On detection of a real sinusoid with short data record

In this paper, we investigate two binary detection problems for a single real tone in additive white Gaussian noise using short data records. In the first hypothesis-testing scenario, we decide if a sinusoid is present in the received signal where both cases of known and unknown sinusoidal frequency will be examined. In the second problem, differentiation between two distinct noisy tones is considered. Simulation results show that the nonlinear least squares and maximum likelihood methods give identical detection performance and they outperform the periodogram approach.