Correlation matrix distance

Computes the correlation matrix distance between two correlation matrices

cmd(x, y)

Arguments

x

First correlation matrix
y

Second correlation matrix

Value

Returns the correlation matrix distance, which is a value between 0 and 1. The correlation matrix distance becomes zero for equal correlation matrices and unity if they differ to a maximum extent.

References

Herdin, M., and Czink, N., and Ozcelik, H., and Bonek, E. (2005). Correlation matrix distance, a meaningful measure for evaluation of non-stationary mimo channels. IEEE VTC.

Examples


m1 <- matrix(rep(1, 16), 4)
m2 <- matrix(c(1, 0, .5, .5, 0, 1, .5, .5, .5, .5, 1, .5, .5, .5, .5, 1), 4)
m3 <- matrix(c(1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1), 4)
cmd(m1, m1)
#> [1] 0
cmd(m1, m2)
#> [1] 0.1174774
cmd(m2, m3)
#> [1] 0.3594874