Optical Signal-to-noise Ratio Research Articles

Enabling ultra-high bit rate transmission with CFBG as dispersion compensator in an OptiSpan 240 km DWDM network

Abstract In this paper, a dispersion compensation technique for an ultra-long haul optical network utilizing a chirped fiber Bragg grating (CFBG) is presented. A high bit-rate signal of 40 Gbps is inputted into each channel. The CFBG, employed for dispersion compensation, is positioned after demultiplexing, enabling effortless network upgrades. The grating parameters of the implemented CFBG are mathematically analyzed and optimized to counteract net dispersion of over 3153 ps/nm across the channel. The design is verified using the OptiSystem software, resulting in a successful transmission up to 240 km with an average Q-factor of 8.09, utilizing an amplification gain of 49.5 dB. Additionally, the achieved optical signal-to-noise ratio (OSNR) level using the symmetrical amplification technique surpasses the acceptable value, with an average bit error rate of 10−16.

Mitigation of atmospheric losses using dual‐polarized 16‐QAM MIMO technique in free‐space optical system in various weather conditions

SummaryThe technique to overcome the challenge while implementing the fiber optical link is investigated using an alternative optical link called a free‐space optical (FSO) link with advanced modulation and signal processing techniques. A dual‐polarized 16‐quadrature amplitude‐modulated signal is transmitted over single and multi‐FSO channels under various atmospheric attenuation conditions. High bandwidth and data rates (up to 10 Gbps), unlicensed spectrum (above 300 GHz), and simplicity of deployment are significant benefits of the FSO system. However, the weather conditions of haze, rain, and fog cause signal attenuation when the optical carrier wave is transmitted over free space, and atmospheric turbulence is a challenge to FSO implementation, which degrades the transmission performance of optical signals for long‐distance communication. For 120 Gbps data transmission, the performance of a multi‐input and multi‐output (MIMO) FSO system is evaluated by observing the bit error rate (BER) and received signal constellation diagram. Optical signal‐to‐noise ratio (OSNR) parameters were iterated to determine the optimal value for back‐to‐back, single‐input, single‐output (SISO), and MIMO systems. Moreover, we examined the proposed system's output with recent articles, including MIMO, multiplexing, and various modulation techniques. The comparison of results shows that the suggested MIMO‐FSO model has enhanced the performance with the lower BER as less than 3.8 × 10−3 (log of BER is −2.42) forward error correction (FEC) limit for 18.7 km link range in clear air with 0.54 dB/km attenuation, 4.8, 4.5, 1.35, and 0.57 km under haze, light fog, medium, and heavy fog with 4.6, 6.9, 28.9, and 75 dB/km attenuations.

Investigation of IEEE 802.16e LDPC Code Application in PM-DQPSK System

With the development of the Internet and information technology, optical fiber communication systems need to meet people’s information demand for large capacity and high speed. High-order phase modulation and channel multiplexing can improve the capacity and data rate of optical fiber communication systems, but they also bring the problem of bit error. To improve the transmission quality and reliability of optical fiber communication systems, forward error correction (FEC) coding techniques are commonly used, which serve as the fundamental approach to enhance the quality and reliability of fiber optic communication systems, ensuring that the received data remain accurate and reliable. The FEC in optical fiber communication systems is divided into three generations. The first generation FEC is mainly hard decision codewords, represented as RS code. The second generation FEC is mainly cascaded code, which stands for interleaved cascaded code. The third generation of FEC mainly refers to soft decision codes, which are represented as low-density parity-check (LDPC) codes. As a kind of FEC, LDPC codes stand out as pivotal contributors in the field of optical communication and have gained remarkable attention due to exceptional error correction performance and low decoding complexity. Based on IEEE802.16e standard, LDPC code with specific code length and rate is compiled and simulated in MATLAB and VPItransmissionMaker 10.1 and successfully incorporated into polarization multiplexed differential quadrature phase shift keying (PM-DQPSK) coherent optical transmission system. The simulation results indicate that the bit error rate (BER) can be reduced to 10−3 when the optical signal-to-noise ratio (OSNR) reaches 14.2 dB, and the BER experiences a reduction by nearly three orders of magnitude when the OSNR is 17.2 dB. These findings underscore the efficacy of LDPC codes in significantly improving the performance of optical communication systems, particularly in scenarios demanding robust error correction capabilities. This study provides valuable, significant results regarding the potential of LDPC codes for enhancing the reliability of optical transmission in real-world applications.

