  Recent advances in random matrix theory have spurred the adoption of
eigenvalue-based detection techniques for cooperative spectrum sensing in
cognitive radio. Most of such techniques use the ratio between the largest and
the smallest eigenvalues of the received signal covariance matrix to infer the
presence or absence of the primary signal. The results derived so far in this
field are based on asymptotical assumptions, due to the difficulties in
characterizing the exact distribution of the eigenvalues ratio. By exploiting a
recent result on the limiting distribution of the smallest eigenvalue in
complex Wishart matrices, in this paper we derive an expression for the
limiting eigenvalue ratio distribution, which turns out to be much more
accurate than the previous approximations also in the non-asymptotical region.
This result is then straightforwardly applied to calculate the decision
threshold as a function of a target probability of false alarm. Numerical
simulations show that the proposed detection rule provides a substantial
performance improvement compared to the other eigenvalue-based algorithms.
