  Spectrum sharing backscatter communication systems are among the most
prominent technologies for ultralow power and spectrum efficient
communications. In this paper, we propose an underlay spectrum sharing
backscatter communication system, in which the secondary network is a
backscatter communication system. We analyze the performance of the secondary
network under a transmit power adaption strategy at the secondary transmitter,
which guarantees that the interference caused by the secondary network to the
primary receiver is below a predetermined threshold. We first derive a novel
analytical expression for the cumulative distribution function (CDF) of the
instantaneous signal-to-noise ratio of the secondary network. Capitalizing on
the obtained CDF, we derive novel accurate approximate expressions for the
ergodic capacity, effective capacity, and average bit error rate. We further
validate our theoretical analysis using extensive Monte Carlo simulations.
