An upper bound on the average number of iterations of the LLL algorithm
Theoretical Computer Science - Special issue on number theory, combinatorics and applications to computer science
A course in computational algebraic number theory
A course in computational algebraic number theory
The optimal LLL algorithm is still polynomial in fixed dimension
Theoretical Computer Science - Latin American theoretical informatics
On the complexity of sphere decoding in digital communications
IEEE Transactions on Signal Processing
On the sphere-decoding algorithm I. Expected complexity
IEEE Transactions on Signal Processing - Part I
Closest point search in lattices
IEEE Transactions on Information Theory
On maximum-likelihood detection and the search for the closest lattice point
IEEE Transactions on Information Theory
Systematic and optimal cyclotomic lattices and diagonal space-time block code designs
IEEE Transactions on Information Theory
An algebraic family of complex lattices for fading channels with application to space-time codes
IEEE Transactions on Information Theory
LLL Reduction Achieves the Receive Diversity in MIMO Decoding
IEEE Transactions on Information Theory
Extended LLL algorithm for efficient signal precoding in multiuser communication systems
IEEE Communications Letters
Augmented lattice reduction for MIMO decoding
IEEE Transactions on Wireless Communications
User selection criteria for multiuser systems with optimal and suboptimal LR based detectors
IEEE Transactions on Signal Processing
Prevoting cancellation-based detection for underdetermined MIMO systems
EURASIP Journal on Wireless Communications and Networking
Loop-reduction LLL algorithm and architecture for lattice-reduction-aided MIMO detection
Journal of Electrical and Computer Engineering - Special issue on Implementations of Signal-Processing Algorithms for OFDM Systems
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Recently, lattice-reduction-aided detectors have been proposed for multiinput multioutput (MIMO) systems to achieve performance with full diversity like the maximum likelihood receiver. However, these lattice-reduction-aided detectors are based on the traditional Lenstra-Lenstra-Lovász (LLL) reduction algorithm that was originally introduced for reducing real lattice bases, in spite of the fact that the channel matrices are inherently complex-valued. In this paper, we introduce the complex LLL algorithm for direct application to reducing the basis of a complex lattice which is naturally defined by a complex-valued channel matrix. We derive an upper bound on proximity factors, which not only show the full diversity of complex LLL reduction-aided detectors, but also characterize the performance gap relative to the lattice decoder. Our analysis reveals that the complex LLL algorithm can reduce the complexity by nearly 50% compared to the traditional LLL algorithm, and this is confirmed by simulation. Interestingly, our simulation results suggest that the complex LLL algorithm has practically the same bit-error-rate performance as the traditional LLL algorithm, in spite of its lower complexity.