6buu+93NIPNrLK5CV0uEbSVpBlmNj7dcXQ23+/Mk6n77vvdfl405JxzGc4TgXPOZbhMSAQ3pjuANPH9zjyZuu++3+3U7esInHPOJZcJVwTOOeeS8ETgnHMZrlsnAklHS5ojaZ6kS9IdT1wkDZT0jKTZkmZJ+mY4vpekJyW9G/7vme5Y4yApW9Jrkh4Lh4dKejk87veFzaB3K5LKJT0o6R1Jb0v6WCYcb0nfCs/xmZLukVTQHY+3pFslrZA0M2Fcs8dXgT+F+/+mpP3aur1umwgkZQPXAscAY4DTJY1Jb1SxqQO+bWZjgInA18N9vQR4ysxGAk+Fw93RN4G3E4Z/BfzezEYAa4Fz0hJVvP4I/MvM9gDGEex/tz7ekvoD3wDGm9neBM3bf5buebxvB45uMq6l43sMMDL8Ow+4vq0b67aJADgAmGdmC8ysBrgXmJzmmGJhZkvN7NXw9QaCL4X+BPt7RzjbHcBJaQkwRpIGAMcBN4fDAj4BPBjO0u32W1IZ8HGC/jwwsxozW0cGHG+CpvMLwx4Ni4CldMPjbWbPE/TRkqil4zsZuNMCLwHlknZvy/a6cyLoDyxMGF4UjuvWJA0B9gVeBvqa2dJw0jKgb7riitEfgO8BDeFwb2CdmdWFw93xuA8FVgK3hUViN0sqppsfbzNbDPwW+JAgAawHXqH7H+9GLR3fdn/XdedEkHEklQAPAReZWVXitLAL0G51r7Ck44EVZvZKumPpZDnAfsD1ZrYvsIkmxUDd9Hj3JPj1OxToBxSzc/FJRujo49udE8FiYGDC8IBwXLckKZcgCfzFzB4ORy9vvEQM/69IV3wxOQg4UdL7BEV/nyAoOy8Piw6gex73RcAiM3s5HH6QIDF09+N9BPCema00s1rgYYJzoLsf70YtHd92f9d150QwHRgZ3lGQR1CpNCXNMcUiLBe/BXjbzK5KmDQFODt8fTbwaGfHFiczu9TMBpjZEILj+7SZnQE8A5wSztYd93sZsFDS6HDU4cBsuvnxJigSmiipKDznG/e7Wx/vBC0d3ynAWeHdQxOB9QlFSNGYWbf9A44F5gLzgR+mO54Y9/NggsvEN4HXw79jCcrLnwLeBf4N9Ep3rDG+B5OAx8LXw4BpwDzgASA/3fHFsL8fAWaEx/wRoGcmHG/gp8A7wEzgLiC/Ox5v4B6CepBagivAc1o6voAI7pCcD7xFcFdVm7bnTUw451yG685FQ8455yLwROCccxnOE4FzzmU4TwTOOZfhPBE451yG80TgugxJJul3CcPfkXR5B637dkmntD5nu7dzatha6DNxb8u5qDwRuK5kK/BpSRXpDiRRwlOtUZwDnGtmh8UVT6M2xuUymCcC15XUEfTT+q2mE5r+ope0Mfw/SdJzkh6VtEDSlZLOkDRN0luShies5ghJMyTNDdsxauzr4DeSpodtvZ+fsN7/SJpC8HRr03hOD9c/U9KvwnE/Jnj47xZJv2ky/ySF/SmEw9dI+kL4+koFfU28Kem34bhKSQ+FcU2XdFA4/nJJd0l6EbhL0l7hvr4eLj+y7W+76+78F4Praq4F3pT06zYsMw7Yk6BZ3wXAzWZ2gIIOfC4ELgrnG0LQfPlw4BlJI4CzCB7Z/6ikfOBFSU+E8+8H7G1m7yVuTFI/gjby9ydoH/8JSSeZ2RWSPgF8x8xmRAlcUm/gU8AeZmaSysNJfyRog/8FSYOAx8N9hKD/jYPNbLOkq4E/mtlfwqZWsiO9Yy6jeCJwXYqZVUm6k6CDks0RF5tuYdsrkuYDjV/kbwGJRTT3m1kD8K6kBcAewFHA2ISrjTKCDkBqgGlNk0Doo8CzZrYy3OZfCPoPeCRivInWA1sIriIeAxqvGo4AxgRN7gDQI2x9FmCKmTW+N/8Dfhj22/Cwmb2bQgyum/OiIdcV/YGgrL04YVwd4fksKQtI7K5wa8LrhoThBnb8MdS0vRUjaMflQjP7SPg31MwaE8mm9uxEE9viDxUAWNDO/gEELYweD/wrnJ4FTEyIq7+ZbWwal5n9FTiRIGlODa9InNuBJwLX5ZjZGuB+duyS8H2CohgIvvhyU1j1qZKywnqDYcAcgiKXr4bNfCNpVNgJTDLTgEMlVSjoMvV04LlWlvmA4Bd+flj8c3i4vRKgzMymEtSNjAvnf4KgWItwvo80t1JJw4AFZvYngtYqx7YSh8tAXjTkuqrfARckDN8EPCrpDYJfzan8Wv+Q4Eu8B/AVM9si6WaCuoNXw6aPV9JKV4hmtlTSJQTNIwv4h5klbRrZzBZKup+gVc33gNfCSaXhfhWE67o4HP8N4FpJbxJ8jp8HvtLMqk8DPi+plqBXq18mi8NlJm991DnnMpwXDTnnXIbzROCccxnOE4FzzmU4TwTOOZfhPBE451yG80TgnHMZzhOBc85luP8HWO7VWITtenoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 5\n",
    "\n",
    "K_values = np.array(range(1,100))\n",
    "deltas = np.zeros(len(K_values))\n",
    "\n",
    "for i,K in enumerate(K_values) :\n",
    "    ach_rat = measure_achievement_ratio(K,32*1e3,10**(7/10),100)\n",
    "    deltas[i] = np.mean(ach_rat)\n",
    "\n",
    "print(deltas)\n",
    "print(f'The maximum number of users on the network is {K_values[np.sum(deltas>=0.9)]}')\n",
    "\n",
    "plt.plot(K_values,deltas)\n",
    "plt.title('Condition achievement rate by the number of users')\n",
    "plt.xlabel('Number of users')\n",
    "plt.ylabel('Proportion of users over SINR threshold')\n",
    "plt.axhline(0.9,color='0')\n",
    "plt.axvline(K_values[np.sum(deltas>=0.9)],color='0')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.22.4\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, clear_output\n",
    "print(np.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "vscode": {
     "languageId": "latex"
    }
   },
   "source": [
    "$$ \n",
    "F = \\begin{pmatrix} \n",
    "        0, \\frac{g_2}{R_1g_1}, \\cdots, \\frac{g_k}{R_1g_1} \\\\\n",
    "        \\frac{g_1}{R_2g_2}, 0, \\ddots, \\vdots \\\\\n",
    "        \\vdots, \\ddots, \\ddots, \\vdots \\\\\n",
    "        \\frac{g_1}{R_kg_k}, \\cdots, \\cdots, 0\n",
