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Abstract-Recently, lattice reduction has been widely used for signal detection in multiinput multioutput (MIMO) communications. In this paper, we present three novel lattice reduction algorithms. First, using a unimodular transformation, a significant improvement on an existing Hermite-Korkine-Zolotareff-reduction algorithm is proposed. Then, we present two practical algorithms for constructing Minkowski-reduced bases. To assess the output quality, we compare the orthogonality defect of the reduced bases produced by LLL algorithm and our new algorithms, and find that in practice Minkowski-reduced basis vectors are the closest to being orthogonal. An error-rate analysis of suboptimal decoding algorithms aided by different reduction notions is also presented. To this aim, the proximity factor is employed as a measurement. We improve some existing results and derive upper bounds for the proximity factors of Minkowski-reduction-aided decoding (MRAD) to show that MRAD can achieve the same diversity order with infinite lattice decoding (ILD).

The standard approaches to solving an overdetermined linear system Ax ≈ b find minimal corrections to the vector b and/or the matrix A such that the corrected system is consistent, such as the least squares (LS), the data least squares (DLS) and the total least squares (TLS). The scaled total least squares (STLS) method unifies the LS, DLS and TLS methods. The classical normwise condition numbers for the LS problem have been widely studied.However, there are no such similar results for the TLS and the STLS problems. In this paper, we first present a perturbation analysis of the STLS problem, which is a generalization of the TLS problem, and give a normwise condition number for the STLS problem. Different from normwise condition numbers, which measure the sizes of both input perturbations and output errors using some norms, componentwise condition numbers take into account the relation of each data component, and possible data sparsity. Then in this paper we give explicit expressions for the estimates of the mixed and componentwise condition numbers for the STLS problem. Since the TLS problem is a special case of the STLS problem, the condition numbers for the TLS problem follow immediately from our STLS results. All the discussions in this paper are under the Golub-Van Loan condition for the existence and uniqueness of the STLS solution.

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Abstract-Recently, an efficient lattice reduction method, called the effective LLL (ELLL) algorithm, was presented for the detection of multiinput multioutput (MIMO) systems. In this letter, a novel lattice reduction criterion, called diagonal reduction, is proposed. The diagonal reduction is weaker than the ELLL reduction, however, like the ELLL reduction, it has identical performance with the LLL reduction when applied for the sphere decoding and successive interference cancelation (SIC) decoding. It improves the efficiency of the ELLL algorithm by significantly reducing the size-reduction operations. Furthermore, we present a greedy column traverse strategy, which reduces the column swap operations in addition to the size-reduction operations.