Leveraging LLM Agents for Automated Optimization Modeling for SASP Problems: A Graph-RAG based Approach

Automated optimization modeling (AOM) has evoked considerable interest with the rapid evolution of large language models (LLMs). Existing approaches predominantly rely on prompt engineering, utilizing meticulously designed expert response chains or structured guidance. However, prompt-based techniques have failed to perform well in the sensor array signal processing (SASP) area due the lack of specific domain knowledge. To address this issue, we propose an automated modeling approach based on retrieval-augmented generation (RAG) technique, which consists of two principal components: a multi-agent (MA) structure and a graph-based RAG (Graph-RAG) process. The MA structure is tailored for the architectural AOM process, with each agent being designed based on principles of human modeling procedure. The Graph-RAG process serves to match user query with specific SASP modeling knowledge, thereby enhancing the modeling result. Results on ten classical signal processing problems demonstrate that the proposed approach (termed as MAG-RAG) outperforms several AOM benchmarks.

Fast Fractional Programming for Multi-Cell Integrated Sensing and Communications

This paper concerns the coordinate multi-cell beamforming design for integrated sensing and communications (ISAC). In particular, we assume that each base station (BS) has massive antennas. The optimization objective is to maximize a weighted sum of the data rates (for communications) and the Fisher information (for sensing). We first show that the conventional beamforming method for the multiple-input multiple-output (MIMO) transmission, i.e., the weighted minimum mean square error (WMMSE) algorithm, has a natural extension to the ISAC problem scenario from a fractional programming (FP) perspective. However, the extended WMMSE algorithm requires computing the $N\times N$ matrix inverse extensively, where $N$ is proportional to the antenna array size, so the algorithm becomes quite costly when antennas are massively deployed. To address this issue, we develop a nonhomogeneous bound and use it in conjunction with the FP technique to solve the ISAC beamforming problem without the need to invert any large matrices. It is further shown that the resulting new FP algorithm has an intimate connection with gradient projection, based on which we can accelerate the convergence via Nesterov's gradient extrapolation.