We study joint transmit-waveform and receive-filter design for a multi-user downlink integrated sensing and communication (ISAC) system under practical constant-modulus and similarity constraints. We cast the design as a unified multi-objective program that balances communication sum rate and sensing signal-to-interference-plus-noise ratio (SINR). To address this, we introduce an efficient algorithm that use consensus alternating direction method of multipliers (ADMM) framework to alternately update the transmit waveform and radar filter. The proposed method effectively handles the non-convex fractional sensing's SINR formulation and ensures fast convergence. Simulation results demonstrate that the proposed approach achieves better trade-offs between communication sum rate and sensing's SINR compared to existing benchmark schemes.
The concept of integrated sensing and communication (ISAC) has emerged as a transformative approach for nextgeneration wireless systems, particularly in the context of 5G and beyond. ISAC systems enable the simultaneous use of the same waveform for both radar sensing and communication, offering significant advantages in terms of spectrum efficiency, latency reduction, and system resource sharing. By incorporating sensing and communication into a unified framework, ISAC holds the potential to significantly enhance the performance of next generation wireless systems, especially in applications like Internet of Things (IoT) and intelligence transportation systems. However, optimizing performance in ISAC systems remains a big challenge due to the dual nature of the tasks involved. Both radar sensing and communication tasks have distinct requirements, such as the need for high sensitivity in radar target detection and robust signal reception for communication systems. Thus, designing a transmit waveform that meets both these objectives while managing interference and resource constraints is nontrivial. One of the primary challenges in ISAC design is waveform optimization, where the transmitted waveform must satisfy both radar sensing and communication objectives. In radar systems, this involves optimizing the waveform for target detection, while in communication systems, the focus shifts to efficient data transmission. Striking the right balance between these competing goals requires advanced techniques for managing the shared resources.
Recent advancements in ISAC have been demonstrated across multiple studies. In particular, [1] introduces a penaltybased iterative beamformer optimization using block coordinate descent and weighted minimum mean square error for a full-duplex monostatic ISAC system, achieving up to 60 dB self-interference cancellation and significant improvements in both radar and communication performance. Following this direction, two cross-domain waveform optimization strategies-communication-centric and sensing-centric-are presented in [3], jointly optimizing time, frequency, power, and delay-Doppler domains to suppress sidelobes, reduce peak-toaverage power ratio (PAPR), and enhance both sensing accuracy and communication efficiency. Meanwhile, a hardwareefficient massive multiple-input multiple-output (MIMO) ISAC framework is developed in [2], employing quantized constantenvelope constraints and low-resolution digital-to-analog converters, where an inexact augmented Lagrangian method with block successive upper-bound minimization effectively reduces beampattern mean squared error (MSE) and symbol error rate, highlighting the potential of massive MIMO for future radar performance enhancement. In addition, [4] proposes two waveform designs-DSSS and OFDM-where DSSS with pseudorandom coding offers simplicity but suffers from Doppler and low data rates, whereas OFDM symbol-domain processing mitigates interference, accurately estimates multi-target range and velocity, and supports high-speed communication. To further enhance ISAC performance, [5] explores the integration of reconfigurable intelligent surface (RIS), jointly optimizing beamforming and RIS phase configuration to improve both target illumination power and user SINR, thereby maintaining effective operation even when the direct path is degraded or blocked. Finally, when the direct transmission path is obstructed, [6] demonstrates that coordinated optimization of beamforming and RIS phase for both radar and communication continues to enhance user signal-to-interference-plus-noise ratio (SINR) and radar target illumination, ensuring reliable dual-function performance even without a direct link.
In this paper, we present a novel waveform design framework for ISAC systems that jointly optimizes radar sensing and communication performance under practical hardware constraints using consensus alternating direction method of multipliers (ADMM) [9]. The designed waveform problem is formulated as a multi-objective optimization task that balances target detection capability and communication efficiency. To address its non-convex nature, a novel algorithm based on consensus ADMM is developed, enabling alternating optimization of the transmit waveform and receive filter while enforcing constantmodulus (CM) and similarity constraints. Simulation results verify that the proposed method achieves better trade-offs between radar and communication performance, demonstrating its practicality, scalability, and effectiveness for next-generation ISAC implementations.
Fig. 1 illustrates the overall architecture of a ISAC system in which the transmitter is equipped with a uniform linear array (ULA) of T elements. The system simultaneously supports downlink communication to M single-antenna user equipments (UE) and transmits radar probing waveforms to detect pointlike targets. In addition, it is assumed that the ISAC system includes a dedicated receive ULA
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