International audienceIn this paper, we address the problem of determining the order of MISO channels by means of a series of hypothesis tests based on scalar statistics. Using estimated 4th-order output cumulants, we exploit the sensitiveness of a Chi-square test statistic to the non Gaussianity of a stochastic process. This property enables us to detect the order of a linear finite impulse response (FIR) channel. Our approach leads to a new channel order detection method and we provide a performance analysis along with a criterion to establish a decision threshold, according to a desired level of tolerance to false alarm. Afterwards, we introduce the concept of MISO channel nested detectors based on a deflation-type procedure using the 4th-order output cumulants. The nested detector is combined with an estimation algorithm to select the order and estimate the parameters associated with different transmitters composing the MISO channel. By treating successively shorter and shorter channels, it is also possible to determine the number of sources
Resumo-A diversidade de cooperação e a multiplexação por divisão de frequências ortogonais (orthogonal frequency division multiplexing-OFDM) são duas das principais tecnologias para os sistemas de comunicação sem fio. Neste artigo, propõe-se um receptorótimo, no sentido da razão sinal ruído (signal-tonoise ratio-SNR), para um sistema OFDM cooperativo não linear. O modelo de sistema utilizado inclui um transmissor com amplificador de potência não linear e um repetidor (relay) do tipo amplifica-e-encaminha (amplify-and-forward-AF), sendo esteúltimo também equipado com um amplificador de potência não linear. Usando a técnica de diversidade por combinação de razão máxima (maximum ratio combining-MRC) para tratar os sinais recebidos, o receptor proposto considera tanto as informações oriundas do caminho direto (fonte-destino) como as provenientes do repetidor. Resultados numéricos de simulação são apresentados, evidenciando o desempenho do receptor proposto. Palavras-Chave-OFDM, diversidade de cooperação, amplificador não linear, receptorótimo, MRC.
Resumo-Este artigo apresenta duas novas técnicas de redução de PAPR (Peak-to-Average Power Ratio) em sistemas de comunicação cooperativos OFDM (Orthogonal Frequency Division Multiplexing) usando seleção de relays do tipo amplifica e encaminha (AF, do inglês Amplify-and-Forward). As técnicas propostas são baseadas em uma técnica clássica de seleção de relay que usa a capacidade de canal como critério de escolha. Entretanto, os novos métodos apresentados consideram não apenas a capacidade de canal, mas também a PAPR na escolha do relay. Resultados de simulações numéricas são apresentados para avaliar o desempenho das técnicas propostas.
In this paper, we exploit the symmetry properties of fourthorder cumulants to develop a new blind identification algorithm for multiple-input multiple-output (MIMO) instantaneous channels. The proposed algorithm utilizes the Parallel Factor (Parafac) decomposition of the 4th-order cumulant tensor by solving a single-step (SS) least squares (LS) problem. This approach is shown to hold for channels with more sources than sensors. A simplified approach using a reduced-order tensor is also discussed. Computer simulations are provided to illustrate the performance of the proposed identification algorithms.
I. THE BLIND IDENTIFICATION PROBLEMCumulants of order higher than two can be viewed as tensors with a highly symmetrical structure. For about two decades, exploiting the cumulant symmetries with a tensor formalism has been an important research topic. The Parallel Factor (Parafac) decomposition of a Pth-order tensor with rank Q consists in decomposing it into a sum of Q rank-one tensors [1]. The keypoint in the use of the Parafac decomposition is its uniqueness property, which can be assured under simple conditions, stated by the Kruskal Theorem [2]. Parafac does not induce neither rotational ambiguities nor orthogonality constraints, as it is the case with matrix singular value decomposition. For that reason, the use of cumulant tensor factorization allows for avoiding the pre-whitening step, a time-consuming operation responsible for increased estimation errors [3].The alternating least squares (ALS) algorithm consists in fitting a Pth-order Parafac model by iteratively minimizing, in an alternate way, P least squares (LS) cost functions. Our focus in this paper is to exploit the redundancies of the parallel factors of the 4th-order cumulant tensor in the minimization problem in order to develop a new blind channel identification (BCI) algorithm. We consider the problem of blind multiple-input multiple-output (MIMO) channel (mixture) identification in the context of a multiuser system characterized by instantaneous complex-valued channels. We introduce new algorithms based on the Parafac decomposition of cumulant tensors, as an extension of the algorithms proposed in [4] for the case of single-input single-output FIR channels. Our main contribution consists in exploiting the redundancies in the Parafac components to estimate the channel matrix by solving a single LS minimization problem. This approach greatly simplifies the estimation problem and allows us to introduce a new blind MIMO channel estimation algorithm based on a single-step (SS) LS optimization procedure.During the two last decades, several BCI methods making use of the redundancies in the 4th-order cumulants have been proposed [5]. Such approaches include, for instance, the popular joint approximate diagonalization of eigenmatrices (JADE) algorithm [6], which is based on second and fourth-order statistics. It is now well-known that in the case of linear mixtures the BCI problem is closely related to the (simultaneous) diagonalization of symmetric cum...
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