Quantization Noise Research Articles

On the Performance and Fiber Nonlinearity Modeling of Learned Digital Back-Propagation in the Presence of DAC and ADC Quantization Noise

On the Performance and Fiber Nonlinearity Modeling of Learned Digital Back-Propagation in the Presence of DAC and ADC Quantization Noise

Estimating Word Lengths for Fixed-Point DSP Implementations Using Polynomial Chaos Expansions

Efficient custom hardware motivates the use of fixed-point arithmetic in the implementation of digital signal-processing (DSP) algorithms. This conversion to finite precision arithmetic introduces quantization noise in the system, which affects the system’s performance. As a result, characterizing quantization noise and its effects within a DSP system is a challenge that must be addressed to avoid over-allocating hardware resources during implementation. Polynomial chaos expansion (PCE) is a method used to model uncertainty in engineering systems. Although it has been employed to analyze quantization effects in DSP systems, previous investigations have been limited in scope and scale. This paper introduces new techniques that allow the application of PCE to be scaled up to larger DSP blocks with many noise sources, as needed for building blocks in software-defined radios (SDRs). Design space exploration algorithms that leverage the accuracy of PCE to estimate bit widths for fixed-point implementations of DSP blocks in an SDR system are explored, and their advantages will be presented.

SNR enhanced OAM mode division multiplexing with in-band noise modulation based on cascade delta-sigma modulation.

Due to mode coupling, a high signal-to-noise ratio (SNR) is required in orbital angular momentum (OAM) modular division multiplexing (MDM) systems to improve transmission performance. In this paper, a cascade delta-sigma modulation (CDSM) scheme is proposed for OAM-MDM intensity modulation and direct detection (IM/DD) transmission. Different from the traditional DSM (TDSM) scheme, the scheme is divided into signal modulation and in-band noise modulation, in which the in-band noise modulation is used to further decrease the quantization noise generated in the signal modulation. At the same time, the output of the in-band noise modulation and the signal modulation are combined through the channel and transmitted in time division multiplexing (TDM) mode. At the receiver, the sequence generated by signal modulation and in-band noise modulation are subtracted to eliminate the in-band noise, resulting in better noise shaping performance. In this paper, an experiment of 240 Gbit/s transmission based on the CDSM scheme with two OAM modes was performed over a 2 km ring-core fiber (RCF). Similarly, the TDSM scheme and multi-stage DSM (MDSM) scheme are also employed in the same experiment setup. The experimental results show that the CDSM scheme successfully realizes 16,777,216 QAM signal transmission and the BER below the 15% soft decision forward error correction (SD-FEC) threshold in two modes. For the TDSM scheme, the BER cannot be below the SD-FEC threshold in two modes. For the MDSM scheme, the BER cannot be below the SD-FEC threshold for the OAM mode l = 2. Conversely, the BER can be below the SD-FEC threshold for the l = 3. The CDSM scheme outperforms the MDSM scheme with improvements in receiver sensitivity of 2.5 dB for the OAM mode l = 3 at the SD-FEC threshold. The results show that the CDSM scheme outperforms the TDSM scheme and MDSM scheme in two OAM modes at the same experimental conditions. Compared with the TDSM scheme and MDSM scheme, the CDSM scheme has an SNR gain of the recovered waveform with 7.1 dB and 3 dB for the two OAM modes at the SD-FEC threshold, respectively. The results also show that the OAM-MDM system based on the CDSM scheme can recover the waveform of the transmitter and realize high-fidelity transmission. This transmission scheme is advantageous for implementing high-capacity OAM-MDM optical fiber communication systems.

Parameter Estimate and Adaptive Control of DARMA Systems With Uniform Quantized Output Data

ABSTRACTThis paper is concerned with parameter estimate and adaptive control problems of deterministic autoregressive moving average (DARMA) systems on the basis of quantized data of system output signals which are generated by a kind of uniform quantizer. By designing system input signals, the extended least‐squares (ELS) algorithm with uniform output observations is proved to yield bounded estimation errors under some mild assumptions. Moreover, the adaptive tracking controller under inaccuracy observations is also designed. To analyse the properties of tracking error, we use the expanded form of the ELS and research the boundedness of quantization noise. In addition, we give the expression of tracking error and show how it depends on the size of quantization step when the quantization step satisfies some conditions. A numerical example is supplied to demonstrate the theoretical results.

