Showing papers on "Continuous phase modulation published in 2016"

Modulation Techniques for Li-Fi

Abstract: Modulation techniques for light fidelity(Li-Fi) are reviewed in this paper.Li-Fi is the fully networked solution for multiple users that combines communication and illumination simultaneously.Light emitting diodes(LEDs) are used in Li-Fi as visible light transmitters,therefore,only intensity modulated direct detected modulation techniques can be achieved.Single carrier modulation techniques are straightforward to be used in Li-Fi,however,computationally complex equalization processes are required in frequency selective Li-Fi channels.On the other hand,multicarrier modulation techniques offer a viable solution for Li-Fi in terms of power,spectral and computational efficiency.In particular,orthogonal frequency division multiplexing(OFDM) based modulation techniques offer a practical solution for Li-Fi,especially when direct current(DC) wander,and adaptive bit and power loading techniques are considered.Li-Fi modulation techniques need to also satisfy illumination requirements.Flickering avoidance and dimming control are considered in the variant modulation techniques presented.This paper surveys the suitable modulation techniques for Li-Fi including those which explore time,frequency and colour domains.

Time-Varying Frequency-Modulated Component Extraction Based on Parameterized Demodulation and Singular Value Decomposition

Abstract: To analyze the valuable frequency component for time-varying frequency-modulated (FM) signals, component extraction is necessary in most applications. Considering the advantage of parameterized demodulation (PD) in transforming FM signals to be stationary, a novel component extraction method based on PD and singular value decomposition (PD-SVD) for both monocomponent and multicomponent signals is proposed. By extending the idea of PD, the time-varying term of the continuous phase function for the interested FM component can be removed, thus resulting in a highly self-correlated component with constant phase. Then, the extraction of the target component from noise or other components can be realized by SVD. Compared with the existing methods, the proposed algorithm is able to analyze the multicomponent signal with crossed instantaneous frequency trajectories and effectively improve the signal-to-noise ratio of the extracted component. The effectiveness of the proposed method is demonstrated by applying it on several numerical signals and the radial vibration signal of a hydroturbine rotor, indicating the potential of analyzing many practical FM signals.

Digital Signal Processing for Dual-Polarization Intensity and Interpolarization Phase Modulation Formats Using Stokes Detection

Abstract: We study and compare two digital signal processing (DSP) approaches to recover the intensity on two orthogonal polarizations and the interpolarization phase modulation using a Stokes-vector direct detection receiver. We focus on higher order modulation of each of the three degrees of freedom allowed in Stokes-vector detection. 2 bits are encoded on each intensity of the two orthogonal polarizations, and 2 bits are encoded in the phase difference between the two polarizations, giving a 6 bits per symbol format. In this study, we propose a novel three-stage DSP algorithm and we compare this new algorithm with our earlier two-stage algorithm using the following metrics: the computational complexity and the bit error rate (BER) performance. Using the three stage approach, waveform filtering and derotation are applied in series rather than in parallel as was done in the two stage algorithm. We show that the three-stage approach exhibits equal BER performance, while significantly reducing the total required number of real additions and real multiplications. Moreover, tracking the state of polarization using the proposed method is m -times more efficient, where m is the number of taps in the first filtering stage.

Sequential quasi-convex-based algorithm for waveform design in colocated multiple-input multiple-output radars

Abstract: This study considers the problem of waveform design for colocated multiple-input multiple-output (MIMO) radars for multiple targets in the presence of multiple interferences in white Gaussian noise. Here, the authors jointly design the transmit waveform and receive beamforming by a sequential algorithm. The proposed sequential algorithm maximises the minimum signal-to-interference-plus-noise ratio (SINR) to design both continuous and finite alphabet phase waveforms. In the case of continuous phase, all phases can be chosen in the waveform space, while in finite alphabet case, phases are only chosen from a confine set. Two important practical constraints of ‘constant envelope’ and ‘similarity’ are considered as well. The authors also have converted the waveform design problem into a quasi-convex optimisation problem which can be effectively solved by using convex optimisation toolbox (CVX). They have evaluated the performance of the matched filter output, beampattern and peak-to-average power ratio via numerical simulations and shown that the proposed sequential method achieves better SINR performance compared with existing MIMO radar transmit waveform design methods, for both single and multiple target scenarios.

