Quaternary Phase-shift Keying Research Articles

Theoretical and Experimental Optimum System Design for LTE-RoF Over Varying Transmission Span and Identification of System Nonlinear Limit

This paper proposes an optimum radio-over-fiber (RoF) system design to extend the coverage of the third-generation partnership program (3GPP) long-term evolution (LTE) base station, i.e., eNodeB. The system is theoretically and experimentally demonstrated as the high-speed interface between eNodeB and a relay node. The LTE signals under test comprise three different modulation schemes, namely, quaternary phase-shift keying (QPSK), 16-quadratic-amplitude modulation (QAM), and 64-QAM, which are modulated onto orthogonal frequency-division multiplexing (OFDM) at 2.6 GHz. The RoF system design is based on the distributed feedback (DFB) laser direct modulation and direct detection receiver. The spurious-free dynamic range (SFDR) considering the third-order intermodulation analysis of the DFB laser achieved 1.93-dB dynamic range gain to improve the modulation efficiency. The practical investigation reveals three distinctive optical power transmission regions, namely, linear, intermixing, and nonlinear regions. The QPSK, 16-QAM, and 64-QAM systems in the intermixing region achieved error vector magnitudes (EVMs) of $\sim$ 1.144%, $\sim$ 1.2%, and $\sim$ 1.21%, respectively, for 10-km transmission, whereas at 60 km, the achieved EVMs are $\sim$ 5.86%, $\sim$ 5.96%, and $\sim$ 6.01%, respectively. The intermixing region for the 10–60-km transmission span achieved the most optimized EVM and within the 3GPP LTE limit of 8%. Additionally, we also demonstrate that nonlinear distortion proportionally increases with linear distortion as the transmission span increases.

A complex-weighted, decision-aided, maximum-likelihood carrier phase and frequency-offset estimation algorithm for coherent optical detection

We present a symbol-by-symbol coherent optical receiver, which employs a novel, complex-weighted, decision-aided, maximum-likelihood (CW-DA-ML) carrier phase and frequency offset estimator. The CW-DA-ML carrier estimator uses a CW transversal filter to generate a carrier reference phasor, and the filter weights are automatically adapted on-line by linear regression on the observed signals. A complete modulo-R reduced frequency offset estimation (FOE) range of ± R/2 is achieved, independent of modulation format, where R is the symbol rate. Carrier phase and frequency tracking is achieved rapidly. The acquisition speed of frequency offset in quaternary phase-shift keying (4-PSK) signals is more than 5 times faster than that of differential FOE. A constant penalty of approximately 1 dB at bit-error rate of 10(-4) is demonstrated for all frequency offsets in 4-PSK signals with laser-linewidth-symbol-duration product of 8 × 10(-5).

Bandwidth-Scalable Long-Haul Transmission Using Synchronized Colorless Transceivers and Efficient Wavelength-Selective Switches

We propose a modular scalable long-haul architecture supporting variable-bandwidth channels with bit rates from 100 Gbit/s to beyond 1 Tbit/s. Colorless transceivers have two operating modes. One transceiver can transmit/receive a conventional narrow-band channel occupying a 30-GHz bandwidth and conveying 100 Gbit/s, or a set of M transceivers can cooperate to transmit/receive a wideband channel occupying an M 50-GHz bandwidth and conveying roughly 160 Gbit/s per 50 GHz (assuming polarization-multiplexed quaternary phase-shift keying). A colorless wavelength-selective switch supports two modes of add/drop (or (de)multiplexing) operation. It can add/drop narrow-band channels (each from/to one port) with minimal loss, or can add/drop wideband channels (each from/to M ports) without spectral gaps, with an additional loss not exceeding 1/3 (-4.8 dB), independent of M. Transceivers can use either single-carrier modulation or orthogonal frequency-division multiplexing (OFDM). We analyze and simulate OFDM-based systems to determine key design requirements, especially for synchronization of cooperating transceivers. A representative design achieves 1520-km reach with 1.4-dB margin in a dispersion-managed network using only erbium-doped fiber amplifiers, improving average spectral efficiency from about 2 to nearly 3 bits/s/Hz.