Broadband tunable single-frequency Yb-doped fiber laser with dual ring subcavity and Sagnac ring filter

We demonstrate a broadband tunable ultra-narrow linewidth single-frequency (SF) Yb-doped fiber laser (YDFL). A dual ring subcavity (DRS) as a filtering component to eliminate the dense longitudinal mode inherent in YDFL and theoretically analyzed its filtering characteristics. By inserting a 0.8 m unpumped polarization-maintaining Yb-doped fiber in the Sagnac ring, a dynamic narrowband grating (DNG) based on the saturable absorption (SA) effect is constructed to ensure SF laser output over the entire wavelength tuning range. We achieve a wide wavelength tunable SF laser output in the range of ∼74 nm, covering 1021.06 nm to 1094.98 nm. The laser has an optical signal-to-noise ratio (OSNR) of more than 62.5 dB, a slope efficiency of 3.57 %, and an ultra-narrow linewidth of 622 Hz over the entire tunable range. In addition, the stability of the wavelength and power fluctuations below 0.018 nm and 0.67 dB, respectively. This tunable SF fiber laser has a compact structure, lower cost, and excellent performance, and is expected to be used in the fields of coherent communications, precision metrology, and so on.

Time-frequency dual-dimension deep neural network (TF-DD-DNN)-based OSNR and XT monitoring in mode-division multiplexing systems

We propose a time-frequency dual-dimension deep neural network (TF-DD-DNN)-based optical performance monitoring (OPM) scheme to jointly monitor the optical signal-to-noise ratio (OSNR) and the mode-coupling induced crosstalk strength (XT) in mode-division multiplexing (MDM) systems, by revealing the diversity of the amplified spontaneous emission (ASE) and XT distortions on optical signals in the time- and frequency-domains. We numerically quantify the predictions of OSNR and XT for a coherent MDM transmission link, achieving the OSNR prediction accuracy of more than 0.99 and the XT prediction accuracy of up to 1 with the root mean square error (RMSE) of 0.11 dB at OSNR = 30 dB @0.1 nm for the case of quadrature-phase-shift keying (QPSK) signals. We evaluate the impacts of the chromatic dispersion (CD) of fibers and the low-pass filter bandwidth on the prediction procedures. The dependency of the modulation formats is also discussed, confirming the robust operation of the proposed scheme. Finally, the TF-DD-DNN scheme is experimental verified. High consistency is obtained between the simulation and experimental results.

Narrow linewidth fiber laser using compound-ring cavity filter and self-injection locked mechanism

Narrow linewidth erbium-doped fiber lasers (EDFLs) hold in significant potential optical fiber sensing, wavelength multiplexing transmission, and optical fiber communication. However, many EDFLs produced outputs with linewidth in several kHz level. Therefore, a high optical signal-to-noise ratio (OSNR), narrow linewidth single-longitudinal-mode (SLM) EDFL was proposed and investigated in this work. The EDFL utilized a combination of compound-ring cavity filter and a self-injection locked mechanism to generate a stable SLM output with an OSNR greater than 72 dB. The maximum wavelength drift and maximum peak power fluctuation over 60 min were maintained at low values of 0.0041 nm and 0.16 dB. Moreover, a narrow linewidth of 1.82 kHz at a measuring time of 0.002 s was realized. Furthermore, the research also investigated output power variations with different pump powers, relaxation oscillation, and the dependence of output central wavelength on the axial strain.

