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One-Bit-Aided Modulo Sampling for DOA Estimation

Qi Zhang, Jiang Zhu, Fengzhong Qu, De Wen Soh

TL;DR

This work tackles DOA estimation under sensor saturation and near-far scenarios by combining modulo sampling with one-bit measurements. It introduces a 1bit-aided-BIF pipeline that uses the arcsin law to estimate a normalized covariance from one-bit data, then applies a blind integer-forcing decoder to unwrap modulo samples, followed by subspace methods for DOA estimation. The approach iteratively refines the covariance estimate and the integer-forcing matrix, enabling robust DOA recovery with low-dynamic-range hardware. The results show that modulo sampling with few bits can match or exceed conventional high-bit ADC performance, particularly in challenging near-far settings, highlighting significant gains for energy-efficient sensor arrays.

Abstract

Modulo sampling has recently drawn a great deal of attention for cutting-edge applications, due to overcoming the barrier of information loss through sensor saturation and clipping. This is a significant problem, especially when the range of signal amplitudes is unknown or in the near-far case. To overcome this fundamental bottleneck, we propose a one-bit-aided (1bit-aided) modulo sampling scheme for direction-of-arrival (DOA) estimation. On the one hand, one-bit quantization involving a simple comparator offers the advantages of low-cost and low-complexity implementation. On the other hand, one-bit quantization provides an estimate of the normalized covariance matrix of the unquantized measurements via the arcsin law. The estimate of the normalized covariance matrix is used to implement blind integer-forcing (BIF) decoder to unwrap the modulo samples to construct the covariance matrix, and subspace methods can be used to perform the DOA estimation. Our approach named as 1bit-aided-BIF addresses the near-far problem well and overcomes the intrinsic low dynamic range of one-bit quantization. Numerical experiments validate the excellent performance of the proposed algorithm.

One-Bit-Aided Modulo Sampling for DOA Estimation

TL;DR

This work tackles DOA estimation under sensor saturation and near-far scenarios by combining modulo sampling with one-bit measurements. It introduces a 1bit-aided-BIF pipeline that uses the arcsin law to estimate a normalized covariance from one-bit data, then applies a blind integer-forcing decoder to unwrap modulo samples, followed by subspace methods for DOA estimation. The approach iteratively refines the covariance estimate and the integer-forcing matrix, enabling robust DOA recovery with low-dynamic-range hardware. The results show that modulo sampling with few bits can match or exceed conventional high-bit ADC performance, particularly in challenging near-far settings, highlighting significant gains for energy-efficient sensor arrays.

Abstract

Modulo sampling has recently drawn a great deal of attention for cutting-edge applications, due to overcoming the barrier of information loss through sensor saturation and clipping. This is a significant problem, especially when the range of signal amplitudes is unknown or in the near-far case. To overcome this fundamental bottleneck, we propose a one-bit-aided (1bit-aided) modulo sampling scheme for direction-of-arrival (DOA) estimation. On the one hand, one-bit quantization involving a simple comparator offers the advantages of low-cost and low-complexity implementation. On the other hand, one-bit quantization provides an estimate of the normalized covariance matrix of the unquantized measurements via the arcsin law. The estimate of the normalized covariance matrix is used to implement blind integer-forcing (BIF) decoder to unwrap the modulo samples to construct the covariance matrix, and subspace methods can be used to perform the DOA estimation. Our approach named as 1bit-aided-BIF addresses the near-far problem well and overcomes the intrinsic low dynamic range of one-bit quantization. Numerical experiments validate the excellent performance of the proposed algorithm.
Paper Structure (8 sections, 15 equations, 4 figures, 1 algorithm)

This paper contains 8 sections, 15 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Algorithm
  4. Estimate the Normalized Convariance Matrix
  5. Integer-Forcing Decoder
  6. 1bit-Aided-BIF Algorithm
  7. Simulation
  8. Conclusion

Figures (4)

  • Figure 1: Computational array signal processing setup using the one-bit-aided modulo sampling/unlimited sensing architecture. Modulo non-linearity maps high-dynamic-range sensor array samples into low-dynamic-range folded samples. The one-bit quantization preserves the sign information of the original measurements. The 1bit-aided-BIF algorithm is used to carry out the estimation of DOAs based on the unified measurement scheme.
  • Figure 2: The performance of 1bit-aided-BIF algorithm in near-far problem with ${\rm SNR}_2 = -10$ dB and $T = 10^4$.
  • Figure 3: The detection probability versus ${\rm SNR}_2$.
  • Figure 4: The detection probability versus the snapshot.