Generalized coherence [signal detection]

The authors introduce a test for detecting the presence of a common signal on M noisy channels that generalizes a popular technique using the magnitude-squared coherence (MSC) estimate for detecting a common signal on two channels. The basis of this test is the generalized coherence estimate, a statistic involving the normalized M×M Gram matrix determinant, which reduces to the MSC estimate for M=2. The distribution of the generalized coherence estimate is derived under the assumptions of independent noise and no common signal on the M channels