Cooperative Spectrum Sensing and Localization in Cognitive Radio Systems Using Compressed Sensing

Algorithm 2

Compressive sampling matching pursuit (CoSaMP) pseudocode.

Require: Measurement matrix Φ, measurement vector 𝑢=Φ𝑥, sparsity level 𝑠

 (1) Initialize: Set 𝑎⁰=0, 𝑣=𝑢, 𝑘=0.

  Repeat the following steps while increasing 𝑘 until achieving halt criterion.

 (2) Signal Proxy: Set 𝑦=Φ^∗𝑣, Ω=supp𝑦_2𝑠 and merge the support 𝑇=Ω⋃supp𝑎^𝑘−1

 (3) Signal Estimation: Solving a least squares problem, set: 𝑏_∣𝑇=Φ^†_𝑇𝑢 and 𝑏_∣𝑇𝑐=0

 (4) Prune: Preparing the next iteration, set 𝑎^𝑘=𝑏_𝑠

 (5) Sample Update: Update the samples by: 𝑣=𝑢−Φ𝑎^𝑘

 (6) return: 𝑠-sparse reconstructed vector 𝑥=𝑎