Analysis Of Quantization Noise Research Articles

Analysis of Quantization Noise in Fixed-Point HDFT Algorithms

Analysis of Quantization Noise in Fixed-Point HDFT Algorithms

Quantization noise analysis in FBMC receivers and its effect on the BER performance

This paper analyzes the fixed-point and floating-point roundoff errors in different Filter Bank MultiCarrier (FBMC) receiver implementations. Two different structures are considered: the polyphase network based and frequency spreading based. Theoretical closed-form formulas for the total Quantization Noise Power (QNP) are derived and verified through simulation. The results show the effects of each parameter and signal processing block on the overall QNP. Also, the results show that the total QNP for an arbitrary set of parameters can be determined using the derived results without performing exhaustive simulations. The effects of the chosen bit-resolution on the bit-error rate performance are also analyzed. Furthermore – based on the theoretical results – FBMC receivers can be designed with an optimal number of bits used in the arithmetic units without significantly affecting the receiver performance.

Analysis of quantization noise in FBMC transmitters

This paper investigates Filter Bank MultiCarrier (FBMC) modulation implemented with frequency spreading and polyphase network-based in terms of the introduced quantization noise. As FBMC is considered one of the future candidates for 5G/6G communication systems due to its advantageous spectral properties, the introduced quantization noise in the implementation is an essential design criterion. Analytical expressions for fixed- and floating-point Quantization Noise Power (QNP) in FBMC transmitter schemes are given. Based on the results, it can be stated that the total QNP depends on the number of carriers, overlapping symbols, and the resolution of the quantizer. The results are verified through simulations. Estimating the quantization noise in FBMC systems in the function of the selected bit resolution and keeping it at an acceptable level is an essential design step. The results can be directly employed in the preliminary hardware design of FBMC transmitters, where the choice of the arithmetical units and the bit resolution is a key factor.

Jitter Modeling in Digital CDR with Quantization Noise Analysis

Phase rotator-based digital clock and data recovery (CDR) using multi-level bang-bang phase detector (ML-BBPD) and time to digital converter (TDC) is analyzed at system and circuit level. A model is proposed for calculating the quantization noise and bit error rate (BER), in order to evaluate the important parameters in CDR design. The jitter analysis is done based on the probability density function achieved from the quantization noise error of the BBPD and TDC. The analysis of ML-BBPD is shown that by increasing the number of sampling clocks, the quantization noise and consequently the jitter and BER are significantly reduced. Also, it is shown that by improving the resolution of the TDC and increasing number of delay cells for the purpose of keeping fixed the dynamic range, the output jitter of TDC is decreased. In the proposed model and also simulation, it is approved that by increasing the ratio of RMS input Gaussian jitter to the quantization step, the output jitter reaches to its saturated value. To prove the jitter model, the goodness of fit test based on Kolmogorov–Smirnov test is used and in addition, the simulation is provided for circuit level CDR. The circuit level simulation is done in TSMC 65 nm CMOS technology. The CDR is worked under 1 V supply voltage at 480Mbit/s bit rate useful for USB2 applications. The CDR dissipates 913 µW power and generates 0.258 ps RMS jitter, while it occupies 166 µm × 104 µm chip area.

Clean Bandwidth Improvement of MPWM Encoding Method for RF All-Digital Transmitter

In radio frequency (RF) all-digital transmitters (ADTs), pulse encoding methods are often used to generate the RF signal of one or several bits, which introduces a large amount of quantization noise (QN). The QN results in a limited clean bandwidth (CBW), which increase the design difficulty of the analog filter significantly. To solve this problem, an optimized mapping pulse width modulation (MPWM) encoding method is presented in this brief. Based on the QN analysis, the concept of noise figure (NF) for MPWM is introduced. Meanwhile, the formulae of the intermedia frequency (IF) and RF QN power in CBW are derived. Then, in the mapping of the IF signal to the RF pulse, the optimized RF pulses are searched by the NF calculation and comparison. Experiments results show that, compared with original MPWM method, the CBW of proposed method is increased by more than 3 times, and it is superior to the other reported approaches.

