Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

TL;DR

This work addresses joint DFRC waveform design for massive MIMO under quantized constant-envelope (QCE) constraints, formulating a CI-based communication QoS objective that minimizes the mean square error between designed and desired beampatterns. A penalty approach converts the discrete QCE constraint into a continuous surrogate, and an inexact augmented Lagrangian method (ALM) solves the resulting problem efficiently with a BSUM-based subroutine that admits closed-form updates. Theoretical convergence guarantees show that ALM iterates converge to stationary points, while numerical results reveal favorable radar and communication performance trade-offs as system and DAC parameters vary, with notable gains over state-of-the-art one-bit/CI-based methods. The framework demonstrates that increasing DAC resolution to a modest level (e.g., 3 bits) yields substantial performance gains, whereas further gains saturate, underscoring the practicality of QCE-enabled massive MIMO DFRC. Overall, the paper provides a scalable, provably convergent design paradigm for integrating sensing and communication in 6G-era systems with hardware-efficient transceivers.

Abstract

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances.

Figures (11)

• Figure 1: A MIMO DFRC system, where there are one BS equipped with $N$ transmit antennas, each employed with a pair of low-resolution DACs, $K$ communication users, and many targets.
• Figure 2: An illustration of the CI metric.
• Figure 3: An illustration of $\mathcal{X}_L^\mathcal{R}$ and $\text{conv}(\mathcal{X}_L^\mathcal{R})$ with $L=8,$ where $\mathcal{X}_L^\mathcal{R}$ is the set of 8 red QCE points and its convex hull $\text{conv}(\mathcal{X}_L^\mathcal{R})$ is the shadow region.
• Figure 4: Convergence behaviors of proposed Algorithms \ref{['alg:alm']} and \ref{['alg:BSUM']}.
• Figure 5: Achieved SERs by the proposed approach versus the safety margin threshold $b$ under different system configurations, where the tuple in the legend represents the system parameter $(N,K,M,L)$ and the SNR is set as $10$ dB. The curves labeled "upper bound" and "lower bound" correspond to the theoretical upper and lower bounds on the SEP in \ref{['upperbound']}, respectively.

Theorems & Definitions (11)

• Proposition 1
• proof
• Definition 1: Stationary point of \ref{['eqn:problem6']}
• Theorem 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Lemma 1