Continuous) Phase Modulation on the Hypersphere

Abstract: We introduce phase modulation on the hypersphere (PMH) for load-modulated multiple-input multiple-output (MIMO) transmitters with a single central power amplifier. In PMH, the peak to average ratio of the sum power before pulse shaping is 1; thus, the central power amplifier of load-modulated MIMO transmitters does not require any back-off. We derive the capacity of PMH on an additive white Gaussian noise channel and show that the input signal should be uniformly distributed on a hypersphere. The mutual information of uniformly distributed PMH input is derived in an uplink multiple-access independent identically distributed Gaussian MIMO channel using the replica method from statistical physics. Furthermore, discrete PMH is introduced using spherical codes and also generalizing minimum shift keying from the complex unit circle to the hypersphere. We investigate different pulse shaping methods for PMH including a novel spherical filtering. Using spherical pulse shaping, the signal stays on the hypersphere. Various filters are investigated, and a tradeoff between spectral shape and peak-to-average-sum-power ratio (PASPR) is found. For as few as four antennas, good spectral properties (similar to root-raised cosine pulses) can be achieved at very low PASPR. Both former and latter further improve with increasing the number of antennas.

Hybrid Maximum Likelihood Modulation Classification for Continuous Phase Modulations

Abstract: In this letter, we propose a hybrid maximum likelihood (HML) classifier for continuous phase modulation (CPM). To the best of our knowledge, the proposed likelihood function is the first one for CPM signals that is based on two of its main features: nonlinear waveform, which is represented with its principal components, and signal memory, which is modeled as a Markov mapping symbol sequence. Unknown channel parameters are estimated through the expectation-maximization (EM) algorithm. An approximation method is further proposed to ensure that the proposed classifier improves classification performance at the cost of a moderate increase in calculations. Numerical results prove the superiority of the proposed approach over the classical HML classifier and feature-based classifier in terms of classifying CPM and linear modulation.

Continuously Phase-Modulated Standing Surface Acoustic Waves for Separation of Particles and Cells in Microfluidic Channels Containing Multiple Pressure Nodes

Abstract: This paper describes continuously phase-modulated standing surface acoustic waves (CPM-SSAW) and its application for particle separation in multiple pressure nodes. A linear change of phase in CPM-SSAW applies a force to particles whose magnitude depends on their size and contrast factors. During continuous phase modulation, we demonstrate that particles with the target dimension are translated in the direction of moving pressure nodes, whereas smaller particles show oscillatory movements. The rate of phase modulation is optimized for separation of target particles from the relationship between mean particle velocity and period of oscillation. The developed technique is applied to separate particles of the target dimension from the particle mixture. Furthermore, we also demonstrate human keratinocyte cells can be separated in the cell and bead mixture. The separation technique is incorporated with a microfluidic channel spanning multiple pressure nodes, which is advantageous over separation in a single pressure node in terms of high throughput.

Experimental demonstration of deep frequency modulation interferometry.

Abstract: Experiments for space and ground-based gravitational wave detectors often require a large dynamic range interferometric position readout of test masses with 1 pm/√Hz precision over long time scales. Heterodyne interferometer schemes that achieve such precisions are available, but they require complex optical set-ups, limiting their scalability for multiple channels. This article presents the first experimental results on deep frequency modulation interferometry, a new technique that combines sinusoidal laser frequency modulation in unequal arm length interferometers with a non-linear fit algorithm. We have tested the technique in a Michelson and a Mach-Zehnder Interferometer topology, respectively, demonstrated continuous phase tracking of a moving mirror and achieved a performance equivalent to a displacement sensitivity of 250 pm/Hz at 1 mHz between the phase measurements of two photodetectors monitoring the same optical signal. By performing time series fitting of the extracted interference signals, we measured that the linearity of the laser frequency modulation is on the order of 2% for the laser source used.

Short baseline GPS multi-frequency single-epoch precise positioning: utilizing a new carrier phase combination method

