Common Phase Error Research Articles

Phase Noise Effects on OFDM Chirp Communication Systems: Characteristics and Compensation

Orthogonal frequency-division multiplexing (OFDM) chirp waveforms are an attractive candidate to be a dual-function signal scheme for the joint radar and communication systems. OFDM chirp signals can not only be employed to transmit communication data through classic phase modulation, but also can perform radar detection by applying linear frequency modulation for subcarriers. However, the performance of the OFDM chirp communication system under the phase noise environment still remains uninvestigated. This paper tries to discuss the influence of phase noise on OFDM chirp communication systems and proposes effective phase noise estimation and compensation methods. We find that the phase noise effect on OFDM chirp communication systems consists of a common phase error (CPE) and an inter-carrier interference (ICI). If not compensated, the performance of the dual-function systems can be seriously degraded. In particular, an exact expression for the signal-plus-interference to noise ratio (SINR) for the OFDM chirp communication system is derived and some critical parameters are analyzed to exhibit the phase noise effects on system performance. Moreover, two low-complexity estimation approaches, maximum likelihood (ML) and linear minimum mean square error (LMMSE), as well as two compensation approaches, the de-correlation and cancellation algorithms, are respectively utilized to eliminate the phase noise impairment. Finally, the phase noise effects and the effectiveness of the compensation approach are verified by extensive numerical results.

C-Band optical 90-degree hybrid using thin film lithium niobate.

The integrated optical 90-degree hybrid is a crucial component for coherent receivers. Here, we simulate and fabricate a 4 × 4 multimode interference coupler as a 90-degree hybrid using thin film lithium niobate (TFLN). The device features low loss (0.37 dB), high common mode rejection ratio (over 22 dB), compact footprint, and small phase error (below 2°) within the whole C-band experimentally, which is promising for integration with coherent modulators and photodetectors for TFLN-based high-bandwidth optical coherent transceivers.

Iterative phase noise suppression for full-duplex communication systems

Oscillator phase noise is one of the bottlenecks that limits the self-interference (SI) cancellation capability of full-duplex systems. In this paper, we propose a method for the suppression of common phase error (CPE) and intercarrier interference (ICI) induced by the phase noise in full-duplex orthogonal frequency division multiplexing (OFDM) systems. First, we regard the effect of CPE as a portion of the SI channel and perform estimation, reconstruction and elimination in the time domain. Then, the ICI signal is estimated and suppressed in the frequency domain. Additionally, by analysing the performance of proposed algorithm, we further develop an iterative mechanism to reduce the parameter estimation error and improve SI cancellation capability. Simulation results show that the proposed method has a significant SI cancellation capability improvement over the traditional SI cancellation schemes.

100 Gbit/s/λ DMT-PON System Based on Intensity Modulation and Heterodyne Coherent Detection

Due to the high receiver sensitivity and linear detection of coherent reception compared to direct detection (DD), the cost-efficient and low-complexity coherent detection based passive optical network (PON) with data rate beyond 100 Gbit/s has drawn great attention. In this letter, we demonstrate a 100 Gbit/s/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> discrete multitone (DMT) PON enabled by intensity modulation and heterodyne coherent detection in simulation. In order to compensate the phase noise, both common phase error (CPE) and RF-pilot (RFP) based schemes are considered and compared. According to the simulation results, the power budgets of our proposed system after 10-km and 20-km single mode fiber (SMF) transmission based on CPE scheme without dispersion management are 32.5-dB and 30.5-dB, while for RFP based scheme, 35-dB and 32.9-dB power budgets can be obtained for 10-km and 20-km SMF transmission, respectively. Our proposed system provides a low cost and low complexity coherent solution for single-wavelength 100 Gbit/s PON.

