  In this paper, the level of sparsity is examined at 6, 26, and 132 GHz
carrier frequencies by conducting channel measurements in an indoor office
environment. By using the Gini index (value between 0 and 1) as a metric for
characterizing sparsity, we show that increasing carrier frequency leads to
increased levels of sparsity. The measured channel impulse responses are used
to derive a Third-Generation Partnership Project (3GPP)-style propagation
model, used to calculate the Gini index for the comparison of the channel
sparsity between the measurement and simulation based on the 3GPP model. Our
results show that the mean value of the Gini index in measurement is over twice
the value in simulation, implying that the 3GPP channel model does not capture
the effects of sparsity in the delay domain as frequency increases. In
addition, a new intra-cluster power allocation model based on measurements is
proposed to characterize the effects of sparsity in the delay domain of the
3GPP channel model. The accuracy of the proposed model is analyzed using
theoretical derivations and simulations. Using the derived intra-cluster power
allocation model, the mean value of the Gini index is 0.97, while the spread of
variability is restricted to 0.01, demonstrating that the proposed model is
suitable for 3GPP-type channels. To our best knowledge, this paper is the first
to perform measurements and analysis at three different frequencies for the
evaluation of channel sparsity in the same environment.