Abstract: Traditional carrier phase combinations are linear functions of the original carrier phases. We develop a new way of carrier phase combination that regards carrier phases of different frequencies as the basis of the carrier phase space. The combined carrier phase is a point of this space. Then, this point, i.e., the combined carrier phase, is mapped back to a single-dimensional carrier phase by a bidirectional mapping. The new single-dimensional carrier phase is called mapped carrier phase. The advantages of this combination approach are a long wavelength and small noise of the mapped carrier phase, which make ambiguity resolution easy. Unfortunately, the mapped carrier phase value is not well determined due to the noise in the observed phases. On the contrary, a set of possible mapped carrier phase values are attained; however, only one value is correct. To reduce the number of candidates and fix the correct value of the mapped carrier phase, the following steps are discussed: (1) The integer nature of the original carrier ambiguity is used to attain an initial set of possible mapped carrier phase values; (2) the distribution of the mapped carrier phase ambiguity is included to reduce the possible values; and (3) the Gaussian least-squares objective function is introduced to fix the correct value. As a result of these steps, a single-epoch positioning algorithm is established. Two experiments are carried out to preliminarily compare the new algorithm with LAMBDA. The results show that the new algorithm is slightly below LAMBDA in resolution success rate, but computationally more efficient than LAMBDA.

Application of SOI microring coupling modulation in microwave photonic phase shifters

Abstract: Phase shifter is one of the key devices in microwave photonics. We report a silicon microring resonator with coupling modulation to realize microwave phase shift. With coupling tuning of the Mach-Zehnder interferometer (MZI) coupler to change the resonator from under-coupling to over-coupling, the device can realize a π phase shift on the incoming microwave signal with a frequency up to 25 GHz. The device can also realize 2.5π continuous phase tuning by manipulating the three DC bias voltages applied on the MZI coupler.

Algebraic Phase Unwrapping Based on Two-Dimensional Spline Smoothing Over Triangles

Abstract: Two-dimensional (2D) phase unwrapping is an estimation problem of a continuous phase function, over a 2D domain, from its wrapped samples. In this paper, we propose a novel approach for high-resolution 2D phase unwrapping. In the first step—SPline Smoothing (SPS), we construct a pair of the smoothest spline functions which minimize the energies of their local changes while interpolating, respectively, the cosine and the sine of given wrapped samples. If these functions have no common zero over the domain, the proposed estimate of the continuous phase function can be obtained by algebraic phase unwrapping in the second step—Algebraic Phase Unwrapping (APU). To avoid the occurrence of common zeros in SPS due to phase noise in the observed wrapped samples, we also propose a denoising step—Denoising by Selective Smoothing (DSS)—as preprocessing, which selectively smooths unreliable wrapped samples by using convex optimization. The smoothness of the proposed unwrapped phase function is guaranteed globally over the domain without losing any desired consistency with all reliable wrapped samples. Numerical experiments for terrain height estimation demonstrate the effectiveness of the proposed 2D phase unwrapping scheme.

Low-Complexity Detection of Binary CPM With Small Modulation Index

Abstract: Binary continuous phase modulation (CPM) with modulation index $h = 0.5$ can be approximated by a linear modulation, which leads to a low-complexity serial receiver. By reconstructing CPM signals generated with a small modulation index into equivalent CPM signals with modulation index $h = 0.5$ , a low-complexity detector (LCD) for binary CPM with small modulation index is proposed. The complexity of the resulting detector is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. In addition, the detector can generate appropriate metrics for the soft decision decoding, which is desirable in a coded CPM system.

Evaluation of Waveforms for Mobile Radio Communications above 6 GHz

Abstract: This paper provides a high level comparison of several multi-carrier and single-carrier waveforms based on the evaluations performed in mmMAGIC project. The waveforms are assessed for the performance indicators that are relevant to mobile radio communication above 6 GHz, specially the millimeter wave frequencies. The evaluations are performed in mmMAGIC waveform simulators under common assumptions on carrier frequencies, waveform parameters, channel and impairment models. The evaluation results reveal that OFDM is suitable for above 6 GHz communication. For above ↑30 GHz communication, OFDM with PAPR reduction and DFTS-OFDM are both promising options. Moreover, some potential enhancements to OFDM (use of window/pulse shape, subband filters, unique word, zero tailing), parametrization of FBMC, and constrained envelop continuous phase modulation for above 6 GHz communication have been discussed.

