  In this paper, a novel amplitude phase shift keying (APSK) modulation scheme
for cooperative backscatter communications aided by a reconfigurable
intelligent surface (RIS-CBC) is presented, according to which the RIS is
configured to modulate backscatter information onto unmodulated or
PSK-modulated signals impinging on its surface via APSK. We consider both
passive and active RISs, with the latter including an amplification unit at
each reflecting element. In the passive (resp. active) RIS-CBC-APSK,
backscatter information is conveyed through the number of RIS reflecting
elements being on the ON state (resp. active mode) and their phase shift
values. By using the optimal APSK constellation to ensure that reflected
signals from the RIS undergo APSK modulation, a bit-mapping mechanism is
presented. Assuming maximum-likelihood detection, we also present closed-form
upper bounds for the symbol error rate (SER) performance for both passive and
active RIS-CBC-APSK schemes over Rician fading channels. In addition, we devise
a low-complexity detector that can achieve flexible trade-offs between
performance and complexity. Finally, we extend RIS-CBC-APSK to multiple-input
single-output scenarios and present an alternating optimization approach for
the joint design of transmit beamforming and RIS reflection. Our extensive
simulation results on the SER performance corroborate our conducted performance
analysis and showcase the superiority of the proposed RIS-CBC-APSK schemes over
the state-of-the-art RIS-CBC benchmarks.
