{"id":538,"date":"2011-09-02T13:58:28","date_gmt":"2011-09-02T13:58:28","guid":{"rendered":"http:\/\/www.raymaps.com\/?p=538"},"modified":"2022-05-31T08:49:28","modified_gmt":"2022-05-31T08:49:28","slug":"ber-of-64-qam-ofdm-in-awgn","status":"publish","type":"post","link":"https:\/\/www.raymaps.com\/index.php\/ber-of-64-qam-ofdm-in-awgn\/","title":{"rendered":"BER of 64-QAM OFDM in AWGN"},"content":{"rendered":"

64-QAM is an important component of the LTE Air Interface that promises higher data rates and spectral efficiencies. Combined with OFDM and MIMO it successfully combats the detrimental effects of the wireless channels and provides data rates in excess of 100Mbps (peak data rate). Here, we discuss a simple example of 64-QAM modulation with OFDM in an AWGN channel. We assume a bandwidth of 1.25MHz which corresponds to an FFT size of 128.<\/p>\n

\n
\n
\"LTE<\/a><\/dt>\n
LTE Bandwidth<\/dd>\n<\/dl>\n<\/div>\n

Given below is the code for this scheme.<\/p>\n

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% FUNCTION TO CALCULATE BER OF 64-QAM OFDM IN AWGN\n% n_bits: Input, number of bits\n% n_fft: Input, FFT size \n% EbNodB: Input, energy per bit to noise PSD\n% ber: Output, bit error rate\n% Copyright RAYmaps (www.raymaps.com)\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nfunction[ber]= M_QAM(n_bits,n_fft,EbNodB);\nEb=7;\nM=64;\nk=log2(M);\nEbNo=10^(EbNodB\/10);\nx=transpose(round(rand(1,n_bits)));\nh1=modem.qammod(M);\nh1.inputtype='bit';\nh1.symbolorder='gray';\ny=modulate(h1,x);\nn_sym=length(y)\/n_fft;\ns_ofdm=zeros(1,n_fft);\nr_ofdm=zeros(1,n_fft);\nfor n=1:n_sym;\ns_ofdm=sqrt(n_fft)*ifft(y((n-1)*n_fft+1:n*n_fft),n_fft);\nwn=randn(1,n_fft)+j*randn(1,n_fft);\nr_ofdm=s_ofdm+sqrt(Eb\/(2*EbNo))*wn.';\ns_est((n-1)*n_fft+1:n*n_fft)=fft(r_ofdm,n_fft)\/sqrt(n_fft);\nend\nh2=modem.qamdemod(M);\nh2.outputtype='bit';\nh2.symbolorder='gray';\nh2.decisiontype='hard decision';\nz=demodulate(h2,s_est.');\nber=(n_bits-sum(x==z))\/n_bits;\nreturn\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n<\/pre>\n
As discussed previously, with proper normalization of IFFT and FFT operations the performance of OFDM in AWGN is the same as the performance of the underlying modulation scheme. We have not even introduced the cyclic prefix in our simulation because without a fading channel there is no ISI and cyclic prefix (CP) is of no use. We will introduce the CP when we turn our attention to fading channels.<\/p>\n
\n
\n
\"OFDM<\/a><\/dt>\n
OFDM 64-QAM<\/dd>\n<\/dl>\n<\/div>\n
It must be noted that although IFFT and FFT are linear inverses of each other proper normalization is required to maintain the signal levels at the transmitter and receiver.<\/p>\n","protected":false},"excerpt":{"rendered":"
64-QAM is an important component of 4G\/5G Air Interface that promises higher data rates and spectral efficiencies. Combined with OFDM and MIMO it successfully combats the detrimental effects of the wireless channels and provides data rates in excess of 100Mbps (peak data rate). Here, we discuss a simple example of 64-QAM modulation with OFDM in an AWGN channel. We assume a bandwidth of 1.25MHz which corresponds to an FFT size of 128.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[189,11,18,219,15],"tags":[34,114],"class_list":["post-538","post","type-post","status-publish","format-standard","hentry","category-5g","category-berp","category-lte","category-modulation","category-wimax","tag-ber","tag-lte"],"_links":{"self":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/538","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=538"}],"version-history":[{"count":10,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/538\/revisions"}],"predecessor-version":[{"id":4060,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/538\/revisions\/4060"}],"wp:attachment":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/media?parent=538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/categories?post=538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/tags?post=538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}