  Ambient Internet of Things networks use low-cost, low-power backscatter tags
in various industry applications. By exploiting those tags, we introduce the
integrated sensing and backscatter communication (ISABC) system, featuring
multiple backscatter tags, a user (reader), and a full-duplex base station (BS)
that integrates sensing and (backscatter) communications. The BS undertakes
dual roles of detecting backscatter tags and communicating with the user,
leveraging the same temporal and frequency resources. The tag-reflected BS
signals offer data to the user and enable the BS to sense the environment
simultaneously. We derive both user and tag communication rates and the sensing
rate of the BS. We jointly optimize the transmit/received beamformers and tag
reflection coefficients to minimize the total BS power. To solve this problem,
we employ the alternating optimization technique. We offer a closed-form
solution for the received beamformers while utilizing semi-definite relaxation
and slack-optimization for transmit beamformers and power reflection
coefficients, respectively. For example, with ten transmit/reception antennas
at the BS, ISABC delivers a 75% sum communication and sensing rates gain over a
traditional backscatter while requiring a 3.4% increase in transmit power.
Furthermore, ISABC with active tags only requires a 0.24% increase in transmit
power over conventional integrated sensing and communication.
