Quantization Noise Power

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A. Lee Swindlehurst - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO
    IEEE Journal on Selected Areas in Communications, 2020
    Co-Authors: Hessam Pirzadeh, Gonzalo Seco-granados, Shilpa Rao, A. Lee Swindlehurst
    Abstract:

    Author(s): Pirzadeh, H; Seco-Granados, G; Rao, S; Swindlehurst, AL | Abstract: IEEE We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta (Σ) sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the Quantization error between adjacent antennas, the method shapes the spatial spectrum of the Quantization Noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the ΣΔ approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial Quantization Noise Power spectrum are derived for the ΣΔ array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the ΣΔ approach for both MRC and zero-forcing receivers.

  • Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO
    eScholarship University of California, 2020
    Co-Authors: Pirzadeh H, Seco-granados G, Rao S, A. Lee Swindlehurst
    Abstract:

    © 1983-2012 IEEE. We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta ( \Sigma \Delta ) sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the Quantization error between adjacent antennas, the method shapes the spatial spectrum of the Quantization Noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the \Sigma \Delta approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial Quantization Noise Power spectrum are derived for the \Sigma \Delta array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the \Sigma \Delta approach for both MRC and zero-forcing receivers

Anne-johan Annema - One of the best experts on this subject based on the ideXlab platform.

  • Using Recursive Multibit Sigma-Delta Modulators to Reduce the Quantization Noise Power
    2004
    Co-Authors: Daniel Schinkel, Adrianus Johannes Maria Van Tuijl, Anne-johan Annema
    Abstract:

    This paper discusses a recursive multibit Σ∆ architecture that enables a high effective quantizer resolution while needing only a limited number of DAC elements. The recursive architecture consists of a set of Σ∆ modulators, whereby each stage cancels the Quantization Noise of the preceding stage. Conventional DEM algorithms can be used in each stage to reduce the sensitivity to mismatch. The architecture enables a significant reduction of both the signal-band and out-ofband Quantization Noise Power, compared to conventional multibit Σ∆ converters.

  • Reducing Quantization Noise With Recursive ΣΔ Modulators
    2004
    Co-Authors: Daniel Schinkel, Ed Van Tuijl, Anne-johan Annema
    Abstract:

    This paper introduces a recursive multibit ΣΔ architecture that enables a high effective quantizer resolution while needing only a limited number of DAC elements. The recursive architecture consists of a set of ΣΔ modulators, whereby each stage cancels the Quantization Noise of the preceding stage. Conventional DEM algorithms can be used in each stage to reduce the sensitivity to mismatch. The architecture enables a significant reduction of both the signal-band and out-of-band Quantization Noise Power, compared to conventional multibit ΣΔ converters.

  • Using Recursive Multibit ΣΔ Modulators to Reduce the Quantization Noise Power
    2004
    Co-Authors: Daniel Schinkel, Ed Van Tuijl, Anne-johan Annema
    Abstract:

    This paper discusses a recursive multibit ΣΔ architecture that enables a high effective quantizer resolution while needing only a limited number of DAC elements. The recursive architecture consists of a set of ΣΔ modulators, whereby each stage cancels the Quantization Noise of the preceding stage. Conventional DEM algorithms can be used in each stage to reduce the sensitivity to mismatch. The architecture enables a significant reduction of both the signal-band and out-of-band Quantization Noise Power, compared to conventional multibit ΣΔ converters.

  • Reducing Quantization Noise with recursive /spl Sigma//spl Delta/ modulators
    2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), 1
    Co-Authors: D. Schinel, Ed Van Tuijl, Anne-johan Annema
    Abstract:

    This paper introduces a recursive multibit /spl Sigma//spl Delta/ architecture that enables a high effective quantizer resolution while needing only a limited number of DAC elements. The recursive architecture consists of a set of /spl Sigma//spl Delta/ modulators, whereby each stage cancels the Quantization Noise of the proceeding stage. Conventional DEM algorithms can be used in each stage to reduce the sensitivity to mismatch. The architecture enables a significant reduction of both the signal-band and out-of-band Quantization Noise Power, compared to conventional multibit /spl Sigma//spl Delta/ converters.

