{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# AFSK Digital Correlator Demodulator\n", "\n", "This notebook contains a Python implementation of the 1200 baud AFSK demodulator\n", "used in the Mobilinkd TNC3.\n", "\n", "This started out as a short demo in Python of the demodulator presented in\n", "[PSoC ® 1 - Simplified FSK Detection (AN2336)](http://www.cypress.com/go/AN2336)\n", "by Dennis Seguine for Cypress Semiconductor. It has grown quite a bit since.\n", "This now expands on that application note to show a complete HDLC packet\n", "demodulator/decoder.\n", "\n", "The purpose of this design is to demodulate 1200 baud amateur radio\n", "packet data. This encompasses the following topics:\n", "\n", " * AFSK Demodulation (the topic of the above mentioned appliction note)\n", " * Clock Recovery\n", " * Data Carrier Detection\n", " * HDLC Decoding\n", " * AX.25 Packet Parsing\n", "\n", "## AFSK Basics\n", "\n", "AFSK -- audio frequency shift keying -- is a method of sending data by\n", "alternating two tones, called *mark* and *space*, to transmit binary\n", "data.\n", "\n", "Amateur radio packet data uses the [Bell 202 modem specification](https://en.wikipedia.org/wiki/Bell_202_modem), which specifies a 1200 baud data rate, 1200Hz mark and 2200Hz space tones, a\n", "+/- 10Hz accuracy, and a 1dB flatness for the audio signal. Bell 202 is a\n", "phase-continuous modulation scheme, meaning that there are no abrupt phase\n", "changes when switching between mark and space tones.\n", "\n", "### NRZI\n", "\n", "The tones themselves do not encode 0/1 directly. Rather a [non-return\n", "to zero, inverted (NRZI)](https://en.wikipedia.org/wiki/Non-return-to-zero)\n", "scheme is used. What this means in laymans terms is that rather than the\n", "tones themselves encoding 0s and 1s, it is a change or no change in tone\n", "that encodes the data. In NRZI, a change in tone encodes a 0 and no change\n", "in tone encodes a 1.\n", "\n", "## AFSK Challenges\n", "\n", "Digital signal processing of AFSK data presents a number of challenges.\n", "At the most rudimentary level we have to deal with noise in the signal\n", "and have to overcome low SNR. In practice, low SNR is actually the least\n", "of our worries. we are focused on AFSK over FM, which provides a fairly\n", "low SNR until it hits a cliff and falls off very fast.\n", "\n", "A much more serious problem we face is twist. Twist is the amplitude\n", "difference between mark and space tones. Recall that the Bell 202 spec\n", "requires a 1dB flatness. Over an amateur radio voice channel, at its\n", "worst we can have twist of +/-9dB and absolutely must handle twist of\n", "6dB.\n", "\n", " 1. The voice channel is emphasized on transmission and de-emphasized on\n", " reception. Pre-emphasis adds about 6dB to the space tone and then\n", " subtracts 6dB during de-emphasis.\n", " 2. Not all radios do pre-emphasis. This can cause up to 6dB in twist\n", " when received on a radio that does de-emphasis.\n", " 3. Radios that do pre-emphasis may clip the signal after emphasis. This\n", " causes the higher tone to be lower in amplitude when de-emphasized.\n", " This can cause up to 6dB in twist when de-emphasized.\n", " 4. Some people may use radios that do not apply de-emphasis. This may\n", " present 6dB twist to the modem in the other direction.\n", "\n", "Because AFSK is sent over a voice channel, and is sent and received\n", "using equipment designed for voice communication, we have to deal with\n", "audio processing artifacts that are typically avoided in data transmission.\n", "The audio filters, pre-emphasis and de-emphasis filters and limiters used\n", "can cause phase shifts in audio that is imperceptible to human ears but\n", "which can lead to inter-symbol interference (ISI) when sending data.\n", "\n", "At least one major TNC manufacturer substituted V.23 modem chips (rather\n", "than Bell 202) in their product for a time, causing tones to by out of\n", "spec by 100Hz.\n", "\n", "All modern digital communications standards use some form of forward\n", "error correction (FEC). 1200 baud packet radio uses no FEC. A one-bit\n", "error will prevent a packet from being properly decoded.