Carrier Phase Estimation in Multi-Subcarrier Coherent Optical Systems

Abstract: In this letter, we analyze three different carrier phase estimation approaches for coherent optical systems based on multi-subcarrier modulation, comparing them in terms of both performance and complexity. Averaging the estimated values on the subcarriers (SCs) significantly increases the laser linewidth tolerance at the expense of additional complexity, while using a single SC for carrier phase estimation yields a complexity reduction without any substantial performance loss with respect to performing a separate phase estimation on all SCs

On frame synchronization in aeronautical telemetry

Abstract: Frame synchronizers, suitable for use with continuous phase modulation (CPM) in the presence of phase and frequency offsets, are derived for periodically inserted preamble bits in continuous-mode transmission. The resulting frame synchronizers involve single or double correlations of the received samples with a local copy of the CPM samples corresponding to the preamble bits. Of particular interest in aeronautical telemetry is shaped offset QPSK, telemetry group version (SOQPSK-TG), with the preamble defined in the integrated network enhanced telemetry (iNET) standard. Two low-complexity versions that leverage the special properties of the iNET preamble and SOQPSK-TG operating at 2 samples/bit are developed. Simulation results show that most frame synchronizers are capable of achieving acceptable performance for Eb/N0 ≥ 0 dB and the maximum frequency offset that can be tolerated increases with Eb/N0 to about 3%of the bit rate.

Design and Performance Analysis of Multiuser CPM With Single User Detection

Abstract: This paper focuses on the design and performance analysis of single user detectable multiuser systems based upon continuous phase modulation. This problem is formulated as a special application of mismatched receiver theory, where a closed-form expression for achievable Euclidean distance can be derived. This expression inspires the constructions of two classes of spectrally efficient multiuser designs: nonorthogonal and orthogonal designs. They are both confirmed to offer strong robustness against nonlinear hardware impairment in downlink and uplink transmissions, but differ in spectral efficiency, complexity and achievable minimum Euclidean distance. Moreover, the proposed designs are able to reduce the convergence threshold in serially concatenated multiuser systems. As a general approach to constructing orthogonal and near-orthogonal signals, the proposed techniques find potential applications in multiantenna systems, and full-duplex communications. Compared with existing continuous phase modulated multiuser designs, the proposed techniques offer improved spectral efficiency and significantly reduced detection complexity.

A Dual Frequency Carrier Phase Error Difference Checking Algorithm for the GNSS Compass

Abstract: The performance of the Global Navigation Satellite System (GNSS) compass is related to the quality of carrier phase measurement. How to process the carrier phase error properly is important to improve the GNSS compass accuracy. In this work, we propose a dual frequency carrier phase error difference checking algorithm for the GNSS compass. The algorithm aims at eliminating large carrier phase error in dual frequency double differenced carrier phase measurement according to the error difference between two frequencies. The advantage of the proposed algorithm is that it does not need additional environment information and has a good performance on multiple large errors compared with previous research. The core of the proposed algorithm is removing the geographical distance from the dual frequency carrier phase measurement, then the carrier phase error is separated and detectable. We generate the Double Differenced Geometry-Free (DDGF) measurement according to the characteristic that the different frequency carrier phase measurements contain the same geometrical distance. Then, we propose the DDGF detection to detect the large carrier phase error difference between two frequencies. The theoretical performance of the proposed DDGF detection is analyzed. An open sky test, a manmade multipath test and an urban vehicle test were carried out to evaluate the performance of the proposed algorithm. The result shows that the proposed DDGF detection is able to detect large error in dual frequency carrier phase measurement by checking the error difference between two frequencies. After the DDGF detection, the accuracy of the baseline vector is improved in the GNSS compass.

Separation of Signals Consisting of Amplitude and Instantaneous Frequency RRC Pulses Using SNR Uniform Training

Abstract: This work presents sample mean and sample variance based features that distinguish continuous phase FSK from QAM and PSK modulations. Root raised cosine pulses are used for signal generation. Support vector machines are employed for signals separation. They are trained for only one value of SNR and used to classify the signals from a wide range of SNR. A priori information about carrier amplitude, carrier phase, carrier offset, roll-off factor and initial symbol phase is relaxed. Effectiveness of the method is tested by observing the joint effects of AWGN, carrier offset, lack of symbol and sampling synchronization, and fast fading.

Over-sampled polyphase code design for physical implementation with spectral and correlation consideration

Abstract: This paper presents an approach for designing continuous phase modulation (CPM) waveform with good spectral compatibility and low correlation properties. The suggested approach is to first design over-sampled polyphase code with stopband and correlation constraint, and then transform the polyphase code into CPM waveform. Applying over-sampling ensures that the resulting CPM waveform would well inherit the spectral and correlation properties from the designed polyphase code. To cope with such over-sampled code optimization, special considerations on both spectral and correlation penalty function are illustrated, and an efficient alternating projection method based on (I)FFT is proposed accordingly. Numeric results validate both the CPM waveform design approach and the over-sampled polyphase code optimization method.

