High-Resolution Distributed Sampling of Bandlimited Fields With Low-Precision Sensors

The problem of sampling a discrete-time sequence of spatially bandlimited fields, with a bounded dynamic range, in a distributed, communication-constrained processing environment is studied. A central unit having access to the data gathered by a dense network of low-precision sensors, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying “conservation of bits” principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics.