Common Phase Error Research Articles

The Effect and Compensation of Phase Noise on Orthogonal Frequency Division Multiplexing (OFDM) System

Orthogonal Frequency Division Multiplexing (OFDM) is characterized by its high data rate. However, the modulation method used in the system is subject to the influence of phase noise due to the need of time synchronization. In this paper, an algorithm based on MMSE (minimum mean square error) is developed to compensate the influence of both the common phase error (CPE) and inter carrier interference (ICI), which are two aspects of phase noise, under common Gaussian white noise. The result of noise cancellation is presented in signal-to-noise ratio (SNR) and symbol error rate (SER). Like digital signal in general, SNR can reduce SER with or without phase noise compensation. The compensation of phase noise significantly reduces the SER of the decoded signal. However, the bandwidth of phase noise still determines the signal accuracy. Under high bandwidth of phase noise, increasing SNR will only slightly increase SER, which is not efficient.

Positioning of spacecraft with VLBI inverse phase reference

For positioning of spacecraft with VLBI phase-reference, an extragalactic radio source was usually served as phase reference. After fringe fitting on the radio source, the solutions including delays and rates mainly from the propagation media were adapted to calibrate the observed phase of the spacecraft. The common phase errors of the nearby source pair were significantly reduced in their differential phases, allowing accurate relative position measurement. However, this traditional phase-reference method requires strong and nearby extragalactic radio source, which is hard to fulfill due to the lack of strong calibrators on the sky. Since the radio flux density from the spacecraft is much stronger than that of the extragalactic radio source, it is possible to use the spacecraft as phase reference. In this paper, we investigated the feasibility and advantages of this so called inverse phase reference method, based on real VLBI observations. We compared the data analysis results using the two phase reference methods, it proved that the inverse phase reference is capable to measure accurate relative positions, and could achieve better results that the traditional methods, especially when the extragalactic radio source was weak.

Joint Channel and Phase Noise Estimation in MIMO-OFDM Systems

The combination of multiple-input multiple-output (MIMO) techniques withorthogonal frequency division multiplexing (OFDM), MIMO-OFDM, is a promising way ofachieving high spectral efficiency in wireless communication systems. However, the performanceof MIMO-ODFM systems is highly degraded by radio frequency (RF) impairments such asphase noise. Similar to the single-input single-output (SISO) case, phase noise in MIMO-OFDMsystems results in a common phase error (CPE) and inter carrier interference (ICI). In this paperthe problem of joint channel and phase noise estimation in a system with multiple transmit andreceive antennas where each antenna is equipped with its own independent oscillator is tackled.The technique employed makes use of a novel placement of pilot carriers in the preamble anddata portion of the MIMO-OFDM frame. Numerical results using a 16 and 64 quadratureamplitude modulation QAM schemes are provided to illustrate the effectiveness of the proposedscheme for MIMO-OFDM systems.

Impacts of Phase Noise on Digital Self-Interference Cancellation in Full-Duplex Communications

In full-duplex (FD) radios, phase noise leads to random phase mismatch between the self-interference (SI) and the reconstructed cancellation signal, resulting in possible performance degradation during SI cancellation. To explicitly analyze its impacts on the digital SI cancellation, an orthogonal frequency division multiplexing (OFDM)-modulated FD radio is considered with phase noises at both the transmitter and receiver. The closed-form expressions for both the digital cancellation capability and its limit for the large interference-to-noise ratio (INR) case are derived in terms of the power of the common phase error, INR, desired signal-to-noise ratio (SNR), channel estimation error and transmission delay. Based on the obtained digital cancellation capability, the achievable rate region of a two-way FD OFDM system with phase noise is characterized. Then, with a limited SI cancellation capability, the maximum outer bound of the rate region is proved to exist for sufficiently large transmission power. Furthermore, a minimum transmission power is obtained to achieve β-portion of the cancellation capability limit and to ensure that the outer bound of the rate region is close to its maximum.

