Designing Low-Complexity Detectors Based on Seysen's Algorithm

Abstract

Lattice reduction (LR) has been applied to linear equalizers and decision feedback equalizers to improve their performance. Recently, Seysen's algorithm (SA) has been proposed as an alternative LR method to the well-documented LLL algorithm. In this paper, we first provide a tree-search implementation method of SA which enables flexible performancecomplexity trade-offs. Based on this tree structure, SA-aided hard-output and soft-output detectors are proposed to enhance performance. The diversity and complexity of the proposed methods are also studied. Thorough comparisons of SA and other LR algorithms are provided. Our analysis of complexity and numerical simulations provide insights that are useful to system designers.

A Seysen's algorithm–based incremental lattice reduction

“…If the condition in (16) is satisfied by an estimation̂i nt , this vector will be used as the final estimation, and the remaining iterations of CLLL will not be executed. As the SA-based linear detector outperforms the CLLL-based one, 34 an ILR algorithm with SA is of great interest. Before adopting SA to the ILR, we have to validate that it is feasible to terminate the SA during its execution process while the detector can still provide the same performance with the intermediate parameters.…”

“…In this paper, we focus on the latter as it is more efficient in complexity and convergence speed. 8,34 The detailed algorithm can be found in the work of Seethaler et al 29…”

Designing low-complexity detectors for generalized SC-FDMA systems

“…To find the transformation matrix T and the new channel matrixH, different methods have been proposed, e.g., CLLL algorithm in [6] and Seysen's algorithm (SA) in [9], [10]. After obtaining T, the ZF equalization can be performed with the new channel matrixH as…”

“…When comes to the number of arithmetic operations of each algorithm, SA has highest operations than those of CLLL and ELR. This is because SA requires (128n − 18) arithmetic operations per basis update [5], [10], which is much higher than CLLL and ELR ones. Our proposed ELR one requires (31n − 7) arithmetic operations per basis update, including 16n + 8 for Eqs.…”

“…Compared with the well adopted CLLL [6], [7] and Seysen's algorithm [9], [10], our proposed ELR algorithm has a different design goal, which tries to minimize the asymptotic pairwise error probability (PEP). Simulations are conducted to show that the proposed ELR method attains comparable error performance to the state-of-the-art LR algorithms and requires lower complexity in terms of the number of arithmetic operations.…”