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We have studied the noise properties of a semiconductor optical amplifier (SOA) under the injection of a pump laser. The laser wavelength is set within the transparency region of SOA. The noise figure (NF) is found to decrease, strongly depending on the relative injection direction of signal and pump (i.e., copropagating or counterpropagating beams). In the copropagating scheme, an improvement in NF is obtained, ranging from 2.5 dB in the low current regime (40 mA, 13-dB chip gain) to 0.5 dB at high currents (150 mA, 23-dB chip gain). In the counterpropagating scheme, NF improvement is less pronounced. We explain the effect by an advantageous carrier redistribution along the SOA under the presence of the pump beam at transparency. A detailed simulation reproduces the observed results.