Differential Quaternary Phase Shift Keying Research Articles

New Accurate Approximation for Average Error Probability

This paper proposes new accurate approximations for average error probability (AEP) of a communication system employing either $M$ -phase-shift keying (PSK) or differential quaternary PSK with Gray coding (GC-DQPSK) modulation schemes over generalized fading channel. Firstly, new accurate approximations of error probability (EP) of both modulation schemes are derived over additive white Gaussian noise (AWGN) channel. Leveraging the trapezoidal integral method, a tight approximate expression of symbol error probability for $M$ -PSK modulation is presented, while new upper and lower bounds for Marcum $Q$ -function (MQF) of the first order, and subsequently those for bit error probability (BEP) under DQPSK scheme, are proposed. Next, these bounds are linearly combined to propose a highly refined and accurate BE P’s approximation. The key idea manifested in the decrease property of modified Bessel function $I_{v}$ , strongly related to MQF, with its argument $v$ . As an application, these approximations are used to tackle AEP’s approximation under $\kappa -\mu $ shadowed fading. Numerical results show the accuracy of the presented approximations compared to the exact ones.

Multiplexed terrestrial free space optic system design using dual polarized multicarrier transmission technique

A hybrid technique for terrestrial free space optic (FSO) system has been proposed in this paper. The hybrid technique is a combination of 8 × 40 Gbps dense wavelength-division multiplexing and a multicarrier transmission (MCT) scheme such as coherent optical orthogonal frequency-division multiplexing (CO-OFDM). The prime design objective is to minimize the issues related to the terrestrial FSO-based system for atmospheric turbulence, bandwidth management, and receiver sensitivity. The cyclic prefix bits have been added with the data symbols of CO-OFDM, which minimizes the effect of nonlinearity due to atmosphere and reduces intersymbol interference. The dual-polarized quadrature phase-shift keying (DP-QPSK) sequence is used to modulate the subcarriers of the MCT system. DP-QPSK is very well known for its optical signal-to-noise ratio tolerance. It has been found that, by the incorporation of a hybrid scheme in the FSO system, a propagation range of 2.2 km in atmospheric turbulence regime for the targeted bit error rate (BER) of 3.8 × 10 − 3 or log of BER of −2.42 is achieved. A contrast performance comparison has also been carried out for the proposed hybrid system with different advanced modulation schemes such as differential quaternary phase-shift keying and four-level quadrature amplitude modulation. The Gamma-Gamma-type distribution function is considered for estimating the turbulence effect of the free space channel. Mathematical modeling related to the proposed system has also been incorporated for better analysis. This type of hybrid technique for the FSO system with the incorporation of DP-QPSK modulation format will give more technical feasibility to the modern communication system.

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.

Terrestrial Trunked Radio (TETRA) exposure of neuronal in vitro networks

Terrestrial Trunked Radio (TETRA) is a worldwide common mobile communication standard, used by authorities and organizations with security tasks. Previous studies reported on health effects of TETRA, with focus on the specific pulse frequency of 17.64Hz, which affects calcium efflux in neuronal cells. Likewise among others, it was reported that TETRA affects heart rate variability, neurophysiology and leads to headaches. In contrast, other studies conclude that TETRA does not affect calcium efflux of cells and has no effect on people's health.In the present study we examine whether TETRA short- and long-term exposure could affect the electrophysiology of neuronal in vitro networks. Experiments were performed with a carrier frequency of 395MHz, a pulse frequency of 17.64Hz and a differential quaternary phase-shift keying (π/4 DQPSK) modulation. Specific absorption rates (SAR) of 1.17W/kg and 2.21W/kg were applied.In conclusion, the present results do not indicate any effect of TETRA exposure on electrophysiology of neuronal in vitro networks, neither for short-term nor long-term exposure. This applies to the examined parameters spike rate, burst rate, burst duration and network synchrony.