\n", "\n", "So, to summarize, our modem must deal with:\n", "\n", " * Low SNR -- noise on top of the actual data signal\n", " * High twist -- large differences in amplitude between mark and space tones\n", " * Phase distortion -- mark and space tones not arriving at symbol boundaries\n", " * Inter-symbol interference -- mark and space tones overlapping due to phase distortion\n", " * Frequency distortion -- large differences in tone frequency and data rate\n", " * No error correction -- one bit errors are fatal\n", "\n", "These issues make demodulating a packet radio signal more challenging\n", "than 1200 baud over POTS. In order to acheive best in class performance\n", "the demodulator needs to address all of these issues.\n", "\n", "## AFSK Demodulation\n", "\n", "As mentioned above, there are a number of steps necessary in order to get to\n", "a decoded packet. The first step is demodulation -- turning the tones into\n", "bits. This is a digital correlator demodulator. It is very simple to implement.\n", "It consumes very little resources which is important when running on low-power\n", "emdedded devices. And it is fairly tolerant of twist.\n", "\n", "### What is a Digital Correlator\n", "\n", "The correlator involves little more than multiplying the input signal with a\n", "delayed copy of itself. It is a [comb filter](https://en.wikipedia.org/wiki/Comb_filter).\n", "It causes the signal to destructively and constructively interfere with\n", "itself in such a manner as to demodulate the encoded bitstream. By adjusting\n", "the delay, we can maximize the difference between mark and space tones.\n", "\n", "A digital correlator invovles converting the analog signal into a digital\n", "one by way of a zero-crossing detector, and then applying the same delay\n", "as one would with an analog comb filter.\n", "\n", "An analog comb filter is sensitive to twist and is more costly to implement\n", "than a digital one. A digital correlator is more sensitive to low-frequency\n", "noise and simpler to implement in code or digital circuitry.\n", "\n", "-----\n", "\n", "Note: it may be cheaper to deal with the twist issues with an analog comb filter.\n", "\n", " $y[n]=x[n]+\\alpha x[n-K]$\n", "\n", "$\\alpha$ is a scaling factor that involves a single multiply per sample.\n", "\n", "### Finding the Right Delay\n", "\n", "As mentioned above, we are designing a comb filter where the goal is to maximize\n", "the difference between mark and space tones. This is a problem summed up by:\n", "\n", "$y[d] = cos(2\\pi f_L d) - cos(2 \\pi f_H d)$\n", "\n", "where $f_L$ is the low freqency, $f_H$ is the high frequency and $d$ is the delay.\n", "\n", "We can graph this equation. When we do, we should see what delays provides the biggest\n", "differences between the two tones." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "%matplotlib notebook\n", "import matplotlib.pyplot as plt\n", "\n", "def plot_to_notebook(time_sec,mark_signal,space_signal,corr_signal,n_samples):\n", " plt.figure()\n", " plt.subplot(1, 1, 1)\n", " plt.xlabel('Time (msec)')\n", " plt.grid()\n", " plt.plot(time_sec[:n_samples]*1000,mark_signal[:n_samples],'y-',label='Mark signal')\n", " plt.plot(time_sec[:n_samples]*1000,space_signal[:n_samples],'g-',label='Space signal')\n", " plt.plot(time_sec[:n_samples]*1000,corr_signal[:n_samples],'r-',linewidth=2,label='Correlation')\n", " plt.legend()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of samples: 1000\n" ] }, { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " evt.data.type = \"image/png\";\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src);\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " evt.data);\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig[\"handle_\" + msg_type];\n", " } catch (e) {\n", " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n", " }\n", " }\n", " };\n", "}\n", "\n", "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function(e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e)\n", " e = window.event;\n", " if (e.target)\n", " targ = e.target;\n", " 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 overridden (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", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\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