Dario Petri - One of the best experts on this subject based on the ideXlab platform.

  • Integral non-linearity in memoryless A/D converters
    Measurement, 2008
    Co-Authors: Antonio Moschitta, Dario Petri
    Abstract:

    This paper investigates the statistical properties of Quantization Noise. In particular, a theoretical model is discussed, which evaluates the Power of Quantization Noise introduced by a memoryless Analog to Digital Converter (ADC) as a function of both the converted signal distribution and the ADC thresholds positioning. Expressions have also been derived to express the Integral Non-Linearity (INL) contribution to Quantization Noise Power as an additive term, and to evaluate such a term with a simple formula. Simulation results that validate the proposed expression are provided.

  • Spectral Estimation of Wideband Noise in Delta–Sigma Modulators
    IEEE Transactions on Instrumentation and Measurement, 2006
    Co-Authors: Elisabetta Nunzi, Paolo Carbone, Dario Petri
    Abstract:

    Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored Noise has not yet been fully characterized. In this paper, the effect of the windowing process on the estimate of the in-band DeltaSigma-shaped Quantization-Noise Power spectral density is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window and proves the necessity of the windowing process in order to reduce the in-band Noise Power estimation bias. Moreover, an a priori criterion for designing the optimal window that reduces the shaped-Noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived

  • Spectral Estimation of Wideband Noise in
    2006
    Co-Authors: Elisabetta Nunzi, Paolo Carbone, Dario Petri
    Abstract:

    Spectral leakage is a well-known phenomenon in- duced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored Noise has not yet been fully characterized. In this paper, the effect of the windowing process on the estimate of the in-band ∆Σ-shaped Quantization- Noise Power spectral density is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window and proves the necessity of the windowing process in order to reduce the in-band Noise Power estimation bias. Moreover, an ap rioricriterion for designing the optimal window that reduces the shaped-Noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived.

  • Spectral Estimation of Wide-band Noise in Delta-Sigma Modulators
    2005 IEEE Instrumentationand Measurement Technology Conference Proceedings, 2005
    Co-Authors: Elisabetta Nunzi, R. Carbone, Dario Petri
    Abstract:

    Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored Noise has not been fully characterized, yet. In this paper the effect of the windowing process on the estimate of the in-band DeltaSigma -shaped-Quantization Noise Power spectral density (PSD) is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window. Moreover, an a-priori criterion for designing optimal window that reduces shaped Noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived

  • Stochastic properties of Quantization Noise in memoryless converters affected by integral non-linearity
    Proceedings of the 20th IEEE Instrumentation Technology Conference (Cat. No.03CH37412), 2003
    Co-Authors: Antonio Moschitta, Dario Petri
    Abstract:

    This paper is focused on the stochastic properties of Quantization Noise introduced by non-ideal memoryless converters. In particular, overloading effects and integral nonlinearity (INL) are considered. A theoretical model is given, which accurately describes the Quantization Noise probability density function in presence of overloading Noise and both deterministic and stochastic INL. The model is also extended to derive Quantization Noise Power as a function of both input signal and INL stochastic properties. Finally, the results are applied to a memoryless converter affected by Gaussian distributed INL, analyzing the properties of Quantization Noise.

Hessam Pirzadeh - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO
    IEEE Journal on Selected Areas in Communications, 2020
    Co-Authors: Hessam Pirzadeh, Gonzalo Seco-granados, Shilpa Rao, A. Lee Swindlehurst
    Abstract:

    Author(s): Pirzadeh, H; Seco-Granados, G; Rao, S; Swindlehurst, AL | Abstract: IEEE We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta (Σ) sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the Quantization error between adjacent antennas, the method shapes the spatial spectrum of the Quantization Noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the ΣΔ approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial Quantization Noise Power spectrum are derived for the ΣΔ array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the ΣΔ approach for both MRC and zero-forcing receivers.

Daniel Menard - One of the best experts on this subject based on the ideXlab platform.