High-Speed, High-Performance DQPSK Optical Links with Reduced Complexity VDFE Equalizers

Optical transmission technologies optimized for optical network segments sensitive to power consumption and cost, comprise modulation formats with direct detection technologies. Specifically, non-return to zero differential quaternary phase shift keying (NRZ-DQPSK) in deployed fiber plants, combined with high-performance, low-complexity electronic equalizers to compensate residual impairments at the receiver end, can be proved as a viable solution for high-performance, high-capacity optical links. Joint processing of the constructive and the destructive signals at the single-ended DQPSK receiver provides improved performance compared to the balanced configuration, however, at the expense of higher hardware requirements, a fact that may not be neglected especially in the case of high-speed optical links. To overcome this bottleneck, the use of partially joint constructive/destructive DQPSK equalization is investigated in this paper. Symbol-by-symbol equalization is performed by means of Volterra decision feedback-type equalizers, driven by a reduced subset of signals selected from the constructive and the destructive ports of the optical detectors. The proposed approach offers a low-complexity alternative for electronic equalization, without sacrificing much of the performance compared to the fully-deployed counterpart. The efficiency of the proposed equalizers is demonstrated by means of computer simulation in a typical optical transmission scenario.

Noncoherent detection of DQPSK in OFDM systems using predictive VA

Noncoherent detection of differential quaternary phase shift keying (DQPSK) signals in OFDM systems is efficiently implemented using a predictive Viterbi algorithm (VA) operating on a trellis with just ST = MP−1 states instead of MP states, where M denotes an M-ary PSK constellation and P denotes the order of the prediction filter. The prediction filter coefficients are generated based on the channel DFT alone making a high SNR approximation, since the estimation of the noise-variance using training symbols results in loss of throughput.

32 channel DQPSK DWDM-PON for local area network using dispersion compensation fiber

In the contest to improving optical channel rates in dense wavelength multiplexing (DWDM) service to realize 40Gb/s, different adjustment and coherent detection plans are being investigated. In this paper, we present differential quaternary phase-shift keying (DQPSK) balance for the arrangement of a 32-channel DWDM in a Local Area Network (LAN).

Concise SER Analysis of Differential Quaternary Phase Shift Keying with Gray Coding Over Composite Multipath Shadowing Channels

To effectively assess the symbol error rate (SER) performance achieved by π/4 differential quaternary phase shift keying (π/4-DQPSK) with Gray coding over Rician-Nakagami fading channels, a simple closed-form asymptotic SER formula is derived, which is much simpler than the existing exact SER expression. From the proposed simple closed-form formula, we can obtain some useful insights into the achievable error rate performance for the DQPSK modulation with Gray coding for various channel conditions in the high signal-to-noise ratio (SNR) regions.

Mitigation of Fiber Nonlinearity Effects in Ultra High-Dense WDM System by Using Fractional Fourier Transform for 32 Channel System

The optical signal is severely degraded when transmitted in the fiber due to both the linear and nonlinear distortions. It is well known that, the linear distortions in single mode fiber include chromatic dispersion (CD) and polarization-mode dispersion (PMD) while self-phase modulation (SPM), cross phase modulation (XPM) and four-wave mixing (FWM) are considered the most among nonlinear distortions. A method called Fractional Fourier Transform (FRFT) has been applied to mitigate fiber nonlinearity impairments. In this work, 10 Gb/s optical fiber system with five spans, each of length 60 km, for three types of modulation formats (Return-to-Zero Differential Phase Shift Keying (RZ-DPSK), Return-to-Zero Differential Quaternary Phase Shift Keying (RZ-DQPSK) and Carrier-Suppressed Return-to-Zero (CSRZ)), single and multi-channel transmission systems are designed and simulated using “OptiSystem (2011) version 10.0” software package. The BER of thirty two channel systems (channel No.16) at bit rate 10 Gb/s per channel, 300 km link length of CSRZ modulation format with channel spacing of 50 GHz at SNR 10 dB without FRFT is 10-4.6 and 10-6.4 with FRFT. The BER of thirty two channel system (channel No.16) at bit rate 10 Gb/s per channel, 300 km link length of CSRZ modulation format with channel spacing of 25 GHz at SNR 10 dB without FRFT is 10- 2.56 and 10-3.24 with FRFT.

