[Paper Review] Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

N. N. Srinidhi, Saif Khan Mohammed+2 more|ArXiv.org|Jan 13, 2009

Advanced Wireless Communication Techniques13 references4 citations

TL;DR

This paper proposes a reactive tabu search (RTS) algorithm for low-complexity, near-maximum-likelihood (near-ML) decoding of large non-orthogonal space-time block codes (STBCs) from cyclic division algebras (CDA), achieving near-SISO AWGN performance and near-capacity coded BER with only 0.5 dB SNR gap at 12×12 STBC size and 18 bps/Hz spectral efficiency.

ABSTRACT

Non-orthogonal space-time block codes (STBC) with {\em large dimensions} are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) {\em as well as} full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of $12 imes 12$ STBC from CDA and 4-QAM with 288 real dimensions achieves $i)$ $10^{-3}$ uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and $ii)$ a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.

Motivation & Objective

• To address the challenge of high decoding complexity in large non-orthogonal STBCs with hundreds of real dimensions.
• To develop a low-complexity decoding algorithm that achieves near-ML performance for large STBCs from cyclic division algebras (CDA).
• To evaluate performance under practical conditions, including imperfect channel state information and spatial correlation.
• To compare the proposed RTS-based decoding with prior low-complexity methods like likelihood ascent search (LAS).

Proposed method

• The RTS algorithm performs heuristic search in the signal space to find the closest STBC codeword to the received signal, avoiding exhaustive search.
• It uses a tabu list to prevent revisiting previously explored solutions, enhancing search efficiency and avoiding local minima.
• Reactive mechanisms dynamically adjust tabu tenure and search intensity based on search history and performance feedback.
• The algorithm incorporates a stopping criterion based on convergence of the objective function and iteration limits.
• An iterative RTS decoding/channel estimation scheme is employed with training pilots to handle imperfect channel state information.
• Spatial correlation is modeled using the Gesbert et al. MIMO fading model to assess robustness under realistic propagation conditions.

Experimental results

Research questions

• RQ1 Can reactive tabu search achieve near-ML performance for large non-orthogonal STBCs with hundreds of real dimensions at affordable complexity?
• RQ2 How does RTS-based decoding compare to the likelihood ascent search (LAS) algorithm in terms of BER performance and dimensionality scaling?
• RQ3 What is the performance of RTS decoding under imperfect channel state information, particularly with training-based channel estimation?
• RQ4 How does spatial correlation in MIMO channels affect the BER performance of RTS decoding for large STBCs?

Key findings

• RTS decoding of a 12×12 non-orthogonal STBC from CDA with 4-QAM achieves an uncoded BER of 10⁻³ at only 0.5 dB SNR gap from SISO AWGN performance.
• With a rate-3/4 turbo code, RTS achieves coded BER within approximately 5 dB of the theoretical MIMO capacity at 18 bps/Hz spectral efficiency.
• RTS outperforms the LAS algorithm in achieving near-SISO AWGN performance with fewer dimensions, albeit at slightly higher complexity.
• When using a training-based iterative RTS decoding/channel estimation scheme, BER performance with estimated CSIR approaches that of perfect CSIR, especially for large coherence times (e.g., Nd=20).
• Spatial correlation in the MIMO channel reduces diversity gain, but increasing receive antenna count (Nr=14 vs. Nr=12) mitigates this performance loss.
• The RTS algorithm maintains strong performance with 16-QAM, indicating its applicability to higher-order constellations and larger STBCs.