  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.