    "    \\end{pmatrix}       \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RSVslDRRZv0LSc5IeDH4uDa27WNJjwc/F0abcRSE8hgKmj6FoNABk/SKW5DaGdm//yZLYAoikDuBzwLnAicC7JJ1YZNObzOyU4Of6YN9DgU8ApwOnAZ+QNC+ipLsILV/Uyz0DSzm5d+60u/RGA0CWL2JJb2No5/afrImzBHIasNXMnjCzvcAQsKzKfc8G7jSzF8xsB3AncE6L0ukSqNEAkOWLWBKq58qpNAuwSw+ZWTwHli4EzjGzS4P37wZON7PLQtusAFYBzwFbgA+Z2c8kfQSYZWafCrb7S2DczP53keOsBFYC9PT0nDo0NATA2NgYs2fPbmEO49Eu+Rodn2BkxzhTob/fGRK987ro7uqs6jNHxyfYvnM3eyenmNkxg565s6ret1m2bNnCwoULm/qZm0Z2llx3cu/cph6rlHb5O8yKSvlasmTJBjPrK1ye9F5Y3wK+amZ7JP0RcCOwtJYPMLPVwGqAvr4+6+/vB2B4eJj86yxpp3wl9Ul/tdi2bVvTv68rB9cX7b3W293FB36/uccqpZ3+DrOg3nzFGUBGgKNC748Mlu1nZs+H3l4PfCa0b3/BvsNNT6FrWCsv8j7NRnGXn33CtC7KkJ3qOZcscbaB3A8cL+lYSTOBi4B14Q0kLQi9PQ94OHh9B3CWpHlB4/lZwTKXIElvzM0qb2NwUYmtBGJm+yRdRu7C3wHcYGabJV0NPGBm64A/lXQesA94AVgR7PuCpL8iF4QArjazFyLPhCvLB4zFx0tnLgqxtoGY2W3AbQXLPh56fQVwRYl9bwBuaGkCXUMa6Wp7QNXX6yYr7uOci1bSG9FdilWaiqSUYtOMjOyYZO3Gkf0PYkp743mS+fl11fIA0maivDjU25hbrOprymz/OIY457DKurjnCHPp4nNhtZGoG7XrbcwtV/WV9EFyaefn19XCSyBtJI5G7Xoac8tVfWV9Dqtioiw1tuP5dfXzEkgbScvFodg0IzMkLj/7hEzPYVVM1KXGdju/rjEeQNpIWi4Oxaq+eud1sXxRb6bnsCom6iqldju/rjFehdVG0jRCubDqa3h4eP9yoG16CUVdamy38+sa4wGkjWTl4pCEQXJRtUvU2xW6EUk4vy4dPIC0Gb84NK6Wrq6NBpo0lRpd+/E2EOdqVG27RDMawH1eK5dkXgJpcz7quHbVtks0q9u0lxpdUnkJpI35bLn1qbY3W1q6TTtXLw8gbcxHHden2q6uaek2nVVrN46weHA9xw7cyuLB9X5j1AIeQNqY3yHXp9p2CR9TER8vXUfD20DaWBxdRLOimnaJrHSbTiN/Fk00PIC0Me8i2nzFOiXcM7C0aZ/lF7/q1Fq69nNdHw8gbSyOO+Qs/6M2cyp0n1a9MbWUrv1c188DSJuLsoto1v9Rm1ltkqYqmGI3Bd0xp6mW0nWaznXSxNqILukcSY9K2ippoMj6D0v6iaQfSbpL0tGhdZOSHgx+1kWbclePrPf6amanhLR0cCjVWD06PhFrumoZgJmWc51EsZVAJHUAnwPeDDwF3C9pnZn9JLTZRqDPzHZJeh/wGeCdwbpxMzslyjS7xmT9H7WZnRLS0sGh1E3B9p3xBhCornS9duMIMyQmzQ5Yl7RznURxlkBOA7aa2RNmthcYApaFNzCzu81sV/D2XuDIiNPomijr4yKa2W03LV2ASwX/vZNTEaekdvnSU7HgkcRznUSyIicvkgNLFwLnmNmlwft3A6eb2WUltv8s8IyZfSp4vw94ENgHDJrZ2hL7rQRWAvT09Jw6NDQEwNjYGLNnz25mlhIhyfkaHZ9gZMc4U6G/uRkSvfO66O7qLLtvYb5GxyfYvnM3eyenmNkxg565syp+RhRqTdeWLVtYuHBhUz4rDo8+82LRYLHgZTB/3twYUlS9UmkX4shDi/9NJvn/qxGV8rVkyZINZtZXuDwVjeiS/gDoA94UWny0mY1IOg5YL2mTmT1euK+ZrQZWA/T19Vl/fz+Qe75E/nWWRJGvRnpS1btvOF9rN45wxV2bGJ+YQb4Q3dU5yarzT0xdo+e2bdtS9XdY+P0tefUx3LJh5IDG6lW/2ZH4fF0ycCtWpBJGwJODby66j183poszgIwAR4XeHxksm0bSmcCVwJvMbE9+uZmNBL+fkDQMLAIOCCCuvFov6I32pGpGry/vNROPYt/9LRtGuODUXu5+5LnpvbB2PhZzaitLSztTksXZBnI/cLykYyXNBC4CpvWmkrQI+AfgPDN7NrR8nqSDg9fzgcVAuPHdVaGe6R6S0JMq643xSVXqu7/7kee4Z2ApTw6+lXsGlqYmiKelnSnJYgsgZrYPuAy4A3gY+JqZbZZ0taTzgs2uBWYDXy/orvsa4AFJDwF3k2sD8QBSo3qCQRIu3llvjE+qJHz3zeTPWmlcrG0gZnYbcFvBso+HXp9ZYr/vAye3NnXZV88FoZpif6tHm/sULPFoRpVP0mYi8GetNMZn421j9dzJVyr2RzELqt85xqPRKh+fITd7UtELy7VGPXfylebPiqqB2+8coxf+jkdGx+mQplV5Vvo+vPND9ngAaWP1TqZY7uKdtXpyN13+e6+nJ57/bWSPB5A21+w7ee8amX31liT8byN7vA3ENZV3jcy+eksS/reRPV4CcU3lT+HLvnpLEv63kT0eQFzTeQN3tjXSjdr/NrLFA4hzriZeknB5HkCca0DSBsZFxUsSDjyAuAa16wUUsv+IXucq8QDi6tbuF1AfGNeYdr75yAoPIK5u7X4B9YFx9avl5sMDTXL5OBBXt3a/gPqswPWrdiZonz8r2TyAuLq1+wXUB8bVr9qbj1Y9f2btxhEWD67n2IFbWTy43gNSnTyAuLq1+wXUZwWuX7U3H60o5XqppnkqtoFI+gDwZTPbEUF6XIr4eADvzlqvagcjtmL+rHZvu2umakogPcD9kr4m6RxJanWiXHosX9SbyseZxurxx+H974c5c+DnP8/9fv/7c8vbRLWlt1aUckuVXkZGx70UUqOKJRAz+5ikvwTOAi4BPivpa8AXzax9/uKda4bbb4cLL4SJidwPwIsvwvXXw403ws03w7nnRp6sOHo6lSq9FablglN7ufuR55qWtlKlGqCtuqE3Q1VtIGZmwDPBzz5gHnCzpM80cvCgRPOopK2SBoqsP1jSTcH6+yQdE1p3RbD8UUlnN5IO51pt7cYR3nH5l9l13u/Arl0vBY+8iYnc8gsvjLwkkqQ2gWJpuWXDCJeffULTSrnFSjV5zWigbycVA4ik/yVpA/AZ4B7gZDN7H3AqcEG9B5bUAXwOOBc4EXiXpBMLNnsvsMPMXgVcB3w62PdE4CLgJOAc4PPB57kC3tskfvmL4tvv+ioHTe0rv/HEBFx3XTQJC7Sqp1NS05KvPiulXbqhN0M1JZBDgfPN7Gwz+7qZTQCY2RTwtgaOfRqw1cyeMLO9wBCwrGCbZcCNweubgTOCNphlwJCZ7TGzJ4Gtwee5kCTdWbaz/EVx+ea7mTk1WX7jiQn453+OJmGBJI3niSotyxf10tvm3dCbQbnaqRgOLF0InGNmlwbv3w2cbmaXhbb5cbDNU8H7x4HTgauAe83sy8HyLwK3m9nNRY6zElgJcPjhh5+6atUqAPbu3cvMmTNbl8GYhPP1i7E9TE4d+P12zBDzZx8cddIakubva/svdwPQM/bCAeueP+ggXrGvSKnkiCNanaz9WvF3Uu/3FeXf7O6JSX65ex/ha6Ak5sw6iFklqrjS/HdYTqV8XXLJJRvMrK9weeanMjGz1cBqgL6+PluxYgUAw8PD9Pf3x5ewFgnn69iBWyl2eyDgycG3RpmshqX5+1o8uJ6R0XE2XfdhDtk7/U56zTXXsOLKK6fvMGcO7NwZWfoKpxWBXE+nRsa01Pt9tSItlY5XS+eBNP8dllMpX5dccknR5XEGkBHgqND7I4NlxbZ5StJBwFzg+Sr3bXtJewZ1u85plB/zsPakJbzzoTvKV2N1dsK73x1d4kjWeJ6o0+LjeBoTZwC5Hzhe0rHkLv4XAb9XsM064GLgB8CFwHozM0nrgH+R9DfAEcDxwA8jS3lKNPLkuGZr55l78/n7l93v4oJNd1UOIB/6UEQpe0mSLqRJSosrL7apTMxsH3AZcAfwMPA1M9ss6WpJ5wWbfRF4haStwIeBgWDfzcDXgJ8A/wb8iZlVaJ1sP0maaiNJPX3isHxRL1+79g948Lp/ZLxzFntnFNSxd3bCy16WGwfyylfGk0jnahRrG4iZ3QbcVrDs46HXu4HfLbHvNcA1LU1gBiTlbi5JPX3isnbjCFdsP4zDLvk73nv/Ws7ffDcAEy8/hM4V78mVPDx4uBTxyRRdJNIwc2+rx8zkS2H/PW8BnzjrfZz8oa+xffah9H9sLXz2sx48XOpkvheWS4YktccUWrtxhKvWbWZ0/KXR4a1oo/FSmMsaL4G4SCSpPSYs37gfDh55zW6jSUMpzLlaeAnERSYp7TFhxRr3w5pZOihWCpOUiFKYc/XwAOLaWqUA0czSQbExDnNmHZS4oOpecsDYpdd5Z88wDyCurZWb2rsVbTSFpbA1a9Y09fNd8xQbuzSyY5K1G0c86Ae8DcS1tVJTe897WWci2mhK8VmWW69Y9eaUWduMXaqGl0BcW0vSNB7VSsuo/rRPXeO95irzAOLaXhIb98tJwzO9R8cnuOKu+INcI0EsaXPJJZFXYTmXMmm4M96+c3fsU9c0+jycYtWbM7zX3DQeQJxLmTSMJ9k7OVV0eZRBrtH514qNXeqd15WYUl4SeBWWi0Ta68OTJMmj+vNmdhS/N40yyDWjpFZYvTk8PNxosjLFA4irST2BIC2NvmmRhob/nrmz6OqcjDXIeRtG63kAcVWrNxCkodE3bZLe8N/d1cmq80+MNciloaSWdh5AXNXqDQRpaPR1zRd3kEtDSS3tPIC4qtUbCLwqwcUl7iCWdd4Ly1Wt3t4/xbpDelWCc+nnAcRVrd5AkNSp3J1zjYmlCkvSocBNwDHANuAdZrajYJtTgC8Ac4BJ4BozuylYtwZ4E7Az2HyFmT3Y+pS3t0bqlL0qwbnsiasNZAC4y8wGJQ0E7z9asM0u4D1m9pikI4ANku4ws9Fg/eVmdnN0SXbggcA595K4AsgyoD94fSMwTEEAMbMtodc/l/QscBgwGkkKnWsCH0DpskxmFv1BpVEz6w5eC9iRf19i+9PIBZqTzGwqqMJ6A7AHuAsYMLM9JfZdCawE6OnpOXVoaAiAsbExZs+e3awsJYbnKzlGxycY2THOVOh/bIZE77wuurs6AdiyZQsLFy6MK4k1Gx2fYPvO3eydnGJmxwx65s7an5ewNH5f1WjXfC1ZsmSDmfUVLm9ZCUTSd4HDi6y6MvzGzExSySgmaQHwz8DFZpafYOcK4BlgJrCaXOnl6mL7m9nqYBv6+vqsv78fyE1JkH+dJZ6v5Fg8uJ6R0QOfNdLb3cE9A/0AbNu2LTX5WrtxJJhhdwb5/jddnZOsOv/EA0pVafy+quH5mq5lAcTMziy1TtJ2SQvM7OkgQDxbYrs5wK3AlWZ2b+iznw5e7pH0T8BHmph055oiawMomzWjgFfrZUdc3XjXARcHry8Gvlm4gaSZwDeALxU2lgdBJ1/9tRz4cSsT2078SXfNk4ZZc2vRjIDY6BTrLlniCiCDwJslPQacGbxHUp+k64Nt3gG8EVgh6cHg55Rg3VckbQI2AfOBT0Wa+ozK4j93nAExawMomxEQG51i3SVLLL2wzOx54Iwiyx8ALg1efxn4con9l7Y0gW0qS5Mert04wie/tZkduyb2L4t6FuA0zcVUTbVSMyYnzFq1XrvzubDcfs2qooj7glk4a3BY1AExDeNmis2y/KGbHuSDNz1Ib+g7bEZA9HnRssUDiNuv0X/upDz3o1hJKszvdqcrdr7y3SILv8NGA6JPsZ4tPheW26/ROvuk1G9XMztwu6imDajS+Wrmd+jzomWLl0Dcfo1WUSSlfrtUSQra62632hJhufOV18zvMA3Veq46HkDcNI38cyelfrtYNQnknpJ31Xknpebi1Wh7UrWdIkqdr7B2KrW56nkAcdM0ctFKSv12mno/ldKM9qRqS4Th8zUyOo54qQ0E2qvU5mrjAcTt1+hFK0kX7rRXkzSjS3UtJcLw+UpCTzqXDh5A3H7NuGil/cKdFM1oT6q3ROjfoauWBxC3X1IawV1z2pOaXSL0kokr5AHE7VftRcsvJK3XrPakZpUmkjLGxyWLjwNx+1UzDiSL82UlUdLGSyRljI9LFi+BuP2qqfLI0nxZSZektgiv3nTFeABx01S6aEVxISlWRdbdxM9KykU5TZIyxscli1dhuZq0+hkXparIRscnKu5b7Wd5dVvtsjY1vWsODyCuJq2+kJSqItu+c3fTPsvr7WuXtDYZlwxeheVq0urBgqWqwvZOTjXts7zevj5JapNxyeABxNWslReSuV2dRaurOmao5s/yenvnWsursFyiqEScqD18eL19EsX5iGHXfLEEEEmHSrpT0mPB73kltpsMPQ99XWj5sZLuk7RV0k2SZkaXetdKo7uKN5bvm7Kiy8vxevtk8U4N2RNXFdYAcJeZDUoaCN5/tMh242Z2SpHlnwauM7MhSX8PvBf4QstS6yJTqtppZkd99zpJrLcPdy3+kyP3sHbjSOLS2Ao+hih74qrCWgbcGLy+EVhe7Y6SBCwFbq5nf5dspaqdeubOiilFzVV4Fz45ZW1zF+6dGrJHZrVXDTR8UGnUzLqD1wJ25N8XbLcPeBDYBwya2VpJ84F7zexVwTZHAbeb2WtLHGslsBKgp6fn1KGhIQDGxsaYPXt2k3MWvyzka3R8gu07d7N3coqZHTPomTuLgyb3pD5fAI8+8+K0HmUzfvk0U3MWMLNjBiccfkiMKWuuYn+HhXnPS1Pes/D/VUylfC1ZsmSDmfUVLm9ZFZak7wKHF1l1ZfiNmZmkUlHsaDMbkXQcsF7SJmBnLekws9XAaoC+vj7r7+8HYHh4mPzrLPF8JdslA7dioYL/+46AL2w6CAFPDvbHlq5aVRrhX+z7Gi2YkBFypctV559Mf0qqsLLyd1io3ny1LICY2Zml1knaLmmBmT0taQHwbInPGAl+PyFpGFgE3AJ0SzrIzPYBRwLZL/+7TIiza3G5i34tU77UOzNvkh445pojrkb0dcDFwGDw+5uFGwQ9s3aZ2Z6g2mox8JmgxHI3cCEwVGp/55Iorsf+lrvoAzUFhEYaw5PYqcHVL65G9EHgzZIeA84M3iOpT9L1wTavAR6Q9BBwN7k2kJ8E6z4KfFjSVuAVwBcjTb1zdSrsWtwxQ5F0LS530a91yhdvDHd5sZRAzOx54Iwiyx8ALg1efx84ucT+TwCntTKNzoU1c1bf8F34mjVrIrkjr+eiX2qdj/B3eT4S3bkKsjAArtwsyrXOsOwj/F2eBxAXiTRPYZGFWX3LXfRrDQg+wt/l+WSKruXS/jztLNT5V/u0yWqr6FrRGO4P/0ofDyCu5dI+hUVW6vzLXfTj7h2V9puMduVVWK7l0n4H73X+rZeFasJ25CUQ17BKVQ9pv4P3AXCtl/abjHblAcQ1pJqqh7gGzzVT3FU8zZLUdoa032S0K6/Ccg2ppurBe+0kQ5K7I3s1YTp5CcQ1pNqqh6zcwadZkjszeDVhOnkAcQ3xqof0SHo7g99kpI9XYbmGeNVDetQ64ty5SjyAuIZ4+0Z6eLB3zeZVWK5hXvWQXIW9ri44tZe7H3nO2xlcU3gAcS6jinWxvmXDiJcQXdN4FZZzGeWju12reQnEtb2kDq5rVNJ7Xbn08xKIa2tJHlzXKO915VrNA4hra1mu5vFeV67VYgkgkg6VdKekx4Lf84pss0TSg6Gf3ZKWB+vWSHoytO6UqPPgsiHL1Tzexdq1WlxtIAPAXWY2KGkgeP/R8AZmdjdwCuQCDrAV+E5ok8vN7OZokuuyKusj6b2LtWuluKqwlgE3Bq9vBJZX2P5C4HYz29XKRLnoxf2oW6/mca5+MrPoDyqNmll38FrAjvz7EtuvB/7GzL4dvF8DvAHYA9wFDJjZnhL7rgRWAvT09Jw6NDQEwNjYGLNnz25SjpIjTfkaHZ9gZMc4U6G/wRkSvfO66O7qnLZtK/M1Oj7B9p272Ts5xcyOGfTMnXXA8Vtly5YtLFy4MJJjFSqX70bPSZr+DmvRrvlasmTJBjPrK1zesiosSd8FDi+y6srwGzMzSSWjmKQFwMnAHaHFVwDPADOB1eSqv64utr+ZrQ62oa+vz/r7+wEYHh4m/zpL0pSvxYPrGRntOGB5b3cH9wz0T1uWpnzVYtu2bbHka+3GEa64axPjEzPIV0R0dU6y6vwTAUquq7Y6LKvfl+drupYFEDM7s9Q6SdslLTCzp4MA8WyZj3oH8A0zmwh99tPByz2S/gn4SFMS7SKVlAbsrI4DKadS77OkTvvukiWuRvR1wMXAYPD7m2W2fRe5Esd+oeAjcu0nP25ROl0LxdWAHQ4Yc7s6+dXefUxM5grBxZ6oWGrfNAebeoJ3FnqmueaKqxF9EHizpMeAM4P3SOqTdH1+I0nHAEcB/16w/1ckbQI2AfOBT0WRaNdccTRgFw4cHB2f2B888kqNA8nSoMNygwx9AKKrViwBxMyeN7MzzOx4MzvTzF4Ilj9gZpeGtttmZr1mNlWw/1IzO9nMXmtmf2BmY1HnwTUujnEKxapuiil2t/3Jb23OzKDDcsHbe6a5avlcWC5WUY9TqLYapvBue+3GEXbsmii6bRqrdqp5hGwWqupca3kAcW2lVLtLWLG77XKljLRW7ZQL3j4A0VXD58JybaVY9UznDDHvZbkxDh3S/mqpcNtGuVKGV+24duUBxLWVYu0u1/7u6/jE20+iq7ODSZveGysfREqVMrq7Ov1O3bUtr8JybadY9cziwfVlxz5cfvYJ057uB7mqrqvOO+mAz89KV1/nKvEA4hyVx0VU0+gMxR8jW25ciXNp5gHEOaob1FhNw3K5Ed4eQFzWeBuIczRvUGNSpmdxLgoeQJyjeYMafRS3aydeheVcoBljH0o1tntXX5dFHkCca6JqG9udywIPIM41mY/idu3C20Ccc87VxQOIc865ungAcc45VxcPIM455+riAcQ551xdZGaVt8oISc8BPw3ezgd+EWNyWsXzlS6er3Rp13wdbWaHFS5sqwASJukBM+uLOx3N5vlKF89Xuni+pvMqLOecc3XxAOKcc64u7RxAVsedgBbxfKWL5ytdPF8hbdsG4pxzrjHtXAJxzjnXAA8gzjnn6tI2AUTS70raLGlKUsnuapK2Sdok6UFJD0SZxnrUkK9zJD0qaaukgSjTWA9Jh0q6U9Jjwe95JbabDL6rByWtizqd1ap0/iUdLOmmYP19ko6JIZk1qyJfKyQ9F/qOLo0jnbWQdIOkZyX9uMR6SfrbIM8/kvTrUaexHlXkq1/SztB39fGKH2pmbfEDvAY4ARgG+spstw2YH3d6m5kvoAN4HDgOmAk8BJwYd9or5OszwEDwegD4dIntxuJOaxV5qXj+gfcDfx+8vgi4Ke50NylfK4DPxp3WGvP1RuDXgR+XWP8W4HZAwG8A98Wd5iblqx/4di2f2TYlEDN72MwejTsdzVZlvk4DtprZE2a2FxgClrU+dQ1ZBtwYvL4RWB5fUhpWzfkP5/dm4AxJijCN9Ujj31VFZvYfwAtlNlkGfMly7gW6JS2IJnX1qyJfNWubAFIDA74jaYOklXEnpkl6gZ+F3j8VLEuyHjN7Onj9DNBTYrtZkh6QdK+k5dEkrWbVnP/925jZPmAn8IpIUle/av+uLgiqem6WdFQ0SWupNP4/VesNkh6SdLukkyptnKknEkr6LnB4kVVXmtk3q/yY3zKzEUm/Btwp6ZEgcsemSflKnHL5Cr8xM5NUqr/50cH3dRywXtImM3u82Wl1dfsW8FUz2yPpj8iVspbGnCZX3H+R+38ak/QWYC1wfLkdMhVAzOzMJnzGSPD7WUnfIFdMjzWANCFfI0D4zu/IYFmsyuVL0nZJC8zs6aB64NkSn5H/vp6QNAwsIlcvnyTVnP/8Nk9JOgiYCzwfTfLqVjFfZhbOw/Xk2rbSLpH/T40ys1+GXt8m6fOS5ptZyUkWvQorRNLLJR2Sfw2cBRTtsZAy9wPHSzpW0kxyjbSJ7bEUWAdcHLy+GDigpCVpnqSDg9fzgcXATyJLYfWqOf/h/F4IrLegZTPBKuaroG3gPODhCNPXKuuA9wS9sX4D2Bmqbk0tSYfn290knUYuPpS/iYm7Z0CEPRB+h1xd5R5gO3BHsPwI4Lbg9XHkepI8BGwmV0UUe9obzVfw/i3AFnJ352nI1yuAu4DHgO8ChwbL+4Drg9e/CWwKvq9NwHvjTneZ/Bxw/oGrgfOC17OArwNbgR8Cx8Wd5ibla1Xwv/QQcDfw6rjTXEWevgo8DUwE/1vvBf4Y+ONgvYDPBXneRJlenUn6qSJfl4W+q3uB36z0mT6ViXPOubp4FZZzzrm6eABxzjlXFw8gzjnn6uIBxDnnXF08gDjnnKuLBxDnnHN18QDinHOuLh5AnIuRpNcHEw3OCmZC2CzptXGny7lq+EBC52Im6VPkRqJ3AU+Z2aqYk+RcVTyAOBezYB6p+4Hd5KaPmIw5Sc5VxauwnIvfK4DZwCHkSiLOpYKXQJyLWfAs9yHgWGCBmV0Wc5Kcq0qmngfiXNpIeg8wYWb/IqkD+L6kpWa2Pu60OVeJl0Ccc87VxdtAnHPO1cUDiHPOubp4AHHOOVcXDyDOOefq4gHEOedcXTyAOOecq4sHEOecc3X5/2mdCjNGll/LAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1.a\n",
    "\n",
    "def sample_users(K,R):\n",
    "    v = np.random.uniform(low=0,high=R**2,size=K)\n",
    "    theta = np.random.uniform(low=0,high=2*np.pi,size=K)\n",
    "    r = np.sqrt(v)\n",
    "    x,y = r*np.cos(theta), r*np.sin(theta)\n",
    "    return x,y\n",
    "\n",
    "for K in [20,30,50,100]:\n",
    "    # Example usage\n",
    "    R = 1\n",
    "    x, y = sample_users(K, R)\n",
    "\n",
    "    plt.scatter(x, y)\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.title(f\"User Locations (K={K})\")\n",
    "    plt.axhline(0, color='gray', linewidth=0.5)\n",
    "    plt.axvline(0, color='gray', linewidth=0.5)\n",
    "    plt.axis('equal')\n",
    "    plt.gca().set_aspect('equal')\n",
    "    plt.grid(True)\n",
    "    plt.scatter(0, 0, color='red', s=100)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92\n"
     ]
    }
   ],
   "source": [
    "# 1.b\n",
    "# K = np.array([20, 30, 50, 100],dtype=np.int32)\n",
    "K = np.array(range(10,100,2), dtype=np.int32)\n",
    "R = 1\n",
    "r1,r2 = 15*1e3,32*1e3\n",
    "W = 3.84*10**6\n",
    "theta = 0.4\n",
    "gamma1, gamma2  = 10**(5/10), 10**(7/10)\n",
    "Rho = np.array([])\n",
    "\n",
    "def generate_F(k,R,r1,r2,gamma1,gamma2,W,theta):\n",
    "    x,y = sample_users(k,R)\n",
    "    r = np.concatenate((r1*np.ones(k//2),r2*np.ones(k//2)))\n",
    "    gamma = np.concatenate((gamma1*np.ones(k//2),gamma2*np.ones(k//2)))\n",
    "    lamda = 0.5\n",
    "    h = np.random.exponential(1/lamda,k)\n",
    "    d = np.sqrt(x**2+y**2)\n",
    "    L = -128.1 - 37.6*np.log10(d)\n",
    "    l = 10**(L/10)\n",
    "    g = l*h\n",
    "    G1,G2 = np.meshgrid(gamma*r*g,g)\n",
    "    F = (theta/W)*G1 / G2\n",
    "    F[np.eye(k,dtype=bool)] = 0\n",
    "    return F, r, gamma, g\n",
    "\n",
    "for k in K:\n",
    "    F,_,_,_ = generate_F(k,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "    rho = np.max(np.abs(np.linalg.eigvals(F)))\n",
    "    Rho = np.append(Rho,rho)\n",
    "\n",
    "Kmax = np.max(K[Rho<1])\n",
    "print(Kmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[28.16665678  6.86250169 20.71464779 18.84900969  5.55326503 20.26449124\n",
      " 18.5940011  22.53251589 10.8578652   5.84853617 15.24183855 30.84545035\n",
      " 10.5792318  33.70498719 29.24888039 17.25597702 16.96352345 18.71285413\n",
      " 16.87350927 20.90320268 19.08188648 16.72779185 24.40954399 15.50125749\n",
      " 26.33456371 17.77436252 22.1659222  16.01064378 19.96822014 25.66662887\n",
      " 30.59317692 35.32767581 18.90044914 17.32921501 17.94490598 13.92232916\n",
      "  9.26279138  9.88947905 10.04367335 25.50658171 22.76623012 16.83294348\n",
