Analytical Origin and Mitigation of Third-Order Tones in 4-Phase BLE Backscatter

This paper reports a repeatable spectral artifact observed in 4-phase (I/Q) BLE backscatter transmitters operating with single-sideband modulation. Despite nominal 90° Hilbert phasing, a dominant third-order spur appears near the image sideband. We show that this artifact originates from the four-step phase staircase combined with the short periodicity of the {2,3}-tick fractional-divider dwell pattern used for BLE subcarrier generation. While the fundamental tone is mapped to the desired sideband, the third harmonic is deterministically placed on the opposite sideband. To mitigate this effect without disturbing BLE timing or CPFSK modulation, a frame-dithered 2/3-dwell mapping technique is proposed. It preserves the exact per-bit dwell budgets while breaking frame-to-frame phase coherence. Measurement results demonstrate a reduction of the third-order spur from −61.8/−63.5 dBm to −66.9/−66.6 dBm and corresponding improvements in SFDR to 15.7/15.5 dBc and IRR to 15.5 dB, with negligible impact on the fundamental tone.