{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# COS 463 Wireless Networks - Spring 2019\n",
"# Lab 2: Synchronization and MAC protocols\n",
"\n",
"In class we've learned about different MAC (medium access control) protocols that determine when devices get to transmit (these protocols *control* *access* to the *medium*). For all but the simplest MAC protocols, the participating devices need to be synchronized in time. The way this is done in practice is to have one node transmit a signal (called a \"preamble\" or \"beacon\") and the other nodes will listen for this signal. Since wireless signals travel at the speed of light, all nodes can agree that they will hear the preamble at nearly exactly the same time.\n",
"\n",
"First, we will explore how nodes can listen for a specific preamble to achieve time synchronization. Then, we will use this method to synchronize to a preamble using the HackRF hardware. Finally, we will wrap up with a Monte Carlo simulation of the capacities of the slotted-ALOHA MAC protocol."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib notebook\n",
"\n",
"from matplotlib import pyplot\n",
"import numpy\n",
"import SoapySDR\n",
"from SoapySDR import SOAPY_SDR_RX, SOAPY_SDR_CF32"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 1: Correlation and Preambles"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A preamble is a waveform sent at the beginning of a packet that is used to indicate the start of a packet. The preamble waveform is agreed to ahead-of-time, so the signal carries no data. Receivers will listen for the preamble, and when it's detected the receivers will start to demodulate the rest of the packet. Preambles can also be used to synchronize multiple clients for MAC protocols that require synchronization.\n",
"\n",
"In this part, we will explore how to detect and synchronize to a preamble. Both detection and synchronization can be done using a **correlation**. A correlation of two discrete signals $x$ and $y$ is an infinite-length discrete signal which is defined as\n",
"$$ (x \\star y)[k] = \\sum_{n = -\\infty}^{\\infty}x^*[n] \\cdot y[n + k]$$\n",
"In other words, at each index $k$, you take conjugate of the first signal $x$ and offset the second signal $y$ by $k$ indices and then sum the resulting two signals. Intuitively, the correlation measures the similarity of two signals for every offset of the one signal relative to the other. For signals with finite length, the correlation is zero for sufficiently large $|k|$, so often we'll consider the correlation to be finite as well."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 1.1: Autocorrelation (5 pts)\n",
"The autocorrelation of a signal $x$ is the correlation of $x$ with itself. For a uniform random signal $x$ think about what the autocorrelation would look like.\n",
"\n",
"- **Plot the signal and its autocorrelation. Use `numpy.correlate` with `mode='full'`, and plot the absolute value of the autocorrelation.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"X_len = 1000\n",
"X = numpy.random.random(X_len) + 1j * numpy.random.random(X_len)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So how do we use the correlation to detect a preamble? Let $x$ be the preamble signal, and let $y$ be the signal that the receiver receives. For now, we'll let $y$ be finite length. If the preamble is not received, then we can model $y$ as a random signal, and the correlation between $x$ and $y$ will also be random. However, if the receiver did receive the preamble in the signal $y$, then we can model $y$ as $x$ with some offset plus noise. The correlation between $x$ and $y$ will then have a large amplitude at the time in $y$ when the preamble started. So if we look for large peaks in the correlation we can detect and then also synchronize to a given preamble."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 1.2: Preamble detection using correlation (10 pts)\n",
"Implement preamble detection and synchronization using the correlation.\n",
"\n",
"- **Fill in the `detect_preamble` function below. The function should take two signals and return `None` if the preamble is not found, otherwise it should return the index where the preamble starts.**"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [],
"source": [
"# Compare the correlation magnitude against this value to determine whether there is a preamble or not\n",
"threshold = 100\n",
"def detect_preamble(preamble, signal):\n",
" pass"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [],
"source": [
"# This cell will test your implementation of `detect_preamble`\n",
"preamble_length = 100\n",
"signal_length = 1000\n",
"preamble = (numpy.random.random(preamble_length) + 1j * numpy.random.random(preamble_length))\n",
"signalA = numpy.random.random(signal_length) + 1j * numpy.random.random(signal_length)\n",
"signalB = numpy.random.random(signal_length) + 1j * numpy.random.random(signal_length)\n",
"preamble_start_idx = 123\n",
"signalB[preamble_start_idx:preamble_start_idx + preamble_length] += preamble\n",
"\n",
"numpy.testing.assert_equal(detect_preamble(preamble, signalA), None)\n",
"numpy.testing.assert_equal(detect_preamble(preamble, signalB), preamble_start_idx)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Handling Frequency Offsets\n",