Switchable Dual-Wavelength Thulium-Doped Fiber Laser Based on Polarization-Maintaining Fiber Bragg Grating and Compound Cavity Filter

This paper presents experimental evidence regarding a novel switchable dual-wavelength thulium-doped fiber laser (TDFL). Wavelength switching is achieved by combining a polarization-maintaining fiber Bragg grating (PM-FBG) with a polarization controller (PC). The three-coupler double-ring compound cavity (TC-DRC) structure, acting as a mode-selection filter, is designed to select a single longitudinal mode (SLM) from the dense longitudinal modes. This paper introduces the design and fabrication method of the TC-DRC filter and analyzes, in detail, the mechanism for SLM selection. The experimental results demonstrate that the designed filter exhibits excellent performance. By adjusting the PC, the TDFL achieves stable SLM operation at the wavelengths of 1940.54 nm and 1941.06 nm, respectively. The optical signal-to-noise ratio (OSNR) is superior to 65 dB. When the TDFL is tested at room temperature, there is no significant wavelength drift, and power fluctuations are less than 1.5 dB. The operation of the SLM is verified through the self-heterodyne method, and the laser maintains stable SLM states for both wavelengths after continuous operation for an hour. Furthermore, based on the phase noise demodulation method, the linewidths of both wavelengths are measured to be less than 10 kHz at the integration time of 0.001 s.

High-efficiency single-frequency DBR fiber laser at 1091 nm utilizing a Yb:YAG crystal-derived silica fiber

A single-frequency distributed Bragg Reflector (DBR) fiber laser operating at 1091 nm was demonstrated by using a Yb:YAG crystal-derived silica fiber (YDSF). The YDSF was prepared via the molten core (MC) method, with a Yb2O3 doping concentration of 5.60 wt.% in the core, resulting in a gain coefficient of 1.45 dB/cm at 1091 nm. Employing 0.8 cm of the YDSF, we attained a single-frequency laser with a maximum output power of 145 mW and a slope efficiency of 31.8%. The laser exhibited an optical signal-to-noise ratio (OSNR) exceeding 71 dB, a linewidth of ∼34 kHz, and a stabilized relative intensity noise (RIN) at -132 dB/Hz for frequencies over 4.5 MHz. The fiber laser could serve as an outstanding seed source for high-power, narrow-linewidth fiber amplifiers operating at 1091 nm.

Combined modulation format identification and optical signal-to-noise ratio monitoring with high accuracy and generalizability based on a proposed fused module few-shot learning algorithm in dynamic coherent optical transmissions

Modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring are important portions of optical performance monitoring (OPM) for future dynamic optical networks. In this paper, we proposed a fusion module few-shot learning (FMFSL) algorithm as an improvement upon the ordinary few-shot learning algorithms for image recognition with the specialty in adopting a combination of a dilated convolutional group and an asymmetric convolutional group to advance the feature extraction. FMFSL algorithm is applied in MFI and OSNR monitoring in coherent optical communication systems with its performance investigated in both back-to-back and fiber transmission scenarios using small-scale constellation diagrams. The results show that FMFSL algorithm can achieve 100% accuracy in MFI and higher OSNR monitoring accuracy compared to the few-shot learning algorithms Deep Nearest Neighbor Neural Network (DN4) and Prototypical Nets (PN) with 2.14% and 4.28% for 64QAM and 3.38% and 8.06% for 128QAM, respectively, without much increase in time consumption. Furthermore, the trained FMFSL algorithm remains excellent in MFI and OSNR monitoring without retraining while employed in back-to-back transmission scenarios with smaller OSNR intervals and fiber transmission scenarios with different amounts of Kerr nonlinearity, demonstrating its high capabilities in generalization and robustness. FMFSL algorithm provides a potential solution for OPM in future dynamic optical networks as a novel machine learning tool.

