Detection Schemes with Low-Resolution ADCs and Spatial Oversampling for Transmission with Higher-Order Constellations in the Terahertz Band

TL;DR

This work addresses the challenge of achieving high data rates at THz frequencies under strict ADC power constraints by combining low-resolution quantization with spatial oversampling. It develops an optimal ML detector for oversampled, quantized reception across arbitrary quantization resolutions, and compares it to several suboptimal detectors, all under a fixed power budget that ties quantization bit-depth to oversampling. A key finding is that $1$-bit quantization can outperform higher-bit quantization at low SNR, and that constellation optimization for $1$- and $2$-bit ADCs can dramatically reduce SER for higher-order constellations, with results validated in both simplified LoS and realistic indoor THz channels. These insights offer practical design guidance for ADC choice, detector implementation, and constellation shaping in high-bandwidth THz links, highlighting significant performance gains possible even with aggressive quantization.

Abstract

In this work, we consider Terahertz (THz) communications with low-resolution uniform quantization and spatial oversampling at the receiver side, corresponding to a single-input multiple-output (SIMO) transmission. We fairly compare different analog-to-digital converter (ADC) parametrizations by keeping the ADC power consumption constant. Here, 1-, 2-, and 3-bit quantization is investigated with different oversampling factors. We analytically compute the statistics of the detection variable, and we propose the optimal and several suboptimal detection schemes for arbitrary quantization resolutions. Then, we evaluate the symbol error rate (SER) of the different detectors for 16- and 64-ary quadrature amplitude modulation (QAM). The results indicate that there is a noticeable performance degradation of the suboptimal detectors compared to the optimal detector when the constellation size is larger than the number of quantization levels. Furthermore, at low signal-to-noise ratios (SNRs), 1-bit quantization outperforms 2- and 3-bit quantization, respectively, even when employing higher-order constellations. We confirm our analytical results by Monte Carlo simulations. Both a pure line-of-sight (LoS) and a more realistically modeled indoor THz channel are considered. Then, we optimize the input signal constellation with respect to SER for 1- and 2-bit quantization. The results give insights for optimizing higher-order constellations for arbitrary quantization resolutions and show that the minimum SER can be lowered significantly by appropriately placing the constellation points.

Figures (17)

• Figure 1: SIMO LoS THz channel with analog phase shifters, VGA, uniform quantizers, linear filter, and detector at the receiver side.
• Figure 2: Law $\mathcal{Q}_b\{\cdot\}$ of $b$-bit uniform midrise quantizer with step size $\Delta$.
• Figure 3: PMF $p_{d|x}(d|x)$ (\ref{['eq:d_pmf']}) and (scaled) continuous approximation $f_{d|x,\text{CLT}}(d|x)$ (\ref{['eq:d_pdf_clt']}) for $\mathcal{X}'=\{\pm1,\pm3\}$ at $\text{SNR}=0\,$dB.
• Figure 4: Thresholds between the decision regions for $x=+1$ and $x=+3$ according to the detectors (\ref{['eq:ML_det_exact']}), (\ref{['eq:ML_det_CLT']}), and (\ref{['eq:subopt_det']}) for $b=1$, $\Delta=2$, $N=64$, and $\mathcal{X}'=\{\pm1,\pm3\}$ at $\text{SNR}=0\,$dB. The colored discrete markers and continuous lines represent the PMF $p_{d|x}(d|x)$ (\ref{['eq:d_pmf']}) and (scaled) continuous approximation $f_{d|x,\text{CLT}}(d|x)$ (\ref{['eq:d_pdf_clt']}), respectively.
• Figure 5: Analytical SER (solid lines) and simulated SER (markers) for the ML detector (\ref{['eq:ML_det_exact']}), CLT-based detector (\ref{['eq:ML_det_CLT']}), minimum distance detector (\ref{['eq:subopt_det']}), and fully optimum detector without filtering (\ref{['eq:z_ML_det']}) under 16-QAM transmission with $\mathcal{X}'=\{\pm1,\pm3\}$. Furthermore, the ML detection performance for the unquantized case with the same oversampling factor is shown.