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

Algorithm 1

Orthogonal matching pursuit (OMP) pseudocode.

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

 (1) Initialize: As a first step, initialize 𝐼=∅and the residual 𝑟=𝑢 repeat 𝑠 times:

 (2) Identify: Select the largest coordinate 𝜆 of 𝑦=Φ^∗𝑟 in absolute value. Break ties lexicographically.

 (3) Update: Add the coordinate 𝜆 to the index set: 𝐼←𝐼⋃𝜆 and update the residual according to:

         𝑥=argmin_𝑧𝑢−Φ_∣𝐼𝑧₂;𝑟=𝑢−Φ𝑥

 (4) return: Index set 𝐼∈1,…,𝑑