      "  5.8447057  20.45764339 28.15794973 17.09403185 20.92933376  8.15692142\n",
      " 22.09419991 22.58831    20.75625269 32.90413606 23.3908391  23.04813658\n",
      " 20.5434783  28.44204695 23.80893325 13.43379353 11.54665306 21.40922606\n",
      " 23.7260069  14.92430548 15.09423377  5.16109012 21.82039109 23.00013506\n",
      " -3.03496525 10.79476481 25.52802375  6.17862929 -9.94205266 23.84591141\n",
      " 24.64791867 22.59839311 17.33067306 26.95989872 30.23779763 23.22757386\n",
      " 24.90262049 16.1683794  27.01378274  6.01056962 18.61707171 19.51201893\n",
      " 20.93116309 25.15624382 16.50106947 19.84520124 28.90858081 20.52741387\n",
      " 23.97496784 -5.96362622]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZkqSuDBP8S4FVwGXAW4EzgPd3WZQkqTvDnNWztr35ygU0XTxXV5VdPZK0kZo1+JPsC/xP4Dqa8fh3TfLWqvpO18VJkubeMBdwfRp4UVVdC5Dk8cDpgMEvSRuhYfr4V0+Efut6YHVH9UiSOjbtEX+S17eTy5OcAZxE08f/BuCHI6hNktSBmbp6Xj0wfQvwwnZ6FbBFZxVJkjo1bfBX1cEbsuEkxwKvAm6tqqe087YFTgQWASuA/avq9g1pR5K0boYZq2fXJEclOSXJaROPIbZ9HLDPpHlLgbOqanfgrPa5JGmEhjmr51TgGJqrddcOu+GqOjfJokmz9wP2aqePB84B3jvsNiVJG26Y4P9tVf3dHLW3fVWtbKdvBrafo+1KkoY0TPD/tySHA98D7pmYWVUXb0jDVVVJpr0COMkhwCEAO+/snR8lwaKlp4+l3RWf2Hcs7XZlmOD/Y+DNwIu5r6un2ufr6pYkC6tqZZKFwK3TrVhVRwNHAyxZssQhIiRpjgwT/G8AHjc4NPMGOA04CPhE++8352CbkqR1MMyVu5cDW6/rhpOcAPw/4IlJbkzyFprA3zvJNcBL2+eSpBEa5oh/a+CqJD/k/n38r5npRVV1wDSLXjJ0dZKkOTdM8B/eeRWSpJEZZjz+ZaMoRJI0GsOMx7+a++6x+1BgM+Duqnpkl4VJkroxzBH/VhPTSUJz9e2zuyxKktSdYc7q+YNqnAq8vJtyJEldG6ar5/UDTx8CLAF+21lFkqRODXNWz+C4/GtohlPer5NqJEmdG6aPf4PG5ZckPbjMdOvFD87wuqqqIzuoR5LUsZmO+O+eYt4jgLcAjwIMfknaCM1068VPT0wn2Qo4FDgY+Crw6eleJ0l6cJuxj7+9R+5/Bg6kuWPW071HriRt3Gbq4/9b4PU0Y+L/cVXdNbKqtFEa100yYP7dKEPq0kwXcL0b2AF4P/CLJHe2j9VJ7hxNeZKkuTZTH/86XdUrSdo4GO6S1DMGvyT1jMEvST1j8EtSzxj8ktQzw4zOKT3ojfMaAmlj4xG/JPWMwS9JPWPwS1LPGPyS1DMGvyT1jMEvST1j8EtSzxj8ktQzBr8k9YzBL0k9Y/BLUs8Y/JLUMwa/JPXMWEbnTLICWA3cC6ypqiXjqEOS+micwzK/qKpuG2P7ktRLdvVIUs+MK/gL+F6Si5IcMqYaJKmXxtXV87yquinJo4Ezk1xVVecOrtD+QjgEYOeddx5HjZI0L43liL+qbmr/vRX4BvDMKdY5uqqWVNWSBQsWjLpESZq3Rh78SR6RZKuJaeBlwOWjrkOS+mocXT3bA99IMtH+V6rqH8dQhyT10siDv6quB5466nYlSQ1P55SknjH4JalnDH5J6plxDtkgSRuFRUtPH1vbKz6x75xv0yN+SeoZg1+Sesbgl6SeMfglqWcMfknqGYNfknrG4JeknjH4JalnDH5J6hmDX5J6xuCXpJ4x+CWpZwx+SeoZg1+Sesbgl6SeMfglqWcMfknqmXl/B675duccSdpQHvFLUs8Y/JLUMwa/JPWMwS9JPWPwS1LPGPyS1DMGvyT1zLw/j3+cxnUNgdcPSJqJR/yS1DMGvyT1jMEvST1j8EtSzxj8ktQzYwn+JPskuTrJtUmWjqMGSeqrkQd/kk2A/wG8AtgDOCDJHqOuQ5L6ahxH/M8Erq2q66vqd8BXgf3GUIck9dI4LuDaEbhh4PmNwLMmr5TkEOCQ9uldSa5ez/a2A25bz9dulPLJaRf1bl/MwH1xH/fF/T2o9scMP8/D2GWqmQ/aK3er6mjg6A3dTpLlVbVkDkra6Lkv7uO+uI/74v76sD/G0dVzE7DTwPPHtvMkSSMwjuD/IbB7kl2TPBR4I3DaGOqQpF4aeVdPVa1J8g7gu8AmwLFVdUWHTW5wd9E84r64j/viPu6L+5v3+yNVNe4aJEkj5JW7ktQzBr8k9cy8DP4kb0hyRZK1SZZMWvZf2qEirk7y8nHVOGp9HiYjybFJbk1y+cC8bZOcmeSa9t9txlnjqCTZKcnZSX7S/owc2s7v3f5IsnmSC5Nc2u6LD7Xzd01yQfuzcmJ7Esq8Mi+DH7gceD1w7uDMdmiINwJPBvYBPt8OITGvOUwGx9F83oOWAmdV1e7AWe3zPlgDvLuq9gCeDby9/b/Qx/1xD/DiqnoqsBjYJ8mzgU8Cn6mq3YDbgbeMr8RuzMvgr6orq2qqK333A75aVfdU1c+Aa2mGkJjvej1MRlWdC/xy0uz9gOPb6eOB146ypnGpqpVVdXE7vRq4kuZq+t7tj2rc1T7drH0U8GLg6+38ebkv5mXwz2Cq4SJ2HFMto9TX9z2T7atqZTt9M7D9OIsZhySLgKcBF9DT/ZFkkySXALcCZwLXAXdU1Zp2lXn5s/KgHbJhNkm+DzxmikXvq6pvjroebbyqqpL06rzmJFsCJwPvqqo7k/xhWZ/2R1XdCyxOsjXwDeBJ461oNDba4K+ql67Hy/o6XERf3/dMbkmysKpWJllIc8TXC0k2own9L1fVKe3s3u4PgKq6I8nZwHOArZNs2h71z8uflb519ZwGvDHJw5LsCuwOXDjmmkbBYTIe6DTgoHb6IKAXfyWmObQ/Briyqo4aWNS7/ZFkQXukT5ItgL1pvvM4G/jTdrV5uS/m5ZW7SV4HfA5YANwBXFJVL2+XvQ/4C5qzG95VVd8ZV52jlOSVwGe5b5iMj463otFJcgKwF81wu7cAhwOnAicBOwM/B/avqslfAM87SZ4HnAdcBqxtZx9G08/fq/2R5N/SfHm7Cc1B8ElV9eEkj6M5AWJb4EfAm6rqnvFVOvfmZfBLkqbXt64eSeo9g1+Sesbgl6SeMfglqWcMfknqGYNfvZPk3iSXJLk8ydeSPHyKdZLk/yZ55BTLjkjy1+30cUl+1m7vqiSHr2MtC5L84/q/G2ndGfzqo99U1eKqegrwO+BtU6zzSuDSqrpziO29p6oW04zweFB7ceBQqmoVsDLJnsO+RtpQBr/67jxgtynmH8jAFZtJ3pfkp0nOB544zbY2b/+9u33NiiQfb/8aWJ7k6Um+m+S6JIO/bE5t25NGwuBXbyXZlOYeBZdNsXhP4KJ2vT+hGeZiMc1fAs+YtO7ftiM83kgz7PfgODf/0v41cB7NfQH+lGYc/A8NrLMceP4GvRlpHRj86qMt2qBeDvwLzdg1k23bjlcPTSh/o6p+3Xb9TB7naKKr5zHAS5I8d2DZxLqXARdU1eq2e+eeiXFiaAZE22ED35M0tI12dE5pA/ymDeqZrEnykKpaO8t6f1BVdyU5B3ge8E/t7IkxXtYOTE88n/j52xz4zbDtSBvKI35palcDj2unzwVem2SLJFsBr57qBW3X0bNobuaxLp5Ac7tQaSQMfmlqp9OM6El7q8ITgUuB79AMcz1ooo//xzRdOqewbl7UtieNhKNzSlNob0by91W19wjaOhfYr6pu77otCTzil6bU3n/2i1NdwDWXkiwAjjL0NUoe8UtSz3jEL0k9Y/BLUs8Y/JLUMwa/JPWMwS9JPfP/Ab3RPuAtiKHUAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#1.c\n",
    "k = Kmax\n",
    "\n",