A Digital Two-Stage Phase Noise Compensation and rCFO/rSCO Tracking Module for mmW Single Carrier Systems

This article proposes a digital two-stage phase noise (PN) compensation and residual carrier frequency offset (rCFO) and residual sampling clock offset (rSCO) tracking module in the baseband receiver side for single carrier (SC) systems in the millimeter-wave (mmW) band. The proposed two-stage PN compensation and rCFO/rSCO tracking module (2STG-PNC&T) includes a correlation-based linear interpolation method for the common phase error (CPE) of the low-frequency PN, a subsymbol CPE compensation with a reformed low-complexity $\boldsymbol {\pi /4}$ robust PN slicer for the high-frequency PN, and a tracking mechanism for rCFO and rSCO estimation on 64-QAM under the harsh PN condition of the frequency synthesizers used in the mmW band. The proposed module can restrict the maximum rCFO/rSCO within ±0.4 ppm and track the phase error caused by the PN successfully. Besides, the compensated power spectral density of the residual PN is reduced from −90 to −125 dBc/Hz at 1-MHz offset. A four-time parallelism architecture of the new 2STG-PNC&T is proposed to work at a 625-MHz clock rate under 64-QAM for 15 Gb/s transmission. The gate count/power of the proposed design is only 4.0%/6.9% of the overall digital baseband, respectively.

Efficient Cross-Correlation Algorithm for Correction of Common Phase Error Employing Preamble for Orthogonal Frequency Division Multiplexing (OFDM) Receivers

In this paper, we propose a cross-correlation algorithm for correction of common phase error (CPE) in orthogonal frequency division multiplexing (OFDM) systems with high implementation efficiency. CPE resulting from the impairment of orthogonality among subcarriers is due to phase noise. It leads to the offset of demodulated data and increases the bit error rate (BER) of the receivers. As a result, it significantly degrades the performance of wireless communication systems that use OFDM. Therefore, offset compensation algorithm must be adopted in the OFDM system. The phase offset is traditionally estimated and compensated by introducing pilots in each OFDM symbol. However, the BER performance of the traditional algorithm PCP is poor because it is limited by the quantity of the pilot constraints of the wireless communication standard. A novel CPE correction algorithm involved in time and frequency domain can be developed to solve this problem. The proposed algorithm takes advantage of preamble sequences to remove the limitation of the pilots and improve the BER performance. Numerical analyses show that the proposed algorithm presents better estimation performance in additive white Gaussian noise (AWGN) channel. And the mean square error (MSE) is reduced to 10−3, which is lower than that of the traditional algorithm (10−2) at 10 dB signal-to-noise ratio (SNR). The BER is approximately down to10−5 at 12 dB SNR. The proposed algorithm can be easily implemented with low complexity of hardware for practical applications.

Decimeter Level Indoor Localization Using Hybrid Measurements of a Distributed Single Receiver

Recently, indoor localization using a single receiver has received significant attention. Despite the improvement of this, developing an accurate and universal system is still heavily required. In this article, we design and implement BiLoc, a decimeter level indoor localization system with hybrid measurements of a distributed single receiver. Specifically, different from the existing single receiver-based localization system, in BiLoc, some antennas of the array on the single receiver are distributed at different locations. To this end, BiLoc is based on the fact that the paths recorded on the same receiver incur common phase errors that are caused by nonsynchronization between the transmitter and the receiver. In BiLoc, first, some antennas of the antenna array are moved to different locations to locate the target. Then, BiLoc uses the 2-D matrix pencil (MP) to estimate the Angle of Arrival (AoA) and Time of Flight (ToF) of the multipath signals, which reduces the computational complexity effectively. After that, BiLoc constructs a nonlinear localization model by using the ToFs of the paths received at different antennas and AoAs measured at the antenna array, and then, an iterative algorithm based on the gradient of the localization objective function is used to solve this nonlinear problem. Because of combining hybrid AoA and ToF measurements, the proposed localization method is no longer sensitive to the selection of the initial guess of the target location. Finally, we implement BiLoc on the software-defined radio (SDR) X310 devices, and the designed prototype has six antennas with a maximum signal bandwidth of 100 MHz. The extensive experiments conducted in the practical indoor environments show that BiLoc achieves a median accuracy of 5 dm, which is comparable to the existing localization systems with decimeter level accuracy, and the localization delay is less than 100 ms. We believe that BiLoc can perform better in the emerging networks, such as 5G, because wider bandwidth and more antennas can be provided.

Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System.

