Performance Analysis for Channel Estimation With 1-Bit ADC and Unknown Quantization Threshold

Abstract

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with 1-bit output resolution and an unknown quantization threshold is considered. Singlecomparator ADCs are energy-efficient and can be operated at ultra-high sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by 2/π (−1.96 dB) when comparing to an ideal ∞-bit converter. Due to hardware imperfections, low-complexity 1-bit ADCs will in practice exhibit an unknown threshold different from zero. Therefore, we study the accuracy which can be obtained with receive data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with inter-symbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models.

Low-Resolution ADCs for Wireless Communication: A Comprehensive Survey

“…Moreover, these two schemes can help substantially reduce the training overhead while achieving considerable estimation accuracy. Stein et al (2018) [110] concentrated on the problem of pilot-based channel parameter estimation from 1-bit quantized data with an unknown hard-limiting threshold. In their work, they considered a hybrid model [111]- [115] where the channel parameters are random and distributed according to a known probability distribution function, while the quantization offset is modeled as a deterministic unknown nuisance parameter.…”

On Quasi-Isometry of Threshold-Based Sampling

“…State-of-the-art signal reconstruction methods rely on assumptions or estimations of characteristics like spectral moments or signal bandwidth [9,[11][12][13][14]. Deviations or inaccurate estimates can impair the quality of the signal reconstruction.…”

When Less Is More$\ldots$ Few Bit ADCs in RF Systems

“…cations; ultrawideband spectrum monitoring [30] and channel estimation [31], [32]; digital RF memory (DRFM) and electronic warfare (EW) receivers [33]- [39]; and even biological sensing and computation [40]- [43]. The motivations for restricting a receiver design to only a few bits can vary widely to include: maximizing sample rate [38], minimizing power dissipation [25], achieving insensitivity to clock jitter over long coherent integration times [9], [10], [44] and, perhaps most importantly, dramatically reducing digital processing throughput requirements in large scale systems [18], [45]- [77].…”