A novel dimensionality metric for multi-antenna systems

We propose a novel dimensionality metric for multi-antenna systems. Being SNR- independent, the metric is suitable for multipath richness comparison of several scenarios having their channel matrices Frobenius-normalized. The metric is based on the equivalence between the given singular values distribution of the normalized channel matrix and those of equi-contribution parallel sub-channels. Under 3 different equivalence criteria (mean, variance or Mean-Square-Error with respect to the optimum singular value), the proposed metric yields the same value, namely, the squared mean of the Frobenius- normalized singular values scaled by a factor (min/max) of the number of the transmit/receive elements.