# Bang Bang Spectrum Sensing

### EasyChair Preprint no. 4887

17 pages•Date: January 11, 2021### 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