{"id":168,"date":"2011-06-23T09:55:06","date_gmt":"2011-06-23T09:55:06","guid":{"rendered":"http:\/\/www.raymaps.com\/blog\/?p=168"},"modified":"2011-08-08T07:27:38","modified_gmt":"2011-08-08T07:27:38","slug":"shannon-capacity-of-a-gsm-channel-mbps","status":"publish","type":"post","link":"https:\/\/www.raymaps.com\/index.php\/shannon-capacity-of-a-gsm-channel-mbps\/","title":{"rendered":"Shannon Capacity of a GSM Channel"},"content":{"rendered":"<p>We know that GSM bit rates can vary from a few kbps to a theoretical maximum of 171.2kbps (GPRS). But what is the actual capacity of a 200kHz GSM channel. We can use the Shannon Capacity Theorem to find this capacity.<\/p>\n<p>C=B*log2(1+SNR)<\/p>\n<p>or<\/p>\n<p>C=B*log2(1+P\/N)<\/p>\n<p>The noise power can be found by using the following formula:<\/p>\n<p>N=B*No=k*T*B=(1.38e-23)*(293)*(200e3)=8.08e-16W=-121dBm<\/p>\n<p>Let us now assume a signal power 0f -90dBm. This gives us an SNR of 31dB or 1258.9 on linear scale. The capacity can thus be calculated as:<\/p>\n<p>C=200e3*log2(1+1258.9)=2.06Mbps<\/p>\n<p>This is the capacity if all time slots are allocated to a single user. If only one time slot is allocated to a user the capacity would be reduced to 257.48kbps.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We know that GSM bit rates can vary from a few kbps to a theoretical maximum of 171.2kbps (GPRS). But what is the actual capacity of a 200kHz GSM channel. We can use the Shannon Capacity Theorem to find this capacity. C=B*log2(1+SNR) or C=B*log2(1+P\/N) The noise power can be found by using the following formula: N=B*No=k*T*B=(1.38e-23)*(293)*(200e3)=8.08e-16W=-121dBm Let us now assume a signal power 0f -90dBm. This gives us an SNR of 31dB or 1258.9 on linear scale. The capacity can thus be calculated as: C=200e3*log2(1+1258.9)=2.06Mbps This is the capacity if all time slots are allocated to a single user. If [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[30,28,29],"class_list":["post-168","post","type-post","status-publish","format-standard","hentry","category-capacity","tag-gsm","tag-shannon-capacity","tag-snr"],"_links":{"self":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/168","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=168"}],"version-history":[{"count":7,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/168\/revisions"}],"predecessor-version":[{"id":226,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/168\/revisions\/226"}],"wp:attachment":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/media?parent=168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/categories?post=168"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/tags?post=168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}