Frequency-Agile Multiband Quadrature Sigma-Delta Modulator for Cognitive Radio: Analysis, Design and Digital Post-Processing

A quadrature ΣΔ analog-to-digital converter (ADC) is a promising solution for intermediate frequency digitizing software defined cognitive radio (CR) receivers because of, e.g., multiband capability and power efficiency. However, inherent coefficient mismatches between the in-phase and quadrature rails can severely damage the performance of such receiver by creating mirror-frequency interference (MFI). In this article, a novel frequency-agile and reconfigurable transfer function design, allowing digital post-compensation of the MFI, is proposed. The design is based on a novel closed-form transfer function model for higher-order quadrature ΣΔ modulators (QΣΔMs) under implementation inaccuracies, proposed herein. By doing the compensation in digital domain, it is possible to take into account all error-sources of the receiver chain at once, including, e.g., a quadrature mixer before the ADC. This capability is obtained by preserving the mirror-band signal information and using the noise transfer function of a QΣΔM to remove quantization noise from therein. This is demonstrated in a multiband scenario aimed for CR receivers, where a number of frequency channels can be received and detected in parallel. Practical examples of the transfer function analysis under implementation inaccuracies and the post-compensation performance are given with a two-stage QΣΔM, having stage-orders of four, allowing eighth-order noise shaping.