Uncoded Space-Time Labeling Diversity

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The Golden code has full rate and full diversity. The Golden codeword matrix contains two pairs of super symbols. Based on one pair of super symbols, two modulation schemes, Golden codeword-based M-ary quadrature amplitude modulation (GC-MQAM) and component-interleaved GC-MQAM (CI-GC-MQAM), are proposed for single-input multiple-output (SIMO) systems. Since the complexities of the maximum likelihood detection for the proposed GC-MQAM and CI-GC-MQAM are proportional to O(M 2 ) and O(M 4 ), respectively, low complexity detection schemes for the proposed GC-MQAM and CI-GC-MQAM are further proposed. In addition, the theoretical average bit error probabilities (ABEPs) for the proposed GC-MQAM and CI-GC-MQAM are derived. The derived ABEPs are validated through Monte Carlo simulations. Simulation and theoretical results show that the proposed GC-MQAM can achieve the error performance of signal space diversity. Simulation and theoretical results further show that the proposed CI-GC-16QAM, -64QAM, and -256QAM with three receive antennas can achieve approximately 2.2, 2.0, and 2.1 dB gain at a bit error rate of 4 × 10 −6 compared with GC-16QAM, -64QAM, and -256QAM, respectively. KEYWORDS Alamouti codes, diversity gain, maximum likelihood detection, multiplexing gain, STBC, uncoded space-time labeling diversity Int J Commun Syst. 2019;32:e3963.wileyonlinelibrary.com/journal/dac antennas transmit four symbols in two time slots, the Golden code achieves full rate. The Golden code also achieves full diversity. This is because each pair of these two super symbols is transmitted by a different antenna and in a different time slot. Based on the concept of space-time labeling diversity (STLD), the Golden code can also be regarded as one type of STLD. 4 This is because two super symbols in each pair conveys the same information. An important application of the Golden codes has been incorporated in the IEEE 802.16e WiMAX standard. 5 The Golden code has also been applied to trellis-coded modulation and space-time block-coded modulation. 6,7 The Golden code was proposed for multiple-input multiple-output (MIMO) systems in the literature. To the authors' best knowledge, the Golden code has never been applied in SIMO systems. The same bandwidth efficiency is kept compared with the conventional SIMO system if a pair of super symbols is transmitted in two time slots in a SIMO system. However, an extra diversity gain is achieved if a pair of super symbols is transmitted in two time slots in a SIMO system. This motivates us to propose Golden codeword-based modulation for a SIMO system. In this paper, when M-ary quadrature amplitude modulation (MQAM) is employed in the SIMO system, the scheme is referred to as Golden codeword-based MQAM (GC-MQAM). The diversity gain achieved by GC-MQAM is identical to that achieved by SSD. This is because two super symbols in a pair are transmitted in independent fading channel. In order to further achieve diversity gain, based on GC-MQAM, we borrow the concept of SSD and propose another modulation scheme, c...

Section: Error Performance Analysis Of Ci-gc-mqammentioning

confidence: 99%

Golden codeword–based modulation schemes for single‐input multiple‐output systems

Pillay

2019

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“…Although the BER performance of SM was significantly enhanced by the application of STBC, further improvement via the application of labeling diversity can be realised. As demonstrated in Xu et al, the BER performance of the conventional STBC system was significantly improved via the use of labeling diversity. Hence, this motivates for the application of labeling diversity to STBC‐SM, hereinafter referred to as STBC‐SM‐LD, which, to the best of the authors' knowledge, has not been reported in the literature.…”

Section: Introductionmentioning

confidence: 95%

“…A 2 × N r STLD system is shown in Figure , where N r is the number of receive antennas. The STLD system is a modification of the conventional 2 × N r STBC system, where the fundamental idea is to transmit a mapped symbol pair in the second time slot instead of the complex conjugates . The STLD system generates the 2 × 2 STBC based on 2 mappers:

