Capacitive Crossbar Array as a Non-Iterative Least-Squares Solver in Real-Time Broadband Beamforming

Abstract

This work demonstrates a compute-in-memory (CIM) capacitive crossbar array that solves the core least-squares problems of broadband Slepian beamforming non-iteratively for batch processing and in real-time for streaming data, eliminating the need for iterative algorithms, auxiliary crossbars, or complex digital peripherals. Our analog CIM architecture directly computes the solution to $\boldsymbol {A}\boldsymbol {\alpha } =\boldsymbol {b}$ through charge-domain matrix inversion. The design exploits non-volatile ferroelectric capacitors (nvCAPs) to store matrix weights, enabling in-situ computation with zero static power and $1000\times $ higher energy efficiency than the resistive CIM counterpart. SPICE simulations show 0.1% normalized mean squared error (MSE) and < 0.5 dB beamforming gain loss. By circumventing iterative algorithms and machine learning (ML)’s data dependency, this work provides a physics-based, hardware-efficient path for real-time broadband beamforming.