Analysis of the Error Signal of the LMS Algorithm.

An analysis of the error signal of the Least-Mean- Square (LMS) algorithm is conducted from the robust control theory viewpoint. The difference equation that relates the input of the LMS algorithm and the error signal is presented. This equation is used to build the matrix that maps the input vector to the error vector. It is shown that has at least one singular value greater than 1. Therefore, the system may amplify noise at high frequencies. Nevertheless, the tap-weight vector may be chosen to prevent that noise amplification and improve the disturbance rejection performance of the LMS algorithm

A novel scheme of multicarrier modulation with the discrete cosine transform

In this work, we derive a novel multicarrier modulation based on the Type-I even discrete cosine transform (DCT1e), which includes new procedures to carry out both the channel estimation and the signal reconstruction. By using a small number of training symbols, we achieve an accurate estimation of the channel's impulse response (CIR) using a novel mirror, replicate and add (MIRA) procedure. The proposed scheme does not require knowing the length of the CIR and is valid even in the presence of spectral nones. We provide the theoretical results that guarantee the validity of the developed technique. After the estimation process, the transmitted symbols are also reconstructed by means of the DCT1e using the same novel MIRA scheme. The conditions that ensure a perfect reconstruction in the absence of noise are also provided in this case. Numerical simulations illustrate the excellent behaviour of the proposed approach, both in terms of channel estimation and recovery of the transmitted information.Ministerio de Economía y Competitivida

DCT Type-III for Multicarrier Modulation

In this paper we propose the use of Discrete Cosine Transform Type-III (DCT3) for multicarrier modulation. There are two DCT3 (even and odd) and, for each of them, we derive the expressions for both prefix and suffix to be appended into each data symbol to be transmitted. Moreover, DCT3 are closely related to the corresponding inverse DCT Type-II even and odd. Furthermore, we give explicit expressions for the 1-tap per subcarrier equalizers that must be implemented at the receiver to perform the channel equalization in the frequency-domain. As a result, the proposed DCT3-based multicarrier modulator can be used as an alternative to DFT-based systems to perform Orthogonal Frequency-Division Multiplexing or Discrete Multitone Modulatio

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

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm

On the use of discrete cosine transforms for multicarrier communications

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 redun-dancy (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

Diseño e igualación de canal en sistemas multiportadora basados en la DCT-III

Análisis matemático e implementación de la transformada del coseno tipo 3 para transmisión de señales mediante sistemas multiportador

Channel Estimation Based on the Discrete Cosine Transform Type-III Even

In this work, we address the problem of channel estimation in multicarrier communications. We present a procedure which employs the Type-III even DCT (DCT3e) at both the transmitter and the receiver. By using any symmetric training symbol we show how to estimate the channel’s impulse response without a prior knowledge of its exact length. Theoretical results are provided in order to guarantee the validity of the proposed technique, whereas simulations illustrate the good behavior of the proposed estimation algorithm

On the Feasibility of SISO /MIMO-PLC based on the Discrete Cosine Transform Type-III even

During the last decades, power line communications (PLC) has emerged as an alternative to other wired line and wireless technologies. In particular, PLC has gained large acceptance for in-home scenarios, where it has become a competitive alternative to WiFi. Most PLC approaches are based on Multicarrier Modulation (MCM) using the Discrete Fourier Transform (DFT) as the basis to construct the multiple orthogonal channels. In this work, we explore the construction of MCM-PLC schemes based on the Discrete Cosine Transform Type-III even (DCT3e). We consider both SISO (single input single output) and MIMO (Multiple Input Multiple Output) PLC schemes, showing that they are a feasible alternative for in-home PLC applications