Digitally Adaptive High-Fidelity Analog Array Signal Processing Resilient to Capacitive Multiplying DAC Inter-Stage Gain Error

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 66; no. 11; pp. 4095 - 4107
• Main Authors: Joshi, Siddharth, Kim, Chul, Thomas, Chris M., Cauwenberghs, Gert
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive arrays; Adaptive systems; analog signal processing (ASP); Array signal processing; Arrays; Beamforming; Capacitors; Computational geometry; Convergence; Convexity; Digital to analog conversion; Digital to analog converters; Error analysis; Hardware; Internet-of-Things (IoT); least-mean-squares (LMS) adaptive filtering; Mathematical analysis; Matrix algebra; Matrix methods; MIMO (control systems); mixed-signal matrix-vector multiplication (MVM); multi-input multi-output (MIMO); Multiplying digital-to-analog conversion (MDAC); non-convex optimization; Optimization; Signal processing; Signal processing algorithms; Topology
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2019.2926447

This paper studies multi-stage capacitive mixed-signal matrix-vector multiplying digital-to-analog (MDAC) conversion topologies for highly energy-efficient, high-resolution, and high-dimensional MIMO analog processing systems. In order to mitigate nonlinearity due to radix errors and capacitive mismatch encountered in compact low-power MDAC realizations, we introduce stochastic successive approximation, or S 2 A, as an online optimization algorithm for adaptive array analog signal processing amenable to efficient implementation in massively parallel mixed-signal hardware. S 2 A offers a direct alternative to stochastic gradient descent overcoming several of its shortcomings, such as its sensitivity to model error, while improving on the rate and quality of convergence. S 2 A overcomes non-convergence typically encountered with gradient descent for non-convex optimization landscapes induced by a mismatch in capacitive multiplying digital-to-analog converter components when applied to adaptive analog signal processing. Experimental validation of S 2 A in mixed-signal hardware for real-time RF adaptive beamforming demonstrates 65 dB of over-the-air, multipath interferer suppression in fewer than 25 S 2 A iterations.