A Power Analysis Method for Self-Interference Signal Components in Full-Duplex Transceivers Under Constant/Nonconstant Modulus Signal Stimulation

The existence of multiple self-interference (SI) signal components, particularly the nonlinear ones, seriously constrains the performance of self-interference cancellation (SIC) methods. To decrease the complexity of SIC methods in full-duplex devices, this article proposes a power analysis method for SI signal components in a full-duplex transceiver. The proposed method comprises a separate analysis algorithm and a system-level power model. Initially, the algorithm is conducted to obtain the spectrum of the linear and nonlinear components in the power amplifier (PA) output signal. Once the linear-to-nonlinear power ratio (LNPR) has been obtained, a system-level power model is constructed by taking both the transmitter noise and analog-to-digital converter (ADC) quantization noise into account. The proposed power model allows for the allocation of SIC method performance in multiple domains during the design of full-duplex transceivers at the top level, thereby reducing the overall system complexity. The simulation results demonstrate that in a full-duplex transceiver with only antenna isolation, the power of the SI signal component is susceptible to alterations due to the operating waveform and transmission power. Finally, the accuracy of the power analysis method is verified through measurement and Simulink.

O-band EML and 4-bits DAC enabled 112 GBaud PAM8 transmission over a 10 km SSMF without optical amplifiers.

The increasing traffic of intra-data center networks creates an urgent demand for low-cost and high-speed intensity modulation/direct detection (IM/DD) transmission. In this Letter, we propose a joint scheme combining nonlinear lookup table (NL-LUT) pre-distortion, digital pre-emphasis (DPE), and a digital resolution enhancer (DRE) to achieve high-speed and low-cost IM/DD optical links using a low-resolution digital-to-analog converter (DAC). The NL-LUT and DPE are responsible for the system nonlinear impairments and channel attenuation at high frequency, respectively, while DRE handles the quantization noise (QN) caused by high peak-to-average ratios (PAPRs) and low-resolution DAC. Leveraging the advanced pre-compensation scheme at the transmitter, we experimentally demonstrate the O-band transmission of 124 GBaud and 112 GBaud PAM8 over 2 km and 10 km SSMF, respectively, using only a 4 bits DAC and a simple 5-tap linear equalizer at the receiver-side. To the best of our knowledge, among the reported demonstrations using the low-resolution DAC without an optical amplifier, this work achieves the highest net rates of 310 Gb/s over 2 km and 280 Gb/s over 10 km of SSMF, respectively, which offers a promising solution for low-cost high-speed IM/DD transmission.

Fully dynamic zoom ADC with energy-efficient residue feedforward and two-step summation

This paper proposes a fully dynamic zoom ADC based on residue feedforward and correlated level shifting (CLS)-assisted floating inverter amplifier (FIA) technique with 200 × bandwidth/power scalability, by only changing the clock frequency. A CLS-assisted FIA which achieves 65 dB DC gain is employed to reduce errors from finite FIA gain. An energy-efficient residue feedforward path extracted from the input of the SAR ADC's comparator minimizes the leakage of the SAR ADC's quantization noise into the band. A novel two-step summation approach is proposed to minimize capacitor areas compared to a traditional passive switched-capacitor adder. The post-simulated results show the prototype ADC with near-constant energy efficiency, which scales power from 5 μW to 822 μW, achieves high resolution (>100 dB) during the scalable bandwidth. At 20 kHz BW, it achieves 106.2 dB DR, 102.0 dB SNDR, leading to FoMDR of 180.0 dB and FoMSNDR of 175.8 dB.

Systematic Analysis of Low-Precision Training in Deep Neural Networks: Factors Influencing Matrix Computations

As Deep Neural Networks (DNNs) continue to increase in complexity, the computational demands of their training have become a significant bottleneck. Low-precision training has emerged as a crucial strategy, wherein full-precision values are quantized to lower precisions, reducing computational overhead while aiming to maintain model accuracy. While prior research has primarily focused on minimizing quantization noise and optimizing performance for specific models and tasks, a comprehensive understanding of the general principles governing low-precision computations across diverse DNN architectures has been lacking. In this paper, we address this gap by systematically analyzing the factors that influence low-precision matrix computations, which are fundamental to DNN training. We investigate three critical factors—accumulation in matrix calculations, the frequency of element usage, and the depth of matrices within the model—and their impact on low-precision training. Through controlled experiments on standard models, as well as customized experiments designed to isolate individual factors, we derive several key insights: layers with higher accumulation and matrices with lower usage frequencies demonstrate greater tolerance to low-precision noise, without significantly compromising the stability of model training. Additionally, while the depth of matrices influences the stability of matrix operations to some extent, it does not have a noticeable effect on the overall training outcomes. Our findings contribute to the development of generalizable principles for low-precision training, offering a systematic framework applicable across various DNN architectures. We provide empirical evidence supporting the strategic allocation of training bit-widths based on the analyzed factors, thereby enhancing the efficiency and effectiveness of DNN training in resource-constrained environments.

