This work studies inference-based resource allocation in ultra low-power, large-scale backscatter sensor networks (BSNs). Several ultra-low cost and power sensor devices (tags) are illuminated by a carrier and reflect the measured information towards a wireless core that uses conventional Marconi radio technology. The development of multi-cell BSNs requires few multi-antenna cores and several low-cost scatter radio devices, targeting at maximum possible coverage. The average signal-to-interference-plus-noise ratio (SINR) of maximum-ratio combining (MRC) and zero-forcing (ZF) linear detectors is found and harnessed for frequency sub-channel allocation at tags, exploiting long-term SINR information. The resource allocation problem is formulated as an integer programming optimization problem and solved through the Max-Sum message-passing algorithm. The proposed algorithm is fully parallelizable and adheres to simple message-passing update rules, requiring mainly addition and comparison operations. In addition, the convergence to the optimal solution is attained within very few iteration steps. Judicious simulation study reveals that ZF detector is more suitable for large scale BSNs, capable to cancel out the intra-cell interference. It is also found that the proposed algorithm offers at least an order of magnitude decrease in execution time compared to conventional convex optimization methods.