M-ary Differential Phase-shift Keying Research Articles

M-ary DPSK coded binary to gray, BCD to gray, and octal to binary all-optical code converters based on SOA-MZI configuration at 500 Gb/s.

Gray codes are broadly used as the cyclic codes to assist error correction in optical communications. In this paper, we have proposed the novel design of three different types of all-optical gray code converters based on the semiconductor optical amplifier (SOA) Mach-Zehnder interferometer (MZI) configuration. The XOR and OR gates are the basic devices used for the proposed design of binary to gray, binary-coded decimal (BCD) to gray, and octal to binary code converters. For the first time, to the best of the authors' knowledge, a high data rate of 500 Gbps is achieved for the three types of all-optical code converters using the SOA-MZI configuration by exploiting an M-ary differential phase shift keying (DPSK) modulation scheme. The performance factors of the proposed all-optical code converters like extinction ratio, bit error rate, and quality factor are calculated.

An MDPSK homodyne receiver with adaptive phase-diversity

ABSTRACT We propose an adaptive phase-diversity method for optical M-ary differential phase-shift keying (MDPSK) homodyne receivers, to achieve coherent optical communication. This method involves eliminating the random fluctuations in the phase differences between the signal light and local oscillator and the in-plane and quadrature signal (IQ) imbalance compensation. For the former, a phase-diversity method, which can theoretically eliminate all phase-related noise, is proposed. The gain and phase imbalances between the I and Q channels can be compensated completely by using automatic phase- and gain-control systems. The core idea is the adaptability of the receiver to the local phase shift of the local oscillator. The performance of the receiver is not sensitive to environmental factors such as temperature and vibrations. Our simulation results show that the imbalances between the IQ channels can be completely compensated over a wide imbalance range, and the baseband signals can be accurately recovered using the proposed scheme.

Hybrid two-level MPPM-MDPSK modulation for high-speed optical communication networks.

A hybrid optical modulation approach is described, which layers a continuous wave $M$M-ary differential phase-shift keying ($M{\rm DPSK}$MDPSK) and a two-level ($2L$2L) multipulse pulse-position modulation (MPPM) intensity-modulated signal for improved spectral efficiency. These $2L$2L techniques are a generalization of earlier hybrid MPPM-$M{\rm DPSK}$MDPSK techniques and have the added advantage of reducing transmitter and detector complexities over previous hybrid modulation approaches. The spectral and power efficiencies for the proposed $2L$2L-MPPM-$M{\rm DPSK}$MDPSK modulation techniques are formulated and shown to have the highest spectral efficiency in comparison to other hybrid techniques with lower implementation complexity. The performance of the proposed $2L$2L hybrid techniques is quantified over free-space optical (FSO) networks as well as fiber networks and verified using Monte Carlo simulation. For FSO channels, the proposed $2L$2L-MPPM-$M{\rm DPSK}$MDPSK technique outperforms the traditional MPPM-$M{\rm DPSK}$MDPSK scheme by approximately 2 dB at a bit-error rate (BER) of ${10^{-4}}$10-4 and a spectral efficiency of 2.5 bit/s/Hz. Similarly, in optical fiber, the proposed scheme relaxes the impact of nonlinearity in comparison to traditional MPPM-$M{\rm DPSK}$MDPSK. Specifically, at a ${\rm BER}{=10^{-3}}$BER=10-3, the $2L$2L-MPPM-$M{\rm DPSK}$MDPSK technique outreaches the MPPM-$M{\rm DPSK}$MDPSK by 2000 km at a spectral efficiency of 2.5 bit/s/Hz and an average transmit power of $-{3}\,\,{\rm dBm}$-3dBm.

Short Non-Binary Low-Density Parity-Check Codes for Phase Noise Channels

This work considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK) modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1:2 dB from finite-length bounds is obtained, down to a CER of 1e-3.

Performance of adaptive subcarrier modulated MIMO wireless optical communications in Malaga turbulence

Abstract Space diversity of multiple-input multiple-output (MIMO) system combined with the adaptive subcarrier modulation technique can effectively reduce the atmospheric channel fading effects. Malaga turbulent probability density function is obtained based on the MeijerG function. The asymptotic expression of average bit error rate in non-adaptive and adaptive modulated MIMO wireless optical systems are derived respectively, and M-ary phase shift keying (MPSK) and M-ary differential phase shift keying (MDPSK) modulation are used in these two kinds of systems. Under moderate turbulence conditions, error performances are analyzed with numerical simulations between these two systems. The results show that the average bit error performance in the adaptive modulated system can be significantly better than the non-adaptive modulated system. But under the same conditions of modulation order and target bit error rate, error performance of non-adaptive modulation is easier to be affected by transmit and receive aperture number than adaptive modulation in MIMO system.