Realization of 4 × 200 Gbps 4-QAM OFDM-OWC System Using Higher Order OAM Modes for HAP-to-Satellites Scenario

Recently, there has been an increase in interest in using optical wireless communication (OWC) links on high-altitude platforms (HAPs) for satellite applications. We implement an orbital angular momentum (OAM) multiplexed orthogonal frequency division multiplexing (OFDM) system using an OWC link. A space-to-air scenario is considered in which transmission pointing errors, geometric loss, turbulence, and additional link losses are taken into account to extend the transmission range, system capacity, and throughput. At 200 Gbps per channel data rate, four different OAM modes are implemented with higher order Laguerre–Gaussian (LG) modes of [0,0], [0,13], [0,40], and [0,80]. An aggregate 800 Gbps data rate can deliver a maximum OWC range of 3300–5000 km for all channels. The maximum received power over the 1000 km range is −19.34 to −32.59 dBm with an additional gain of 0–2.5 dB. It is also possible to obtain a better performance over large distances of 500–3500 km with an error vector magnitude of 2.98–17.5%. Furthermore, a high gain of −40.80 dB, a signal-to-noise ratio (SNR) of 55.21 dB, and an optical SNR of 67.25 dB can be achieved for varied transmitter pointing errors of 0.1 rad. As compared to other literature, this system exhibits a superior performance.

تأثير ثلاث خطط مختلفة على المرحلة الثانية من الشبكات الضوئية في الجيل القادم

Abstract: In this work, a simulative analysis of 40 Gb/s downstream time and wavelength division multiplexing-passive optical network (TWDM-PON) for next-generation passive optical network second stage (NG-PON2) had been designed and demonstrated. The performance of three different wavelength plans in TWDM-PON are evaluated as the solution to NG-PON2 to support 40Gbit/s bandwidth requirement. A four 10-Gb/s TWDM-PON signals are stacked using four different wavelengths in the downstream direction and externally modulated. The system performance is observed using Bit Error Rate (BER) and Optical Signal-to-Noise Ratio (OSNR) with respect to the design parameters such as distance, number of users and received optical power. Thus, the proposed system was able to support 512 number of users and 80 km transmission distance. When the system is tested upon transmission of triple play services over 80km distance with 512 users, it is shown that BER of 8.9 × 10-10, 3.9 × 10-9 and 1.3 × 10-4 are achieved for data, voice and video, respectively.

Tunable narrow linewidth fiber laser based on parity-time symmetric double rings and variable optical attenuator

A tunable narrow linewidth fiber ring laser based on parity-time (PT) symmetric double rings and variable optical attenuator (VOA) is demonstrated. The laser is composed of a fiber loop mirror (FLM), which creates two coupled rings: the reflective ring and the transmissive ring. The loss of the transmissive ring can be controlled by tuning the VOA, which balances with the gain of the reflective ring. When the PT symmetry is broken, a single-longitudinal-mode (SLM) laser is realized. The laser can be tuned by an optical tunable filter (OTF), and the tuning range is 38 nm, spanning from 1525 nm to 1563 nm. In the whole tuning process, the linewidth of the laser is at the sub-kHz level, and the optical signal to noise ratios (OSNR) is over 53 dB. The fluctuation of wavelength and power are less than 0.02 nm and 0.52 dB in an hour, respectively.

FrFT-based estimation of linear and nonlinear impairments using Vision Transformer

To comprehensively assess the conditions of an optical fiber communication system, it is essential to implement joint estimation of the following four critical impairments: nonlinear signal-to-noise ratio (SNRNL), optical signal-to-noise ratio (OSNR), chromatic dispersion (CD), and differential group delay (DGD). However, current studies only achieve identifying a limited number of impairments within a narrow range, due to a lack of high-performance computing algorithms and a unified representation of impairments. To address these challenges, we adopt time-frequency signal processing based on the fractional Fourier transform (FrFT) to achieve the unified representation of impairments, while employing a Transformer-based neural network (NN) to break through network performance limitations. To verify the effectiveness of the proposed estimation method, numerical simulations were conducted on a five-channel polarization-division-multiplexed quadrature phase shift keying (PDM-QPSK) long haul optical transmission system with the symbol rate of 50 GBaud per channel. The mean absolute error (MAE) for SNRNL, OSNR, CD, and DGD estimation is 0.091 dB, 0.058 dB, 117 ps/nm, and 0.38 ps, and the monitoring window ranges from 0−20dB, 10−30dB, 1700−51,000ps/nm, and 0−100ps, respectively. Our proposed method achieves accurate estimation of linear and nonlinear impairments over a broad range, representing a significant advancement in the field of optical performance monitoring (OPM).

