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Analysis of Quantization Noise Suppression Gains in Digital Phased Arrays

Erik Kennerland, Bengt Lindoff, Emil Björnson

Abstract

Digital phased arrays have often been disregarded for millimeter-wave communications since the analog-to-digital converters (ADCs) are power-hungry. In this paper, we provide a different perspective on this matter by demonstrating analytically and numerically how the ADC resolution can be reduced when using digital phased arrays. We perform a theoretical analysis of the quantization noise characteristics for an OFDM signal received and processed by a digital phased array, using Gaussian approximation of the OFDM signal. In particular, we quantify the quantization noise suppression factor analytically and numerically. This factor describes how much the coherent combining reduces the quantization noise as a function of the number of antennas, which allows for reducing the ADC bit resolution. For instance in a 8-16 antenna digital phased array the ADC resolution can be reduced with 1-2 bits compared to the ADC required for an analog phased array.

Analysis of Quantization Noise Suppression Gains in Digital Phased Arrays

Abstract

Digital phased arrays have often been disregarded for millimeter-wave communications since the analog-to-digital converters (ADCs) are power-hungry. In this paper, we provide a different perspective on this matter by demonstrating analytically and numerically how the ADC resolution can be reduced when using digital phased arrays. We perform a theoretical analysis of the quantization noise characteristics for an OFDM signal received and processed by a digital phased array, using Gaussian approximation of the OFDM signal. In particular, we quantify the quantization noise suppression factor analytically and numerically. This factor describes how much the coherent combining reduces the quantization noise as a function of the number of antennas, which allows for reducing the ADC bit resolution. For instance in a 8-16 antenna digital phased array the ADC resolution can be reduced with 1-2 bits compared to the ADC required for an analog phased array.
Paper Structure (13 sections, 23 equations, 4 figures)

This paper contains 13 sections, 23 equations, 4 figures.

Table of Contents

  1. Background
  2. Related work
  3. Organization
  4. ADC Quantization Error Properties of Bivariate Gaussian Signals
  5. Optimal Clipping Level
  6. Quantization Noise Covariance
  7. Quantization Error Covariance Analysis for Digital Phased Arrays
  8. Two-Element Phased Array
  9. Multiple Antenna Digital Phased Arrays
  10. Approximations of the Noise Suppression Factor
  11. Simulation Results
  12. Implications for Digital Phased Arrays
  13. Conclusions

Figures (4)

  • Figure 1: The partition of $\mathbb{R}^2$ which the covariance is evaluated over. For legibility, $\mathcal{I}$ denotes $\bigcup_{m,n = 1}^{2^k}\mathcal{I}_{m,n}$. The edge region $\mathcal{E}$ has been partitioned further into $\mathcal{E} = \bigcup_{i =1}^{4}\mathcal{E}_i$, the reason that is explained in the appendix.
  • Figure 2: Simulated correlation of the quantization noise compared to the approximation (\ref{['psiApprox']}), normalized by $\sigma^2$ to represent the correlation.
  • Figure 3: The noise suppression factor for various $k$. The dashed line represents the ideal noise suppression, or equivalently the minimal value of the noise suppression factor, being $\frac{1}{N}$, while the gray curves are approximations calculated by applying the more refined approximation of applying (\ref{['psiApprox']}) to (\ref{['suppression']}). The dots are noise suppression levels for simulated OFDM-transmissions.
  • Figure 4: The comparison between the simple and refined approximation to the noise suppression.