A Noncoherent Multiuser Large-Scale SIMO System Relying on M-Ary DPSK and BICM-ID

A new constellation is designed for the multiuser noncoherent large-scale single-input multiple-output uplink system based on M-ary differential phase-shift keying, which is combined with a bit interleaved coded modulation-iterative decoding scheme for attaining improved performance. We conceive a new approach for constructing EXIT charts parameterized by the number of antennas used for optimizing the design. Finally, the system performance is analyzed and compared to previous work. This evaluation shows an overall improvement of two orders of magnitude demonstrating a dramatic reduction in the required number of antennas.

Average SEP of AF Relaying in Nakagami‐m Fading Environments

This paper is devoted to an investigation of an exact average symbol error probability (SEP) for amplify and forward (AF) relaying in independent Nakagami‐m fading environments with a nonnegative integer plus one‐half m, which covers many actual scenarios, such as one‐side Gaussian distribution (m = 0.5). Using moment generating function approach, the closed‐form SEP is expressed in the form of Lauricella multivariate hypergeometric function. Four modulation modes are considered: rectangular quadrature amplitude modulation (QAM), M‐ary phase shift keying (MPSK), M‐ary differential phase shift keying (MDPSK), and π/4 differential quaternary phase shift keying (DQPSK). The result is very simple and general for a nonnegative integer plus one‐half m, which covers the same range as integer m. The tightness of theoretical analysis is confirmed by computer simulation results.

Performance of SIM-MDPSK FSO Systems With Hardware Imperfections

This paper studies the error performance of free-space optical (FSO) systems, employing subcarrier intensity modulation (SIM) with M-ary differential phase-shift keying (MDPSK). Novel analytical expressions for the symbol error probability are derived, based on the Fourier series approach. The irradiance fluctuations of the received optical signal are modeled by considering both Gamma-Gamma atmospheric turbulence and pointing errors. In addition, hardware imperfections of DPSK demodulator, as the phase noise of local oscillator at the receiver, are considered. It is illustrated that the phase noise significantly degrades the system performance, especially when the optical signal transmission is impaired by weak atmospheric turbulence and weak pointing errors effect. Furthermore, the phase noise results in an unrecoverable error-rate floor, which is an important limiting factor for SIM-DPSK FSO systems.

Rician-Nakagami 페이딩 채널에서 M-PSK와 M-DPSK 시스템에 대한 효과적인 점근적 심볼 에러 확률 성능 분석

Using the existing exact but quite complicated symbol error rate (SER) expressions for M-ary phase shift keying (M-PSK) and M-ary differential phase shift keying (M-DPSK), we derive effective and concise closed-form asymptotic SER formulas especially in Rician-Nakagami fading channels. The derived formulas can be utilized to efficiently verify the achievable error rate performances of M-PSK and M-DPSK systems for the Rician-Nakagami fading environments. In addition, by exploiting the modulation gains directly obtained from the asymptotic SER formulas, we also theoretically demonstrate that M-DPSK suffers an asymptotic SER performance loss of 3.01dB with respect to M-PSK for a given M in Rician-Nakagami fading channels at high signal-to-noise ratio (SNR).

Asymptotic BER Comparison of MPSK and MDPSK in Lognormal Fading Channels

The bit error rate (BER) performance loss of $M$ -ary differential phase-shift keying (MDPSK) with respect to $M$ -ary phase-shift keying (MPSK) in wireless fading channels has been extensively studied, but the understanding of this problem in lognormal fading channels has been limited. The most recent work has shown the asymptotic BER performance losses of BDPSK and QDPSK with respect to BPSK and QPSK, respectively, in the lognormal fading channels. However, it is not known how the modulation order increases. In this paper, we derive the general expression of the relative BER performance loss of MDPSK with respect to MPSK for arbitrary $M$ over the lognormal fading channels in high signal-to-noise ratio regimes. We start our analysis by investigating the asymptotic BER performance losses of MDPSK with respect to MPSK for $M=\mbox{4}, \mbox{8}, \mbox{and} \mbox{16}$ . Using the regularity of these results, we obtain the general closed-form expression of the relative BER performance loss in the lognormal fading channels.