"In practice, radios will disagree on their center frequencies. This is because a radio's center frequency is determined by a local oscillator (which is fed into the \"mixer\"), and these oscillators have some error. What this means is that a signal that's transmitted by one radio will be received with a \"frequency offset\" by another radio.\n",
"\n",
"Unfortunately, if the receiving radio doesn't know what the frequency offset is, then this can cause the correlation to fail. Consider the demonstration below:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def shift_frequency(signal, freq_shift):\n",
" \"\"\"\n",
" Applies a frequency shift to a signal. `freq_shift` is in radians per sample, and should be between 0 and 2𝛑.\n",
" \n",
" A frequency offset is simply an addition of a linearly increasing phase. Note that you could have taken the DFT,\n",
" circularly shifted the spectrum, and then taken the IDFT, and you would have gotten the same result.\n",
" \"\"\"\n",
" return signal * numpy.exp(1j * freq_shift * numpy.arange(len(signal)))"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
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"\n",
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"\n",
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"\n",
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" }\n",
"\n",
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" fig.updated_canvas_event();\n",
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" return;\n",
" }\n",
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"\n",
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"\n",
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"\n",
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" else if (e.srcElement)\n",
" targ = e.srcElement;\n",
" if (targ.nodeType == 3) // defeat Safari bug\n",
" targ = targ.parentNode;\n",
"\n",
" // jQuery normalizes the pageX and pageY\n",
" // pageX,Y are the mouse positions relative to the document\n",
" // offset() returns the position of the element relative to the document\n",
" var x = e.pageX - $(targ).offset().left;\n",
" var y = e.pageY - $(targ).offset().top;\n",
"\n",
" return {\"x\": x, \"y\": y};\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys (original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object')\n",
" obj[key] = original[key]\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function(event, name) {\n",
" var canvas_pos = mpl.findpos(event)\n",
"\n",
" if (name === 'button_press')\n",
" {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * mpl.ratio;\n",
" var y = canvas_pos.y * mpl.ratio;\n",
"\n",
" this.send_message(name, {x: x, y: y, button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event)});\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"}\n",
"\n",
"mpl.figure.prototype.key_event = function(event, name) {\n",
"\n",
" // Prevent repeat events\n",
" if (name == 'key_press')\n",
" {\n",
" if (event.which === this._key)\n",
" return;\n",
" else\n",
" this._key = event.which;\n",
" }\n",
" if (name == 'key_release')\n",
" this._key = null;\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.which != 17)\n",
" value += \"ctrl+\";\n",
" if (event.altKey && event.which != 18)\n",
" value += \"alt+\";\n",
" if (event.shiftKey && event.which != 16)\n",
" value += \"shift+\";\n",
"\n",
" value += 'k';\n",
" value += event.which.toString();\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, {key: value,\n",
" guiEvent: simpleKeys(event)});\n",
" return false;\n",
"}\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
" if (name == 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message(\"toolbar_button\", {name: name});\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.close = function() {\n",
" comm.close()\n",
" };\n",
" ws.send = function(m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function(msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data'])\n",
" });\n",
" return ws;\n",
"}\n",
"\n",
"mpl.mpl_figure_comm = function(comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = $(\"#\" + id);\n",
" var ws_proxy = comm_websocket_adapter(comm)\n",
"\n",
" function ondownload(figure, format) {\n",
" window.open(figure.imageObj.src);\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy,\n",
" ondownload,\n",
" element.get(0));\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element.get(0);\n",
" fig.cell_info = mpl.find_output_cell(\"\");\n",
" if (!fig.cell_info) {\n",
" console.error(\"Failed to find cell for figure\", id, fig);\n",
" return;\n",
" }\n",
"\n",
" var output_index = fig.cell_info[2]\n",
" var cell = fig.cell_info[0];\n",
"\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function(fig, msg) {\n",
" var width = fig.canvas.width/mpl.ratio\n",
" fig.root.unbind('remove')\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable()\n",
" $(fig.parent_element).html('');\n",
" fig.close_ws(fig, msg);\n",
"}\n",
"\n",
"mpl.figure.prototype.close_ws = function(fig, msg){\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"}\n",
"\n",
"mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width/mpl.ratio\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] = '';\n",
