We consider the problem of enabling a passive sensor to communicate, by integrating wireless power transfer and ambient backscatter transmission. The passive sensor collects energy from the radio-frequency signal emitted by an existing (legacy) transmitter, and uses such an energy to modulate its information by reflecting the legacy signal. In particular, we study the case when the intended receiver of the sensor information is co-located with the legacy transmitter. The achievable data rate of the sensor transmission is optimized as a function of the available resources, subject to limits on the mean square error of the channel estimate, symbol error rate, and harvested energy. The performance of both the legacy and sensor systems are further corroborated by means of Monte Carlo simulations.