    "x,y = sample_users(k,R)\n",
    "r = np.concatenate((r1*np.ones(k//2),r2*np.ones(k//2)))\n",
    "gamma = np.concatenate((gamma1*np.ones(k//2),gamma2*np.ones(k//2)))\n",
    "lamda = 0.5\n",
    "h = np.ones(k)\n",
    "h = np.random.exponential(1/lamda,k)\n",
    "d = np.sqrt(x**2+y**2)\n",
    "L = -128.1 - 37.6*np.log10(d)\n",
    "l = 10**(L/10)\n",
    "g = l*h\n",
    "G1,G2 = np.meshgrid(gamma*r*g,g)\n",
    "F = (theta/W)*G1 / G2\n",
    "F[np.eye(k,dtype=bool)] = 0\n",
    "\n",
    "sigma2 = 10**(-104/10)/1000\n",
    "b = sigma2*(1/(3.84*10**6))*r*gamma/g\n",
    "P =  np.linalg.inv(np.eye(k) - F)@b\n",
    "\n",
    "print(10*np.log10(P*1000)) # display the power allocation in dBm\n",
    "\n",
    "def SINR(W,R,P,G,theta,sigma2):\n",
    "    alpha = W/R\n",
    "    pg = P*G\n",
    "    p,_ = np.meshgrid(P,P)\n",
    "    p[np.eye(len(p),dtype=bool)] = 0\n",
    "    sm = np.sum(p,axis=1)*G\n",
    "    return alpha*pg/(theta*sm+sigma2)\n",
    "\n",
    "plt.hist(10*np.log10(P*1000))\n",
    "plt.title('Power allocation distribution')\n",
    "plt.ylabel('Number of users')\n",
    "plt.xlabel('P (dBm)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k=10, num_iteration=4\n",
      "k=12, num_iteration=5\n",
      "k=14, num_iteration=6\n",
      "k=16, num_iteration=4\n",
      "k=18, num_iteration=3\n",
      "k=20, num_iteration=7\n",
      "k=22, num_iteration=5\n",
      "k=24, num_iteration=4\n",
      "k=26, num_iteration=6\n",
      "k=28, num_iteration=7\n",
      "k=30, num_iteration=6\n",
      "k=32, num_iteration=13\n",
      "k=34, num_iteration=9\n",
      "k=36, num_iteration=10\n",
      "k=38, num_iteration=9\n",
      "k=40, num_iteration=10\n",
      "k=42, num_iteration=11\n",
      "k=44, num_iteration=13\n",
      "k=46, num_iteration=11\n",
      "k=48, num_iteration=11\n",
      "k=50, num_iteration=16\n",
      "k=52, num_iteration=20\n",
      "k=54, num_iteration=11\n",
      "k=56, num_iteration=19\n",
      "k=58, num_iteration=14\n",
      "k=60, num_iteration=19\n",
      "k=62, num_iteration=16\n",
      "k=64, num_iteration=13\n",
      "k=66, num_iteration=19\n",
      "k=68, num_iteration=19\n",
      "k=70, num_iteration=23\n",
      "k=72, num_iteration=38\n",
      "k=74, num_iteration=27\n",
      "k=76, num_iteration=51\n",
      "k=78, num_iteration=33\n",
      "k=80, num_iteration=41\n",
      "k=82, num_iteration=42\n",
      "k=84, num_iteration=31\n",
      "k=86, num_iteration=54\n",
      "k=88, num_iteration=105\n",
      "k=90, num_iteration=125\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#1.d\n",
    "K_list = np.array(range(10,Kmax,2), dtype=np.uint32)\n",
    "epsilon = 0.1\n",
    "iteration_list = np.zeros(len(K_list))\n",
    "\n",
    "for idx in range(len(K_list)):\n",
    "    k = K_list[idx]\n",
    "    p = np.ones(k)\n",
    "    new_p = np.ones(k)*0.1\n",
    "    num_iteration = 0\n",
    "    _, r, gamma, g = generate_F(k,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "    while not np.all(np.abs(p - new_p) < epsilon):\n",
    "        p = new_p\n",
    "        pg = p*g\n",
    "        pg1,_ = np.meshgrid(pg,pg)\n",
    "        pg1[np.eye(len(pg),dtype=bool)] = 0\n",
    "        sm = np.sum(pg1,axis=1)\n",
    "        new_p = (r*gamma*(theta*sm + sigma2))/(W*g)\n",
    "        num_iteration += 1\n",
    "    iteration_list[idx] = num_iteration\n",
    "    print(f\"k={k}, num_iteration={num_iteration}\")\n",
    "\n",
    "plt.plot(K_list, iteration_list, marker='o')\n",
    "plt.xlabel('Number of Users (k)')\n",
    "plt.ylabel(f'Number of Iterations with epsilon={epsilon}')\n",
    "plt.title('Number of Iterations vs Number of Users')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2567. 1859. 1473. 1227. 1055.  929.  831.  752.  689.  635.  590.  551.\n",
      "  518.  488.  462.  438.  417.  398.]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of iterations')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1.e\n",
    "\n",
    "def iterativeE(gamma,beta,tol,seed):\n",
    "    p=seed.copy()\n",
    "    p_old = np.inf*np.ones_like(p)\n",
    "    iter = 0\n",
    "    while np.sum(abs(p-p_old))>=tol:\n",
    "        p_old = p.copy()\n",
    "        sinr = SINR(W,r,p,g,theta,sigma2)\n",
    "        p = (1-beta)*p + beta*gamma/sinr*p\n",
    "        iter +=1\n",