Phase Noise Estimation and Suppression for PDM CO-OFDM/OQAM Systems

Phase noise induced common phase error and inter-carrier-interference are serious impairments for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. As have been discussed in previous publications, extra signal-to-noise-ratio (SNR) penalty is required to maintain the system performance under the interference of laser phase noise. The SNR penalty is proportional to the laser linewidth, the time duration of an OFDM symbol, and the system SNR. Therefore, the phase noise induced interference remains the bottleneck for CO-OFDM systems, especially for those systems employing high-order modulation formats, or with long fast Fourier transform window. Thanks to the usage of specially designed filter banks, CO-OFDM/offset quadrature amplitude modulation (CO-OFDM/OQAM) systems demonstrate lower out-of-band leakage and higher spectral efficiency compared with conventional CO-OFDM systems. Recently, both theoretical studies and experimental demonstrations for CO-OFDM/OQAM systems have been widely reported. With the relaxation of orthogonal condition from the complex field to the real field, phase noised induced interference in CO-OFDM/OQAM systems is more complicated than that in conventional CO-OFDM systems. To our best knowledge, there have been no studies on the phase noise estimation and suppression methods for CO-OFDM/OQAM systems. In this paper, we systematically study and analyze phase noise induced interference for CO-OFDM/OQAM systems. Based on the theoretical analysis and the concept of orthogonal basis expansion, we develop a time-domain phase noise estimation and suppression method for polarization-division-multiplexed CO-OFDM/OQAM systems. As shown in numerical Montel Carlo simulations, the proposed method can improve the system robustness against phase noise effectively.

Optimized Phase Noise Compensation Technique using Neural Network

Objectives: The paper designs a technique to optimize the phase noise compensation in the multiple inputs multiple output orthogonal frequency division multiplexing by using the neural network. Methods/Statistical Analysis: The phase noise compensation in the orthogonal frequency division multiplexing consists of two parts, one is the inter-carrier interference and other is the common phase error. This paper represents a neural network and Jaya algorithm based technique for the estimation of phase noise. The neural network has been used to remove the common phase error while inter-carrier interference has been removed by the Jaya algorithm. Findings: The proposed technique has been compared with three states of art techniques on different block size by using bit error rate. The reduced bit error rate can be identified for each block size. The effectiveness of the technique can be recognized by analyzing the results. Application/Improvements: The proposed technique can be used to facilitate the high data rate with better QoS during transmission.

On the Achievable Rates of OFDM with Common Phase Error Compensation in Phase Noise Channels

This paper considers the problem of analytically assessing the maximum achievable rates (capacity) of orthogonal frequency division multiplexing (OFDM) transmissions when the receiver, for complexity reasons, only accounts for the common phase error (CPE) effect due to phase noise impairments with inter-carrier interference (ICI) treated as noise. By recognizing that the functional form of the CPE with respect to the phase noise realization is actually a free design parameter, determination of the capacity is posed as a functional optimization problem with respect to the, so-called, CPE function. A simple lower bound of the capacity is obtained, revealing the performance degradation due to the unknown CPE at the receiver, as well as the suboptimal performance achieved in severe phase noise conditions by the conventional CPE function that is routinely employed in previous works. The existence of an optimal number of subcarriers that balances the effects of the (unknown) CPE and ICI is highlighted and critical system design/operation issues, such as selection of the CPE function and effect of unknown channel on the achievable rate, are discussed. The analysis in this paper can be employed for determining the suitability of OFDM in phase noise channels and provides a tractable utility function for resource allocation purposes.

Common phase error estimation in coherent optical OFDM systems using best-fit bounding box.

In this paper, we investigate and characterize a new approach of adopting best-fit bounding box method for common phase error estimation in coherent optical OFDM systems. The method is based on the calculation of the 2-D convex hull of the received signal constellation, which is generally adopted in image processing area to correct the skew of images. We further perform detailed characterizations including root mean square error analysis, laser linewidth tolerance, noise tolerance, and computation complexity analysis, via numerical simulations and experiments. The results show the proposed method achieves much improved spectral efficiency and comparable system performance than the pilot-aided method, while it exhibits good estimation accuracy and reduced complexity than the blind phase searching method.

Proposal of DCS-OFDM-PON upstream transmission with intensity modulator and collective self-coherent detection

Abstract We introduce digital coherent superposition (DCS) into optical access network and propose a DCS-OFDM-PON upstream transmission scheme using intensity modulator and collective self-coherent detection. The generated OFDM signal is real based on Hermitian symmetry, which can be used to estimate the common phase error (CPE) by complex conjugate subcarrier pairs without any pilots. In simulation, we transmit an aggregated 40 Gb/s optical OFDM signal from two ONUs. The transmission performance with DCS is slightly better after 25 km transmission without relative transmission time delay. The fiber distance for different ONUs to RN are not same in general and there is relative transmission time delay between ONUs, which causes inter-carrier-interference (ICI) power increasing and degrades the transmission performance. The DCS can mitigate the ICI power and the DCS-OFDM-PON upstream transmission outperforms the conventional OFDM-PON. The CPE estimation is by using two pairs of complex conjugate subcarriers without redundancy. The power variation can be 9 dB in DCS-OFDM-PON, which is enough to tolerate several kilometers fiber length difference between the ONUs.

