{"id":28924,"date":"2026-06-16T14:16:51","date_gmt":"2026-06-16T06:16:51","guid":{"rendered":"http:\/\/localhost\/wordpress\/?p=28924"},"modified":"2026-06-18T15:29:47","modified_gmt":"2026-06-18T07:29:47","slug":"blog202602","status":"publish","type":"post","link":"http:\/\/localhost\/wordpress\/2026\/06\/16\/blog202602\/","title":{"rendered":"Blog202602"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"28924\" class=\"elementor elementor-28924\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-279f440 e-flex e-con-boxed e-con e-parent\" data-id=\"279f440\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d36d179 elementor-widget elementor-widget-text-editor\" data-id=\"d36d179\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.17.0 - 01-11-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<div id=\"stacks_out_4904195\" class=\"stacks_out\">\n<div id=\"stacks_in_4904195\" class=\"stacks_in com_elixir_stacks_foundryImage_stack\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"modal-header\">\n<div class=\"closer_x\">\n<div class=\"modal-header\">\n<h4 id=\"myModalLabel\" class=\"modal-title text-xs-left\">2026.06<\/h4>\n<h4 class=\"modal-title text-xs-left\">Frequency-Modulated Continuous-Wave (FMCW) Radar<\/h4>\n<p>\u6587\/Pouya Torkaman<br>\u7de8\/\u6881\u701a\u53cb<\/p>\n<\/div>\n<h5><strong>Abstract<\/strong><\/h5>\n<p>&nbsp; &nbsp; Frequency-Modulated Continuous-Wave (FMCW) radar is a crucial technology in modern sensing applications, offering high-resolution distance and velocity measurements with low power consumption. Unlike traditional pulsed radar systems, FMCW radar continuously transmits a frequency-modulated signal, analyzing the frequency shift in the reflected wave to determine target range and motion. This article explores the fundamental principles of FMCW radar, including its signal processing techniques, chirp modulation, and data analysis methods. Additionally, we examine its historical development and its widespread applications in autonomous vehicles, aviation, industrial sensing, and medical imaging. With advancements in digital signal processing and semiconductor technology, FMCW radar continues to evolve, enabling more precise and efficient sensing solutions for next-generation technologies.<\/p>\n<h5><strong>Short History of Radar<\/strong><\/h5>\n<p>&nbsp; &nbsp; The foundations of radar can be traced back to the late 19th century when James Clerk Maxwell formulated electromagnetic wave theory in the 1860s. Later, in 1886, Heinrich Hertz experimentally demonstrated that radio waves could be reflected off metallic objects, laying the groundwork for radar technology. As the 20th century began, researchers explored the properties of radio wave reflection and detection. In 1904, German engineer Christian H\u00fclsmeyer invented the \u201cTelemobiloscope,\u201d an early radar-like system designed to detect ships in foggy environments. Although primitive, this invention demonstrated the feasibility of using radio waves for object detection.<\/p>\n<p>&nbsp; &nbsp; By the 1920s, various researchers, including Guglielmo Marconi, were exploring radio wave propagation and reflection, but practical radar systems had not yet been developed. The rapid advancement of radar occurred during World War II, with multiple nations developing radar independently. Notable developments include:<\/p>\n<ul>\n<li>United Kingdom: The British developed Chain Home, the first operational radar system, which played a critical role in the Battle of Britain.<\/li>\n<li>United States: The MIT Radiation Laboratory advanced radar research, leading to airborne and naval radar systems.<\/li>\n<li>Germany and Japan: Both countries developed radar technologies but did not achieve the same level of operational effectiveness as the Allies.<\/li>\n<\/ul>\n<p>&nbsp; &nbsp; Pulsed radar systems became the standard during this period, using high-power bursts of radio waves to detect objects at long distances.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:553\/1*N74S7_lE3gzUT1GOGDsFhQ.png\"><\/p>\n<p style=\"text-align: center;\"><em>Fig 1.&nbsp;<a class=\"z or\" href=\"https:\/\/mecorad.com\/celebrating-120-years-of-radar-christian-huelsmeyers-historic-telemobiloscope-demonstration\/\" target=\"_blank\" rel=\"noopener ugc nofollow\">Christian H\u00fclsmeyer\u2019s historic Telemobiloscope demonstration<\/a><\/em><\/p>\n<p>&nbsp; &nbsp; Following World War II, radar technology transitioned into civilian use, finding applications in air traffic control, weather monitoring, and scientific research. Advances in microwave technology, solid-state electronics, and Doppler radar significantly improved radar capabilities.