  We investigate the potential of quickest detection based on the eigenvalues
of the sample covariance matrix for spectrum sensing applications. A simple
phase shift keying (PSK) model with additive white Gaussian noise (AWGN), with
$1$ primary user (PU) and $K$ secondary users (SUs) is considered. Under both
detection hypotheses $\mathcal{H}_0$ (noise only) and $\mathcal{H}_1$ (signal +
noise) the eigenvalues of the sample covariance matrix follow Wishart
distributions. For the case of $K = 2$ SUs, we derive an analytical formulation
of the probability density function (PDF) of the maximum-minimum eigenvalue
(MME) detector under $\mathcal{H}_1$. Utilizing results from the literature
under $\mathcal{H}_0$, we investigate two detection schemes. First, we
calculate the receiver operator characteristic (ROC) for MME block detector
based on analytical results. Second, we introduce two eigenvalue-based quickest
detection algorithms: a cumulative sum (CUSUM) algorithm, when the
signal-to-noise ratio (SNR) of the PU signal is known and an algorithm using
the generalized likelihood ratio, in case the SNR is unknown. Bounds on the
mean time to false-alarm $\tau_\text{fa}$ and the mean time to detection
$\tau_\text{d}$ are given for the CUSUM algorithm. Numerical simulations
illustrate the potential advantages of the quickest detection approach over the
block detection scheme.
