Multi-dimensional Goodness-of-Fit tests for spectrum sensing based on stochastic distances

In this paper, we study two multi-dimensional Goodness-of-Fit tests for spectrum sensing in cognitive radios. The multi-dimensional scenario refers to multiple CR nodes, each with multiple antennas, that record multiple observations from multiple primary users for spectrum sensing. These tests, viz., the Interpoint Distance (ID) based test and the 〈h,φ〉 distance based tests are constructed based on the properties of stochastic distances. The ID test is studied in detail for a single CR node case, and a possible extension to handle multiple nodes is discussed. On the other hand, the 〈h, φ〉 test is applicable in a multi-node setup. A robustness feature of the KL distance based test is discussed, which has connections with Middleton's class A model. Through Monte-Carlo simulations, the proposed tests are shown to outperform the existing techniques such as the eigenvalue ratio based test, John's test, and the sphericity test, in several scenarios.