EM-Based Phase Noise Estimation in Vector OFDM Systems Using Linear MMSE Receivers

Vector orthogonal frequency-division multiplexing (V-OFDM) for single-transmit-antenna systems is a generalization of OFDM where single-carrier frequency-domain equalization and OFDM are just two special cases. Phase noise in a V-OFDM system leads to a common vector block phase error (CVBPE) and an intervector block carrier interference effect. Severe performance degradation may occur if these two effects are not estimated and compensated well. In this paper, blind and semiblind phase noise estimation and compensation in a V-OFDM system is investigated by using the expectation-maximization (EM) algorithm. This is motivated by the fact that the conventional frequency-domain phase noise suppression schemes based on pilot-aided common phase error (CPE) or CVBPE estimation and compensation are not spectrally efficient as the vector block size is increased. Two novel schemes are proposed: One estimates the CVBPE only, and the other estimates the entire phase noise sequence in the time domain. General closed-form formulas for the maximization step of the EM algorithm for the two schemes are derived, and their computational complexity values are analyzed. The performances of the two schemes are investigated by using linear-minimum-mean-square-error (LMMSE) receivers. Simulations show that the two proposed schemes are very effective in estimating and compensating for phase noise in V-OFDM systems. It turns out that the second proposed scheme not only outperforms the traditional CPE or CVBPE schemes but is computationally efficient as well when applied to V-OFDM systems.

A Wavelet Multiplexing to Reduce Phase Noise Effects in OFDM based DVB-t

Orthogonal Frequency Division Multiplexing (OFDM) is a highly recommended multiplexing/modulation scheme for high data rate communications due to its high spectrum efficiency and robustness against Inter Symbol Interference (ISI). The OFDM is based on dividing the available spectrum into narrow band orthogonal subcarriers and modulating data on each subcarrier. Due to long symbol period, OFDM system is more sensitive to phase noise of the oscillator compared to single carrier systems. The Phase noise of oscillators used in the transmitters & receivers results in two effects, Common Phase Error (CPE) & Inter Carrier Interference (ICI). These effects results in increasing SNR requirement at the receiver to achieve certain BER. The design & simulation of OFDM based DVB-t system with wavelet multiplexing & demultiplexing and analysis of phase noise effects on BER is presented in this paper. The performance of simulated DVB-t system is analysed by considering SNR requirement to achieve certain BER in the presence of oscillator instabilities on AWGN & mobile radio channels. The modelled Wiener phase noise is generated for different 3dB bandwidths of noise spectrum. The simulation results shows that, the SNR required to achieve a bit rate of 10-2 in wavelet multiplexing is around 6dB lower as compared to FFT counterpart. The result also reveal that PAPR is also less, however wavelet multiplexing computational intensive.

Low-complexity optical phase noise suppression in CO-OFDM system using recursive principal components elimination.

A low-complexity optical phase noise suppression approach based on recursive principal components elimination, R-PCE, is proposed and theoretically derived for CO-OFDM systems. Through frequency domain principal components estimation and elimination, signal distortion caused by optical phase noise is mitigated by R-PCE. Since matrix inversion and domain transformation are completely avoided, compared with the case of the orthogonal basis expansion algorithm (L = 3) that offers a similar laser linewidth tolerance, the computational complexities of multiple principal components estimation are drastically reduced in the R-PCE by factors of about 7 and 5 for q = 3 and 4, respectively. The feasibility of optical phase noise suppression with the R-PCE and its decision-aided version (DA-R-PCE) in the QPSK/16QAM CO-OFDM system are demonstrated by Monte-Carlo simulations, which verify that R-PCE with only a few number of principal components q ( = 3) provides a significantly larger laser linewidth tolerance than conventional algorithms, including the common phase error compensation algorithm and linear interpolation algorithm. Numerical results show that the optimal performance of R-PCE and DA-R-PCE can be achieved with a moderate q, which is beneficial for low-complexity hardware implementation.

