Amplitude Phase Shift Keying Constellation Research Articles

Circularly Symmetric Companding Quantization-Inspired Hybrid Constellation Shaping for APSK Modulation to Increase Power Efficiency in Gaussian-Noise-Limited Channel

In this paper we address hybrid probabilistic-geometric constellation shaping (HCS) of amplitude phase shift keying (APSK) constellation based on the reversed model of optimal companding quantization for circularly symmetric sources with the goal to increase the constellation power efficiency in Gaussian-noise-limited channel. To empirically optimize the proposed APSK constellation such that a symbol-error rate (SER) reaches its minimum under given constraints with respect to signal-to-noise ratio (SNR) and the prior probabilities of constellation points, for various settings of constellation parameters, we investigate SER dependence on SNR and determine the constellation parameters achieving minimum SER. The SER dependence on SNR we estimate theoretically by deriving approximate formula for SER of uncoded APSK constellation in Gaussian-noise-limited channel and practically by performing simulation. The obtained results are well-matched verifying the accuracy of approximate SER formula. The results also show that our APSK constellation outperforms some previous APSK and M-ary QAM constellations in terms of power efficiency. Thus, for SER equal to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> the gain in power efficiency amounts up to 2.35 dB, 2.23dB and 1.64 dB compared with the maximum mutual information-optimized 4+12-APSK, 4+12+16-APSK and 4+12+20+28-APSK constellations, respectively. This means that by employing APSK constellation we propose instead the traditional APSK constellations the transmitted signal power can be reduced by a third enabling lower power consumption. The improved power efficiency of our APSK constellation makes it suitable for application in power-limited communications such as fiber-optic communications, satellite communications, power-line communications, and multiple-input multiple-output wireless transmissions.

A New APSK-Based M-Ary Differential Chaos Shift Keying Modulation System

In this letter, a new amplitude phase shift keying (APSK) based ${M}$ -ary differential chaos shift keying (A- ${M}$ -DCSK) system is proposed. The theoretical symbol error rate (SER) and bit error rate (BER) expressions of A- ${M}$ -DCSK system for two constellations are derived and verified for both AWGN and multipath Rayleigh fading channels. Numerical results reveal that A- ${M}$ -DCSK system provides near or better BER with much lower peak-to-average power ratio (PAPR) as compared to quadrature amplitude modulation (QAM) based ${M}$ -DCSK (Q- ${M}$ -DCSK) system. Furthermore, A- ${M}$ -DCSK system shows better robustness against channel estimation error than Q- ${M}$ -DCSK system. At last, with APSK constellation rotation, the BER of A- ${M}$ -DCSK system is enhanced with a slightly increased PAPR.

APSK-CSK Systems Based on Kite and Color Wheel Constructions

Visible light communications (VLC) technology has emerged as a solution for the radio frequency relief and can be implemented, for example, through light fidelity. In most applications, VLC relies on a backbone technology due to its short-range nature. Hence, a combination technique is required to join the backbone network and VLC, preferably in an amplify-and-forward scenario, to reduce the implementation cost. In this paper, leveraging on the robustness of amplitude phase-shift keying (APSK) against channel nonlinearities, we propose a design framework consisting of a mapping technique using APSK and color shift keying (CSK), referred to as hybrid APSK-CSK scheme, to link a backbone network to VLC. The APSK constellation, made of two rings, is based on the kite structure. The ratio of inner by outer rings radii, $\beta$ , combined with four other parameters, namely, the attenuation coefficient of the backbone channel, $\alpha$ , the amplification coefficient of inner signal, $\delta _i$ , the amplification coefficient of outer signal, $\delta _o$ , and the ratio of the APSK-CSK inner by outer rings, $\gamma$ , are exploited to control lighting, color rendering, and the communication performance. Results reveal that the scheme performance is based on the obtained characteristic equations and provides better lighting comfort as the constellation size increases.