Iterative estimation of phase using complex cepstrum representation

Abstract: This paper presents a method to iteratively estimate phase information from speech in the cepstrum domain. It assumes that correct markings of pitch periods, which may not correspond to glottal closure instants (GCI), are available and can be used to extract the smooth spectral envelope of speech. By using this information, the minimum-phase cepstrum is derived and used as prior information in a modified version of a previously proposed scheme of complex cepstrum analysis based on the mean squared error. Experiments with an emotional database show that the proposed method achieves better performance in terms of continuous phase spectrum estimation, when compared with approaches that rely on accurate GCI markings and high-resolution phase unwrapping mechanisms. In addition, similar results to the full optimization of the complex cepstrum vector are reached, at a lower computational complexity.

Performance analysis of a joint estimator for timing, frequency, and phase with continuous-phase modulation

Abstract: Performance analysis is presented for the joint estimation of symbol timing, frequency offset, and phase offset with continuous-phase modulation. In this study, undesirable influences on parameters to be estimated, which arise from the inaccuracy of the already estimated parameters, are computed mathematically. Based on performance analysis, a conditional Cramer-Rao bound (CRB) is put forward, and a hypothesise is made that phase offset variance with frequency error present should match with the conditional CRB for any digital phase modulation. Moreover, the hypothesis is manifested by analysing the log-likelihood function in a more general mathematical manner. To alleviate the influences, a data-aided acquisition and phase-locked loop tracking algorithm is proposed. The results of Monte Carlo simulations are presented, showing good agreement with theoretical analysis. Simulation results also show that the proposed algorithm can improve performance in terms of phase error variance at the expense of a high signal-to-noise ratio threshold.

Performance of analog and digital modulation schemes under sweep jamming

Abstract: Wireless Communications is used in various applications and the number of wireless devices has also increased over the past several decades. However, wireless communication systems may be significantly affected by interference signal. In this paper, the carrier to noise ratio (CNR) or the bit error rate (BER) performance of Amplitude Modulation (AM), Frequency Modulation (FM), MPSK (M-array Phase Shift Keying), MFSK (M-array Frequency Shift Keying), Minimum Shift Keying (MSK) and Gaussian Minimum Shift Keying (GMSK) have been evaluated under sweep jamming as an intended interference. In addition, we measured the quality of received audio signal by perceptual evaluation of speech quality (PESQ). From the result of performance analysis, we concluded that orthogonal frequency-division multiplexing (OFDM) sweep jamming severely affects power of the transmission signal and chirp sweep jamming provided a strong influence over the phase and frequency of the transmission signal. By using our simulators, it is possible to determine an appropriate modulation scheme according to the channel environment. In addition, we know the parameter of jammer for blocking the unnecessary communications.

Digital Adaptive Carrier Phase Estimation in Multi-Level Phase Shift Keying Coherent Optical Communication Systems

Abstract: The analysis of adaptive carrier phase estimation is investigated in long-haul high speed n-level phase shift keying (n-PSK) optical fiber communication systems based on the one-tap normalized least-mean-square (LMS) algorithm. The close-form expressions for the estimated carrier phase and the bit-error-rate floor have been derived in the n-PSK coherent optical transmission systems. The results show that the one-tap normalized LMS algorithm performs pretty well in the carrier phase estimation, but will be less effective with the increment of modulation levels, in the compensation of both intrinsic laser phase noise and equalization enhanced phase noise.

LTV equalization of CPM signals over doubly-selective aeronautical channels

Abstract: In this paper, transmission of continuous phase modulated (CPM) signals over time- and frequency-selective (i.e., doubly-selective) channels is considered. Leveraging on the well-known Laurent representation for a CPM signal, we design a two-stage receiver, composed of a linear time-varying (LTV) equalizer, followed by a detector: the former one aims at mitigating the channel dispersion and it is synthesized under the zero-forcing (ZF) or minimum mean-square error (MMSE) criterion; the latter one recovers the transmitted symbols from the pseudo-symbols of the Laurent representation in a simple recursive manner. Relying on a Basis Expansion Model (BEM) of the doubly-selective channel, we derive frequency-shift (FRESH) versions of the proposed LTV equalizers, discussing also their complexity issues and proposing simplified implementations. Monte Carlo simulation results, carried out in two typical aeronautical scenarios (arrival/takeoff and en-route), show that the proposed approach is able to work satisfactorily also over rapidly time-varying channels.

