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We numerically and experimentally investigate the high-speed small-signal cross-gain modulation (XGM) characteristics of a quantum-dot (QD) semiconductor optical amplifier (SOA). From a p-doped QD SOA operating at 1.3 mum, high-speed small-signal XGM responses up to 40 GHz are measured from low to high injection currents and improve at high injection currents. In the numerical model, we set up about six hundred coupled rate equations, where the carrier dynamics of QD electron and hole states are considered separately and the enhanced hole occupation due to p-type doping is included. The high-speed small-signal XGM spectra are calculated at various modulation frequencies and pump-probe detunings. We identify how the two separate XGM mechanisms of total carrier density depletion (TCDD) at low injection current and spectral hole burning (SHB) at high injection current affect the high-speed small-signal XGM behavior. From the measured and calculated results, we show that high-speed small-signal XGM responses of QD SOAs can be improved by injecting more carriers to the QD excited states, which enhances high-speed XGM induced by SHB rather than by TCDD.