Cognitive Radio Transceivers: RF, Spectrum Sensing, and Learning Algorithms Review

Algorithm 2

Steps of the CAF symmetry-based detector.

Initialize: Acquire 𝑛 data samples from the spectrum sensing interval formed by 𝑁

samples and set (𝑙+1) the number of OMP iterations, and (𝑀) the number of delays 𝜏s

For  𝑀 different values of 𝜏,

 (a) Calculate the autocorrelation vector 𝐟_𝜏0 given by:

  𝐟_𝜏=[𝑓_𝜏(0),𝑓_𝜏(1),...,𝑓_𝜏(𝑁−1)]^𝑇,

where 𝑓_𝜏(𝑡)=𝑦(𝑡)𝑦(𝑡+𝜏).

  (b) Calculate the elements of the matrix 𝐴 performing the IDFT transform:

     𝑎_(𝑝,𝑞)𝑒^{2𝑖𝜋(𝑝−1)(𝑞−1)/𝑁}

   The OMP algorithm

 (c) Estimate the cyclic autocorrelation vector by solving the following system of

 equations: 𝐴𝐫_𝜏=𝐟_𝜏 by using an iterative optimization technique called

  Orthogonal Matching Pursuit (OMP) that delivers an approximated solution 𝐫̂_𝜏.

   Symmetry check

  (d) Calculate the symmetry index for this value of 𝜏, by ignoring the first amplitude that

 corresponds to the first iteration of OMP, and measuring the mean value of the abscissa

 of the remaining (𝑙−1) non zero elements in 𝐫̂_𝜏. The symmetry index is given by:

     IDN^(𝜏)_sym=1𝑙^𝑙_𝑖∑₌₁𝐫̂_𝜏𝑖.

End For

Equivalent symmetry check:

  IDN^(equ)_sym=1𝑀^𝑀_𝑖∑₌₁|IDN^(𝜏𝑖)_sym|<0.