Continuous-time nonlinear closed-loop in-memory computing for high-accuracy massive MIMO detection

Analog in-memory computing (IMC) has emerged as a promising approach for accelerating matrix operations by exploiting the intrinsic physics of memory arrays. To date, however, most IMC architectures have focused on linear algebra workloads in which computation is encoded in the equilibrium state of a physical system. Extending these principles to nonlinear optimization remains challenging and typically relies on iterative algorithms composed of repeated linear operations. Here, we introduce a continuous-time nonlinear closed-loop IMC architecture for box-constrained zero-forcing (BCZF) decoding in massive multiple-input multiple-output (MIMO) systems. The proposed architecture embeds the decoding problem directly within the dynamics of a nonlinear feedback network of memory arrays and supply-limited operational amplifiers, allowing solutions to emerge through continuous-time physical optimization. We derive a compact analytical model of the circuit and show that its trajectories minimize an equivalent energy function. Experimental emulation using a fabricated IMC chip confirms the predicted dynamics under realistic hardware nonidealities for up to 16x16 MIMO systems. To overcome the finite precision of analog hardware, we extend mixed-precision iterative refinement from linear algebra to nonlinear continuous-time optimization, enabling reliable detection of high-order modulation formats including 256-QAM. Benchmark projections indicate operation from ultra-low-energy approximate decoding to high-accuracy massive MIMO detection. Together, these results extend closed-loop IMC from equilibrium-based linear algebra to continuous-time nonlinear optimization and establish a pathway toward efficient physical accelerators for high-accuracy wireless communications.