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This article addresses the design, analysis, and parameterization of reconfigurable multi-band noise and signal transfer functions (NTF and STF), realized with multistage quadrature ΣΔ modulator (QΣΔM) concept and complex-valued in-phase/quadrature (I/Q) signal processing. Such multi-band scheme was already proposed earlier by the authors at a preliminary level, and is here developed further toward flexible and reconfigurable A/D interface for cognitive radio (CR) receivers enabling efficient parallel reception of multiple noncontiguous frequency slices. Owing to straightforward parameterization, the NTF and the STF of the multistage QΣΔM can be adapted to input signal conditions based on spectrum-sensing information. It is also shown in the article through closed-form response analysis that the so-called mirror-frequency-rejecting STF design can offer additional operating robustness in challenging scenarios, such as the presence of strong mirror-frequency blocking signals under I/Q imbalance, which is an unavoidable practical problem with quadrature circuits. The mirror-frequency interference stemming from these blockers is analyzed with a novel analytic closed-form I/Q imbalance model for multistage QΣΔMs with arbitrary number of stages. Concrete examples are given with three-stage QΣΔM, which gives valuable degrees of freedom for the transfer function design. High-order frequency asymmetric multi-band noise shaping is, in general, a valuable asset in CR context offering flexible and frequency agile adaptation capability to differing waveforms to be received and detected. As demonstrated by this article, multistage QΣΔMs can indeed offer these properties together with robust operation without risking stability of the modulator.

Multistage Quadrature Sigma-Delta Modulators for Reconfigurable Multi-Band Analog-Digital Interface in Cognitive Radio Devices