"}\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function() {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message(\"ack\", {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () { fig.push_to_output() }, 1000);\n",
"}\n",
"\n",
"mpl.figure.prototype._init_toolbar = function() {\n",
" var fig = this;\n",
"\n",
" var nav_element = $('')\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items){\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) { continue; };\n",
"\n",
" var button = $('');\n",
" button.click(method_name, toolbar_event);\n",
" button.mouseover(tooltip, toolbar_mouse_event);\n",
" nav_element.append(button);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = $('');\n",
" nav_element.append(status_bar);\n",
" this.message = status_bar[0];\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = $('');\n",
" var button = $('');\n",
" button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
" button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
" buttongrp.append(button);\n",
" var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
" titlebar.prepend(buttongrp);\n",
"}\n",
"\n",
"mpl.figure.prototype._root_extra_style = function(el){\n",
" var fig = this\n",
" el.on(\"remove\", function(){\n",
"\tfig.close_ws(fig, {});\n",
" });\n",
"}\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function(el){\n",
" // this is important to make the div 'focusable\n",
" el.attr('tabindex', 0)\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" }\n",
" else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager)\n",
" manager = IPython.keyboard_manager;\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which == 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_save = function(fig, msg) {\n",
" fig.ondownload(fig, null);\n",
"}\n",
"\n",
"\n",
"mpl.find_output_cell = function(html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i=0; i= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] == html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"}\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel != null) {\n",
" IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
"}\n"
],
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""
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"source": [
"X_with_freq_offset = shift_frequency(X, 0.1)\n",
"X_autocorr = numpy.correlate(X, X, mode='same')\n",
"X_autocorr_freq_offset = numpy.correlate(X, X_with_freq_offset, mode='same')\n",
"pyplot.figure()\n",
"pyplot.plot(abs(X_autocorr), label=\"Normal correlation\")\n",
"pyplot.plot(abs(X_autocorr_freq_offset), label=\"Correlation with frequency offset\")\n",
"pyplot.legend()\n",
"pyplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, the correlation with a frequency offset doesn't have a large peak anywhere. This is because the frequency offset causes the received signal to \"look\" significantly different from the transmitted signal, and so the correlation fails to detect the preamble.\n",
"\n",
"The way this is handled in practice is by using a method called \"Schmidl-Cox\" synchronization. The intuition is that the frequency offset \"corrupts\" our signal such that we can't detect it using correlation, but if we were to send two copies of the preamble back-to-back, then we would receive two copies of the corrupted preamble back-to-back. Then, instead of searching for a specific signal, we can search for any signal that repeats in time.\n",
"\n",
"Let $L$ be the length of the repeated segment. Then the preamble has length $2L$. At each index $d$ of the signal $s$, the Schmidl-Cox algorithm calculates the following two values:\n",
"$$ P(d) = \\sum_{m=0}^{L - 1} s_{d + m}^* s_{d + m + L} $$\n",
"$$ R(d) = \\frac{1}{2} \\sum_{m=0}^{2L - 1} \\left| s_{d + m} \\right|^2 $$\n",
"\n",
"Then the metric calculated at each index is\n",
"\n",
"$$ M(d) = \\frac{\\left| P(d) \\right|^2}{R(d)^2} $$\n",
"\n",
"Intuitively, $P$ is a correlation between the next $L$ samples and the following $L$ samples and $R$ is a normalization factor. Once the value of $M$ increases beyond a threshold, the preamble is detected. Note that $P$ also has a recursive form:\n",
"\n",
"$$ P(d + 1) = P(d) + (s_{d + L}^* s_{d + 2L}) - (s_{d}^* s_{d + L}) $$\n",
"\n",
"**Food for thought**: How could we use a Schmidl-Cox preamble to estimate the frequency offset? This may not be immediatly obvious, but we will do this in Lab 4 to estimate and then correct frequency offsets for when we're receiving data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 1.3 Schmidl-Cox Preamble Detection (10 pts)\n",
"- **Implement the Schmidl-Cox preamble detector below.**\n",
"\n",
"You can use either the iterative or recursive formulations for calculating $P$. Return the index $d^*$ that maximizes $M(d)$ if $M(d^*)$ is greater than the threshold, otherwise return None."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [],
"source": [
"schmidl_cox_threshold = 0.5\n",
"def detect_preamble_with_freq_offset(signal, short_preamble_len):\n",
" pass"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"# This cell will test your implementation of `detect_preamble`\n",
"short_preamble_length = 100\n",
"signal_length = 1000\n",
"short_preamble = numpy.exp(2j * numpy.pi * numpy.random.random(short_preamble_length))\n",
"preamble = numpy.tile(short_preamble, 2)\n",
"noise = numpy.random.normal(size=signal_length) + 1j * numpy.random.normal(size=signal_length)\n",