Digitization method for a photonic analog-to-digital converter with phase-shifted optical quantization.

This Letter proposes a novel, to the best of our knowledge, matrix digitization method for a photonic analog-to-digital converter with phase-shifted optical quantization (PSOQ-ADC). This method overcomes the issues of excessive bit width of the output code and the generation of invalid codes encountered by the traditional direct digitization method. A PSOQ-ADC was fabricated on a lithium niobate on insulator (LNOI) platform, and an experimental platform was built. The results show that RF signals at 1/2/5 GHz, which were sampled by a 50GS/s optical pulse train, were digitized successfully with the matrix digitization method, producing 5-bit codes without invalid codes. In comparison, the direct digitization method yields 10-bit codes, and as the optical signal-to-noise ratio (OSNR) decreases, the ratio of invalid codes increases in the direct digitization method; even with Hamming distance correction, its effective number of bits (ENOB) remains smaller than that of the matrix digitization.

All-Optical format conversion from PAM4 to QPSK based on non-degenerate Phase-Sensitive amplification and pump assisted nonlinear optical loop mirror

An all-optical format conversion (AOFC) scheme from 4-ary pulse amplitude modulation (PAM4) to quadrature phase shift keying (QPSK) based on the non-degenerate phase-sensitive amplification (PSA) and the pump assisted nonlinear optical loop mirror (PA-NOLM) is proposed and numerically simulated for the first time. The input unipolar PAM4 signal with equal amplitude distance (UPAM4-A) is coupled with two input pump lights and injected into the symmetric interferometric fiber optic parameter amplifier (FOPA) to achieve the separation of the UPAM4-A and the new pump light generated at the signal frequency based on the non-degenerate PSA. When the filtered out UPAM4-A is coherent added with the new generated pump, the UPAM4-A signal to the biplolar PAM4 (BPAM4) signal. When the converted BPAM4 is sent into the PA-NOLM after adjusting its power, the BPAM4 signal could be converted into the QPSK signal. The error vector magnitude (EVM) and bit error ratio (BER) performance of the system are measured before and after AOFC with different input and receiver optical signal to noise ratio (OSNR). For the input UPAM4-A signal with an input OSNR of 27 dB, there is about 8.2 dB BER performance improvement in receiver OSNR for the final converted QPSK signal. Additionally, the proposed non-degenerate PSA configuration can be extended to realize the AOFC from one QPSK to two on–off keying (OOK) signals. The scheme can be applied in the optical gateway connecting the long-haul and the short-reach optical networks with suitable modulation formats.

Across-dimensional optical constellation de-aggregations from QAMs to PAMs in optical transparent networks

In this paper, an across-dimensional optical constellation de-aggregation scheme is proposed and verified. This de-aggregation scheme builds flexible optical connections between core and edge networks and fills the lack of the conversions between quadrature amplitude modulation (QAM) and pulse amplitude modulation (PAM) formats. 10G Baud quadrature phase shift keying/9QAM/16QAM-to-2×on off keying (OOK)/PAM3/PAM4 constellation de-aggregations are achieved. The enabled constellation manipulations contain polarization-assisted quadrature de-multiplexing and bi-directional vector moving. The key research status of QAM/PAM de-aggregations and adopted theoretical derivations are analyzed and expressed in detail. The signal spectrum, constellations, eye diagrams, transfer characteristics curves, error vector magnitudes and bit error ratios (BERs) during the de-aggregation process are calculated to measure the system performances. With the input optical signal-to-noise ratio (OSNR) of 10 dB/15 dB/20 dB, the de-aggregated OOK/PAM3/PAM4 signals show the receiver OSNR of 19.1 dB/21.9 dB/31.2 dB, respectively, at the BER of 10−3. The proposed scheme presents excellent format scalability and has potential applications in flexible all-optical connections, across-dimensional optical transmissions, and optical transparent networks.