    "    return p, iter\n",
    "\n",
    "Beta = np.arange(0.1,1,0.05)\n",
    "Niter = np.zeros_like(Beta)\n",
    "_, r, gamma, g = generate_F(Kmax,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "\n",
    "seed = np.ones(Kmax)\n",
    "for b in range(len(Beta)):\n",
    "    p,iter = iterativeE(gamma,Beta[b],1e-3,seed)\n",
    "    Niter[b] = iter\n",
    "\n",
    "print(Niter)\n",
    "\n",
    "plt.plot(Beta,Niter)\n",
    "plt.title('Number of iterations before convergence by beta')\n",
    "plt.xlabel('Beta')\n",
    "plt.ylabel('Number of iterations')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5000. 5000. 5000. 5000. 5000. 5000. 5000.]\n"
     ]
    }
   ],
   "source": [
    "# 1.f\n",
    "\n",
    "def iterativeF(gamma,alpha,tol,seed,maxIter):\n",
    "    p = seed.copy()\n",
    "    p_old = np.inf*np.ones_like(p)\n",
    "    iter = 0\n",
    "    while (np.sum(abs(p-p_old))>=tol) & (iter<maxIter):\n",
    "        p_old = p.copy()\n",
    "        sinr = SINR(W,r,p,g,theta,sigma2)\n",
    "        p[sinr<gamma] = alpha*p_old[sinr<gamma]\n",
    "        p[sinr>gamma] = p_old[sinr>gamma]/alpha\n",
    "        iter +=1\n",
    "    return p, iter\n",
    "\n",
    "Alpha = 10**(np.linspace(0.25,1.5,7)/10)\n",
    "Niter = np.zeros_like(Alpha)\n",
    "_, r, gamma, g = generate_F(Kmax,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "\n",
    "seed = np.ones(Kmax)\n",
    "for a in range(len(Alpha)):\n",
    "    p,iter = iterativeF(gamma,Alpha[a],1e-3,seed,5e3)\n",
    "    Niter[a] = iter\n",
    "\n",
    "print(Niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5000. 5000. 5000. 5000. 5000. 5000. 5000.]\n"
     ]
    }
   ],
   "source": [
    "# 1.g\n",
    "def iterativeG(gamma,alpha,tol,maxIter):\n",
    "    p = np.ones(Kmax)\n",
    "    p_old = np.inf*np.ones_like(p)\n",
    "    iter = 0\n",
    "    while (np.sum(abs(p-p_old))/Kmax>=tol) & (iter<maxIter):\n",
    "        p_old = np.copy(p)\n",
    "        sinr = SINR(W,r,p,g,theta,sigma2)\n",
    "        p[sinr > alpha*gamma*p_old] = p_old[sinr > alpha*gamma*p_old]/alpha\n",
    "        p[sinr < gamma*alpha**(-1)] = p_old[sinr < gamma*alpha**(-1)]*alpha\n",
    "        iter += 1\n",
    "    return p, iter\n",
    "\n",
    "Alpha = 10**(np.linspace(0.25,1.5,7)/10)\n",
    "#Alpha = [10**(0.25/10), 10**(0.25/10), 10**(0.25/10)]\n",
    "Niter = np.zeros_like(Alpha)\n",
    "_, r, gamma, g = generate_F(Kmax,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "epsilon = 5e-3\n",
    "\n",
    "for a in range(len(Alpha)):\n",
    "    p_alpha,iter = iterativeG(gamma,Alpha[a],epsilon,5e3)\n",
    "    Niter[a] = iter\n",
    "\n",
    "print(Niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.\n",
      " 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000. 1000.]\n",
      "[0.00108582 0.00064746 0.00234666 0.00363168 0.0011197  0.00317839\n",
      " 0.00247856 0.00200685 0.00372026 0.00263357]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Proportion of users satisfying SINR condition')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2.a\n",
    "\n",
    "\n",
    "def generate_F2(k,R,r1,r2,gamma1,gamma2,W,theta):\n",
    "    x,y = sample_users(k,R)\n",
    "    r = np.concatenate((r1*np.ones(k//2),r2*np.ones(k//2)))\n",
    "    gamma = np.concatenate((gamma1*np.ones(k//2),gamma2*np.ones(k//2)))\n",
    "    d = np.sqrt(x**2+y**2)\n",
    "    L = -128.1 - 37.6*np.log10(d)\n",
    "    l = 10**(L/10)\n",
    "    return r, gamma, l\n",
    "\n",
    "def iterativeE(gamma,beta,tol,seed,k,l,r,lim_iteration):\n",
    "    p=seed.copy()\n",
    "    p_old = np.inf*np.ones_like(p)\n",
    "    iter = 0\n",
    "    lamda = 0.5\n",
    "    while lim_iteration > iter:\n",
    "\n",
    "        h = np.random.exponential(1/lamda,k)\n",
    "        g = l*h\n",
    "\n",
    "        p_old = p.copy()\n",
    "        sinr = SINR(W,r,p,g,theta,sigma2)\n",
    "        p = ((1-beta)*p + p*beta*gamma/sinr)\n",
    "        iter +=1\n",
    "        \n",
    "    return p, iter, sinr\n",
    "\n",
    "lim_iteration = 1000\n",
    "K = 10\n",
    "Beta = np.arange(0.05,1,0.01)\n",
    "Niter = np.zeros_like(Beta)\n",
    "ach_rat = np.zeros_like(Beta)\n",
    "r, gamma,l = generate_F2(K,R,r1,r2,gamma1,gamma2,W,theta)\n",
    "\n",
    "seed = np.ones(K)\n",