Performance Analysis of DWDM System for Different Modulation Schemes Using Variations in Channel Spacing

AbstractThis paper reflects the analytical study of dense wavelength division multiplexed optical network with different number of channels at various channel spacing in order to achieve higher data rates by means of few advanced modulation schemes. Bit error rate and quality factor are being analyzed with the variation in number of channels, channel spacing and transmission length of fiber. Advanced modulation schemes being compared here are carrier suppressed return to zero (CSRZ), duobinary return to zero (DRZ), modified duobinary return to zero (MDRZ), 33 % differential phase shift keying (33 % DPSK), 66 % DPSK and differential quaternary phase shift keying (DQPSK). It is keenly observed that CSRZ scheme with 100 GHz channel spacing serves best performance in terms of max. Q factor, min. BER and maximum transmission coverage upto 4,000 km for 16 and 32 channels DWDM system since CSRZ is high tolerant to nonlinear effects. On the other hand, MDRZ scheme with 75 GHz channel spacing exhibits transmission coverage upto 4,000 km and 4,500 km for 16 and 32 channels respectively, but with degraded signal due to effect of inter symbol interference (ISI).

High SNR BER Comparison of Coherent and Differentially Coherent Modulation Schemes in Lognormal Fading Channels

Using an auxiliary random variable technique, we prove that binary differential phase-shift keying and binary phase-shift keying have the same asymptotic bit-error rate performance in lognormal fading channels. We also show that differential quaternary phase-shift keying is exactly 2.32 dB worse than quaternary phase-shift keying over the lognormal fading channels in high signal-to-noise ratio regimes.

Common-Channel Optical Physical-Layer Network Coding

We propose and experimentally demonstrate a coherent optical physical-layer network coding scheme on polarization-multiplexed differential quaternary phase-shift keying (PM-DQPSK) signals, in which the two PM-DQPSK signal components in the network-coded signal occupy the same channel and cannot be separated by conventional means of demultiplexing. In the scheme, network coding at intermediate nodes is realized by combining the two PM-DQPSK signals with a coupler. For network decoding at terminal nodes, one of the signal components is reconstructed and subtracted from the network-coded signal to obtain the other signal component. From its known bit sequence, waveform reconstruction of the signal to be subtracted is implemented by a lookup table. Carrier phase estimation for the reconstructed waveform utilizes the property that DQPSK signals have constant modulus at the sampling point. Experimental results show that, for 12-GBd PM-DQPSK signals, network decoding at a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> can be achieved, with 2.1-dB optical signal-to-noise ratio penalty relative to back-to-back transmission.

Design of adaptive dispersion compensation and demodulation system for 40 Gbps RZ-DQPSK optical fiber communication receivers

An adaptive terminal dispersion compensation and demodulation scheme based on dual-feedback strategy for 40Gbps return-to-zero differential quaternary phase shift keying (RZ-DQPSK) fiber communication receivers is proposed to achieve high reliability receiving performances. In the receiving system introduced in this paper we utilize both the balanced receiver feedback and framer error rate to achieve accurate RZ-DQPSK optical signal demodulation and adaptive dispersion compensation. Compared to traditional RZ-DQPSK receivers, the proposed design combines the chromatic dispersion (CD) compensation and Mach-Zehnder interferometer (MZI) adjusting and automatically estimates the dispersion compensation parameters without human intervention. And another improvement is introducing the framer error rate as feedback quantity to ensure the accuracy of CD and MZI adjusting. Finally, we present the performance of the designed receiver by showing the simulations and experiment results in actual telecommunication engineering projects.

