An SQNR Improvement Technique Based on Magnitude Segmentation for Polar Quantizers

IEEE Transactions on Circuits and Systems I: Regular Papers, 2000

This thesis presents the theory and analysis of IF polar receiver (PRX) architecture. By using new quantization techniques in the polar domain, the proposed receiver can boost the signal to quantization noise ratio (SQNR) compared to a traditional rectangular (I/Q) receiver. The proposed PRX is composed of a magnitude and a phase quantizer. The magnitude quantizer is similar to the conventional rectangular quantizer in voltage domain. The phase quantizer employs a time-todigital converter (TDC) for phase detection. Furthermore, an intuitive graphical method is used to analyze the quantization properties of the polar quantization. A 10 bit polar quantizer is designed and fabricated in 130nm CMOS, and achieves 2-to 5-dB of SQNR improvement compared to rectangular quantizer for signal bandwidths as high as 20MHz.

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2011

PurposeThe purpose of this paper is to address the problem of polar quantization optimization. Particularly, the aim is to find the method for the optimal resolution‐constrained polar quantizer design.Design/methodology/approachThe new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed.FindingsAt high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2 dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal‐to‐quantization ratio is derived.Practical implicationsSince circularly symmetric sources and complex presentation of signals a...

Electronics and Electrical Engineering, 2013

In this paper a novel two-stage quantizer with the embedded G.711 quantizer is proposed for speech signal processing. The first processing stage, where the input signal is quantized with the G.711 quantizer, is followed by the second stage where the segmental uniform quantizer performs the reduction of the quantization error introduced in the first stage. In this way higher signal quality, measured by signal to quantization noise ratio, is achieved in comparison with the G.711 quantizer while no bit rate reduction is performed. Particularly, in the second stage two additional bits are introduced. Although the expected quality gain, as a result of increasing the overall bit rate for 2 bit/sample, is around 12 dB, the gain achieved with the proposed quantizer is 14 dB. This additional quality gain of 2 dB proves the advantage of the proposed two-stage quantizer. Index Terms-G.711 quantizer, speech signal quality improvement, two-stage quantizer model.

IEEE Signal Processing Letters, 2000

In this letter, in order to outperform the existing method for unrestricted polar quantizer (UPQ) design in terms of signal to quantization noise ratio, the asymptotic approximations of Rayleigh distributed function are applied to all magnitude regions of the UPQ, except to the last one. Given the constraint, the UPQ is designed to provide the minimum of the asymptotic mean-squared error distortion for the Gaussian source of unit variance. The effects of this constraint are studied for different bit rates . The accuracy of the derived formulas is assessed and the reasonable accuracy is observed for bit/sample.

The paper analysis probability density of the quantization noise given by the sine and cosine functions of the phase , when the phase is uniform distibuted in the interval 0 2 ]. By the Monte Carlo simulation, the phase error given by the quantization of sin and cos is determined and compared with the error obtained by uni rm quantization of the phase.

IEEE Transactions on Circuits and Systems I: Regular Papers, 2000

The drive signals for radio frequency switch mode amplifiers can be directly generated by digital circuits using pulsewidth modulation and pulse position modulation. The quantisation noise that occurs when the pulsewidths are quantised to the timing grid can be shaped using sigma delta (Σ∆) modulation combined with polar quantisation. This paper analyses the behaviour of the resulting non-uniform polar quantisation and predicts the signal to noise ratio (SNR) performance of both Cartesian and polar filtered Σ∆ architectures. Practical measurements and simulations support the analysis. Orthogonal frequency division multiplexing and wideband code division multiple access signals are shown to have an increasing SNR with signal strength of 0.5 dB/dB at low signal levels, and 1 dB/dB at medium signal levels prior to entering the overload region. The schemes trade-off improved quantiser fidelity for higher oversampling requirements. They have reduced transitions, better coding efficiency and generally outperform the traditional bandpass Σ∆ scheme. Their complexity grows linearly with the number of quantisation points.

Signal Processing, 2018

This paper describes two approaches to optimization of the key design parameters, the support region threshold and the number of magnitude representation levels, of product polar companded quantizer (PPCQ) for Gaussian source of unit variance. The first approach is based on the exact performance analysis of PPCQ and on distortion optimization with respect to the key design parameters. Due to the optimization problem complexity we encountered with the first approach, some suitable approximations are introduced with the second one. As a result, much simpler asymptotic closed-form formula for distortion of PPCQ is derived as a function of the support region threshold. Although with this approach the closed-form formula for the support region threshold cannot be derived, the results of this approach indicate the useful support region threshold form. By combining the results of both approaches we propose, the worthy closed-form formulas for the support region threshold and signal to quantization noise ratio of a nearly optimal PPCQ are provided. Moreover, from the results of both analyses the lower and upper bound expressions for the number of magnitude representation levels are provided. The analysis presented in the paper is useful for designing PPCQ and is of great theoretical and practical importance.

British Journal of Mathematics & Computer Science, 2013

In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based on the obtained approximative quadratic spline functions, the design for companding quantizer for Gaussian source is done. The support region of proposed companding quantizer is divided on segments of unequal size, where the optimal value of segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by the companding quantizer proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.

Information Sciences, 2013

This paper considers the application of variable-length coding using two unrestricted polar quantizers (UPQs) for performance improvement of unrestricted polar quantization for bivariate Gaussian source. We propose the use of two UPQs, both designed for the bivariate Gaussian source of unit variance, having different sizes of codebooks and different optimal compressor functions. We show that the fixed-rate UPQ is a subset of our model, and we perform rigorous optimization procedure in order to obtain optimal parameter values maximizing the signal to quantization noise ratio (SQNR) for the given average bit rate. In addition, we study how gain in SQNR over the fixed-rate UPQ depends on the average bit rate and we show that the gain ranges from 0.619 dB to 0.869 dB depending on the average bit rate. Discussion is also provided about the proposed quantizer complexity and its performance in comparison to Shannon limit. The proposed UPQ provides a sophisticated choice of average bit rate compared to the fixed-rate UPQ. Features of the proposed quantizer indicate that the obtained model should be of high theoretical and practical significance.

STIN, 1977

The well-known algorithm of Max is used to determine the minimum distortion quantizers for normal, two-sided exponential, and specialized two-sided gamma input distributions and for mean-square, magnitude, and relative magnitude error distortion criteria. spaced quantizers are found, with the resulting quantizer distortion and entropy. The quantizers, and the quantizers with entropy coding, are compared to the rate distortion bounds for mean-square and magnitude error. The optimum equally-spaced and unequally