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Integer forcing is an alternative approach to conventional linear receivers in multiple-antenna systems. In the integerforcing scheme, the receivers try to extract integer combinations of messages from the received matrix before recovering each message individually. Recently, the integer-forcing approach was generalized to a block fading scenario. Among the decoding methods described, the one which achieves higher rates has the drawback that no efficient algorithm to find the best choice of integer linear combinations is known. In this paper, we propose a sub-optimal scheme to find those combinations with a lower complexity. Simulation results show that the proposed method outperforms other existing low-complexity methods.

Abstract-Integer forcing is an alternative approach to conventional linear receivers for multiple-antenna systems. In an integer-forcing receiver, integer linear combinations of messages are extracted from the received matrix before each individual message is recovered. Recently, the integer-forcing approach was generalized to a block fading scenario. Among the existing variations of the scheme, the ones with the highest achievable rates have the drawback that no efficient algorithm is known to find the best choice of integer linear combination coefficients. In this paper, we propose several sub-optimal methods to find these coefficients with low complexity, covering both parallel and successive interference cancellation versions of the receiver. Simulation results show that the proposed methods attain a performance close to optimal in terms of achievable rates for a given outage probability. Moreover, a low-complexity implementation using root LDPC codes is developed, showing that the benefits of the proposed methods also carry on to practice.

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Resumo-A técnica de pré-codificação de forçagem a inteiros (IF) é uma alternativa às técnicas tradicionais de pré-codificação linear em canais downlink MIMO com múltiplos usuários (MU-MIMO). A pré-codificação IF aproxima o canal efetivo, observado por cada usuário, em uma combinação linear inteira dos vetores transmitidos, generalizando métodos tradicionais de précodificação linear. Recentemente, Silva et al. propuseram um método para encontrar parâmetros ótimos para pré-codificação IF em alta SNR, porém restrito ao caso de K = 2 usuários. Nesse artigo, propomos um método para encontrar bons parâmetros para K ≥ 2 usuários com complexidade O(K 3 ). Resultados de simulação mostram que o método proposto atinge um desempenho muito superior aos métodos tradicionais de pré-codificação linear.Palavras-Chave-MIMO com múltiplos usuários, canal downlink, forçagem a inteiros, pré-codificação linear.Abstract-Integer-Forcing (IF) precoding is an alternative to traditional methods of linear precoding in multiuser MIMO (MU-MIMO) downlink channels. The IF precoding tries to convert the effective channel, as it is seen by each receiver, into an integer linear combination of the transmitted vectors, generalizing traditional linear precoding. Recently, Silva et al. proposed a method to find optimal parameters for IF precoding in high SNR, restricted, however, to K = 2 users. In this paper, we propose a method to find good parameters for K ≥ 2 users with complexity O(K 3 ). Simulations results show that the proposed method can outperform traditional methods of linear precoding.