On Sorted Lattice Reduction Algorithm for Integer Forcing Receiver

Considering a single-user multiple-input multiple-output (MIMO) wireless system, this paper puts forward a novel sorted lattice reduction (SLR) algorithm for integer forcing (IF) linear receiver, which reduces the 2-norm of each lattice basis using a series of column-addition operations.The lower complexity and excellent performance of IF receivers are from the closed-loop property of integer domain and the optimization techniques of maximizing the signal-to-interference-noise-ratio (SINR) of each layer, which is equivalent to a famous NP-Hard problem, referred to as shortest independent vector problem (SIVP), in lattice theory.Thesorted lattice reduction algorithm in this paper can effectively alleviate the complexity of this problem in spite of a little orthogonality performance loss, which goes especially well with large MIMO systems. Computer simulations show that the proposed algorithm not only outperforms the famous LLL algorithm in terms of the length of the maximal lattice basis, but also has a relative lower practical complexity. Moreover, the integer forcing receiver based on the sorted lattice reduction algorithm defeats most linear receivers in terms of the bit-error-ratio (BER) performance and is closed to that of the optimal maximal likelihood (ML) receiver.