{ "cells": [ { "cell_type": "markdown", "id": "5d97bd4b-cd65-4602-8152-bb8c772eb938", "metadata": {}, "source": [ "# Distributed Power Control\n", "This method helps to find a stable configuration for the Cellular power levels of Mobile Devices. It also applies more generally to **Signals** and **Interferences** too.\n", "\n", "The crux of the problem is as such: imagine that you are in a cocktail party and wish to speak to your friend.\n", "\n", "Your friend is right beside you, but you cannot hear them properly and so you increase your volume. Simultaneously though, all other pairs in the room have the same idea and also increase their volume.\n", "\n", "In turn, your friend cannot hear you either because your voice becomes drowned out by the increased voice of other people. All-in-all this process continues ad-infinitum until everyone is shouting." ] }, { "cell_type": "markdown", "id": "908b2042-8a48-4b14-9b35-c023a7dc9518", "metadata": {}, "source": [ "## The Cocktail Party Problem\n", "The problem was outlined in the previous cell, but clearly this is not how a Cocktail Party usually transpires. Instead, everyone finds a suitable and polite volume at which to speak so that everyone may be heard despite conversations happening everywhere else. \n", "\n", "This is the crux of the Distributed Power Control Algorithm. And as can be expected, it is **iterative**." ] }, { "cell_type": "markdown", "id": "a2d40490-748a-4f73-ba06-cae1265f0bde", "metadata": {}, "source": [ "## Mathematically\n", "We have $N$ transmitter / receiver pairs indexed by $i$. The transmitter is your phone a.k.a a Mobile Station, and the receiver is the tower, a.k.a Base Station.\n", "\n", "The transmit power of this link $i$ is $p_i$. Note that the transmitted power from any MS (Mobile Station) just equates to interference for another MS.\n", "\n", "We can create a Matrix $G$ to encode this transmitter signal / interference where\n", "\\begin{align}\n", "G_{ii} &= \\text{direct channel gain from transmitter i to receiver i}\\\\\n", "G_{ij} &= \\text{interference channels}\n", "\\end{align}\n", "\n", "Thus we can then encode:\n", "\n", "\\begin{equation*}\n", "\\text{SIR}_i = \\frac{G_{ij}p_i}{\\sum_{j\\neq i}G_{ii}p_j +n_i}\n", "\\end{equation*}\n", "\n", "where the received power of the intended transmission at the receiver is $G_{ii} p_i$ (gain multiplied however much of there there is).\n", "and the interference is the sum of $G_ii p_j$ over all transmitters $j$ (other than the intended receiver $i$). also there is a noise $n_i$ in the receiver electronics for each receiver $i$.\n", "\n", "Then given we index $[t]$ as discrete _time_ slots, we know we need to maintain a minimum level of $\\text{SIR}_i \\geq \\gamma_i$ because otherwise the receiver wouldn't understand our message.\n", "\n", "We use this iterative algorithm:\n", "\n", "$$\n", "p_i[t+1] = \\frac{\\gamma_i}{\\text{SIR}_i [t]}p_i[t]\n", "$$\n", "\n", "Note that when eventually the $\\text{SIR}_i$ becomes equal to the desired $\\gamma_i$, the above algorithm equilibriates.\n", "\n", "### Optimisation\n", "\n", "The problem of finding an optimal configuration of powers can be found be solving:\n", "\n", "\n", "\\begin{align}\n", "&\\!\\min_{\\mathbf{p}} &\\qquad& \\sum_i p_i\\\\\n", "&\\text{subject to} & & \\text{SIR}_i(\\mathbf{p}) \\geq \\gamma_i, \\forall i\\\\\n", "\\end{align}\n", "\n", "\n", "\n", "which if we plug the SIR equation in from above we get:\n", "\n", "$$\n", "\\begin{align}\n", "&\\!\\min_{\\mathbf{p}} &\\qquad& \\sum_i p_i\\\\\n", "&\\text{subject to} & & \\frac{G_{ii}p_i}{\\sum_{j\\neq i}G_{ij}p_j +n_i}\\geq \\gamma_i, \\qquad\\forall i\\\\\n", "\\end{align}\n", "$$\n", "\n", "which is equal to:\n", "\n", "$$\n", "\\begin{align}\n", "&\\!