Signal Processing Methods to Enhance the Energy Efficiency of In-Memory Computing Architectures

This paper presents signal processing methods to enhance the energy vs. accuracy trade-off of in-memory computing (IMC) architectures. First, an optimal clipping criterion (OCC) for signal quantization is proposed in order to minimize the precision of column analog-to-digital converters (ADCs) at iso-accuracy. For a Gaussian distributed signal, the OCC is shown to reduce the column ADC precision requirements by 3 bits at an signal-to-quantization noise ratio (SQNR) of 22.5 dB over the commonly used full range (FR) quantizer. Next, the input-sliced weight-parallel (ISWP) IMC architecture is presented as a generalization of the popular bit-serial bit-parallel (BSBP) architecture. Quantization noise analysis of the ISWP indicates that its accuracy is comparable to BSBP while providing an order-of-magnitude reduction in energy consumption due to fewer array invocations and smaller ADC precision. Combining OCC and ISWP noise analysis, we map popular DNNs such as VGG-9 (CIFAR-10), ResNet-18 (CIFAR-10), and AlexNet (ImageNet) on a OCC-enabled ISWP architecture and show a reduction in energy consumption by an order-of-magnitude at iso-accuracy over the BSBP architecture that employs FR-based ADCs.

Analysis of quantization noise and state estimation with quantized measurements

The approximate correction of the additive white noise model in quantized Kalman filter is investigated under certain conditions. The probability density function of the error of quantized measurements is analyzed theoretically and experimentally. The analysis is based on the probability theory and nonparametric density estimation technique, respectively. The approximator of probability density function of quantized measurement noise is given. The numerical results of nonparametric density estimation algorithm demonstrate that the theoretical conclusion is reasonable. Based on the analysis of quantization noise, a novel algorithm for state estimation with quantized measurements also is proposed. The algorithm is based on the least-squares estimator and unscented transform. By least-squares estimator, the effective information is extracted from the quantized measurements. Also, using the information to update the estimated state can give a better estimation under the influence of quantization. The root mean square error (RMSE) of the proposed algorithm is compared with the RMSE of the existing methods for a typical tracking scenario in wireless sensor networks systems. Simulations provide a strong evidence that this tracking algorithm could indeed give us a more precise estimated result.

Statistical Analysis of Quantization Noise in an End-to-End OFDM Link

Quantization is an important operation in digital communications systems. It not only introduces quantization noise but also changes the statistical properties of the quantized signal. Furthermore, quantization noise cannot be always considered as an additive source of Gaussian noise as it depends on the input signal probability density function. In orthogonal-frequency-division-multiplexing transmission the signal undergoes different operations which change its statistical properties. In this paper we analyze the statistical transformations of the signal from the transmitter to the receiver and determine how these effect the quantization. The discussed process considers the transceiver parameters and the channel properties to model the quantization noise. Simulation results show that the model agrees well with the simulated transmissions. The effect of system and channel properties on the quantization noise and its effect on bit-error-rate are shown. This enables the design of a quantizer with an optimal resolution for the required performance metrics.

Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters

This paper considers the problem of reconstructing a class of nonuniformly sampled bandlimited signals of which a special case occurs in, e.g., time-interleaved analog-to-digital converter (ADC) systems due to time-skew errors. To this end, we propose a synthesis system composed or digital fractional delay filters. The overall system (i.e., nonuniform sampling and the proposed synthesis system) can be viewed as a generalization of time-interleaved ADC systems to which the former reduces as a special case. Compared with existing reconstruction techniques, our method has major advantages from an implementation point of view. To be precise, (1) we can perform the reconstruction as well as desired (in a certain sense) by properly designing the digital fractional delay filters, and (2) if properly implemented, the fractional delay filters need not be redesigned in case the time skews are changed. The price to pay for these attractive features is that we need to use a slight oversampling. It should be stressed, however, that the oversampling factor is less than two as compared with the Nyquist rate. The paper includes error and quantization noise analysis. The former is useful in the analysis of the quantization noise and when designing practical fractional delay filters approximating the ideal filters.