A blind discrete-cosine-transform-based phase noise compensation (BD-PNC) is proposed to compensate the inter-carrier-interference (ICI) in the coherent optical offset-quadrature amplitude modulation (OQAM)-based filter-bank multicarrier (CO-FBMC/OQAM) transmission system. Since the phase noise sample can be approximated by an expansion of the discrete cosine transform (DCT) in the time-domain, a time-domain compensation model is built for the transmission system. According to the model, phase noise compensation (PNC) depends only on its DCT coefficients. The common phase error (CPE) compensation is firstly performed for the received signal. After that, a pre-decision is made on a part of compensated signals with low decision error probability, and the pre-decision results are used as the estimated values of transmitted signals to calculate the DCT coefficients. Such a partial pre-decision process reduces not only decision error but also the complexity of the BD-PNC method while keeping almost the same performance as in the case of the pre-decision of all compensated signals. Numerical simulations are performed to evaluate the performance of the proposed scheme for a 30 GBaud CO-FBMC/OQAM system. The simulation results show that its bit error rate (BER) performance is improved by more than one order of magnitude through the mitigation of the ICI in comparison with the traditional blind PNC scheme only aiming for CPE compensation.

DeepWiPHY: Deep Learning-Based Receiver Design and Dataset for IEEE 802.11ax Systems

In this work, we develop DeepWiPHY, a deep learning-based architecture to replace the channel estimation, common phase error (CPE) correction, sampling rate offset (SRO) correction, and equalization modules of IEEE 802.11ax based orthogonal frequency division multiplexing (OFDM) receivers. We first train DeepWiPHY with a synthetic dataset, which is generated using representative indoor channel models and includes typical radio frequency (RF) impairments that are the source of nonlinearity in wireless systems. To further train and evaluate DeepWiPHY with real-world data, we develop a passive sniffing-based data collection testbed composed of Universal Software Radio Peripherals (USRPs) and commercially available IEEE 802.11ax products. The comprehensive evaluation of DeepWiPHY with synthetic and real-world datasets (110 million synthetic OFDM symbols and 14 million real-world OFDM symbols) confirms that, even without fine-tuning the neural network’s architecture parameters, DeepWiPHY achieves comparable performance to or outperforms the conventional WLAN receivers, in terms of both bit error rate (BER) and packet error rate (PER), under a wide range of channel models, signal-to-noise (SNR) levels, and modulation schemes.

Relaxation of the Radio-Frequency Linewidth for Coherent-Optical Orthogonal Frequency-Division Multiplexing Schemes by Employing the Improved Extreme Learning Machine

A coherent optical (CO) orthogonal frequency division multiplexing (OFDM) scheme gives a scalable and flexible solution for increasing the transmission rate, being extremely robust to chromatic dispersion as well as polarization mode dispersion. Nevertheless, as any coherent-detection OFDM system, the overall system performance is limited by laser phase noises. On the other hand, extreme learning machines (ELMs) have gained a lot of attention from the machine learning community owing to good generalization performance, negligible learning speed, and minimum human intervention. In this manuscript, a phase-error mitigation method based on the single-hidden layer feedforward network prone to the improved ELM algorithm for CO-OFDM systems is introduced for the first time. In the training step, two steps are distinguished. Firstly, pilots are used, which is very common in OFDM-based systems, to diminish laser phase noises as well as to correct frequency-selective impairments and, therefore, the bandwidth efficiency can be maximized. Secondly, the regularization parameter is included in the ELM to balance the empirical and structural risks, namely to minimize the root mean square error in the test stage and, consequently, the bit error rate (BER) metric. The operational principle of the real-complex (RC) ELM is analytically explained, and then, its sub-parameters (number of hidden neurons, regularization parameter, and activation function) are numerically found in order to enhance the system performance. For binary and quadrature phase-shift keying modulations, the RC-ELM outperforms the benchmark pilot-assisted equalizer as well as the fully-real ELM, and almost matches the common phase error (CPE) compensation and the ELM defined in the complex domain (C-ELM) in terms of the BER over an additive white Gaussian noise channel and different laser oscillators. However, both techniques are characterized by the following disadvantages: the CPE compensator reduces the transmission rate since an additional preamble is mandatory for channel estimation purposes, while the C-ELM requires a bounded and differentiable activation function in the complex domain and can not follow semi-supervised training. In the same context, the novel ELM algorithm can not compete with the CPE compensator and C-ELM for the 16-ary quadrature amplitude modulation. On the other hand, the novel ELM exposes a negligible computational cost with respect to the C-ELM and PAE methods.