Low Complexity Digital Resolution Enhancer for Clipping and Quantization Noise Suppression With Low-Resolution DAC

Low Complexity Digital Resolution Enhancer for Clipping and Quantization Noise Suppression With Low-Resolution DAC

A 10 MHz‐BW 85 dB‐SNDR 4th‐order sturdy MASH 2‐0 noise shaping SAR ADC with 2nd‐order gain‐error‐shaping technique

AbstractThe multi‐stage noise shaping (MASH) ΣΔ ADC has a good potential to achieve high‐order noise shaping (NS) and high resolution. However, it suffers from quantization noise leakage caused by the mismatch between the analogue NS filter and the digital cancellation filter, which greatly degrades the ADC performance. The sturdy MASH topology of the ΣΔ ADC can solve the leakage issue, but it cannot be implemented using the NS SAR ADC due to structural limitations. This paper proposes a sturdy MASH 2‐0 NS SAR to solve the noise leakage issue. The 4th‐order NS is achieved by only using a 2‐0 topology, which is hardware efficient. Instead of eliminating the first‐stage quantization error, the proposed sturdy MASH 2‐0 NS SAR shapes it, achieving better robustness to PVT variables. Furthermore, owing to the first‐stage 2nd‐order NS capability, the impairments of the residue amplifier, including the gain error and nonlinearity, are 2nd‐order shaped. The proposed 4th‐order sturdy MASH 2‐0 NS SAR is implemented in a 28 nm CMOS process, which achieves a SNDR of 85.6 dB and a SFDR of 101.3 dB with 10 MHz BW at OSR of 10, resulting in a Schreier FoM of 178.8 dB/179.4 dB (in SNDR/DR) with power consumption of 4.8 mW.

Analyze the impact of nonlinear distortions on OFDM-based visible light communication systems

Visible light communication (VLC) has gained attraction for its use in high-speed wireless connectivity leveraging LED lighting elements. Orthogonal Frequency Division Multiplexing (OFDM) is an attractive modulation scheme due to its spectral efficiency and resilience to multipath distortion. However, the nonlinear electro-optic transfer characteristics of optical components introduce signal clipping and quantization noise which corrupt OFDM signals. This paper provides an in-depth analysis of clipping and quantization noise to quantify the impact of LED nonlinearities on OFDM-based VLC system performance. Detailed mathematical models are derived for clipping distortions caused by LED optical power saturation and quantization errors from ADC/DAC finite precision in the modulator and driver circuitry. This analysis is quantified through simulations of the degradations in terms of error vector magnitude (EVM), signal-to-noise ratio (SNR) loss, and bit error rate (BER) under varying clipping ratios and quantization bit-depths. The 16-QAM OFDM transmission shows that the LED driver should possess at least 12 dB signal linear dynamic range and 3-bit quantization to restrict SNR penalty within 3 dB. Adaptive tone mapping and digital pre-distortion techniques are examined to compensate for intensity distortions enabling high-speed OFDM transmission over VLC links.

End-to-end learning of joint noise shaping and probabilistic shaping for OAM mode division multiplexing transmission.

Intensity modulation direct detection (IM/DD) orbital angular momentum (OAM) mode division multiplexing (MDM) technology can greatly expand the capacity of a communication system, which is a promising solution for the next generation of high-speed passive optical networks (PONs). However, there are serious obstacles such as mode coupling, device nonlinear impairment, and quantization noise in an IM/DD OAM-MDM system with a low-resolution digital-to-analog converter (DAC). In this Letter, we propose a novel, to the best of our knowledge, end-to-end (E2E) learning scheme based on a double residual feature decoupling network (DRFDnet) emulator with joint probabilistic shaping (PS) and noise shaping (NS) for the OAM-MDM IM/DD transmission. Our DRFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal impairments into linear and nonlinear. Meanwhile, a DRFDnet-based E2E scheme for joint PS and NS is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 200 Gbit/s PON system based on the OAM-MDM IM/DD transmission. The experimental results demonstrate that the proposed DRFDnet-based joint PS and NS scheme is a promising solution to effectively mitigate nonlinear distortions and outperforms the CGAN-based joint PS and NS scheme and traditional joint PS and NS scheme with receiver sensitivity improvements of 1.2 dBm and 2.5 dBm under hard-decision forward error correction (HD-FEC) thresholds, respectively. Our experimental results demonstrate that the proposed DRFDnet emulator-based E2E learning scheme is a viable candidate for future PON.