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

Vector Precoding for Gaussian MIMO Broadcast Channels: Impact of Replica Symmetry Breaking

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

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.

Performance Analysis of Linear and Non-Linear Equalizer in Rician Channel

In this paper, equalization algorithms applying soft–decision feedback, designed for quaternary phase–shift keying (QPSK) and 8PSK (phase–shift keying) transmission are introduced. The method employed is a minimum mean– squared error (MMSE) in which each iteration is done in order to refine the data estimates. The rule for generating soft decisions is adapted continuously to the current state of the algorithm. We show that standard Decision Feedback Equalization (DFE-Non linear Equaliser) methods are clearly outperformed the minimum mean–squared error (MMSE linear Equaliser). We use the MATLAB to show that the MMSE-DFE provide better performance with the increasing value of SNR in scattering environment.

Blind detection of M-ary quaternary phase shift keying signals by a complex Hopfield neural network with amplitude-phase-type hard-multistate-activation-function

Considering the disadvantage of the algorithms based on statistics, a novel algorithm based on complex Hopfield neural network with amplitude-phase-type hard-multistate-activation-function (CHNN-APHM) is proposed to detect M-ary quaternary phase shift keying (MPSK) signals blindly. An amplitude-phase-type hard-multistate-activation-function is constructed. The stabilities of the CHNN-APHM with asynchronous and synchronous operating mode are also analyzed separately. While the weighted matrix of CHNN-APHM is constructed by the complementary projection operator of received signals, the problem of quadratic optimization with integer constraints can be successfully solved with the CHNN-APHM, and the MPSK signals are blindly detected. Simulation results show that the algorithm reaches the real equilibrium points with shorter received signals and if is applicable for channel with common zeros.

Experimental demonstration of flexible bandwidth networking with real-time impairment awareness

We demonstrate a flexible-bandwidth network testbed with a real-time, adaptive control plane that adjusts modulation format and spectrum-positioning to maintain quality of service (QoS) and high spectral efficiency. Here, low-speed supervisory channels and field-programmable gate arrays (FPGAs) enabled real-time impairment detection of high-speed flexible bandwidth channels (flexpaths). Using premeasured correlation data between the supervisory channel quality of transmission (QoT) and flexpath QoT, the control plane adapted flexpath spectral efficiency and spectral location based on link quality. Experimental demonstrations show a back-to-back link with a 360-Gb/s flexpath in which the control plane adapts to varying link optical signal to noise ratio (OSNR) by adjusting the flexpath's spectral efficiency (i.e., changing the flexpath modulation format) between binary phase-shift keying (BPSK), quaternary phase-shift keying (QPSK), and eight phase-shift keying (8PSK). This enables maintaining the data rate while using only the minimum necessary bandwidth and extending the OSNR range over which the bit error rate in the flexpath meets the quality of service (QoS) requirement (e.g. the forward error correction (FEC) limit). Further experimental demonstrations with two flexpaths show a control plane adapting to changes in OSNR on one link by changing the modulation format of the affected flexpath (220 Gb/s), and adjusting the spectral location of the other flexpath (120 Gb/s) to maintain a defragmented spectrum.

Frequency-Domain Turbo Equalization with Soft Successive Interference Cancellation for Single Carrier MIMO Underwater Acoustic Communications

This paper proposes a low-complexity frequency-domain turbo equalizer (FDTE) combined with phase rotation compensation and soft successive interference cancellation (SSIC) for single carrier multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. Different from existing time-domain turbo equalizers in MIMO UWA systems, the proposed receiver implements low-complexity turbo equalization in the frequency domain to combat severe inter-symbol interference (ISI) and employs a layered structure to cope with unbalanced MIMO channels. Soft, rather than hard, successive interference cancellation (SIC) is employed in the layered iterative turbo detection to alleviate co-channel interference (CCI), and phase compensation is utilized within the layered FDTE to mitigate phase rotation. The proposed scheme was evaluated by the SPACE08 experiment conducted in a shallow area of the Atlantic Ocean in October 2008. The 2-transducer 12-hydrophone MIMO system communicated with quaternary phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulation schemes over 200 m and 1000 m ranges, where the proposed FDTE-SSIC scheme achieved low bit error rates (BERs) with only a few iterations. Simulation results also demonstrated that the proposed FDTE-SSIC receiver provided lower BER than one-layer FDTE receivers with comparable complexity.