Quantization noise analysis of sign/logarithm data encoders when excited by speech or sinusoidal inputs

In many digital signal processing applications, the use of sign/logarithm data encoding is valuable. Simple formulas that predict usable dynamic range for systems employing sign/logarithm arithmetic when excited either by speech or sinusoidal inputs are derived.

Reduction of quantization noise in the Notch Fourier transform

The paper considers the problem of quantization noise in the Notch Fourier transform (NFT). Quantization noise analysis is performed and a mixed configuration error spectrum shaping (ESS) technique is applied in order to reduce the quantization noise. The ESS structures are kept simple and efficient while effectively reducing the quantization noise.

Error spectrum shaping in linear phase frequency sampling FIR filters

The paper considers the problem of quantization noise in linear phase frequency sampling FIR filters. After the quantization noise analysis, the error spectrum shaping (ESS) technique is applied in a mixed configuration, depending on the specific noise source. The quantization noise created in the front-end of the filter and amplified in the parallel resonators, is effectively reduced by a unique, efficient comb filter ESS realization. The noise sources at the parallel resonators are compensated by low complexity (multiplication-free or one shift only operations) ESS structures. The mixed ESS configuration achieves substantial noise reduction while minimizing the complexity of the error spectrum shaping network, thus making it attractive for practical implementation. The analysis is confirmed by simulations.

Quantization noise analysis and error feedback implementation in frequency sampling FIR filters

This paper considers the problem of quantization noise in frequency sampling complex FIR filters. The error feedback (EFB) method — in which the discarded part of the word is appropriately fed back to the filter, so as to reduce the total effect, is utilized in order to reduce the quantization noise. We find conditions on the EFB scheme which pertain, separately, to each branch of the frequency sampling structure. These conditions ensure both noise reduction and the prevention of additional quantization, which may be created by EFB itself. The amount of improvement is a function of the filter characteristics and the specific implementation. Formulas for the improvement are developed and confirmed by simulation.

Spectral analysis of quantization noise in a single-loop sigma-delta modulator with DC input

An exact discrete-time analysis of the moments and spectra of the quantization noise of a discrete-time single-loop sigma-delta modulator with a DC input is presented. An exact difference equation for the discrete-time nonlinear system is used to evaluate the first- and second-order moments and power spectrum of the binary quantizer noise and the binary quantizer output for a single-loop sigma-delta encoder with a DC input. It is shown that the sample mean and power of the binary quantization noise are consistent with the common uniform distribution assumption, but that the autocorrelation and power spectrum are not consistent with the white noise assumption. The results are used to evaluate the overall sample average mean squared quantization error as a function of the decimation filter used. >

Quantization noise analysis of a general digital filter

A new, precise modeling technique is presented for the exact representation of digital filters, discrete systems, or computational algorithms. It leads to a method for the determination of the noise variance of the filter output due to quantization errors occurring at multipliers, summers, and the A/D converter. The noise formulae are in either infinite series or closed form and through their use a precise evaluation of an arbitrary filter structure may be obtained. The formulas can be easily computer implemented and require no filter analysis by the designer. The special case of state-space filters is examined in detail. Appropriate numerical examples are included.

Quantization noise analysis for fixed-point digital filters using magnitude truncation for quantization

Two methods are described for the determination of the quantization errors in digital filters using magnitude truncation quantization. The first method is very accurate but rather cumbersome for numerical analysis. The second method overcomes this disadvantage and uses a quasi-linearization technique. Results are given that indicate the very good agreement between computations and results of simulations, both for a second-order and for a tenth-order recursive digital filter.