Common Phase Estimation in Coherent OFDM System Using Image Processing Technique

In a coherent orthogonal frequency division multiplexing system, the possible rotation of the rectangular signal constellation, due to common phase error, is shown to be effectively compensated by applying an skew compensation technique adopted in image processing area. We further propose an improved technique to further reduce the complexity of the algorithm and investigate the effect of the number of required test phases, via numerical simulations. The proposed improved algorithm is also compared with the conventional blind phase searching algorithm. It is shown that by employing only two bits of overhead, it can achieve a comparable performance to that of the traditional pilot aided method.

Cost-Effective and Spectrum-Efficient Coherent TDM-OFDM-PON Aided by Blind ICI Suppression

Digital coherent orthogonal frequency division multiplexing passive optical network (OFDM-PON) is a strong candidate for the 2nd-stage-next-generation PON (NG-PON2). However, as an OFDM system, especially for long-symbol duration OFDM system, it is very sensitive to laser phase noise. The common phase error (CPE) and intercarrier interference (ICI) caused by the laser phase noise severely cut down the performance of the coherent OFDM-PON. To correct the phase noise as well as guarantee high spectral efficiency, in this letter, we propose an advanced pseudo pilot-aided orthogonal basis expansion-based (A-PS-OBE) blind ICI suppression method over both constant and nonconstant modulus modulation, and deployed it in coherent optical time division multiplexing (TDM) OFDM-PON. The numerical results demonstrate the A-PS-OBE method can make the application of the cost-effective lasers possible in the coherent TDM-OFDM-PON and high-order modulation can also be adopted though the laser linewidth is large to 700 kHz.

Performance Investigation of Pilot-Aided Log-Likelihood Ratios for LDPC Coded CO-OFDM

Pilot-subcarrier and pilot-tone aided log-likelihood ratios (PA-LLR, PT-LLR), proposed for LDPC coded coherent optical OFDM (CO-OFDM) system, is reviewed in this paper. The knowledge of common phase error based on pilot-subcarriers or pilot-tone is incorporated into the new PA-LLR or PT-LLR metric, which eliminates the need for prior common phase error estimation and compensation. The formulation of both metrics is presented in a unified way. The performance of both metrics, in their approximate versions, is compared against the approximate conventional LLR (AC-LLR) for different modulation formats using different LDPC codes in a back-to-back case. APA-LLR or APT-LLR outperforms AC-LLR for higher-order QAM, with smaller number of pilot-subcarriers (PSCs) or at smaller pilot-tone-to-signal power ratios (PSRs). A time-domain blind intercarrier interference (BL-ICI) mitigation algorithm is employed to improve the performance, which eliminates the error floor at large laser linewidth. Furthermore, we examine the tolerance of different LLR metrics to linear fiber impairment (chromatic dispersion) or nonlinear phase noise (self-phase modulation), in which case, our metrics still outperform the conventional one. Iterative demodulation using new tentative-decision-based phasor offers almost 1-dB OSNR improvement for smaller number of PSCs. Finally, we also analytically prove that APA-LLR or APT-LLR converges to AC-LLR as the number of PSCs or PSR value increases. The optimal OSNR for calculating noise power is found to be around 10 dB for actual OSNR values beyond 10 dB in either the back-to-back case or after 13 600-ps/nm/km dispersion with channel compensation. APA-LLR and APT-LLR offer better performance than AC-LLR without any increase in complexity.

Analysis and Compensation of Phase Noise in Vector OFDM Systems

Vector orthogonal frequency division multiplexing (V-OFDM) for single transmit antenna systems is a generalization of OFDM where single-carrier frequency domain equalization (SC-FDE) and OFDM are just two special cases. It has been shown to be able to collect multipath diversity and thus generally outperforms OFDM. The performance of OFDM under phase noise has been extensively studied in the literature. These effects can be summarized as introducing a common phase error (CPE) and inter carrier interference (ICI) resulting in poor performance. The performance of V-OFDM under phase noise still remains uninvestigated and in this paper it is shown that phase noise in V-OFDM systems leads to a common vector block phase error (CVBPE) as well as an inter vector block carrier interference (IVBCI) effect. An expression for the signal plus interference noise ratio (SINR) for a V-OFDM system is derived and found to agree closely with simulation results. A pilot vector CVBPE based phase noise estimation technique is derived, and then combined with the maximum likelihood (ML) and the linear minimum mean square error (LMMSE) estimators to estimate the phase noise. It turns out that compared with OFDM, V-OFDM systems can perform phase noise estimation with lower complexity. The decorrelation and cancellation techniques are then used to compensate for the phase noise impairment. Numerical results for both coded and uncoded systems with perfect and practical channel estimation are provided to validate the analysis and effectiveness of the proposed phase noise estimation and compensation methods.

