Mutualistic Mechanism in Symbiotic Radios: When Can the Primary and Secondary Transmissions Be Mutually Beneficial?

In symbiotic radio (SR), a secondary transmitter (STx) transmits messages by modulating its information over the radio frequency (RF) signals received from a primary transmitter (PTx), and in return, the secondary transmission provides multipath gain to the primary transmission. In this paper, we are interested in the fundamental mutualistic mechanism between the primary and secondary transmissions, which describes the condition through which the two systems can benefit each other. Since the symbol period ratio $K$ between secondary and primary transmissions is an important system parameter that affects the mutualistic symbiosis, we first derive the theoretical performance in terms of bit error rate (BER) for both primary and secondary transmissions for arbitrary $K$ by using QPSK modulation scheme at the PTx and BPSK modulation scheme at the STx as an example setup. Then we the obtain closed-form expressions for the condition on $K$ to enable mutualistic symbiosis in SR, which is not related to the specific channel realizations but determined by the average strengths of the direct and backscatter links when the number of receiving antennas is large. Meanwhile, we analyze the average BER performance and the diversity orders for both transmissions in the high signal-to-noise-ratio (SNR) regime. Extensive simulations and numerical results are provided to verify the accuracy of our theoretical analysis and demonstrate the interrelationship between the primary and secondary transmissions.