Transmission Performance Comparison of Direction Detection-Based 100-Gb/s Modulation Formats for Metro Area Optical Networks

Transmission performances of direct detection-based 100-Gb/s modulation formats are investigated and compared for metro area optical networks. The effects of optical signal-to-noise ratio sensitivity, chromatic dispersion, cross-channel nonlinearity, and transmission distance on the performance of differential 8-ary phase-shift keying (D8PSK), differential phase-shift keying plus three-level amplitude-shift keying (DPSK+3ASK), and dual-carrier differential quaternary phase-shift keying (DC-DQPSK) are evaluated. The performance of coherent dual-polarization quadrature phase-shift keying (DP-QPSK) with block phase estimation and coherent DP-QPSK with digital differential detection are also presented for reference. According to our analysis, all three direct detection modulation formats could transmit a 100-Gb/s signal over several hundred kilometers of a single-mode fiber link. The results also show that DC-DQPSK outperforms D8PSK and DPSK+3ASK, and the performance of DC-DQPSK is comparable to that of coherent DP-QPSK with digital differential detection. The maximum transmission distance of DC-DQPSK is over 1,000 km, which is enough distance for metro applications.

Series solutions for π/4-DQPSK BER with MRC

Simple series expressions for bit error rate (BER) of π/4 shifted differential quaternary phase-shift keying (π/4-DQPSK) over some common fading environments (Rayleigh, Rician and Nakagami-m) are derived. Both single- and multi-channel reception scenarios are considered. In case of multi-antenna reception, it is assumed that the fading is independent and identically distributed (IID), and the receiver follows optimum maximal ratio combining (MRC). The derived expressions, computed through probability density function (PDF)-based approach, give an exact match with moment-generating function (MGF)-based solutions but get rid of numerical integrations involved in MGF approach. Further, the analytical results presented in this article consist of finite or rapidly converging infinite series and thus a trade-off between precision and complexity can be easily realised by choosing a specific number of terms. Bounds on the error resulting from truncation of the infinite series are also derived. Moreover, it was shown that the series solutions, when reasonably truncated, still provide better approximations than the previous attempts.

Quantum-Dash Mode-Locked Laser as a Source for 56-Gb/s DQPSK Modulation in WDM Multicast Applications

We investigate wavelength tunable 56-Gb/s differential quaternary phase-shift keying (DQPSK) systems using comb generation in a quantum-dash mode-locked laser for wavelength-division-multiple access (WDM)-based broadcast application. We present relative intensity noise and bit-error-rate measurements for each mode. We demonstrate error-free operation over nine WDM channels with 100-GHz spacing.

Analytical Performance Evaluation of Space Time Coded MIMO OFDM Systems Impaired by Fading and Timing Jitter

An analytical approach is presented to determine the impact of time selective fading, timing jitter and additive white Gaussian noise (AWGN) on the bit error rate (BER) performance of an orthogonal frequency- division multiplexing (OFDM) system with differential quaternary phase-shift keying (DQPSK), differential phase- shift keying (DPSK) and quaternary phase-shift keying (QPSK) modulation. The expression for the conditional BER conditioned on a given timing error and fading, is derived and the average BER is evaluated. The BER performance results are evaluated for different values of fading and jitter. The performance of the OFDM system in Rayleigh and Rician fading channels is also compared. Analytical approach is also developed to evaluate the BER performance of a quasi-orthogonal- space-time block coded OFDM system having multiple transmitting and single receiving antennas. The analysis is extended for a multiple- input multiple-output (MIMO)-OFDM system using the selection method for combining multiple receiving antennas, which offers significant improvement in the system performance. The effects of increase in number of OFDM subcarriers and increase in Doppler frequency are also investigated.

Intersymbol interference in DQPSK fibre‐optic systems

AbstractThe limited bandwidth of high‐speed transmitter and receiver hardware gives rise to intersymbol interference (ISI) in digital communication systems. The influence of such ISI is investigated in a low‐complexity fibre‐optical setting, using differential quaternary phase‐shift keying (DQPSK) modulation. The ISI is approximated by a memoryless, stochastic model, for use in applications where neither equalisation nor sequence detection can be afforded. The channel capacity of this model is calculated and shown to depend strongly on the transmitter calibration. More than 3dB is gained, at a target bit error rate (BER) of 10−6, by allowing the transmitted phase levels to deviate from their nominal multiples of π/2 by up to 7%. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.