Soft-Decision for Differential Amplify-and-Forward over Time-Varying Relaying Channel

Differential detection schemes do not require any channel estimation, which can be employed under user mobility with low computational complexity. In this work, a soft-input soft-output (SISO) differential detection algorithm is proposed for amplify-and-forward (AF) over time-varying relaying channels based cooperative communications system. Furthermore, maximum-likelihood (ML) detector for M-ary differential Phase-shift keying (DPSK) is derived to calculate a posteriori probabilities (APP) of information bits. In addition, when the SISO is exploited in conjunction with channel decoding, iterative detection and decoding approach by exchanging extrinsic information with outer code is obtained. Finally, simulation results show that the proposed non-coherent approach improves detection performance significantly. In particular, the system can obtain greater performance gain under fast-fading channels.

Asymptotic SER Performance Comparison of MPSK and MDPSK in Wireless Fading Channels

We propose a general framework to investigate asymptotic relative performance between M-ary phase-shift keying (MPSK) and M-ary differential phase-shift keying (MDPSK) in wireless fading channels. Using this framework, we provide an alternative derivation for the closed-form expression of the asymptotic performance loss of MDPSK w.r.t. MPSK in an additive white Gaussian noise channel. The same performance loss is also shown to be true for the lognormal fading channels.

Performance of M-QAM, M-DPSK and M-PSK with MRC diversity in a Nakagami-m fading channel

The nature of a wireless communication channel is very unpredictable. To design a good communication link, it is required to know the statistical model of the channel accurately. The average symbol error probability (ASER) was analyzed for different modulation schemes. A unified analytical framework was presented to obtain closed-form solutions for calculating the ASER of M-ary differential phase-shift keying (M-DPSK), coherent M-ary phase-shift keying (M-PSK), and quadrature amplitude modulation (QAM) over single or multiple Nakagami-m fading channels. Moreover, the ASER was estimated and evaluated by using the maximal ratio-combining (MRC) diversity technique. Simulation results show that an error rate of the fading channel typically depends on Nakagami parameters (m), space diversity (N), and symbol rate (M). A comparison between M-PSK, M-DPSK, and M-QAM modulation schemes was shown, and the results prove that M-ary QAM (M-QAM) demonstrates better performance compared to M-DPSK and M-PSK under all fading and non-fading conditions.

Maximum-Likelihood Detector for Differential Amplify-and-Forward Cooperative Networks

The exact maximum-likelihood (ML) detector for amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (DPSK) in Rayleigh fading is derived in a single-integral form, which serves as a benchmark for differential AF networks. Two algorithms are then developed to reduce the complexity of the ML detector. Specifically, the first algorithm can eliminate a number of candidates in the ML search, while causing no loss of optimality of ML detection. In high signal-to-noise ratios (SNRs), this algorithm almost surely identifies a single candidate that amounts to the ML estimate of the signal. For low to medium SNRs with multiple candidates determined, we then derive an accurate closed-form approximation for the integral involved in the likelihood function, which only requires a five-sample evaluation per symbol candidate. Finally, combining these algorithms, we propose a closed-form approximate ML detector, which achieves an almost identical bit-error-rate (BER) performance to the exact ML detector at practical complexity. In particular, it is shown that the proposed approximate ML detector is far less complex than the well-known diversity combiner in high SNRs, while achieving approximately 1.7-dB gain in the 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> BER when the relay is closer to the destination.

Noncoherent Amplify-and-Forward Cooperative Networks: Robust Detection and Performance Analysis

We develop closed-form generalized likelihood ratio test (GLRT) sequence detectors for multi-relay amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (M-DPSK) and noncoherent M-ary frequency-shift keying (M-FSK). The proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels, signal powers, noise variances, and relay functionalities is unavailable to the destination. A comprehensive error probability performance analysis is carried out in Rayleigh fading. Specifically, we derive unified pairwise error probability (PEP) expressions for both detectors in a dual-hop network, which are valid for arbitrary modulation order M and arbitrary sequence length N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . We also derive unified bit-error probability (BEP) expressions for both detectors employing binary signalings in various networks for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 1. It is further shown that both detectors achieve near full diversity orders. Finally, the superiorities of the proposed detectors over the state-of-the-art noncoherent detectors are justified through extensive comparisons in practical scenarios. For example, in a multi-relay network where the relays are uniformly distributed between the source and destination, the proposed detector for noncoherent FSK with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 1 outperforms the well-known maximum energy selector by almost 15 dB in high signal-to-noise ratios.