\\min_{\\mathbf{p}} &\\qquad& \\sum_i p_i\\\\\n", "&\\text{subject to} & & G_{ii}p_i - \\gamma_i (\\sum_{j\\neq i} G_{ij}p_j + n_i) \\geq 0, \\qquad \\forall i\\\\\n", "\\end{align}\n", "$$\n", "\n", "### Game Theory\n", "\n", "It can be done...\n" ] }, { "cell_type": "markdown", "id": "39ff1bc4-5713-4836-906c-7a4a84bf8f04", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "markdown", "id": "a8ef9a5c-c99c-4b4b-8d64-8d2433ddec98", "metadata": {}, "source": [ "### Iteratatively:" ] }, { "cell_type": "code", "execution_count": 148, "id": "5c5cdb68-793e-4967-b6bd-1ebeb6a1431d", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "G = np.array([[1, 0.1, 0.2, 0.3],\n", " [0.2, 1, 0.1, 0.1],\n", " [0.2, 0.1, 1, 0.1],\n", " [0.1, 0.1, 0.1, 1]])\n", "\n", "# each row is the subsequent iteration\n", "# column i represents link i\n", "SIR = np.empty((0, G.shape[1]))\n", "\n", "gamma = [2.0, 2.5, 1.5, 2.0]\n", "P = np.array([[1.0 ,1.0 ,1.0 ,1.0]]) # each row is the subsequent iteration too.\n", "noise = 0.1\n", "\n", "iterations = 20\n", "\n", "for t in range(iterations):\n", " SIR_t = np.array([])\n", " for i in range(G.shape[1]):\n", " SIR_t = np.append(SIR_t, (G[i][i] * P[t][i])/ ( sum([G[i][x]*P[t][x] for x in range(G.shape[1]) if x != i]) + noise))\n", " P = np.vstack([P, np.array(gamma)/SIR_t*np.array(P[t])])\n", " SIR = np.vstack([SIR, SIR_t])" ] }, { "cell_type": "code", "execution_count": 158, "id": "0083fb48-9c7e-4d90-a692-c022c084f2fa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([[1.43, 2. , 2. , 2.5 ],\n", " [2.28, 2.34, 1.28, 1.82],\n", " [1.83, 2.56, 1.55, 1.98],\n", " [2.02, 2.4 , 1.45, 1.97],\n", " [1.96, 2.49, 1.49, 1.97],\n", " [1.98, 2.46, 1.48, 1.98],\n", " [1.98, 2.48, 1.49, 1.98],\n", " [1.98, 2.48, 1.49, 1.99],\n", " [1.99, 2.48, 1.49, 1.99],\n", " [1.99, 2.49, 1.49, 1.99],\n", " [1.99, 2.49, 1.49, 1.99],\n", " [1.99, 2.49, 1.49, 1.99],\n", " [1.99, 2.49, 1.5 , 1.99],\n", " [1.99, 2.49, 1.5 , 2. ],\n", " [2. , 2.49, 1.5 , 2. ],\n", " [2. , 2.5 , 1.5 , 2. ],\n", " [2. , 2.5 , 1.5 , 2. ],\n", " [2. , 2.5 , 1.5 , 2. ],\n", " [2. , 2.5 , 1.5 , 2. ],\n", " [2. , 2.5 , 1.5 , 2. ]]),\n", " array([[1. , 1. , 1. , 1. ],\n", " [1.4 , 1.25, 0.75, 0.8 ],\n", " [1.23, 1.34, 0.88, 0.88],\n", " [1.35, 1.3 , 0.85, 0.89],\n", " [1.33, 1.36, 0.88, 0.9 ],\n", " [1.37, 1.36, 0.89, 0.92],\n", " [1.38, 1.38, 0.9 , 0.92],\n", " [1.39, 1.39, 0.91, 0.93],\n", " [1.4 , 1.41, 0.92, 0.94],\n", " [1.41, 1.42, 0.92, 0.94],\n", " [1.42, 1.42, 0.93, 0.95],\n", " [1.43, 1.43, 0.93, 0.95],\n", " [1.43, 1.43, 0.93, 0.96],\n", " [1.44, 1.44, 0.94, 0.96],\n", " [1.44, 1.44, 0.94, 0.96],\n", " [1.44, 1.45, 0.94, 0.96],\n", " [1.44, 1.45, 0.94, 0.97],\n", " [1.45, 1.45, 0.95, 0.97],\n", " [1.45, 1.45, 0.95, 0.97],\n", " [1.45, 1.45, 0.95, 0.97],\n", " [1.45, 1.45, 0.95, 0.97]]))" ] }, "execution_count": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.around(SIR, 2), np.around(P, 2)" ] }, { "cell_type": "code", "execution_count": 186, "id": "52d84668-36fb-4764-9ea1-770aacc61ce1", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig, (ax1,ax2) = plt.subplots(1,2,figsize=(15,5))\n", "#power to iteration graph\n", "xx = np.linspace(0, 20, 21)\n", "colours = ['blue', 'green', 'red', 'orange']\n", "for i, c in zip(range(G.shape[1]), colours):\n", " yy = P[:,i]\n", " ax1.plot(xx, yy, color=c)\n", "ax1.set_xlabel('iteration')\n", "ax1.set_ylabel('power(mW)')\n", "#sir to it graph\n", "xx = np.linspace(0, 20, 20)\n", "colours = ['blue', 'green', 'red', 'orange']\n", "for i, c in zip(range(G.shape[1]), colours):\n", " yy = SIR[:,i]\n", " ax2.plot(xx, yy, color=c)\n", "ax2.set_xlabel('iteration')\n", "ax2.set_ylabel('SIR')\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:metal]", "language": "python", "name": "conda-env-metal-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }