On the Use of Discrete Cosine Transforms for Multicarrier Communications

Abstract

Abstract-In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redundancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.Index Terms-Carrier-frequency offset (CFO), discrete cosine transform (DCT), discrete multitone modulation (DMT), multicarrier modulation (MCM), multicarrier transceiver, orthogonal frequency-division multiplexing (OFDM).

Simple Algorithms for Estimating the Symbol Timing Offset in DCT‐Based Multicarrier Systems

“…In DCT-MCM, T −1 can be any kind of inverse DCT [16], with two different types of redundancy: symmetric extension (SE) or zero-padding (ZP). This work focuses on Type-II even discrete cosine transform (DCT2e) and Type-IV even discrete cosine transform (DCT4e), assuming SE [2,5].…”

“…Finally, the channel length of ℎ ℎ [ ] is assumed to be less than the length of the redundancy (SE or CP); i.e., ]+1 < . For a more thorough description of DCT-MCM, we refer the reader to [2,5,16].…”

Estimation of Symmetric Channels for Discrete Cosine Transform Type‐I Multicarrier Systems: A Compressed Sensing Approach

“…As OFDM systems present poor behaviour under carrier frequency offset, other multicarrier modulation (MCM) techniques have been investigated, which are related to other transformations different from DFT. Among them, the eight types of Discrete Cosine Transforms (DCTs) have been studied in the literature, and for each one of them the corresponding extension technique has been proposed [ 6 , 8 , 9 , 14 ]. These works focus on MCM signal reconstruction, and they provide good results due to the good properties of the DCTs.…”

“…As we have already mentioned before, the interblock interference is eliminated by introducing as redundancy a left prefix x lp and also a right suffix x rs , both of length ν − 1, into each data symbol to be transmitted. In order to apply DCT1, it is proved in [ 9 , 14 ] that it suffices to consider the extended block x e in ( 3 ) with the choice of prefix x lp and suffix x rs as follows: which means that we apply a whole-point symmetry (WS) on the left and on the right sides of the original symbol. Figure 2 illustrates an example of the WS symmetric extension of x .…”

Spectrum Sensing in multipath fading channels using Cosine Modulated Filter Bank for Cognitive Radio applications

“…Some work has been done on DFT filter bank structures [7]. The advantage of cosine modulation over the FFT based systems is the possibility of designing subbands with desired attenuation and spectral containment [8]. Energy detection is a common choice due to the simplicity and less knowledge requirement on the signal to 978-1-4799-6085-9/15/$31.00 ©2015 IEEE be detected [9].…”