{"id":154607,"date":"2023-08-05T13:27:29","date_gmt":"2023-08-05T07:57:29","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154607"},"modified":"2023-08-05T13:27:31","modified_gmt":"2023-08-05T07:57:31","slug":"a-single-bit-equally-likely-to-be-0-and-1-is-to-be-sent-across-an-additive-white-gaussian-noise-awgn-channel-with-power-spectral-density-%f0%9d%91%810-2","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-single-bit-equally-likely-to-be-0-and-1-is-to-be-sent-across-an-additive-white-gaussian-noise-awgn-channel-with-power-spectral-density-%f0%9d%91%810-2\/","title":{"rendered":"A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density \ud835\udc410\/2."},"content":{"rendered":"\n<p>Q. A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density \ud835\udc41<sub>0<\/sub>\/2. Binary signaling, with<\/p>\n\n\n\n<p>0 \u21a6 \ud835\udc5d(\ud835\udc61) and 1 \u21a6 \ud835\udc5e(\ud835\udc61), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability.<\/p>\n\n\n\n<p>Let \ud835\udf11<sub>1<\/sub>(\ud835\udc61), \ud835\udf11<sub>2<\/sub>(\ud835\udc61) form an orthonormal signal set.<\/p>\n\n\n\n<p>If we choose \ud835\udc5d(\ud835\udc61) = \ud835\udf11<sub>1<\/sub>(\ud835\udc61) and \ud835\udc5e(\ud835\udc61) = \u2212\ud835\udf11<sub>1<\/sub>(\ud835\udc61), we would obtain a certain bit-error probability \ud835\udc43<sub>\ud835\udc4f<\/sub>.<\/p>\n\n\n\n<p>If we keep \ud835\udc5d(\ud835\udc61) = \ud835\udf11<sub>1<\/sub>(\ud835\udc61), but take \ud835\udc5e(\ud835\udc61) = \u221a\ud835\udc38 \ud835\udf11<sub>2<\/sub>(\ud835\udc61), for what value of \ud835\udc38 would we obtain the <strong>same <\/strong>bit-error probability \ud835\udc43<sub>\ud835\udc4f<\/sub>?<\/p>\n\n\n\n<p>(A) 0<\/p>\n\n\n\n<p>(B) 1<\/p>\n\n\n\n<p>(C) 2<\/p>\n\n\n\n<p>(D) 3<\/p>\n\n\n\n<p>Ans: 3<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density \ud835\udc410\/2. Binary signaling, with 0 \u21a6 \ud835\udc5d(\ud835\udc61) and 1 \u21a6 \ud835\udc5e(\ud835\udc61), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let \ud835\udf111(\ud835\udc61), [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154610,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"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-opacity":"","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-opacity":"","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-opacity":"","overlay-gradient":""}},"ast-content-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-opacity":"","overlay-gradient":""},"tablet":{"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-opacity":"","overlay-gradient":""},"mobile":{"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-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154607","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154607","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154607"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154607\/revisions"}],"predecessor-version":[{"id":154611,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154607\/revisions\/154611"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154610"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154607"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154607"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}