The authors derive expressions for the small signal noise properties of the electrode current of a travelling-wave semiconductor optical amplifier when used as a detector. The analysis takes into account spatial variations in the amplifier carrier density and fields. Numerical simulations show that the dominant mechanisms giving rise to the detected current noise are spontaneous-spontaneous and signal-spontaneous beat noise occurring within the amplifier gain medium, and the thermal noise of the load resistor and postamplifier. As the spontaneous emission and amplified signal are generated by the same shared gain medium, beat noises will contain not only beating within longitudinal modes but also beating between distinct modes. In previous analyses this 'extra' noise was neglected which gave rise to errors between experiment and theory. The analysis also shows that there is an optimum amplifier gain which gives the best sensitivity. The bit error rate characteristics show good agreement with previously reported experimental results. Typically, for a 20 dB amplifier with 250 Mbit/s NRZ input data, sensitivities of the order of -27 dBm for a bit error rate of 10(-9) can be achieved.