Subcarrier Intensity Modulated Optical Wireless Communications Using Noncoherent and Differentially Coherent Modulations

Error rate performance is analyzed for subcarrier noncoherent and differentially coherent modulated optical wireless communication systems over atmospheric turbulence channels. Both Gamma-Gamma and negative exponential channels are considered. Using a moment generating function approach, we obtain a unified bit-error rate expression for a family of noncoherent and differentially coherent modulations. We also analyze the symbol-error rate performance of subcarrier <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> -ary differential phase-shift keying and <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> -ary noncoherent frequency-shift keying modulated systems using the same frequency domain approach. Our asymptotic analysis reveals relative error rate performance of <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> -ary differential phase-shift keying and <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> -ary noncoherent frequency-shift keying in different channel conditions.

Effect of Nonlinear Phase Noise on the Performance of $M$-Ary PSK Signals in Optical Fiber Links

The effects of amplified spontaneous emission (ASE) noise and nonlinear phase (NLP) noise on the symbol error rate performance of M-ary coherent phase shift keying (CPSK) and differential phase shift keying (DPSK) are analyzed. Expressions for the symbol error probability (SEP) are derived for the two cases of independent ASE and NLP noises and dependent ASE and NLP noises. Numerical results are presented for 2-, 4-, 8-, and 16-level signaling to demonstrate the applicability of the SEP expressions. Our results indicate that the SEPs for DPSK for the two cases are approximately the same except for M=2. The SEPs for CPSK differ significantly for the two cases for all M , implying that independent phase noise assumption is not valid for CPSK.

Adaptive Demodulation in Differentially Coherent Phase Systems: Design and Performance Analysis

Adaptive Demodulation (ADM) is a newly proposed rate-adaptive system which operates without requiring Channel State Information (CSI) at the transmitter (unlike adaptive modulation) by using adaptive decision region boundaries at the receiver and encoding the data with a rateless code. This paper addresses the design and performance of an ADM scheme for two common differentially coherent schemes: M-DPSK (M-ary Differential Phase Shift Keying) and M-DAPSK (M-ary Differential Amplitude and Phase Shift Keying) operating over AWGN and Rayleigh fading channels. The optimal method for determining the most reliable bits for a given differential detection scheme is presented. In addition, simple (near-optimal) implementations are provided for recovering the most reliable bits from a received pair of differentially encoded symbols for systems using 16-DPSK and 16- DAPSK. The new receivers offer the advantages of a rate-adaptive system, without requiring CSI at the transmitter and a coherent phase reference at the receiver. Bit error analysis for the ADM system in both cases is presented along with numerical results of the spectral efficiency for the rate-adaptive systems operating over a Rayleigh fading channel.

Optimal and Suboptimal Differentially Coherent Reception of MDPSK in Time-Spread WSSUS Channel

A model of the wide-sense stationary uncorrelated scattering (WSSUS) channel with time-spread and additive white Gaussian noise is considered. The general expression for the symbol-by-symbol reception algorithm of M-ary differential phase shift keying (MDPSK), which realizes implicit diversity, is obtained. Depending on the type of impulse response receiver filter (demodulator kernel), the partial cases that follow from this expression are considered: optimal demodulator, conventional differentially coherent demodulator, demodulator with iterative kernel and its special cases. Relations for assessing the bit error probability of the considered demodulators in the case when signals are transmitted with binary and quadrature differential phase shift keying without taking into account intersymbol interference are derived. The performance bounds for the optimized binary and quadrature systems are determined. The results of the calculation of the bit error probability are presented.

Adaptive MDPSK DS/CDMA receivers with performance analysis

AbstractFor direct‐sequence code‐division multiple‐access (DS/CDMA) systems, the multiuser and multipath interferences are always present. When the demodulation is coherent, a coherent carrier reference must be generated prior to demodulation. The generation of coherent reference at low signal‐to‐interference‐and‐noise ratio (SINR) is difficult. In the downlink CDMA communications, numbers of active users transmit information simultaneously by different signature waveform. However, the multipath channel and multiple‐access interference (MAI) limit the system capacity. Adaptive single‐user receivers do not require knowledge of MAI parameters and need fewer computations. In this paper, we propose adaptive receivers with decision‐feedback differential detection (DF‐DD) and compare variations of the receiver structure proposed in Schrober's paper for noncoherent channels. In the absence of knowledge of the carrier phase, we derive the minimum mean square error (MMSE) of the proposed receivers to show that the performances of the proposed receivers with M‐ary differential phase‐shift keying (MDPSK) signals approach that of the coherent receiver with MPSK signal. Some simulation examples are given to demonstrate the effectiveness and compare the performances of the proposed adaptive receivers. Copyright © 2008 John Wiley &amp; Sons, Ltd.