  • Quantization Noise Power Estimation for Floating-Point DSP Circuits
    IEEE Transactions on Circuits and Systems II: Express Briefs, 2016
    Co-Authors: Gabriel Caffarena, Daniel Menard
    Abstract:

    In this brief, we present a semianalytical model of the Quantization Noise Power of floating-point DSP circuits, considering heterogeneous precisions. The use of hardware operators with optimized precisions has proven to provide important cost reductions. However, precision optimization is a time-consuming task, and fast and accurate error estimators are required. Moreover, the use of the signal-to-Quantization Noise ratio (SQNR) as a quality reference is common in DSP design, and there are no proper models to perform fast estimation in the context of floating-point systems with heterogeneous precision. The model presented here accounts for the Quantization produced when the size of the mantissa of a floating-point signal is modified along the datapath and it has negligible dependence with the signal statistics. In addition, the model is appropriate for fast SQNR estimations and can be integrated in current Quantization optimizers. The results show that the semianalytical model has an estimation error of less than 2% when compared to a simulation-based reference, whereas other approaches introduce estimation errors of up to 52%.

  • ICCAD - A polynomial time algorithm for solving the word-length optimization problem
    2013 IEEE ACM International Conference on Computer-Aided Design (ICCAD), 2013
    Co-Authors: Karthick Parashar, Daniel Menard, Olivier Sentieys
    Abstract:

    Trading off accuracy to the system costs is popularly addressed as the word-length optimization (WLO) problem. Owing to its NP-hard nature, this problem is solved using combinatorial heuristics. In this paper, a novel approach is taken by relaxing the integer constraints on the optimization variables and obtain an alternate Noise-budgeting problem. This approach uses the Quantization Noise Power introduced into the system due to fixed-point word-lengths as optimization variables instead of using the actual integer valued fixed-point word-lengths. The Noise-budgeting problem is proved to be convex in the rounding mode Quantization case and can therefore be solved using analytical convex optimization solvers. An algorithm with linear time complexity is provided in order to realize the actual fixed-point word-lengths from the Noise budgets obtained by solving the convex Noise-budgeting problem.

  • A Discrete Model for Correlation Between Quantization Noises
    IEEE Transactions on Circuits and Systems II: Express Briefs, 2012
    Co-Authors: J-c Naud, Gabriel Caffarena, Daniel Menard, Olivier Sentieys
    Abstract:

    The automation of fixed-point conversion requires fast methods to evaluate the numerical accuracy of the system. As an alternative to a simulation-based approach, most of the analytical methods use perturbation theory to provide the expression of the Quantization Noise at the output of a system. Most existing analytical methods do not consider a correlation between Noise sources. This assumption is no longer valid when a unique datum is quantized several times. This brief proposes to study the correlation between Quantization Noises with different Quantization modes (truncation and rounding) and considering the number of eliminated bits. Then, the expression of the Power of the output Quantization Noise is provided when the correlation between the Noise sources is considered. The proposed approach allows improving significantly the estimation of the output Quantization Noise Power compared to the classical approach, with a slight increase of the computation time. In our experiment, the maximal relative estimation error obtained with the proposed approach is less than 2% compared to 84% when a correlation is not taken into account.

  • ACCURACY EVALUATION OF FIXED-POINT BASED LMS ALGORITHM
    Digital Signal Processing, 2010
    Co-Authors: Romuald Rocher, Daniel Menard, Olivier Sentieys, Pascal Scalart
    Abstract:

    The implementation of adaptive filters with fixed-point arithmetic requires computation quality evaluation. The accuracy may be determined by computing the global Quantization Noise Power at the system output. In this paper, a new model for evaluating analytically the global Noise Power in LMS-based algorithms is presented. Thus, the model is developed for LMS and NLMS algorithms. The accuracy of our model is analyzed by simulations.

  • ICASSP - Analytical approach for analyzing Quantization Noise effects on decision operators
    2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010
    Co-Authors: Karthick Parashar, Daniel Menard, Romuald Rocher, Olivier Sentieys
    Abstract:

    The presence of decision operators has proved to be a serious impediment for a fully analytical Noise Power estimation technique. This paper proposes a generalized decision operator which can potentially capture the behavior of all possible types of decision operators and provides a fully analytical technique to handle them while performing Quantization Noise Power estimation. The proposed method is applied to BPSK and 16-QAM decision operators. The total error rate and the PDF of the error signal are found to follow the simulation to a great degree of accuracy.