Carrier recovery in coherent receiver of optical orthogonal frequency division multiplexing system

In this paper, we reviewed our common phase error (CPE) and intercarrier interference (ICI) compensa- tion methods for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. We first presented a unified CPE estimation framework combining decision-aided (DA), pilot-aided (PA) and decision feed- back (DF) algorithms. The DA method is used to estimate the CPE of the current OFDM symbol based on the decision statistics of the previous symbol. DA + PA helps increase the phase noise tolerance of DA and reduce the overhead of PA, while DA + DF reduces the overhead to zero, achieving best performance with one more step of estimation, compensation and demodulation. We also described a modified time-domain blind intercarrier interference (BL-ICI) mitigation algorithm over non- constant amplitude formats. The new algorithm is derived from the BL-ICI algorithm over constant amplitude format for wireless networks. A new power estimation scheme was proposed for the BL-ICI algorithm to adapt to non- constant amplitude format. It has the same order of complexity with frequency domain decision-aided ICI (DA-ICI) compensation method and does not suffer from symbol decision errors. The effectiveness of both CPE and ICI compensation algorithms were demonstrated in a simulated 56-Gbit/s CO-OFDM system with various modulation formats.

Pilot-Tone Assisted Log-Likelihood Ratio for LDPC Coded CO-OFDM System

Pilot-tone assisted log-likelihood ratio (PT-LLR) is derived for low-density parity-check coded, coherent optical orthogonal frequency division multiplexing systems in the presence of linear phase noise. The knowledge of common phase error (CPE) obtained from the pilot-tone is incorporated into the new LLR metric, which eliminates the need for prior CPE estimation and compensation. We compare our metric with the conventional LLR (C-LLR) through extensive simulation using their approximate versions (APT-LLR, AC-LLR). APT-LLR has the same order of complexity as AC-LLR while it outperforms AC-LLR for higher order modulation formats (16-QAM, 64-QAM) at smaller pilot-tone-to-signal power ratios. In addition, we show that with the help of time-domain blind intercarrier interference mitigation, both metrics perform better in the presence of larger laser linewidth.

An effect of phase noise for an indoor wireless system

This paper gives an overview of 60GHz indoor wireless channel characteristics and an effect on phase noise. The performance of OFDM system is severely degraded by the local oscillator phase noise, which causes both common phase error (CPE) and inter-carrier interference (ICI). In this paper, the phase noise suppression (PNS) algorithm in order to reduce the phase noise in OFDM-based 60GHz WPANs is considered. The PNS algorithm is very simple and easily designed to realize system but it requires more effort to reduce the IC.

무선 LAN 시스템 성능개선에 관한 연구

본 논문은 4세대 무선 통신방식의 하나인 OFDM 기반의 60 GHz 무선 랜에서의 위상잡음의 영향에 관하여 논한다. 60 GHz 주파수 대역은 광대역 전송이 가능할 뿐만 아니라 실내 무선 환경에서의 무선 링크를 밀집 시킬 수 있다는 장점이 있다. 본 논문에서는 시스템 구현이 용이한 위상잡음 억제 알고리듬을 OFDM 기반의 60 GHz 무선 랜 시스템에 적용하고 이에 따른 성능을 SER 측면에서 분석하였다. 60 GHz 대역에서 발생하는 위상잡음 환경에서 위상잡음 억제 알고리듬을 적용한 경우, 그렇지 않은 경우에 비해 16-QAM, 64-QAM에서 각각 6 dB, 7.5 dB 정도의 SER 성능 향상을 보였다. We investigate the OFDM-based wireless LAN systems operating in the 60 GHz frequency band as part of the fourth-generation (4G) systems. The 60 GHz band is of much interest since this is the band in which a massive amount of spectral space has been allocated worldwide for dense wireless local communications. This paper gives an overview of 60 GHz band channel characteristics and an effect on phase noise. The performance of OFDM system is severely degraded by the local oscillator phase noise, which causes both common phase error and inter-carrier interference. In this paper, we apply phase noise suppression (PNS) algorithm that is easy for implementation to OFDM based 60 GHz wireless LAN system and analyze the SER performance. In case of using the PNS algorithm, SER performance is improved about 6 dB, 7.5 dB, respectively in 16, 64-QAM.