"signalA = 0.1 * noise\n",
"signalB = 0.1 * noise\n",
"signalC = 0.1 * noise\n",
"preamble_start_idx = 321\n",
"signalB[preamble_start_idx:preamble_start_idx + len(preamble)] += preamble\n",
"signalC[preamble_start_idx:preamble_start_idx + len(preamble)] += shift_frequency(preamble, 0.1)\n",
"\n",
"numpy.testing.assert_equal(detect_preamble_with_freq_offset(signalA, short_preamble_length), None)\n",
"numpy.testing.assert_equal(detect_preamble_with_freq_offset(signalB, short_preamble_length), 321)\n",
"numpy.testing.assert_equal(detect_preamble_with_freq_offset(signalC, short_preamble_length), 321)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 2: Preamble detection with the HackRF"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 2.1 Offline Preamble Detection (20 pts)\n",
"\n",
"There is a Schmidl-Cox preamble being transmitted every second at frequency 1280 MHz. Using the below API, tune to 1280 MHz at a bandwidth of 100 kHz and record two seconds of data. Tune elsewhere (try 1290 MHz) and record another two seconds of data. You may need to play around with the gain value to get a clean reception.\n",
"- **For both signals, plot the signal (real and imaginary components separate) and the values of $M$ from running Schmidl-Cox on each signal**"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [],
"source": [
"class Radio:\n",
" def __init__(self, *args, **kwargs):\n",
" self.sdr = SoapySDR.Device(*args, **kwargs)\n",
"\n",
" def set_sample_rate(self, sample_rate_hz):\n",
" self.sdr.setSampleRate(SOAPY_SDR_RX, 0, sample_rate_hz)\n",
"\n",
" def set_center_frequency(self, freq_hz):\n",
" self.sdr.setFrequency(SOAPY_SDR_RX, 0, freq_hz)\n",
"\n",
" def start_receive(self):\n",
" self.rx_stream = self.sdr.setupStream(SOAPY_SDR_RX, SOAPY_SDR_CF32)\n",
" self.sdr.activateStream(self.rx_stream)\n",
"\n",
" def stop_receive(self):\n",
" self.sdr.deactivateStream(self.rx_stream)\n",
" self.sdr.closeStream(self.rx_stream)\n",
" self.rx_stream = None\n",
"\n",
" def grab_samples(self, rx_buff):\n",
" if self.rx_stream is None:\n",
" raise RuntimeError(\"Need to start receiving before grabbing samples\")\n",
"\n",
" if len(rx_buff) > self.get_buffer_size():\n",
" raise RuntimeError(\"Number of samples cannot be more than the buffer size\")\n",
"\n",
" resp = self.sdr.readStream(self.rx_stream, [rx_buff], numElems=len(rx_buff))\n",
" if resp.ret != len(rx_buff):\n",
" raise RuntimeError('Receive failed: {}'.format(SoapySDR.errToStr(resp.ret)))\n",
"\n",
" def get_buffer_size(self):\n",
" return 131072\n",
" \n",
" def set_receive_gain(self, gain):\n",
" \"\"\"\n",
" `gain` is a value between 0 and 1. Note that `gain` corresponds to a value in decibels,\n",
" so the actual gain is exponential in the value of `gain`.\n",
" \"\"\"\n",
" max_rx_gain = sum(self.sdr.getGainRange(SoapySDR.SOAPY_SDR_RX, 0, gain_type).maximum()\n",
" for gain_type in self.sdr.listGains(SoapySDR.SOAPY_SDR_RX, 0))\n",
" self.sdr.setGain(SoapySDR.SOAPY_SDR_RX, 0, gain * max_rx_gain)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 2.2 Real-time Preamble Detection (Optional) (5 pts)\n",
"Run Schmidl-Cox in real time to detect the preamble. Since performing the calculations in python is slow, to get this to work it is necessary to vectorize the calculation of $P$ and to ignore the normalization term (so this is really a variant of Schmidl-Cox).\n",
"\n",
"To receive the bonus points for this optional problem, demonstrate your real-time preamble detection to a TA during lab hours."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 3: Slotted-ALOHA Capacity\n",
"\n",
"In the idealized slotted aloha model, time is splitted into multiple slots and the packet transmission time is one full slot. All nodes are perfectly syncronized, and transmit at the begining of each slot. The transmission probability for each user for each slot is some value $p$.\n",
"\n",
"For each time slot, three cases may happen. 1): There are more than one nodes transmits, thus resulting in a conflict slot. The receiver cannot receive them correctly. 2): There is only one node transmission and thus the receiver can receive it correctly. 3): No node transmits at the current slot.\n",
"\n",
"In this section, we will verify the slotted-ALOHA capacity curve through Monte-Carlo simulation.\n",
"\n",
"### Problem 3.1 Slotted ALOHA Simulation (10 pts)\n",
"- **Fill in the function below.**\n",
"\n",
"The function will take a number of users, a number of time slots, and a probability $p$ that a given user will transmit on a given timeslot. The function will return the ratio of successful timeslots (timeslots in which a successful transmission occurred) to total number of timeslots."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def simulate_slotted_aloha(num_users, num_timeslots, per_slot_user_prob):\n",
" pass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 3.2 Verifying Slotted ALOHA capacity (5 pts)\n",
"Run your simulation over 1000 values of $p$ between 0 and 1 with 10 users and 10k timeslots.\n",
"- **Plot the timeslot success ratio as a function of $p$ **\n",
"\n",
"Verify that the resulting plot matches the theoretical curve."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
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