Bang Bang Spectrum Sensing

EasyChair Preprint 4887

Abstract

In this research paper, given an upper bound on total number of sensing bands, the problem
of determining number of sensing bands with low and high sensing times (given the total sensing
time as well as traffic over wideband of channels) is formulated and solved. In such formulation, the
optimization criterion is chosen to be (maximization/minimization) average number of sensing bands.
The dual problem deals with optimization (maximization/minimization) of low and high sensing times.
The solution of dual problem readily follows. Hence, a bang bang time optimal spectrum sensing related
results follow readily. It is shown that the variance of a Bernoulli Random variable, Z constitutes a
logistic map in success probability ’P’. This fact is utilized to derive analytic results. Some analytical
results related to number of sensing bands required are proved. Specifically it is shown that when
the values assumed by Z are known integers, there is no value of success probability ’P’ for which
expectation of Z equals the variance of Z.

Keyphrases: Cognitive Radio, Diophantine equation, Sensing Bands, sensing time, spectrum sensing

@booklet{EasyChair:4887,
  author    = {Rama Murthy Garimella and Jagannadha Swamy Tata},
  title     = {Bang Bang  Spectrum  Sensing},
  howpublished = {EasyChair Preprint 4887},
  year      = {EasyChair, 2021}}