One-Bit Autocorrelation Estimation With Non-Zero Thresholds

Abstract

One-bit quantization has received attention due to its simplicity, low cost, and ability to recover the autocorrelation of the unquantized data. In the past, the autocorrelation estimation from one-bit data can be done in two separate stages. One is the power estimation by using one-bit quantizers of non-zero thresholds, while the other focuses on estimating the normalized autocorrelation with one-bit quantizers of a zero threshold. However, the overall hardware cost increases in this approach. This paper presents an autocorrelation estimator based on a one-bit quantizer with a non-zero threshold. The proposed method depends purely on a one-bit quantizer and its output data. Our method first infers the power information and then estimates the normalized autocorrelation by polynomial root-finding. The autocorrelation estimate is obtained by combining the power and the normalized autocorrelation. Numerical simulations show that the proposed method exhibits similar behavior to an estimator based on the unquantized data, with a 5dB loss in the estimation error.

Covariance Recovery for One-Bit Sampled Non-Stationary Signals With Time-Varying Sampling Thresholds

“…As can be seen in Fig. 1, we can accurately estimate the time-varying variance elements of an input signal based on (20) for i = 2 and j = 8 (r 02 = r 08 ). The results are obtained for the number of ensembles N x ∈ {1000, 3000, 6000, 10000}, with fixed d and Σ for each experiment.…”

“…Several numerical results are presented to illustrate the effectiveness of the proposed methodologies. Compared to [20] and the conference version of this work, we can summarize our contributions as follows:…”

“…Based on our discussions in Section III, p 0i and p 0j may be immediately obtained by (20). Then, {p ij } are estimated by formulating a minimization problem.…”

“…In this section, the Gauss-Legendre quadrature approach [25], [41] is adopted to evaluate the integration in (5). This lays the ground for the recovery of {p ij } since p 0i and p 0j are obtained by (20). At first, an approximated version of ( 5) is obtained based on the Gauss-Legendre quadrature technique in Section V-A.…”

“…In particular, the power information of the input signal x is lost in one-bit data with employing zero threshold. Because, there is no difference between the sign of x and that of ηx for η > 0 [20]. As a natural alternative, time-varying thresholds are utilized in recent works which can lead to enhancements in recovery performance [1], [21]- [24].…”