Aumento da Eficiência Espectral de Sistemas com Codificação Wavelet

Abstract

Resumo-O aproveitamento da ortogonalidade entre linhas de uma matriz wavelet tem sido explorada para obter sistemas de comunicac ¸ão sem fio que apresentam desempenho comparável, e em alguns casos superior, aos que utilizam códigos espáciotemporais. Entretanto, uma limitac ¸ão dos sistemas wavelet propostos até o momento é a eficiência espectral (EE) que fica limitada a 1 bit/s/Hz. A combinac ¸ão de símbolos wavelet em um símbolo do canal pode aumentar a eficiência espectral desses sistemas, e neste trabalho propomos o uso da func ¸ão geradora de momentos para, a partir de uma matriz de codificac ¸ão, obter as sequências de símbolos wavelet e suas probabilidades conjuntas, e através de um exemplo, mostra-se que a combinac ¸ão de pares de símbolos wavelet permite aumentar a EE para 2 bits/s/Hz. O método proposto é geral e permite determinar, para uma dada matriz de codificac ¸ão wavelet quais sequências de tamanho N podem ser obtidas, o que abre a possibilidade de realizar combinac ¸ões de sequência de símbolos wavelet para obter sistemas com eficiência espectral maiores.Palavras-Chave-Wavelet, codificac ¸ão, eficiência espectral, func ¸ão geradora, momentos.

Wavelet Channel Coding: An Algebraic Approach

“…The proposed WCC system requires specially designed constellations since generated wavelet symbols are not equiprobable and the alphabet cardinality grows with the wavelet coding matrix order. The construction of special constellations was explored in [7], [8], [13], [14].…”

“…The WCC entropy rate is 1 bit/symbol when the coding rate is unitary and the spectral efficiency is limited to 1 bit/s/Hz [1]. In order to improve this efficiency, a method to increase it to 2 bits/s/Hz by constructing a signal constellation from consecutive pairs of integer wavelet symbols was proposed in [13]. These symbol pairs were directly associated to points in a signal space diagram forming a constellation for transmission.…”

“…In [15], an optimizing effort suggested that these constellations were optimal. The method proposed in [13] could be generalized to blocks of length greater than two to achieve an arbitrary spectral efficiency, however the block-tosignal mapping would not be as simple as in the case of symbols pairs.…”

“…In [13], a probability generating function (PGF) for a wavelet symbol sequence was formulated. This alternative PGF permitted to predict integer symbol pairs generated by a WCC encoder and provided the joint probability distribution of these pairs.…”

“…In general, WCC provides an increase in system performance at the cost of a large increase in the dimensionality of the output code. In order to counteract this drawback, some works propose constellations and increase spectral efficiency to wavelet symbols transmission, as in [8], [12], [13], [15].…”