Nonlinear Effects in Mode-Division-Multiplexed Transmission Over Few-Mode Optical Fiber

Focusing on the essential parameters concerning nonlinear effects between two spatial modes, we give a general estimation of the nonlinear performance in a wavelength-division-multiplexed (WDM) mode-division-multiplexed (MDM) polarization-division-multiplexed (PDM) quaternary phase-shift keying (QPSK) 100-Gb/s coherent transmission system.

Position-based diversity transmission scheme employing optical wireless communication

We propose a position-based diversity transmission scheme for indoor optical wireless communication. In our scheme, the I (in-phase) and Q (Quadrature) signal of QPSK (quaternary phase-shift keying) modulation are transmitted separately to obtain a secure position-based transmission. We analyze probability of error with different mode numbers of the radiation lobe of Lambertian source, and position of the transmitters to attain single or multiple secure area(s). To obtain different secured areas, TDMA (time-division multiple access) with adaptive transmitted power for each time slot is applied. According to analytical results, the signal can be demodulated correctly only in the specific area and high-level security for optical wireless communication systems can then be achieved. In our scheme, the probability that the intruders can get the correct signal is decreased 90%, compared to conventional QPSK.

Influence of imperfect cophasing on performance of EGC receiver of BPSK and QPSK signals transmitted over Weibull fading channel

This paper presents an analysis of maximum ratio combining (MRC) receiver of quaternary phase-shift keying (QPSK) signals transmitted over a Weibull fading channel. We determine the influence of imperfect cophasing and branches unbalance on bit error rate dependence on average signal-to-noise ratio. The performance dependence on diversity order and fading severity is also observed. Keywords — Cophasing, Diversity systems, Error probability, Fading. I. INTRODUCTION N order to reduce the influence of multipath fading on signal detection, it is possible to use spatially separated receiver antennas at the reception and to combine the signals from different branches of the receiver in a certain manner. The optimal combining technique is maximum ratio combining (MRC). This combining technique involves cophasing of the useful signal in all branches, multiplication of the received signal in each branch by the estimated envelope of that particular signal and summing of the received signals from all antennas (1). By cophasing, all the random phase fluctuations of the signal that emerged during the transmission are eliminated. For this process it is necessary to estimate the phase of the received signal. This phase estimation can be performed from the modulated or unmodulated received signal carrier. In previous papers concerning this matter the assumptions of the ideal phase estimation of the incoming signal were mainly used (2), (3). Only in (4) and (5) the influence of the imperfect phase estimation was examined and that was in the case of the equal gain combining (EGC) in the receiver. In paper (4), the influence of the phase error on the error probability in the case of digital binary (BPSK) and quaternary phase-shift keying (QPSK) signal detection was observed. This error probability was calculated applying the Gram-Charlier expansion. The analysis is performed under the assumption of the uncorrelated Rayleigh fading at receiving antennas. In paper (5) closed-form expressions for outage probability and error probability during the BPSK and QPSK signal detection over the Nakagami-m fading channel were obtained. Dual branch EGC technique was applied. In both papers the analysis of the system was done under the assumption that the branches of the receiver are balanced. However, as it is well-known (6), it is very rare to meet in practice the identical propagation paths in each branch. Also, the electrical components in different branches of the receiver are not ideal. Thus, it is also of interest to consider the influence of the branch unbalance in the receiver on system performances. In this paper an analysis of QPSK signal reception is presented. The signal is transmitted over the Weibull fading channel and MRC technique is applied in the receiver, while the receiving branches are assumed unbalanced. The phase estimation is performed from the unmodulated carrier and is not ideal. The difference between the phase of the incoming signal and the estimated phase for that signal is a statistical process and it follows the Tikhonov distribution (4), (5), (7). It is shown in which measure the imperfect phase estimation affects the bit-error rate (BER).