Closed-Form SER Expression for APSK Based on the Kite Structure

In communication systems, amplitude phase shift keying (APSK) arises as a potential solution to mitigate performance degradations due to channel non-linearities. Since it combines the characteristics of PSK and those of amplitude shift keying (ASK), APSK is also likely to be robust in systems influenced by phase noise. It is, therefore, solicited in cascaded systems involving visible light communications (VLC) as the second communication technology. This letter proposes the design of an APSK constellation, based on the kite structure, suitable for such cascaded systems. The constellation design is detailed and the symbol error probability is derived in closed-form. The bit error rate performance is compared with those of quadrature amplitude modulation (QAM) and PSK. Findings reveal that for $ 2\eta = 4$ ( $ \eta $ being the common number of symbols per ring), the proposed APSK scheme has similar performance with ${Q}$ PSK and 4 QAM, and, for $2\eta > 8$ , the APSK scheme outperforms the corresponding PSK, making it a good candidate for cascaded VLC systems. Even though the proposed scheme is outperformed by QAM, it gains up to about 5 dB over the PSK for an error rate of $ 10^{-8} $ .

Polar-coded modulation based on the amplitude phase shift keying constellations

In this paper, we investigate the polarization effect of the amplitude phase shift keying (APSK) constellations. We find that the polarization effect of the APSK constellations is affected by the bit mapping and the bit loading. Traditionally, the Gray mapping is usually adopted in APSK constellations. Based on the given Gray mapping, we firstly propose the bit interleaved coded modulation polar-APSK (BICM-PA) scheme, which neglects the correlations between the bit levels by using the bit interleaver. In the BICM-PA scheme, a new metric called cumulative Bhattacharyya parameter is introduced to optimize the bit loading of the APSK constellations under the Gray mapping. Second, the multilevel coded modulation polar-APSK (MLCM-PA) is proposed to further improve the performance. A two-stage optimization approach is adopted to select the bit mapping and the bit loading in the MLCM-PA scheme. The semi-set partitioning mapping is introduced to achieve a better system performance in the MLCM-PA scheme. Simulation results verify the effectiveness of all the proposed metrics. In addition to this, BICM-PA and MLCM-PA both outperform the coded modulation Turbo-APSK scheme up to 1dB.

A Near-Capacity MIMO Coded Modulation Scheme for Digital Terrestrial Television Broadcasting

Multiple-input multiple-output (MIMO), which can provide ultrahigh data transmission rate, is one of the key technologies for the next generation digital terrestrial television broadcasting (DTTB) standards. This paper proposes a near-capacity MIMO bit-interleaved coded modulation scheme with either independent or iterative demapping (BICM/BICM-ID) for the DTTB system. First, the amplitude phase shift keying (APSK) constellation with Gray mapping is proposed to replace the conventional Gray quadrature amplitude modulation (QAM) counterpart. From the perspective of average mutual information analysis, Gray-APSK has certain shaping gain compared to Gray-QAM for both independent and iterative demapping schemes. Besides the APSK constellation, a novel bit interleaver named bit mapping, which takes into account the unequal error protection of both APSK constellations and low-density parity-check codes, is proposed to further improve the system performance. The tool of extrinsic information transfer chart is utilized to analyze and design the optimal bit mapping for the BICM/BICM-ID scheme. Bit error rate simulations are finally carried out to verify the superiority of the proposed MIMO coded modulation scheme.

Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise

We study the design of amplitude phase-shift keying (APSK) constellations for a coherent fiber-optical communication system where nonlinear phase noise (NLPN) is the main system impairment. APSK constellations can be regarded as a union of phase-shift keying (PSK) signal sets with different amplitude levels. A practical two-stage (TS) detection scheme is analyzed, which performs close to optimal detection for high enough input power. We optimize APSK constellations with 4, 8, and 16 points in terms of symbol error probability (SEP) under TS detection for several combinations of input power and fiber length. For 16 points, performance gains of 3.2 dB can be achieved at a SEP of 10^{-2} compared to 16-QAM by choosing an optimized APSK constellation. We also demonstrate that in the presence of severe nonlinear distortions, it may become beneficial to sacrifice a constellation point or an entire constellation ring to reduce the average SEP. Finally, we discuss the problem of selecting a good binary labeling for the found constellations.

