  In this paper, we examine the error performance of backscatter communication
in the presence of ambient interference, where the backscatter device acts as a
relay. Specifically, the performance comparison of amplify-and-forward (AF) and
decode-and-forward (DF) backscatter relaying is considered for the first time.
Considering energy-based detection for on-off keying (OOK) modulation, we
derive the statistics of the received signal power, from which the detection
thresholds and corresponding bit error rates (BER) are obtained analytically.
For the DF scheme, we allow the source node to transmit continuous-wave signals
during the relay-to-destination transmission phase to power the backscatter
relay. Under a total power budget constraint at the source, we optimize the
power allocation for the transmissions in the source-to-relay and
relay-to-destination phases. Numerical analysis shows that the DF scheme with
optimal power allocation performs similarly compared to the AF scheme, despite
the added complexity of the decoding operation. On the other hand, the AF
scheme significantly outperforms the DF scheme when the reflection coefficients
at the backscatter device do not correspond to perfect OOK. These results
provide valuable insights into the design and deployment of backscatter nodes
with the goal of improving coverage.