    "for b in range(len(Beta)):\n",
    "    p,iter,sinr = iterativeE(gamma,Beta[b],1e-3,seed,K,l,r,lim_iteration)\n",
    "    Niter[b] = iter\n",
    "    ach_rat[b] = np.mean(sinr>=gamma)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(Beta,ach_rat)\n",
    "plt.title('SINR condition achievement rate by beta')\n",
    "plt.xlabel('Beta')\n",
    "plt.ylabel('Proportion of users satisfying SINR condition')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.95   0.95   0.97   0.9275 0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      " 0.     0.     0.     0.     0.     0.     0.     0.     0.    ]\n",
      "The maximum number of users on the network is 5\n"
     ]
    }
   ],
   "source": [
    "# 1)\n",
    "\n",
    "r = 1\n",
    "W = 3.84*10**6\n",
    "theta = 0.4\n",
    "sigma2 = 10**(-104/10)*1e-3\n",
    "P = 10**(40/10)*1e-3\n",
    "\n",
    "def measure_achievement_ratio(K,R,gamma,n_avg=1):\n",
    "    x,y = sample_users(K,r)\n",
    "    d = np.sqrt(x**2+y**2)\n",
    "    L = -128.1 - 37.6*np.log10(d)\n",
    "    l = 10**(L/10)\n",
    "    history = np.zeros((n_avg,1))\n",
    "    for i in range(n_avg):\n",
    "        h = np.random.exponential(0.5,K)\n",
    "        g = l*h\n",
    "        p = P/K\n",
    "        SINR = W/R*p*g/(theta*(K-1)*p*g+sigma2)\n",
    "        history[i] = np.mean(SINR>=gamma)\n",
    "\n",
    "    return history\n",
    "\n",
    "K_values = np.array(range(1,100))\n",
    "deltas = np.zeros(len(K_values))\n",
    "\n",
    "for i,K in enumerate(K_values) :\n",
    "    ach_rat = measure_achievement_ratio(K,240*1e3,10**(10/10),100)\n",
    "    deltas[i] = np.mean(ach_rat)\n",
    "\n",
    "print(deltas)\n",
    "print(f'The maximum number of users on the network is {K_values[np.sum(deltas>=0.9)]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K=10, Average Rate=302435.04, Standard Deviation=55886.00\n",
      "K=20, Average Rate=145715.76, Standard Deviation=25712.58\n",
      "K=30, Average Rate=98592.00, Standard Deviation=17455.12\n",
      "K=40, Average Rate=71969.16, Standard Deviation=14026.13\n"
     ]
    }
   ],
   "source": [
    "# 2)\n",
    "\n",
    "T = 1000\n",
    "I = 50\n",
    "gamma_i = 10**(10/10)\n",
    "R_i = 240e3\n",
    "L = 16                  # = W/R_i\n",
    "P = 10**(40/10)*1e-3\n",
    "K_list = [10, 20, 30, 40]\n",
    "radius = 1\n",
    "lamda = 0.5\n",
    "sigma2 = 10**(-104/10)*1e-3\n",
    "\n",
    "for K in K_list:\n",
    "    try_averages = np.zeros(I)\n",
    "    for idx in range(I):\n",
    "        # Generate K users\n",
    "        x, y = sample_users(K, radius)\n",
    "        # Compute distance and pathloss effect\n",
    "        d = np.sqrt(x**2+y**2)\n",
    "        L = -128.1 - 37.6*np.log10(d)\n",
    "        l = 10**(L/10)\n",
    "        Average_rates = np.zeros(K)\n",
    "\n",
    "        for t in range(T):\n",
    "            h = np.random.exponential(1/lamda,K)\n",
    "            g = l*h\n",
    "            SNR_base = P*g/sigma2\n",
    "            SNR = SNR_base.copy()\n",
    "            C = np.ones(K)\n",
    "            current_rates = np.zeros(K)\n",
    "            proportional_fairness = np.zeros(K)\n",
    "\n",
    "            for i in range(K):\n",
    "                while SNR[i] > gamma_i and C[i] < 15:\n",
    "                    SNR[i] = SNR_base[i]/C[i]\n",
    "                    C[i] += 1\n",
    "                # print(f\"SNR[i] = {SNR[i]} and gamm_i = {gamma_i}\")\n",
    "\n",
    "                current_rates[i] = C[i] * R_i\n",
    "                if Average_rates[i] != 0:\n",
    "                    proportional_fairness[i] = np.argmax(current_rates[i]/Average_rates[i])\n",
    "                else:\n",
    "                    proportional_fairness[i] = np.inf\n",
    "            selected_user = np.argmax(proportional_fairness)\n",
    "            Average_rates[selected_user] += -(1/(t+1))*Average_rates[selected_user] + current_rates[selected_user]/(t+1)\n",
    "            Average_rates[range(K) != selected_user] -= Average_rates[range(K) != selected_user]/(t+1)\n",
    "        try_averages[idx] = np.mean(Average_rates)\n",
    "    print(f\"K={K}, Average Rate={np.mean(try_averages):.2f}, Standard Deviation={np.std(try_averages):.2f}\")"
   ]
  }
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