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Box Decoding with Low-Complexity Sort-free Candidate Pruning for MIMO Detection

Shengchun Yang, Amit Sravan Bora, Emil Matus, Gerhard Fettweis

TL;DR

This work tackles the scalability bottleneck of Box Decoding for large-scale MIMO by introducing three deterministic, sort-free pruning rules (SCP, ICP, SICP) that exploit QAM-grid symmetry and the ZF reference to prune candidate nodes without constellation-wide sorting. The approach preserves QAM-order independence, enables parallel hardware-friendly implementation, and achieves substantial reductions in node visits with negligible BER degradation compared to K-Best. Simulation results demonstrate near–K-Best performance at a fraction of the complexity, suitable for high-order constellations and large MIMO sizes. The proposed pruning strategies thus offer a modulation-independent, scalable solution for high-throughput MIMO detectors with practical hardware implications.

Abstract

Box Decoding is a sort-free tree-search MIMO detector whose complexity does not scale with the QAM order, achieved by searching a fixed candidate "box" around a zero-forcing (ZF) estimate. Prior work primarily reports small dimensions (e.g. 2x2), since the search visits an exponentially growing number of nodes as the MIMO order increases when no pruning is applied. This letter introduces three deterministic pruning rules that exploit QAM-grid symmetry and relative displacement between the ZF estimate and the nearby QAM points to eliminate unlikely branches, avoiding metric sorting and reducing full metric distance calculations. Simulations show large complexity savings with only a small impact on error performance. The resulting detector preserves QAM-order independence, scales to larger MIMO sizes, and maps naturally to parallel hardware implementation.

Box Decoding with Low-Complexity Sort-free Candidate Pruning for MIMO Detection

TL;DR

This work tackles the scalability bottleneck of Box Decoding for large-scale MIMO by introducing three deterministic, sort-free pruning rules (SCP, ICP, SICP) that exploit QAM-grid symmetry and the ZF reference to prune candidate nodes without constellation-wide sorting. The approach preserves QAM-order independence, enables parallel hardware-friendly implementation, and achieves substantial reductions in node visits with negligible BER degradation compared to K-Best. Simulation results demonstrate near–K-Best performance at a fraction of the complexity, suitable for high-order constellations and large MIMO sizes. The proposed pruning strategies thus offer a modulation-independent, scalable solution for high-throughput MIMO detectors with practical hardware implications.

Abstract

Box Decoding is a sort-free tree-search MIMO detector whose complexity does not scale with the QAM order, achieved by searching a fixed candidate "box" around a zero-forcing (ZF) estimate. Prior work primarily reports small dimensions (e.g. 2x2), since the search visits an exponentially growing number of nodes as the MIMO order increases when no pruning is applied. This letter introduces three deterministic pruning rules that exploit QAM-grid symmetry and relative displacement between the ZF estimate and the nearby QAM points to eliminate unlikely branches, avoiding metric sorting and reducing full metric distance calculations. Simulations show large complexity savings with only a small impact on error performance. The resulting detector preserves QAM-order independence, scales to larger MIMO sizes, and maps naturally to parallel hardware implementation.

Paper Structure

This paper contains 19 sections, 10 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Tree-Based MIMO Detection
  4. Box Decoding Algorithm
  5. Low-Complexity Box Candidate Pruning
  6. Efficient PED Comparison Techniques
  7. Local PED Minimum Rule (Metric 1)
  8. Local PED Ordering Rule (Metric 2)
  9. Proposed Candidate Pruning Strategies
  10. Single-Step Candidate Pruning (SCP)
  11. Iterative Candidate Pruning (ICP)
  12. Hybrid SCP-ICP Candidate Pruning (SICP)
  13. Complexity Analysis
  14. Number of Visited Node
  15. Complexity in Hardware Implementation
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Box decoding example (reproduced from box): (a) Box operation on a 16-QAM map grid (positive quadrant); (b) Box decoder tree structure with box size $\mathcal{B}=4$.
  • Figure 2: Block diagram of the proposed box pruning strategies; (a) Box-SCP and (b) Box-ICP with box size $\mathcal{B} = 4$.
  • Figure 3: BER performance of detection schemes ($-\triangledown -$: ZF; $-\triangledown -$: LMMSE; $-\square -$: Box-SCP; $-\diamondsuit -$: Box-SICP$_1$; $-\diamondsuit -$: Box-SICP$_2$; $-\diamondsuit -$: Box-SICP$_3$;$-\bigcirc -$: $K$-Best; $-\Box -$: Box-ICP; $-\bigcirc -$: Box; $-\ast -$: ML for 4-QAM or SD for 16/64-QAM).