Fast Transforms of Fourier Class in Ofdm Technology of Wireless Transmission Systems

Abstract

The ma­in mo­di­fi­ca­ti­ons and stan­dards of OFDM techno­logy that pro­vi­de high qua­lity com­mu­ni­ca­ti­on in mul­ti­path transmis­si­on of the transmit­ted sig­nal are highlighted. It is analyzed in the struc­tu­re of the transmit­ter of the com­mu­ni­ca­ti­on system ba­sed on OFDM techno­logy of exe­cu­ti­on of fast transforms of Fou­ri­er class. The ortho­go­nal freq­uency di­vi­si­on mul­tip­le­xing / de­mul­tip­le­xing functi­on is as­sig­ned to the fast com­pu­ter of transform, and the pre­co­der is used to re­du­ce the high pe­ak fac­tor in­he­rent in OFDM techno­logy. The ba­sic ele­ments and req­ui­re­ments for the com­pu­ters that per­form fast transforms in the struc­tu­ral sche­me of imple­men­ta­ti­on of OFDM techno­logy are de­ter­mi­ned. The re­la­ti­on bet­we­en the num­ber of sub­car­ri­ers and the si­ze of ba­sic transform of OFDM techno­logy is con­si­de­red. The pos­si­bi­lity of using Fou­ri­er, Hartley transforms and co­si­ne transforms in the pre­co­der has be­en fo­und out. The ba­sic sta­ges of the met­hod of construc­ting the struc­tu­ral sche­me of fast Fou­ri­er transforms ba­sed on cyclic con­vo­lu­ti­ons are for­mu­la­ted. The iden­ti­fi­ed steps inclu­de: bu­il­ding a has­hing ar­ray, de­ter­mi­ning a simpli­fi­ed has­hing ar­ray supple­men­ted by an ar­ray of signs, construc­ting and analyzing a ge­ne­ra­li­zed struc­tu­re of the ba­sis mat­rix, bu­il­ding blocks of in­put da­ta in­teg­ra­ti­on, bu­il­ding blocks of cyclic con­vo­lu­ti­ons, bu­il­ding blocks of com­bi­ning re­sults of cyclic con­vo­lu­ti­ons who­se out­puts are re­sults of di­rect/in­di­rect transforms of Fou­ri­er class ba­sed on cyclic con­vo­lu­ti­ons. The sta­ges of construc­ting and analyzing the ge­ne­ra­li­zed struc­tu­re of the ba­sic mat­rix are per­for­med on the ba­sis of a has­hing ar­ray, a simpli­fi­ed has­hing ar­ray, and an ar­ray of signs. The ta­bu­lar as­signment of the block-cyclic struc­tu­re of the ba­sic mat­rix spe­ci­fi­es the co­or­di­na­tes of the pla­ce­ment of the sign and the simpli­fi­ed val­ue of the first ele­ments of the cyclic sub­mat­ri­ces. An example for the ішяу N=16 of de­ter­mi­ning the has­hing ar­ray, the simpli­fi­ed has­hing ar­ray and the sign ar­ray, the block-cyclic struc­tu­re of the ba­sis mat­rix used in construc­ting the struc­tu­ral sche­me of the com­pu­ter is con­si­de­red. An example of a struc­tu­ral sche­me of a DHT-I of si­ze N=20, con­ta­ining fo­ur blocks of exe­cu­ti­on of a 4-po­int cyclic con­vo­lu­ti­on. The techniq­ue of construc­ting the struc­tu­re sche­me of com­pu­ters using cyclic con­vo­lu­ti­on blocks can be used to ef­fi­ci­ent per­form discre­te transforms of Fou­ri­er class in OFDM-ba­sed com­mu­ni­ca­ti­on systems. The pos­si­bi­lity of using struc­tu­ral construc­ti­on techniq­ue to au­to­ma­te the pro­cess of construc­ting struc­tu­ral sche­mes the transforms of Fou­ri­er class ba­sed on cyclic con­vo­lu­ti­ons has be­en es­tab­lis­hed.