A Novel Phase Noise Suppression Scheme Utilizing Gaussian Wavelet Basis Expansion for PDM CO-OFDM Superchannel

In this paper, we propose a novel Gaussian wavelet basis expansion-based phase noise suppression scheme for polarization-division-multiplexing (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) superchannel. We analyze the phase noise suppression principle of Gaussian wavelet basis expansion (GWBE) and experimentally demonstrated it in 400-Gb/s optical PDM-QPSK-OFDM superchannel. Compared with the traditional common phase error (CPE) suppression scheme, a Q-factor improvement of about 1.5∼3.2 dB is achieved when the number of the pilots ranges from 16 to 80. Meanwhile, we evaluate the nonlinear phase noise suppression ability by adjusting the launched power into 160 km standard single mode fiber (SSMF). The results show that the proposed GWBE scheme is obviously superior to CPE and orthogonal basis expansion (OBE) in different nonlinear phase noise scenarios. Furtherly, we extend the GWBE scheme to 800 Gb/s PDM-16QAM-OFDM superchannel. The GWBE scheme can enhance the BER performance from 1.92 E-03 to 5.87 E-04 when the number of pilots is 48.

Performance Enhancement of Coherent Optical OFDM System Using LMS Algorithm

Instability of the local oscillator causes phase noise – a phenomenon that is a disadvantage and is considered to be a major obstacle in the functioning of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An attempt has been made in this paper to reduce the effects of common phase errors generated by phase noise. In this paper, a least mean square (LMS) based algorithm is proposed for estimation of phase noise. Using this proposed algorithm, the major problem of phase ambiguity caused by cycle slip is avoided and the bit error rate is greatly improved. Further, there is no requirement for modifying the frame structure of OFDM using this algorithm. A CO-OFDM system with the 8-PSK technique is used to implement the algorithm concerned. Furthermore, the algorithm, using the 8-PSK modulation technique, is analyzed and compared with the existing QPSK technique and with other algorithms. The investigations reveal that 8-PSK outperforms existing LMS algorithms using other techniques and significantly reduces the bit error rate.

Two-dimensional projection histogram assisted with low-overhead pilots for the common phase error compensation in CO-OFDM system

Abstract In this paper, we demonstrate a two-dimensional projection histogram assisted common phase error (CPE) compensation scheme in coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. With the help of the low overhead pilots, the rough estimation can be obtained, and the π/2 deviation problem of projection histogram (PH) assisted scheme can be efficiently solved, which can improve the estimation accuracy of CPE. And, with the processing of the two-dimensional projection histogram mapping, the fine estimation can be achieved. The numerical CO-OFDM system simulations over the single mode fiber (SMF) transmission are conducted. The corresponding results show that, compared to the pilot-aided (PA) estimation method, only less-overhead pilots were employed for our scheme, but more accurate CPE estimation can be achieved, hence improving the system performance. Moreover, to achieve an optimal transmission performance, the overhead of pilots for the PA method should be set to 20%, while the proposed method can reduce to 1.25%.

Squint-looking differential synthetic aperture ladar: signal processing and experimental demonstration.

Squint-looking differential synthetic aperture ladar (DSAL) is reported with detailed signal processing mathematics and high-resolution experimental demonstrations. Based on the DSAL principle and standard squint-looking synthetic aperture radar theory, the data processing procedures on squint-looking DSAL image formation are obtained. The experimental DSAL setup, operating in "step-stop" strip map mode, adopts a frequency chirped laser with a wavelength of 1550 nm as the illuminating source and a specially designed random phase generator to introduce large common mode random phase error (RPE) into the phase history data of both receiving sub-apertures. High-resolution DSAL images of a cooperative target at a distance of 1.85 m and squint-looking angle of $-{10}^\circ$-10∘ or $+{10}^\circ$+10∘ are demonstrated. The DSAL images, with or without large RPE, are all well focused by straightforwardly following the given data processing steps. The result illustrates that the DSAL technique is robust in removing common mode phase errors in squint-looking configuration.

Pilot-Free Common Phase Error Estimation for CO-OFDM With Improved Spectral Efficiency

We propose an improved pilot free phase noise mitigation algorithm for CO-OFDM systems using weighted multi-level QPSK partitioning and Kalman filtering. Through extensive Monte Carlo simulations, we demonstrate an improvement in spectral efficiency of $>$ 6% in case of 200 Gbps single channel and 1 Tbps multi channel 16QAM CO-OFDM transmission with blind carrier phase estimation. We also experimentally demonstrate the performance of the proposed algorithm against the standard pilot aided algorithm for the transmission of 120 Gbps 16QAM CO-OFDM at different noise levels.

