Error performance of Uncoded Space Time Labelling Diversity in spatially correlated Nakagami‐q channels

Self Cite

Space‐time block code (STBC)–based multiple‐input–multiple‐output techniques have been considered recently to enhance the performance of mobile satellite communication systems in terms of link reliability. Uncoded space‐time labelling diversity (USTLD) is a diversity technique that is a direct extension of the STBC system and further improves its performance. A USTLD system is proposed in this paper that is designed specifically for satellite to mobile station links. The circular M‐ary Amplitude Phase‐Shift Keying (MAPSK) constellation, which is adopted by the most recent satellite broadcasting standard Digital Video Broadcasting standard for nonlinear satellite links (DVB‐S2X), is applied to the USTLD system. The most critical aspect of developing a USTLD system is the design of the secondary mapper to achieve labelling diversity. Existing square M‐ary Quadrature Amplitude Modulation (MQAM) approaches to USTLD mapper design are adapted for appropriate 16APSK and 64APSK constellations from the DVB‐S2X standard. Various metrics are derived to quantitatively compare mapper designs for a Nakagami‐q fading channel. Theoretical results, verified by Monte Carlo simulations, show that the best of the MAPSK USTLD mappers considered achieve a gain of approximately 4 dB for 16APSK and 5 dB for 64APSK when compared to the Alamouti STBC system. Furthermore, a study is conducted to analytically compare USTLD mappers using the derived metrics for both MQAM and MAPSK. It is concluded that a two‐stage approach is the most accurate methodology for comparing USTLD mapper designs.

f_{x} false(x false) = \frac{x ((), 1 + q^{2})}{q} \exp ((), - \frac{x^{2} {((), 1 + q^{2})}^{2}}{4 q^{2}}) I_{0} ((), \frac{x^{2} false(1 - q^{4} false)}{4 q^{2}}),

Section: System Modelmentioning

confidence: 99%

Section: System Modelmentioning

confidence: 99%

“…The full derivation, and its associated assumptions, is shown in appendix A in the work of Patel et al The derivation follows the union bound approach, which is given by

P_{b} false(ρ false) \leq \frac{1}{m 2^{m}} true \sum_{L = 0}^{2^{m} - 1} true \sum_{\begin{matrix} \overset{L}{true} = 0 \\ \overset{L}{true} \neq L \end{matrix}}^{2^{m} - 1} δ false(L, \overset{L}{true} false) P ((), L \to \overset{L}{true}),

where

δ false(L, \overset{L}{true} false)

and

P ((), L \to \overset{L}{true})

are respectively the number of bit errors and the pairwise error probability (PEP) between the transmitted label L and estimated label

\overset{L}{true}

. It was shown by Patel et al that the PEP is an integral defined in terms of the moment‐generating function (MGF) of the fading distribution. The trapezoidal approximation of the PEP is given by

P ((), L \to \overset{L}{true}) \approx \frac{1}{4 n} true \prod_{i = 1}^{2} {([], {scriptM}_{i} ((), \frac{1}{2} {(||, d_{i} false(L, \overset{L}{true} false))}^{2}))}^{N_{R}} + \frac{1}{2 n} true \sum_{j = 1}^{n - 1} true \prod_{i = 1}^{2} ([], {scriptM}_{i} ((), (||, d_{i} false(L, \overset{}{true})))

…”

Section: Mapper Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

USTLD mapper design for APSK constellations over satellite links

Quazi

Patel

2019

Self Cite

An ordered crossover based approach to designing labeling diversity mappers

Solwa

2021

Genetic algorithms (GAs) are population‐based search optimization techniques that mimic the process of evolution and natural selection. GAs are an effective way of finding feasible solutions to complex problems. Recently, GAs were applied to the labeling diversity (LD) problem that produced local optimal mappers for M‐QAM, M‐PSK, and M‐APSK constellations. However, the GA did not implement biological processes during the mating process; hence it could not be classified as a GA, but rather a genetic‐inspired algorithm (GIA). In this article, we investigate the application of six distinct crossover techniques to further improve the GIAs ability to produce more closer‐to‐optimal mapper designs. By using biological crossover techniques, offspring produced acquires genetic diversity from parent chromosomes. Single parent crossover techniques do not produce diversified offspring, thus diversity being acquired only by mutation. The Davis ordered crossover (OX1) was chosen as a suitable technique to be applied to the proposed GA. The proposed GA was tested on 16QAM, 16PSK, 16APSK, and three 16APSK constellations that do not exhibit diagonal symmetry. In the case of the 16QAM and 16PSK constellations, the proposed GA matched but did not improve upon existing mapper designs. In the case of the 16APSK and 11+5APSK constellations, the proposed GA produced mapper designs exhibited diversity gains of ≈0.5 dB over the existing GIA mapper designs at the BER of 10−6. The asymmetric 16APSK and single symmetry 16APSK constellations exhibited diversity gains of ≈4 and ≈2 dB over existing GIA mapper designs at the BER of 10−3 and 10−5. More significantly, the proposed GA achieved a significant improvement in time complexity. However, the proposed GA was shown to have higher computational complexity of O(M!) over the GIA with a complexity of O(M2). Mutation rate studies have shown that for single‐parent crossover techniques, higher mutation rates are needed, thus making the process is purely random. In the case of the two‐parent crossover technique, randomness is reduced and genetic diversity is increased, hence lower mutation rates were required due to a more guided search.

A modified global neighborhood algorithm for designing labeling diversity mappers

Solwa

Ayanda

2022

Genetic algorithms (GAs) have been recently applied to uncoded space‐time labeling diversity systems (USTLD) to improve upon diversity in wireless links. GAs were used to optimize the secondary mappers that are used to encode the information to be transmitted. Existing literature only achieved a local optimal design, at the fraction of the computational costs. Hence, this article focuses on improving upon the GAs for USTLD systems by merging it with a global‐local search technique, called the global neighborhood algorithm (GNA). The GNA algorithm was tested on M‐QAM, M‐PSK, M‐APSK, and asymmetric M‐APSK constellations of modulation order M =16,32$$ =16,32 $$, and 64$$ 64 $$. In the case of M‐QAM constellations, the GNA was able to match, but not improve upon existing mapper designs. In the case of the 64PSK constellation, the GNA was able to produce mapper designs that improved upon the error performance of existing mapper designs by approximately 1 dB. In the case of the 32APSK constellation, the GNA was able to improve upon the error performance of existing mapper designs by approximately 0.5 dB. Moreover, the GNA produced mapper designs for the 11+5APSK and asymmetric 16APSK constellations that improved upon the error performance of existing mapper designs by approximately 0.5 and 4 dB respectively. Finally, the computational complexity of the proposed GNA algorithm was analyzed and the algorithm was shown to be Ofalse(normalM2+Pm,1+Pm,2false)$$ O\left({\mathrm{M}}^2+{P}_{m,1}+{P}_{m,2}\right) $$ which is slightly more complex than the initial GA approach with complexity Ofalse(normalM2false)$$ O\left({\mathrm{M}}^2\right) $$, but significantly less complex than the enhanced GA with complexity Ofalse(normalM!false)$$ O\left(\mathrm{M}!\right) $$. The increased complexity also came with significant gains such as improved LD mapper designs.