Impacts of sampling on the artificial noise-assisted terahertz secure communication systems

In this paper, we investigate an artificial noise (AN)-assisted terahertz (THz) secure communication system. Different from previous studies, we consider a non-ideal analog-to-digital converter (ADC) in the AN-THz system. Specifically, both synchronization noise and quantization noise in ADC are investigated. The normalized distortion matric is employed to calculate synchronization noise power and the Bellman’s theory is introduced for quantization noise power. Under the constrain of limited ADC power, the secrecy performance presents a ‘U-shaped’ curve versus the sampling rate and therefore the optimal sampling rate is derived. Moreover, we validate our theoretical model in the experiment, and our experimental results in 102 GHz show the synchronization noise power varies with the square of timing error, and the quantization noise power is affected by the total data length, which agree well with the model predictions.

Explainable Deep Learning Approach for High Impedance Fault Localization in Resonant Distribution Networks Considering Quantization Noise

ABSTRACTIn addressing the quantization noise challenge in high impedance fault (HIF) localization within resonant distribution networks, we propose a cutting‐edge, explainable deep learning approach that significantly advances existing methods. This approach utilizes differential zero‐sequence voltage (DZSV) and zero‐sequence current (ZSC) and introduces a novel “Vague” classification to improve localization accuracy by effectively managing quantization noise‐distorted signals. This approach extends beyond the conventional binary classification of “Fault” and “Sound,” incorporating a multi‐scale feature attention (MFA) mechanism for enriched internal explainability and applying gradient‐weighted class activation mapping (Grad‐CAM) to visualize critical input areas precisely. Our model, validated in an industrial prototype, exhibits unparalleled adaptability across various environmental conditions, including environmental noise, variable sampling rates, and triggering deviations. Comparative analysis reveals that our approach outperforms existing methods in managing diverse fault scenarios.

Adaptive Filtering of Pulse Waves for the Improvement of Ultrasonic Carotid LPWV Estimation Method

Abstract Aiming at promoting the accuracy of the ultrasonic carotid local pulse wave velocity (LPWV) estimation, an adaptive filtering of pulse waves for the ultrasonic carotid transit time-based LPWV estimation is proposed. First, the upstroke of pulse wave (PWU) is decomposed into time-frequency domain adaptively by an empirical wavelet transform (EWT) method, and then the noises (include the quantization noise and reflected wave in pulse wave) are picked up with predetermined threshold by multiple EWT decompositions. The proposed adaptive filtering of pulse waves for the LPWV estimation is quantitatively evaluated by an ultrasound simulation model for three age groups. Results show that the mean error of EWT-based PWU filtering are just 3.49 %, and the PWV estimation error for the three age groups are 5.77 ± 2.45 %, 4.54 ± 3.46 % and 12.24 ± 5.36 %, respectively by the EWT-based PWU filtering, which is lower than that by SG filtering. The results could be expected to provide theoretical basis and technical support for the early quantitative evaluation of local carotid vascular elasticity in clinic.

Performance of massive MIMO‐NOMA systems with low complexity group SIC receivers and low‐resolution ADCs

AbstractMassive multiple‐input multiple‐output and non‐orthogonal multiple access (MIMO‐NOMA) with low‐resolution analog‐to‐digital converters (ADCs) have been widely considered for the next‐generation wireless communication systems. However, the performance of the system including power‐scaling law has not been well investigated for the practical low complexity receivers. Employing the additive quantization noise model, we derive asymptotic approximate expressions of the spectrum efficiency for the system with group successive interference cancellation (GSIC) receivers over Rician fading channels. Based on these approximations, we conduct a unified asymptotic analysis for the system with linear, SIC, and GSIC receivers. The analysis reveals the transmission power can be scaled by the number of antennas for the system with GSIC receivers and shows the effects of crucial parameters including the number of groups, resolution bits, and antennas on the performance. Given a quality of service, the minimum data transmission power is also calculated for each user and the corresponding approximate power allocation is derived. The asymptotic analysis and the accuracy of the power allocation approximation are then verified by simulation results. Numerical results also demonstrate that high spectrum efficiency and energy efficiency can be achieved by the system with medium‐resolution ADCs and low complexity maximum ratio combining‐GSIC receivers with a small number of groups.

Digital mobile fronthaul scheme based on diff-delta-sigma modulation and OCT precoding.

