The Channel Capacity of General Complex-Valued Load Modulation for Backscatter Communication

Abstract

This paper studies achievable information rates of backscatter communication systems where the tag performs load modulation with a freely adaptable passive termination. We find that the complex phasor of the tag current is constrained to a disk and that the capacity problem can therefore be described with existing results on peak-power-limited quadrature channels. This allows us to state the channel capacity and the capacity-achieving distribution of the load impedance, which is described by non-concentric circles in the right half-plane. For the low-SNR case (SNR < 4.8 dB) we find that channel capacity is achieved by a purely reactive load with Cauchy-distributed reactance. The exposition is based on a system model that abstracts all relevant classes of backscatter communication systems, including RFID. To address practicality, we construct a symbol alphabet that allows for a near-capacity information rate of more than 6 bit per load-switching period at reasonably high SNR. We also find that the rate hardly decreases when typical value-range constraints are imposed on the load impedance.