Quadrature ΣΔ Modulators for Cognitive Radio - I/Q Imbalance Analysis and Complex Multiband Principle

This article discusses the applicability of quadrature ΣΔ modulator (QΣΔM) based analog-to-digital (A/D) conversion in cognitive radio (CR) receivers. First, unavoidable in-phase/quadrature (I/Q) mismatch effects, limiting the dynamic range, are analyzed in closed-form in the case of a first-order modulator. In addition, using the derived analytical converter model, it is shown that notching the signal transfer function (STF) of the modulator at the mirror frequencies of the desired signals will effectively cancel the I/Q imbalance induced mirror-frequency interference (MFI) in case of the modulator feedback mismatch. In practice, such STF design is easy to implement within the existing converter circuitry, as will be demonstrated in this article. The latter part of the article proposes a novel complex multiband QΣΔM scheme, particularly aimed for the CR receivers. This multiband scheme allows parallel reception of scattered frequency chunks in the CR context and is stemming from the additional degrees of freedom in noise transfer function (NTF) design, provided by the QΣΔM principle. Here multiple noise shaping notches on distinct frequencies are effectively realized through proper design of complex NTF. The modulator structure also allows flexible reconfigurability of the notches with straightforward parameterization of the modulator transfer functions. When combined with the above mirror-frequency rejecting STF design, the concept is demonstrated and proved effective and robust against I/Q imbalances using practical radio signal simulations in realistic received signal conditions.