{"id":76,"date":"2011-06-02T11:22:43","date_gmt":"2011-06-02T11:22:43","guid":{"rendered":"http:\/\/www.raymaps.com\/blog\/?p=76"},"modified":"2013-03-22T05:11:17","modified_gmt":"2013-03-22T05:11:17","slug":"bit-error-rate-of-qpsk-in-rayleigh-fading","status":"publish","type":"post","link":"https:\/\/www.raymaps.com\/index.php\/bit-error-rate-of-qpsk-in-rayleigh-fading\/","title":{"rendered":"Bit Error Rate of QPSK in Rayleigh Fading"},"content":{"rendered":"<p style=\"text-align: justify;\">So far we have considered the bit error rate (BER) of BPSK and QPSK in an AWGN channel. Now we turn our attention to a Rayleigh fading channel which is a more realistic representation of a wireless communication channel. We consider a single tap Rayleigh fading channel which is good approximation of a flat fading channel i.e. a channel that has flat frequency response (but varying with time). The complex channel coefficient is given as (a+j*b) where a and b are Gaussian random variables with mean 0 and variance 0.5. We use the envelope of this channel coefficient in our simulation as any phase shift is easily removed by the receiver.<\/p>\n<pre lang=\"matlab\">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\r\nfunction[ber]=err_rate3(l,EbNo)\r\nsi=2*(round(rand(1,l))-0.5);\r\nsq=2*(round(rand(1,l))-0.5);\r\ns=si+j*sq;\r\nn=(1\/sqrt(2*10^(EbNo\/10)))*(randn(1,l)+j*randn(1,l));\r\nh=(1\/sqrt(2))*((randn(1,l))+j*(randn(1,l)));\r\nr=abs(h).*s+n;\r\nsi_=sign(real(r));\r\nsq_=sign(imag(r));\r\nber1=(l-sum(si==si_))\/l;\r\nber2=(l-sum(sq==sq_))\/l;\r\nber=mean([ber1 ber2]);\r\nreturn\r\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/pre>\n<p>It is observed that the BER for a Rayleigh fading channel is much higher than the BER for an AWGN channel. In fact, for Rayleigh fading, the BER curve is almost a straight line!!!<\/p>\n<figure id=\"attachment_77\" aria-describedby=\"caption-attachment-77\" style=\"width: 866px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/www.raymaps.com\/index.php\/bit-error-rate-of-qpsk-in-rayleigh-fading\/ber2\/\" rel=\"attachment wp-att-77\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-77\" title=\"Rayleigh Fading\" alt=\"\" src=\"http:\/\/www.raymaps.com\/wp-content\/uploads\/2011\/06\/ber2.jpg\" width=\"866\" height=\"561\" srcset=\"https:\/\/www.raymaps.com\/wp-content\/uploads\/2011\/06\/ber2.jpg 866w, https:\/\/www.raymaps.com\/wp-content\/uploads\/2011\/06\/ber2-300x194.jpg 300w\" sizes=\"auto, (max-width: 866px) 100vw, 866px\" \/><\/a><figcaption id=\"caption-attachment-77\" class=\"wp-caption-text\">Rayleigh Fading<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">Note:<\/p>\n<p style=\"text-align: justify;\">1. The input EbNo to the function is in dB so it is converted into linear scale by 10^(EbNo\/10).<\/p>\n<p style=\"text-align: justify;\">2. Noise is added in a Rayleigh fading channel as well. Noise is introduced by the receiver front end and is always present.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>So far we have considered the bit error rate (BER) of BPSK and QPSK in an AWGN channel. Now we turn our attention to a Rayleigh fading channel which is a more realistic representation of a wireless communication channel. We consider a single tap Rayleigh fading channel which is good approximation of a flat fading channel i.e. a channel that has flat frequency response (but varying with time). The complex channel coefficient is given as (a+j*b) where a and b are Gaussian random variables with mean 0 and variance 0.5. We use the envelope of this channel coefficient in our [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[34,36],"class_list":["post-76","post","type-post","status-publish","format-standard","hentry","category-berp","tag-ber","tag-qpsk"],"_links":{"self":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/76","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/comments?post=76"}],"version-history":[{"count":23,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/76\/revisions"}],"predecessor-version":[{"id":1915,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/76\/revisions\/1915"}],"wp:attachment":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/media?parent=76"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/categories?post=76"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/tags?post=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}