Synchronous filtering method for improving the optical signal-to-noise ratio of a tunable laser based on the Fabry-Pérot interferometer.

Optical measurements are closely related to the optical signal-to-noise ratio (OSNR) of the laser, which can be improved using a tunable optical filter (TOF) to suppress frequency noise. For an external-cavity tunable laser with a tuning range larger than the TOF bandwidth, the wavelength at the center of the TOF passband must be varied based on the laser tuning. This study proposes a tunable-laser OSNR-enhancement method based on the Fabry-Pérot (FP) interferometer. The FP signal contains the wavelength information of the swept laser, which can be used to determine the real-time driving voltage of the TOF. Notably, the laser needs to be continuously tunable without mode hopping, and the free spectral range of the FP interferometer must be smaller than the TOF bandwidth.

Hierarchical blind phase search for correcting imperfect phase rotation in QAM signals synthesized via optical coherent superposition.

Coherent superposition has been proposed to synthesize high-order quadrature amplitude modulation (QAM) by coherently superposing low-order QAMs in the optical domain. These approaches could effectively relax the digital-to-analog converter resolution and reduce the complexity of the driving electronics. However, in the superposition process, imperfect phase rotations (IPRs) in low-order QAMs will be transferred to the resultant high-order QAM. Importantly, the induced IPR cannot be compensated for by conventional linear equalizers and carrier recovery methods. To combat the induced IPR, herein, we propose a hierarchical blind phase search (HBPS) algorithm to compensate for the IPRs in synthesized high-order QAMs. The proposed HBPS can match the generation mechanism of the IPRs in coherent superposition, by tracing back and estimating the IPR in the QPSK-like constellation of each hierarchy and finally correcting the induced IPRs. Simulation and experimental results verify that this algorithm could effectively compensate for the IPR in the resultant 16-QAMs synthesized using coherent superposition approaches. The proposed HBPS shows significant optical signal-to-noise ratio (OSNR) gains compared to the conventional blind phase search (BPS) method for high-order QAMs coherently superposed using optical signal processing (OSP) and tandem modulators (TMs). Specifically, at the BER of 2.4e-2, the HBPS achieves a 1.5-dB OSNR sensitivity enhancement over the BPS in either OSP or TMs-based schemes, even with an imperfection rotation of up to 20∘.

Non-sweep DC component estimation method for a virtual-carrier assisted Kramers-Kronig receiver

The Kramers-Kronig (KK) receiver has attracted much attention in short-range optical interconnection because of its ability to recover the phase of the signal from the intensity information through KK algorithm. In high-speed KK systems, such as virtual-carrier (VC) assisted ones, an alternating current (AC) coupled photo-detector (PD) is preferred due to relaxing the requirements of analog-to-digital converter (ADC) and electronic amplifier by filtering direct current (DC) component. However, the loss of the DC component will cause the KK algorithm to break down, so it is necessary to accurately recover DC value in the digital domain with multiple-sweep. In this paper, we propose what we believe is a novel non-sweep DC component estimation scheme based on optimized digital carrier-to-signal power ratio (OD-CSPR) method, which can accurately estimate the DC component with only 3-4 iterations in the scenario of VC-assisted KK receiver optical transmission. The scheme utilizes the one-dimensional search optimization algorithm based on golden section search and parabolic interpolation without sweeping. The simulation and experimental results of the proposed non-sweep OD-CSPR method show that the DC component can be estimated accurately in a large CSPR range, and the system performance is close to that of the conventional DC-sweep method. Compared with the typical defined digital CSPR (DD-CSPR) based optimization method, the proposed one can realize optical signal-to-noise ratio (OSNR) gains of 0.9 dB in the back-to-back (B2B) and 0.7 dB under 80 km fiber transmission scenarios respectively with a total bit rate of 160Gb/s.

Geometrically Shaped Odd-Bit QAM Constellations Suitable for Principal Component-Based Phase Estimation

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.