1-Bit Compressive Data Gathering for Wireless Sensor Networks

Algorithm 1

Proposed 1-bit CS framework.

  Sensor node’s operation:

 (1) Sample and buffer sensory data 𝑥, then generate projection 𝑏∈{1,−1}^𝑀 computed from (6);

 (2) Calculate the norm value of original sensory data 𝑛𝑜𝑟𝑚_𝑥=‖𝑥‖₂;

 (3) Send norm_x and projection 𝑏 to base station.

  Base station’s operations:

 (1) After receiving norm_x and projection 𝑏 from the sensor node, base station solves (7)

   and get normalized coefficients 𝑠̂ from blind_1_bit_cs (𝐴, 𝑏), here blind_1_bit_cs function

   can be any blind CS reconstruction algorithm that needs no prior sparse level information.

 (2) Computing the estimated original sensory data

   𝑥^⌢=(Ψ^𝑇∗𝑠)̂×𝑛𝑜𝑟𝑚_𝑥, here Ψ^𝑇 is the transpose of Ψ, and Ψ^𝑇×Ψ=𝐼.