Frequency-coded quantum key distribution using amplitude-phase modulation

Abstract: Design principals of universal microwave photonics system for quantum key distribution with frequency coding are concerned. Its concept is based on the possibility of creating the multi-functional units to implement the most commonly used technologies of frequency coding: amplitude, phase and combined amplitude-phase modulation and re-modulation of optical carrier. The characteristics of advanced systems based on classical approaches and prospects of their development using a combination of amplitude modulation and phase commutation are discussed. These are the valuations how to build advanced systems with frequency coding quantum key distribution, including at their symmetric and asymmetric constructions, using of the mechanisms of the photon polarization states passive detection, based on the filters for wavelength division multiplexing of modulated optical carrier side components.

On the Optimization of a PSP-Based CPM Detection

Abstract: This paper deals with a reduced-complexity per survivor processing-based CPM demodulation. It relies on a trellis with reduced state number and defined from a rational modulation index possibly different from the transmit modulation index and referred to as virtual receiver modulation index. The virtual receiver modulation index should be chosen so as to achieve a tradeoff between error-rate performance and complexity reduction. The main purpose of this paper is the choice of the virtual receiver modulation index. It gives guidelines to discard the values of the virtual receiver modulation index, that degrade the error-rate performance. Two criteria are used. The first one considers the uncoded CPM case and is based on an approximation of the minimal Euclidean distance. The second one is related to the bit interleaved coded CPM case and resorts to an EXIT chart to analyze the convergence of the iterative receiver.

Binary CPMs With Improved Spectral Efficiency

Abstract: We design new continuous phase modulation (CPM) formats, which are based on the combination of a proper precoder with binary input and a ternary CPM. The proposed precoder constrains the signal phase evolution in order to increase the minimum Euclidean distance, and to limit the bandwidth expansion due to the use of a ternary CPM. The resulting schemes are highly spectrally efficient and outperform classical binary and quaternary formats in terms of coded and uncoded performance.

Multiplier-Free Carrier Phase Estimation for Optical Coherent Systems

Abstract: A multiplier-free carrier phase estimation (CPE) algorithm is investigated in this letter. The Viterbi and Viterbi (V&V) algorithm is widely used in CPE, because the V&V algorithm is less complex than many other feed-forward CPE algorithms, including the blind phase search algorithm. In the V&V algorithm, an M th power operation is used to remove the modulated data phase. However, one disadvantage of the $M$ th power operation is its large computational complexity. In this letter, we extend our prior simplified M th power method from frequency offset estimation to CPE and propose an improved V&V algorithm, adopting the absolute operation as an approximation and making the V&V algorithm a multiplier-free CPE algorithm. Using simulations, the improved V&V algorithm is compared with the traditional V&V algorithm in the 32-GBd quadrature phase-shift keying, 8PSK, star-8QAM, and square-16QAM systems for CPE. The results show that the improved V&V algorithm outperforms the traditional V&V algorithm. In addition, the complexity is reduced effectively and no multiplier is required.

Passband Digital Transmission

Abstract: There are a host of reasons why modulation may be required, including transmission of digital data over bandpass channels. In the continuous-wave (CW) modulation, the transmission bits are encoded as a variation of the parameters of a sinusoidal signal, called the carrier wave. The focus of this chapter is on digital CW binary and M-ary modulation schemes. Digital passband modulation is based on variation of the amplitude, phase or frequency of the sinusoidal carrier, or some combination of these parameters. This chapter is concerned with a number of digital modulation techniques that have some common characteristics and yet distinct features.

Carrier Phase Estimation for 32-QAM Optical Systems Using Quasi-QPSK-Partitioning Algorithm

Abstract: In this letter, we propose a quasi-quadrature phase shift keying (QPSK) partitioning to replace the conventional QPSK partitioning in the first stage of the carrier phase estimation (CPE) algorithms for 32-QAM optical systems. By using the proposed quasi-QPSK-partitioning method, the ability of the CPE algorithms to track changes of phase is greatly enhanced. For 1-dB SNR penalty at bit error rate of 1E-2, the proposed method can achieve an improvement of 85% in combined linewidth symbol duration product tolerance when compared with the conventional method for single stage. With the help of the fine estimation stages, the maximum tolerable combined linewidth symbol duration product can be up to 5.1E-5.