A Trade-Off Analysis of Energy Detectors and Partitioned Search for Primary Detection

Cognitive radios aim to coexist in the unused spectrum bands which are licensed to primary users without harming the primary transmission/reception. For a cognitive radio, it is important to detect the band in which the primary is operating as fast as possible and with high reliability in order to adapt its transmission. In this work, we propose
P-partitioning

method
in combination with energy detectors for the search of the band that the primary user is operating. In the P-partitioning method, the spectrum bands are categorized into P groups and the group that the primary band belongs to is detected in a recursive fashion. The energy detector operates on each group and the test statistics is the total energy received in the bands belonging to the group. The proposed search technique has detection time
P
log
_P
(
N
), where
N
is the number of bands in the spectrum. When
P
=
N
, the proposed scheme is equivalent to linear search with detection time N. We study the performance of the proposed scheme for a single non-cooperative radio and also for multiple cooperating radios. For a single cognitive radio, we provide an upper bound on the probability of correct detection which presents two different regimes of operation. In the low SNR regime, although it is counter-intuitive the partitioning improves the probability of detection. This is due an averaging effect when the signal energy in different bands are accumulated to obtain the energy contribution from a group. In the high SNR regime, performance degrades with partitioning. In addition, we observe that user cooperation improves the performance in the high SNR regimes.