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

Algorithm 1

Steps of the MME detector.

Initialize: Acquire 𝐿 consecutive data samples and assume that there are (𝑀≥1) receivers (antennas),

and (𝑁_𝑆) is the total number of collected samples.

 (a) Define the received vector 𝑥_𝑛 given by:

  𝐱(𝑛)=𝑥₁(𝑛),𝑥₂(𝑛),…,𝑥_𝑀(𝑛)^𝑇

 (b) The collection of 𝐿 consecutive outputs 𝐱_𝑛 is defined as:

  𝐱_𝑛=𝐱^𝑇(𝑛),𝐱^𝑇(𝑛−1),…,𝐱^𝑇(𝑛−𝐿+1)^𝑇

 (c) Compute the sample covariance matrix 𝐑(𝑁_𝑆):

  𝑅(𝑁_𝑠1)=𝑁_𝑠^{𝐿−1+𝑁𝑠}_𝑛∑_=𝐿𝐱_𝑛𝐱^𝐻_𝑛

 (d) Compute 𝜆_max and 𝜆_min the maximum and minimum eigenvalues of the matrix 𝐑(𝑁_𝑆).

 (e) Compute the threshold 𝜈 for the test statistics:

𝜈=𝑁_𝑆+√𝑀𝐿²𝑁_𝑆−√𝑀𝐿²1+𝑁_𝑆+√𝑀𝐿^−2/3𝑁_𝑆𝑀𝐿^1/6𝐹₁⁻¹1−𝑃_𝐹𝐴,

 where 𝐹₁ is the Tracy-Widom distribution of order 1 [102].

The decision test:

 (f) Decide on 𝐻₀ or 𝐻₁ by computing the ratio between 𝜆_max and 𝜆_min:

     𝜆_max𝜆_min≷^𝐻1_𝐻0𝜈