ω_{1}^{M}

and

ω_{2}^{M}

as in Xu et al Figures and illustrate the Gray‐coded labeling map

ω_{1}^{16}

and the optimised labeling map

ω_{2}^{16}

for 16‐QAM, while Figures and illustrate the Gray‐coded labeling map

ω_{1}^{64}

and the optimised labeling map

ω_{2}^{64}

for 64‐QAM .…”

Section: System Models and Backgroundmentioning

confidence: 99%

“…Recently, a new diversity technique termed space‐time labeling diversity (STLD) was proposed, which does not require additional transmit or receive antennas. The diversity gain is achieved via the use of labeling maps, which are thoroughly discussed in Xu et al, and used to maximise the minimum product distance of STBC . Furthermore, it was shown that, under identical channel conditions, the STLD system outperforms the STBC system for a given spectral efficiency .…”

Section: Introductionmentioning

confidence: 99%

“…Currently, optimal BER performance of STLD is only guaranteed via maximum‐likelihood (ML) detection. Since labeling diversity can only be applied to high‐order modulation ( M ≥ 16), the receiver computational complexity grows extremely high, making hardware implementation impractical. This motivates for the formulation of an alternative LC detector for STLD, which is then extended to STBC‐SM‐LD.…”

Section: Introductionmentioning

confidence: 99%

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Space‐time block coded spatial modulation with labeling diversity

Govindasamy

Pillay

2017

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SummarySpace-time block coded spatial modulation (STBC-SM) exploits the advantages of both spatial modulation and the Alamouti space-time block code. Meanwhile, space-time labeling diversity has demonstrated an improved bit error rate (BER) performance in comparison to the latter. Hence, in this paper, we extend the application of labeling diversity to STBC-SM, which is termed STBC-SM-LD. Under identical channel assumptions, STBC-SM-LD exhibits superior BER performance compared to STBC-SM. For example, with 4 × 4, 64-quadrature amplitude modulation (64-QAM), STBC-SM-LD has a BER performance gain of approximately 2.6 dB over STBC-SM. Moreover, an asymptotic bound is presented to quantify the average BER performance of M-ary QAM STBC-SM-LD over independent and identically distributed Rayleigh frequency-flat fading channels. Monte Carlo simulations for STBC-SM-LD agree well with the analytical framework. In addition to the above, low-complexity (LC) near-maximum-likelihood detectors for space-time labeling diversity and STBC-SM-LD are presented. Complexity analysis of the proposed LC detectors shows a substantial reduction in computational complexity compared to their ML detector counterparts. For example, the proposed detector for STBC-SM-LD achieves a 91.9% drop in computational complexity for a 4 × 4, 64-QAM system. The simulations further validate the near-maximum-likelihood performance of the LC detectors.

Trellis code‐aided high‐rate M‐QAM space‐time labeling diversity using a unitary expansion

Dlodlo

2018

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Summary In this paper, we present a high‐rate M‐ary quadrature amplitude modulation (M‐QAM) space‐time labeling diversity (STLD) system that retains the robust error performance of the conventional STLD system. The high‐rate STLD is realised by expanding the conventional STLD via a unitary matrix transformation. Robust error performance of the high‐rate STLD is achieved by incorporating trellis coding into the mapping of additional bits to high‐rate codes. The comparison of spectral efficiency between the proposed trellis code‐aided high‐rate STLD (TC‐STLD) and the conventional STLD shows that TC‐STLD with 16‐QAM and 64‐QAM respectively achieves a 12.5% and 8.3% increase in spectral efficiency for each additional bit sent with the transmitted high‐rate codeword. Moreover, we derive an analytical bound to predict the average bit error probability performance of TC‐STLD over Rayleigh frequency‐flat fading channels. The analytical results are verified by Monte Carlo simulation results, which show that the derived analytical bounds closely predict the average bit error probability performance at high signal‐to‐noise ratios (SNR). Simulation results also show that TC‐STLD with 1 additional bit achieves an insignificant SNR gain of approximately 0.05 dB over the conventional STLD, while TC‐STLD with 2 additional bits achieves an SNR gain of approximately 0.12 dB.