Study of Constrained Precoding with Zero-Crossing Modulation for Channels with 1-Bit Quantization and Oversampling

TL;DR

The paper addresses the energy efficiency challenge of MU-MIMO downlinks at millimeter-wave and sub-terahertz bands by employing 1-bit ADCs with receiver oversampling and time-instance zero-crossing (TI ZX) modulation. It introduces a quality-of-service (QOS) constrained temporal precoding framework, formulated as a convex optimization per user and dimension to minimize transmit energy while enforcing a SER-based constraint expressed via a target distance γ to the decision threshold. A semi-analytical symbol error rate (SER) upper bound is derived using a multivariate normal model, enabling SER-based design and an approximate BER bound through BER_{ub} ≈ SER_{ub} / n_s. Numerical results for different oversampling configurations validate that the semi-analytical SER upper bound indeed bounds the actual SER and demonstrate energy savings compared to traditional precoding. The approach offers a viable pathway for reliable, low-power decoding in high-frequency systems with severe quantization and synchronization constraints.

Abstract

Future wireless communications systems are expected to operate at bands above 100GHz. The high energy consumption of analog-to-digital converters, due to their high resolution represents a bottleneck for future wireless communications systems which require low-energy consumption and low-complexity devices at the receiver. In this work, we derive a novel precoding method based on quality of service constraints for a multiuser multiple-input multiple-output downlink system with 1-bit quantization and oversampling. For this scenario, the time-instance zero-crossing modulation which conveys the information into the zero-crossings is considered. Unlike prior studies, the constraint is given regarding the symbol error probability related to the minimum distance to the decision threshold. Numerical results illustrate the performance of the proposed precoding method evaluated under different parameters

Figures (4)

• Figure 1: Multiuser MIMO system model with $N_{\text{u}}$ single antenna users.
• Figure 2: Representation of the $\boldsymbol{c}_{\text{out}}$ sequence for $M_{\text{Rx}}=3$.
• Figure 3: Semi-analytical and numerical SER comparison for the MMDDT precoding method. In (a) $M_{\text{Rx}}= M_{\text{Tx}}= 2$, $N=2$ and $\sigma^2 = 1$. In (b) with $M_{\text{Rx}}= M_{\text{Tx}}= 3$, $N=1$ and $\sigma^2 = 1$.
• Figure 4: Semi-analytical and numerical BER comparison for the MMDDT precoding method. In (a) $M_{\text{Rx}}= M_{\text{Tx}}= 2$, $N=2$ and $\sigma^2 = 1$. In (b) with $M_{\text{Rx}}= M_{\text{Tx}}= 3$, $N=1$ and $\sigma^2 = 1$.