# LMPIT-inspired Tests for Detecting a Cyclostationary Signal in Noise with Spatio-Temporal Structure

## TL;DR

This paper develops and analyzes detectors for identifying cyclostationary signals in noise with specific spatio-temporal structures, improving spectrum sensing in cognitive radio applications.

## Contribution

It derives LMPIT-inspired detectors for structured noise scenarios and demonstrates their performance, especially when noise is spatially uncorrelated.

## Key findings

- LMPITs exist only for spatially uncorrelated noise
- Proposed tests approximate LMPITs and perform well in simulations
- New hypothesis tests for unknown noise structures

## Abstract

In spectrum sensing for cognitive radio, the presence of a primary user can be detected by making use of the cyclostationarity property of digital communication signals. For the general scenario of a cyclostationary signal in temporally colored and spatially correlated noise, it has previously been shown that an asymptotic generalized likelihood ratio test (GLRT) and locally most powerful invariant test (LMPIT) exist. In this paper, we derive detectors for the presence of a cyclostationary signal in various scenarios with structured noise. In particular, we consider noise that is temporally white and/or spatially uncorrelated. Detectors that make use of this additional information about the noise process have enhanced performance. We have previously derived GLRTs for these specific scenarios; here, we examine the existence of LMPITs. We show that these exist only for detecting the presence of a cyclostationary signal in spatially uncorrelated noise. For white noise, an LMPIT does not exist. Instead, we propose tests that approximate the LMPIT, and they are shown to perform well in simulations. Finally, if the noise structure is not known in advance, we also present hypothesis tests using our framework.