Blind adaptive equalization of polarization-switched QPSK modulation

Coherent detection in combination with digital signal processing has recently enabled significant progress in the capacity of optical communications systems. This improvement has enabled detection of optimum constellations for optical signals in four dimensions. In this paper, we propose and investigate an algorithm for the blind adaptive equalization of one such modulation format: polarization-switched quaternary phase shift keying (PS-QPSK). The proposed algorithm, which includes both blind initialization and adaptation of the equalizer, is found to be insensitive to the input polarization state and demonstrates highly robust convergence in the presence of PDL, DGD and polarization rotation.

Bandwidth scalable, coherent transmitter based on the parallel synthesis of multiple spectral slices using optical arbitrary waveform generation

We demonstrate an optical transmitter based on dynamic optical arbitrary waveform generation (OAWG) which is capable of creating high-bandwidth (THz) data waveforms in any modulation format using the parallel synthesis of multiple coherent spectral slices. As an initial demonstration, the transmitter uses only 5.5 GHz of electrical bandwidth and two 10-GHz-wide spectral slices to create 100-ns duration, 20-GHz optical waveforms in various modulation formats including differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK), and eight phase-shift keying (8PSK) with only changes in software. The experimentally generated waveforms showed clear eye openings and separated constellation points when measured using a real-time digital coherent receiver. Bit-error-rate (BER) performance analysis resulted in a BER < 9.8 × 10(-6) for DPSK and QPSK waveforms. Additionally, we experimentally demonstrate three-slice, 4-ns long waveforms that highlight the bandwidth scalable nature of the optical transmitter. The various generated waveforms show that the key transmitter properties (i.e., packet length, modulation format, data rate, and modulation filter shape) are software definable, and that the optical transmitter is capable of acting as a flexible bandwidth transmitter.

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.

Compensation of Frequency Offset for 16-QAM Optical Coherent Systems using QPSK Partitioning

The performance of a feed-forward carrier frequency recovery algorithm for 16-quadrature amplitude modulation (QAM) optical coherent systems is investigated using the quaternary phase-shift keying (QPSK) partition scheme. The frequency estimation technique, which employs only a subset of the 16-QAM symbols with the QPSK partition, is demonstrated to be effective when applied prior to the carrier phase recovery. Frequency offset of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> times the symbol rate is shown to be tolerable at a bit-error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> with combined linewidths symbol duration products of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> .

Adaptive Chromatic Dispersion Compensation for Coherent Communication Systems Using Delay-Tap Sampling Technique

A fast and low-complexity adaptive chromatic dispersion (CD) compensation algorithm based on delay-tap sampling technique for optical coherent systems is proposed. By generating a delay-tap plot from the signal powers after an adaptive CD equalizer, a parameter can be extracted from the delay-tap plot which can be used to estimate CD accurately. Simulation results for coherent polarization-division-multiplexed (PDM) quaternary phase-shift keying (QPSK) as well as 16-quadrature amplitude modulation (QAM) systems with various pulse shapes demonstrate that high CD estimation accuracies using relatively few data symbols can be achieved in presence of other transmission impairments.

Impact of Transmitter Bandwidth on Transmission Performance of Coherent 112-Gb/s PDM-QPSK Systems

We investigate the impact of the transmitter bandwidth on the nonlinear tolerance in a 112-Gb/s polarization-division-multiplexed quaternary phase-shift keying system with coherent detection over a 1200-km dispersion-managed link using standard single-mode fiber. We show that a narrower transmitter bandwidth degrades not only the noise tolerance, but also exacerbates signal degradations due to nonlinearities both in single channel and in wavelength-division-multiplexed configuration. A nonlinear threshold difference of approximately 1 dB is observed.