[Paper Review] Complexity Comparison between Two Optimal-Ordered SIC MIMO Detectors Based on Matlab Simulations

Yanpeng Wu, Hufei Zhu|arXiv (Cornell University)|Mar 8, 2020

Advanced Wireless Communication Techniques5 references4 citations

TL;DR

This paper compares the computational complexity of two optimal-ordered successive interference cancellation (SIC) detectors for MIMO systems using custom Matlab simulations and theoretical analysis. It demonstrates that the detector proposed in [2] requires 9N² more floating-point operations than the one in [1], confirming higher worst-case and average complexity, despite both having the same asymptotic O(MN² + N³) complexity class.

ABSTRACT

This paper firstly introduces our shared Matlab source code that simulates the two optimal-ordered SIC detectors proposed in [1] and [2]. Based on our shared Matlab code, we compare the computational complexities between the two detectors in [1] and [2] by theoretical complexity calculations and numerical experiments. We carry out theoretical complexity calculations to obtain the worst-case complexities for the two detectors in [1] and [2]. Then from the theoretical worst-case complexities, we make the conclusion that the detector proposed in [2] requires 9N 2 more floating-point operations (flops) than the detector proposed in [1], where N is the number of transmit antennas. Our numerical experiments also show that the detector in [2] requires more worst-case and average complexities than the detector in [1].

Motivation & Objective

• To provide a shared, annotated Matlab source code for simulating two optimal-ordered SIC MIMO detectors proposed in [1] and [2].
• To conduct a detailed computational complexity comparison between the two detectors using both theoretical analysis and numerical experiments.
• To determine which detector has lower computational complexity in terms of floating-point operations (flops), particularly in worst-case and average scenarios.
• To validate theoretical complexity bounds through empirical flop counting in the shared Matlab code.

Proposed method

• Implemented a custom Matlab simulation framework where each floating-point operation is manually annotated with flop counts for complex multiplication (cm), complex addition (ca), real multiplication (rm), real addition (ra), real division (rdiv), real square root (rsqrt), and real-complex multiplication (rcm).
• Assigned standard flop weights: cm=6, ca=2, rm=1, ra=1, rdiv=1, rsqrt=1, rcm=2 to convert all operations into total real flops.
• Performed theoretical worst-case complexity analysis using summation identities: ∑i = N²/2 + N/2 and ∑i² = N³/3 + N²/2 + N/6 to derive O(MN² + N³) and O(MN + N²) complexity bounds.
• Executed the Matlab code to collect exact flop counts for both detectors under identical conditions, enabling numerical comparison of worst-case and average complexity.
• Mapped algorithmic steps from [1] and [2] into computational statements, with additional explanations for code components not fully detailed in the original papers.
• Validated the correctness of the complexity model by cross-referencing key equations, such as the update of squared row lengths in the inverse Cholesky factor, using established matrix factorization theory.

Experimental results

Research questions

• RQ1 Which of the two optimal-ordered SIC detectors from [1] and [2] has lower computational complexity in terms of floating-point operations?
• RQ2 Do the theoretical worst-case complexity bounds O(MN² + N³) and O(MN + N²) accurately reflect the actual flop counts in practice?
• RQ3 How do the average and worst-case complexities of the two detectors compare across different numbers of transmit antennas N?
• RQ4 Can the shared Matlab code accurately and reproducibly measure the computational cost of SIC detection algorithms with fine-grained flop accounting?
• RQ5 What is the exact quantitative difference in computational cost between the two detectors, particularly in the worst-case scenario?

Key findings

• The detector proposed in [2] requires 9N² more floating-point operations than the detector in [1] in the worst-case scenario.
• Theoretical analysis confirms that the detector in [1] has a worst-case complexity of O(MN² + N³), while the detector in [2] has O(MN + N²), indicating a significant difference in growth rate.
• Numerical experiments using the shared Matlab code confirm that the detector in [2] exhibits both higher worst-case and average computational complexity than the detector in [1].
• The shared Matlab code enables precise, statement-level flop counting, allowing exact measurement of computational cost for each detector.
• Despite both detectors having the same asymptotic complexity class O(MN² + N³) in some prior analysis, this paper reveals a concrete 9N² difference in actual flop count.
• The complexity difference arises primarily from the way Givens rotations and row length updates are computed, with [2] involving more real multiplications and divisions, which are costly operations.