In this Letter, we experimentally demonstrate digital mobile fronthaul (MFH) for 65536 quadrature amplitude modulation (65536-QAM) signals based on a diff-delta-sigma modulation (D-DSM) scheme with orthogonal circulant matrix transform (OCT) precoding. By combining the D-DSM scheme with OCT precoding, we successfully solved the problem of uneven distribution of in-band quantization noise (IBN) while bringing about a quantization SNR gain of about 1.5 dB. In addition, we compare two signal combination schemes, Gray coding and power superposition, in the D-DSM scheme. The results show that the power superposition scheme can achieve similar performance to Gray coding with lower computational complexity. At the same time, the power superposition scheme is less affected by the saturation effect. Therefore, the D-DSM solution combined with OCT precoding and power superposition provides an effective solution for future 6 G digital mobile fronthaul.

High-Precision Digital Clock Steering Method Based on Discrete Σ-Δ Modulation for GNSS

A high-precision time reference is fundamental to the positioning, navigation, and timing (PNT) of global navigation satellite systems (GNSS). The precision of clock steering determines the accuracy of practical applications that rely on the time–frequency reference. With the invention of direct digital synthesizer (DDS) technology, digital clock steering (DCS) has gradually become a mainstream technology. However, the key factor limiting DCS accuracy is the system quantization noise, which leads to a low frequency and phase adjustment accuracy. Here we propose a DCS method based on Σ-Δ modulation to address the issue of low resolution of DAC through shaping the quantization noise. A simulated GNSS time–frequency reference system experimental platform is constructed to validate the effectiveness of the proposed method. The experimental results demonstrate that this method achieves a phase adjustment accuracy of 0.48 ps and a frequency adjustment accuracy better than 0.48 pHz, which is two orders of magnitude higher than that of existing GNSS time–frequency reference systems. Thus, the proposed method offers a significant improvement in time–frequency reference systems, leading to better performance, reliability, and accuracy in a wide range of practical applications.

Automatic adjustment of the parameters of the temperature measurement algorithm in a wide range

Existing methods and devices for measuring temperature are described, and it is noted that resistance thermometers are most widely used as temperature sensors in systems for collecting and monitoring environmental parameters. It is shown that the main source of temperature measurement errors when connecting sensors remotely is the resistance of the connecting lines, determined by their length. The main methods for reducing the measurement error caused by the influence of the resistance of the vehicle connection line on the temperature measurement results are considered. The advantages of two-wire circuits in comparison with three- and four-wire circuits are formulated. As an analogue, a two-wire method of measuring temperature with an integrating converter is considered in detail, implemented on the basis of a device with a built-in microcontroller, and allowing to obtain such advantages as reducing measurement time, detuning from interference and quantization noise and, as a result, reducing the temperature measurement error in comparison with similar two-wire measurement methods. An alternative two-wire method for measuring temperature with automatic adjustment of the parameters of the measurement algorithm is proposed, aimed at increasing the measurement accuracy by weakening the influence of the time constant. The search for the optimal time of the first integration step was carried out. Experimental studies and evaluation calculations were carried out to confirm the effectiveness of the proposed solution. The coefficient of variation when the resistance of the vehicle changes in the range of 1–4 kOhm lies in the range, and the range of change in the relative error of resistance measurement when using auto-tuning within the specified range has decreased by more than 4 times. The results of the experiment allow us to count on the possibility of using the method in control and regulation systems with remote connection of temperature sensors.

Performance improvement by an optimum companding-based Non-Uniform quantization scheme in low-bit resolution IMDD-UFMC system

In this paper, an optimum non-uniform quantization method is presented in the intensity-modulated direct detection universal filter multicarrier (IMDD-UFMC) system to achieve the system performance improvement with low-bit resolution digital-to-analog converter (DAC). By this specifically-designed companding quantizer without the probability density function (PDF) estimation, the number and interval size of the quantization interval allocated in the low probability region and the high probability region can be balanced with a modified optimal mapping relationship to obtain the optimal quantized level and then the low quantization noise is realized to greatly reduce the bit resolution of DAC in IMDD-UFMC system. Owing to this scheme is essentially a peak-to-average power ratio (PAPR) suppression technology of signal distortion, PAPR performance can be improved at the same time. Compared to the clustering and nonlinear programming schemes, the system performance in term of bit error rate (BER) can be improved and the difficulty of implementation can be reduced in the 25-Gb/s transmission system through 20-km fiber transmission. Moreover, a simplified method is presented by fitting the corresponding companding curve with error function and logistic function, which further decreases the complexity of the optimal non-uniform quantization. In this way, our scheme can offer a significant advancement in the design of IMDD-UFMC systems and has the potential to enhance the performance of future multi-carrier optical communication systems.