<\/p>\n<p>&nbsp; &nbsp; A notable development was Continuous Wave (CW) radar, which operated without pulses but faced limitations in measuring range. To address this, Frequency-Modulated Continuous-Wave (FMCW) radar was introduced. Designed to enhance range resolution and Doppler detection while maintaining low power consumption, FMCW radar differs from pulsed radar by continuously transmitting a frequency-modulated signal. By analyzing the frequency shift in the reflected signal, it can precisely determine both the distance and velocity of a target. Today, FMCW radar is widely utilized in various fields, including automotive systems, aviation, drones, industrial sensing, and medical imaging. With continuous advancements in digital signal processing and semiconductor technology, FMCW radar has become an essential component of modern radar systems, offering high accuracy, low power requirements, and compact designs.<\/p>\n<h5><strong>FMCW Radar Concept<\/strong><\/h5>\n<p>&nbsp; &nbsp; FMCW radar is an advanced radar technique that continuously transmits a signal while varying its frequency over time. Unlike pulsed radar, which emits discrete bursts of energy, FMCW radar sends a continuous waveform with a frequency that changes linearly over a given period, typically in a sawtooth or triangular pattern. This frequency modulation enables precise measurement of target range and velocity with lower power requirements compared to traditional radar systems. The core operation of FMCW radar relies on transmitting a signal that gradually shifts in frequency and comparing it to the reflected wave received from an object which can be seen in figure 2. The difference between the transmitted and received signal frequencies, known as the beat frequency, is directly proportional to the target\u2019s distance. By analyzing this frequency shift, the radar system can accurately determine the range of the object. Additionally, if the target is moving, the Doppler effect introduces an extra frequency shift, allowing the system to calculate velocity.<\/p>\n<h5><strong>Working principle<\/strong><\/h5>\n<p>&nbsp; &nbsp; In an FMCW radar system, the transmitted signal is a chirp signal, meaning its frequency increases linearly over time. This continuous frequency modulation allows the radar to measure range and velocity simultaneously by analyzing the frequency difference between the transmitted and received signals. The transmitted signal is a linear frequency-modulated (LFM) waveform. The frequency increases linearly over a period Tc , resulting in the transmitted signal:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:288\/1*j1xcPB33rUwkKkepwsjddA.png\"><\/p>\n<p><span style=\"font-size: 16px;\">&nbsp; &nbsp; where: <\/span><em class=\"op\">A<\/em>&nbsp;is the amplitude of the signal,&nbsp;<em class=\"op\">f0<\/em>&nbsp;is the starting frequency of the chirp,&nbsp;<em class=\"op\">Bc <\/em>&nbsp;is the total bandwidth of the chirp,&nbsp;<em class=\"op\">Tc<\/em> is the chirp duration, and&nbsp;<em class=\"op\">\u03bc<\/em>&nbsp;is the chirp rate, defined as:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:60\/1*6kc2Mgv-5MgfLSKVDLuxmA.png\"><\/p>\n<p>&nbsp; &nbsp; The frequency of the transmitted signal at any time<em class=\"op\">&nbsp;t<\/em>&nbsp;is:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:156\/1*CfEMB0b5t5l4PUmtObO28g.png\"><\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:700\/1*5b5Y9ph6rYTSB7h-ATek6w.png\"><\/p>\n<p style=\"text-align: center;\"><em>Fig 2. A depiction of contemporary radar sensors featuring multiple identical transmit chirps within a frame, where the digitized IF samples \ud835\udc60 IF [ \ud835\udc58 ] are systematically stored in a data matrix, organized by chirps, for coherent signal processing (Source: Ref [3]).<\/em><\/p>\n<p>&nbsp; &nbsp; When the transmitted signal encounters a target at distance \ud835\udc45, it reflects back to the receiver after a time delay \ud835\udf0f, which is given by:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:103\/1*vgeoDR8R7_sYMnSE2d9XAg.png\"><\/p>\n<p>&nbsp; &nbsp; Where is the speed of light. Therefore, the received signal is a delayed version of the transmitted signal:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/miro.medium.com\/v2\/resize:fit:417\/1*WFkGieSLrTnMls8d_fLtyA.png\"><\/p>\n<p id=\"31d3\" class=\"pw-post-body-paragraph mu mv hp mw b mx my mz na nb nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr hi bg\" data-selectable-paragraph=\"\">&nbsp; &nbsp; Figure 2 illustrates the basic operation of an FMCW radar system. The transmitted signal linearly sweeps across a bandwidth over a fixed time period, with its frequency gradually increasing. The transmitted signal (TX) then propagates through the environment, reflecting off objects in its path. The radar receiver (RX) captures the reflected signals, which return with a slight delay. This delay is proportional to the distance of the target \u2014 closer objects reflect the signal back sooner, while objects farther away introduce a longer delay. Since the received signal is slightly time-shifted compared to the transmitted one, there is a frequency difference between them. This difference, known as the intermediate frequency (IF), is crucial because it contains valuable information about the target\u2019s range and velocity. The larger the delay, the greater the frequency difference, allowing the system to precisely calculate how far away an object is.