We saw that equal gain combining and maximal ratio combining result in tremendous improvement in bit error rate performance in a Rayleigh fading channel. These are receive diversity schemes i.e. schemes that work with multiple receive antennas. Now let us turn our attention to schemes that work with multiple transmit antennas. We know that the main aim of a combining scheme is to coherently add the signals. If the same signal is transmitted from multiple transmit antennas the resulting signals would not add up coherently when they arrive at the receiver (remember that each path introduces a random phase shift). One solution to this problem is that the channel state information (CSI) be fed back to the transmitter. So if this done quickly enough, before the channel state changes, the phase of the signals at the transmit side could be pre-adjusted so that when these signals arrive at the receiver they combine constructively.<\/p>\n
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\r\nfunction[ber]=err_rate5(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\nh1=(1\/sqrt(2))*((randn(1,l))+j*(randn(1,l)));\r\nh2=(1\/sqrt(2))*((randn(1,l))+j*(randn(1,l)));\r\nsr1=(1\/sqrt(2))*s.*(conj(h1).\/abs(h1));\r\nsr2=(1\/sqrt(2))*s.*(conj(h2).\/abs(h2));\r\nr=h1.*sr1+h2.*sr2+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>\nIt is observed that above scheme has exactly the same bit error rate performance as equal gain combining. The reason for this is that in the above scheme the noise at the receiver is halved (single receiver means single noise component) but the transmit power is also halved from each of the transmit antennas (to keep the total transmit power same). Thus it does not matter whether the phase adjustment happens at the receiver or the transmitter. But the important question is that can the channel state information be fed back to the transmitter quickly enough?<\/p>\n","protected":false},"excerpt":{"rendered":"
We saw that equal gain combining and maximal ratio combining result in tremendous improvement in bit error rate performance in a Rayleigh fading channel. These are receive diversity schemes i.e. schemes that work with multiple receive antennas. Now let us turn our attention to schemes that work with multiple transmit antennas. We know that the main aim of a combining scheme is to coherently add the signals. If the same signal is transmitted from multiple transmit antennas the resulting signals would not add up coherently when they arrive at the receiver (remember that each path introduces a random phase shift). […]<\/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":[34,35],"class_list":["post-96","post","type-post","status-publish","format-standard","hentry","category-berp","tag-ber","tag-diversity"],"_links":{"self":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/96","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=96"}],"version-history":[{"count":11,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"predecessor-version":[{"id":1205,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions\/1205"}],"wp:attachment":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}