Experimental Demonstration of the Tradeoff Between Chromatic Dispersion and Phase Noise Compensation in Optical FBMC/OQAM Communication Systems

Filterbank multicarrier based on offset quadrature amplitude modulation (FBMC/OQAM) is a promising candidate for optical fiber communication systems, thanks to its better time/frequency confinement compared to other multicarrier modulations. Among linear impairments, the compensation of fiber-induced chromatic dispersion (CD) and laser-induced phase noise (PN) in FBMC/OQAM systems induces a compromise in terms of the number of used subcarriers. Considering a fixed dedicated signal bandwidth, the number of subcarriers is expected to be large enough to allow a better frequency-domain CD compensation. On the other hand, it should be sufficiently small in order for the compensation of common phase error inherent to the PN to work properly. In this paper, we experimentally demonstrate the tradeoff between CD and PN compensation that we previously highlighted by simulations. More specifically, considering a 20-GHz FBMC/4-OQAM modulation and an aggregated laser linewidth of about 200 kHz, we show that the maximum transmission distance reaches 3100 km with nearly 512 active subcarriers and three-tap equalizers, when a maximum 1-dB optical signal-to-noise ratio penalty at a bit error rate of 3.8 × 10–3 can be tolerated. Moreover, we propose and validate a frame structure and an integrated synchronization/channel equalization architecture to implement a standalone demodulation system.

Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems

In this paper, we present a novel blind common phase error estimation method in coherent orthogonal frequency division multiplexing systems using projection histogram-assisted processing. In the proposed algorithm, the constellation of the signal distorted by common phase noise is regarded as a tilted image, which can be rotated back to the right position by tilt adjustment. Considering the characteristics of the constellation, the tilt adjustment can be realized under the assistance of projection histogram. By simply counting and maximizing the number of the projection points fell into certain intervals, the tile angle can be obtained, which means that the common phase error is known. Compared with the conventional blind phase searching method, the proposed method shows similar performance and reduced complexity. Moreover, we optimized the algorithm by dividing the estimation process into two stages, in which case the complexity can be further reduced without introducing bit error ratio penalty.

Phase Noise Cancelation Based on Polarization Modulation for Massive MIMO-OFDM Systems

In massive multiple-input multiple-output (MIMO) systems, phase noise introduced by oscillators can cause severe performance loss. It leads to common phase error and intercarrier interference in massive MIMO-OFDM uplink. To solve the issue, a novel phase noise cancelation scheme based on polarization modulation for the massive MIMO-OFDM system is proposed. We first introduce the polarization modulation (PM) exploited in massive MIMO-OFDM uplink. Then, by exploiting the zero-forcing detection, we analyze the asymptotically ICI and the distribution of the transformed noise under different XPD values. Furthermore, we demonstrate that phase noise can be asymptotically canceled and only the transformed additive white Gaussian noise exists as the number of antennas at the base station is very large. Moreover, we derive the instantaneous signal-to-noise ratio (SNR) on each subcarrier and analyze the ergodic capacity. To increase the ergodic capacity performance further, a joint modulation scheme combining the PM and 2PSK is proposed and the ergodic capacity performance of the joint modulation is discussed. The simulation results show that the proposed scheme can effectively mitigate phase noise and achieve a higher ergodic capacity.

基于二维投影直方图导频辅助的相干光正交频分复用系统公共相位误差噪声补偿算法

基于二维投影直方图导频辅助的相干光正交频分复用系统公共相位误差噪声补偿算法

Lagrange interpolation based extended Kalman filter for phase noise suppression in CO-OFDM system

Abstract In this paper, for the first time, a novel Lagrange interpolation (LRI) based extended Kalman filter (EKF) is proposed to compensate inter-carrier interference (ICI) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. Owing to the features of Wiener distribution for laser phase noise, our proposed second-order or higher-order LRI is more suitable for phase fitting than sub-symbol block algorithm based on linear interpolation (LI-SCPEC). Furthermore, to compensate the common phase error (CPE), a modified iteration-free blind (MIFB) algorithm is also designed in this paper. Comparing with the existing common IFB scheme, our method avoids phase misjudgment. By combining the MIFB with the LRI scheme, the accuracy of phase noise estimation and spectrum utilization can be effectively improved. The results of Monte Carlo simulation prove that our proposed scheme is effective in phase noise suppression in CO-OFDM system