Survey on spiked models and their application to wireless commcunications

In this talk, we will discuss some problems related to cooperative spectrum sensing, and show how random matrix theory can help to address them. We will propose a simple test for frequency band sensing in wireless networks. The test is based on the analysis of the ratio of the extreme eigenvalues related to the gain matrix of the channel. The novelty relies in the fact that the test does not require the knowledge of the noise statistics. Large random matrix results allow us to build the threshold for the test, and also to study its type II error. This in particular enables us to compare this test with a different although popular test already proposed in the literature. We will show that our test is uniformly more powerful.