EXIT-Chart-Matching-Aided Near-Capacity Coded Modulation Design and a BICM-ID Design Example for Both Gaussian and Rayleigh Channels

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated, wherein a novel method of designing amplitude phase-shift keying (APSK) constellations is proposed, which is capable of outperforming both traditional quadrature amplitude modulation (QAM) and nonuniformly spaced QAM (NU-QAM). It is shown that the channel capacity can be approached by the proposed <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex></formula> -APSK constellation as <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex></formula> tends to infinity. Additionally, a new algorithm is introduced for finding the best bit-to-symbol mapping. Furthermore, when signal space diversity is also employed, our extrinsic information transfer (EXIT) chart analysis and Monte Carlo simulations demonstrate that the proposed BICM-ID schemes exhibit a near-Shannon-capacity performance for transmission over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. For a block length of 64 800 bits, the bit-error-rate (BER) curve of the proposed BICM-ID 16/64-APSK scheme is only about 0.8 and 1.0 dB away from the Gaussian-input Shannon limit over AWGN and Rayleigh fading channels, respectively, at the BER of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{10}^{-5}$</tex> </formula> and for a code rate of 1/2.

Constellation Shaping for Bit-Interleaved LDPC Coded APSK

An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded amplitude phase-shift keying (APSK) system. A subset of the interleaved bits output by a binary LDPC encoder are passed through a nonlinear shaping encoder whose output is more likely to be a zero than a one. The "shaping" bits are used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Because the shaping bits are biased, symbols from lower-energy subconstellations are selected more frequently than those from higher-energy subconstellations. An iterative decoder shares information among the LDPC decoder, APSK demapper, and shaping decoder. Information rates are computed for a discrete set of APSK ring radii and shaping bit probabilities, and the optimal combination of these parameters is identified for the additive white Gaussian noise (AWGN) channel. With the assistance of extrinsic-information transfer (EXIT) charts, the degree distributions of the LDPC code are optimized for use with the shaped APSK constellation. Simulation results show that the combination of shaping, degree-distribution optimization, and iterative decoding can achieve a gain in excess of 1 dB in AWGN at a rate of 3 bits/symbol compared with a system that does not use shaping, uses an unoptimized code from the DVB-S2 standard, and does not iterate between decoder and demodulator.

APSK Constellation with Gray Mapping

Amplitude phase shift keying (APSK) constellation is superior to its quadrature amplitude modulation (QAM) counterpart from the mutual information point of view. However, due to the lack of Gray mapping, it introduces high independent demapping loss. In this letter, a special kind of APSK constellations with Gray mapping (Gray-APSK) is proposed, which provides considerable shaping gain compared with the QAM constellations with Gray mapping (Gray-QAM) in both independent and iterative demapping scenarios, as verified by average mutual information analysis and bit error rate simulations.

Turbo-coded APSK modulations design for satellite broadband communications

This paper investigates the design of power and spectrally efficient coded modulations based on amplitude phase shift keying (APSK) modulation with application to satellite broadband communications. APSK represents an attractive modulation format for digital transmission over nonlinear satellite channels due to its power and spectral efficiency combined with its inherent robustness against nonlinear distortion. For these reasons APSK has been very recently introduced in the new standard for satellite Digital Video Broadcasting named DVB-S2. Assuming an ideal rectangular transmission pulse, for which no nonlinear inter-symbol interference is present and perfect pre-compensation of the nonlinearity, we optimize the APSK constellation. In addition to the minimum distance criterion, we introduce a new optimization based on the mutual information; this new method generates an optimum constellation for each spectral efficiency. To achieve power efficiency jointly with low bit error rate (BER) floor we adopt a powerful binary serially concatenated turbo-code coupled with optimal APSK modulations through bit-interleaved coded modulation. We derive tight approximations on the maximum-likelihood decoding error probability, and results are compared with computer simulations. The proposed coded modulation scheme is shown to provide a considerable performance advantage compared to current standards for satellite multimedia and broadcasting systems. Copyright © 2006 John Wiley & Sons, Ltd.