<\/p>\n<p id=\"38d8\" class=\"pw-post-body-paragraph mu mv hp mw b mx my mz na nb nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr hi bg\" data-selectable-paragraph=\"\">&nbsp; &nbsp; Later, the IF signal is sampled and converted into a digital format using an analog-to-digital converter (ADC). These digital samples are then organized in a structured data matrix, where each row corresponds to an individual chirp. This structured approach allows for efficient processing, helping the system extract key details about the target\u2019s movement and position through advanced signal processing techniques. There are two important time dimensions: \u201cfast time\u201d and \u201cslow time.\u201d Fast time represents the duration of a single chirp, capturing fine details of an object\u2019s range. Slow time, on the other hand, represents the sequence of chirps collected over multiple transmissions. By analyzing how these chirps change over time, the radar system can measure the velocity of moving objects using Doppler processing. The angle detection dimension is crucial for determining the spatial orientation of a target relative to the radar. By utilizing techniques like phased array antennas or synthetic aperture radar, the radar system can measure the direction of arrival (DOA) of the reflected signal. This measurement provides valuable information about the angular position of the target, which can be expressed in terms of azimuth, elevation, or both, depending on the system configuration. The ability to accurately detect the angle of a target allows the radar to distinguish between multiple objects in the same range, improving its ability to track targets in cluttered environments. By combining this angular data with range information from the fast time dimension and the frequency modulation captured in the slow time dimension, the radar system can generate a comprehensive 3D map of the surrounding area. For example, for an antenna array, each receive chain independently processes its data samples and computes a 2D FFT (fast and slow time FFT). To obtain a 3D representation, a final FFT is performed across the antenna elements in the spatial domain. This entire process results in the formation of a Radar data cube, which encapsulates range, Doppler, and angle information. Advanced signal processing techniques, such as beamforming, target clustering, and tracking algorithms, are then applied to extract precise target locations, estimate their velocity, and monitor their movement over time.<\/p>\n<h5><strong>References<\/strong><\/h5>\n<p>[1] https:\/\/mecorad.com\/celebrating-120-years-of-radar-christian-huelsmeyers-historic-telemobiloscope-demonstration<\/p>\n<p>[2] https:\/\/www.ti.com\/video\/5415203482001<\/p>\n<p>[3] A. Santra, S. Hazra, L. Servadei, T. Stadelmayer, M. Stephan, and A. Dubey, Methods and techniques in deep learning: Advancements in mmWave Radar Solutions. John Wiley &amp; Sons, 2022.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><!-- \/wp:paragraph --><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2026.06 Frequency-Modulated Continuous-Wave (FMCW) Rada &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"http:\/\/localhost\/wordpress\/2026\/06\/16\/blog202602\/\"> <span class=\"screen-reader-text\">Blog202602<\/span> \u95b1\u8b80\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28924","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"yrg","author_link":"http:\/\/localhost\/wordpress\/author\/yrg\/"},"uagb_comment_info":0,"uagb_excerpt":"2026.06 Frequency-Modulated Continuous-Wave (FMCW) Rada...","_links":{"self":[{"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/posts\/28924","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/comments?post=28924"}],"version-history":[{"count":8,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/posts\/28924\/revisions"}],"predecessor-version":[{"id":28945,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/posts\/28924\/revisions\/28945"}],"wp:attachment":[{"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/media?parent=28924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/categories?post=28924"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wordpress\/wp-json\/wp\/v2\/tags?post=28924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}