Concatenative Complete Complementary Code Division Multiple Access and its Fast Transform based Implementation

Over multipath channels, \textit{complete complementary code division multiple access} (CC-CDMA) and \textit{convolutional spreading code division multiple access} (CS-CDMA) provide {\it inter-channel interference} (ICI) free transmission with an enhanced {\it spectral efficiency} (SE). However, the {\it convolutional spreading} (CS) operation of the systems is computationally complex and involves a high \textit{peak-to-average power ratio} (PAPR). Address such issues, we propose the \textit{concatenative complete complementary code division multiple access} (CCC-CDMA). Since the CCCCs can be generated from the rows of the Walsh-Hadamard or \textit{discrete Fourier transform} (DFT) matrices, the CS operation can be implemented using corresponding {\it fast transforms} (FTs) to reduce computational complexity. Simulation results shown that enlargement of {\it spreading factor} (SF) strengthens the robustness against clipping noise and the binary CCCC generated by Walsh-Hadamard matrix has excellent robustness against Doppler frequency shifts.

Concatenative Complete Complementary Code Division Multiple Access and its Fast Transform based Implementation

Over multipath channels, \textit{complete complementary code division multiple access} (CC-CDMA) and \textit{convolutional spreading code division multiple access} (CS-CDMA) provide {\it inter-channel interference} (ICI) free transmission with an enhanced {\it spectral efficiency} (SE). However, the {\it convolutional spreading} (CS) operation of the systems is computationally complex and involves a high \textit{peak-to-average power ratio} (PAPR). Address such issues, we propose the \textit{concatenative complete complementary code division multiple access} (CCC-CDMA). Since the CCCCs can be generated from the rows of the Walsh-Hadamard or \textit{discrete Fourier transform} (DFT) matrices, the CS operation can be implemented using corresponding {\it fast transforms} (FTs) to reduce computational complexity. Simulation results shown that enlargement of {\it spreading factor} (SF) strengthens the robustness against clipping noise and the binary CCCC generated by Walsh-Hadamard matrix has excellent robustness against Doppler frequency shifts.

FAST TRANSFORMS OF FOURIER CLASS IN OFDM TECHNOLOGY OF WIRELESS TRANSMISSION SYSTEMS

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.

Fast Transforms in Image Processing: Compression, Restoration, and Resampling

Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet, and alike. They proved to be very efficient in image compression, in image restoration, in image resampling, and in geometrical transformations and can be traced back to early 1970s. The paper reviews these methods, with emphasis on their comparison and relationships, from the very first steps of transform image compression methods to adaptive and local adaptive filters for image restoration and up to “compressive sensing” methods that gained popularity in last few years. References are made to both first publications of the corresponding results and more recent and more easily available ones. The review has a tutorial character and purpose.