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As America's decaying power grid groans under the annual strain of heat waves, such as a recent one in California that led to blackouts in Silicon Valley, demand for power is growing.
Each channel is characterized by independent Rayleigh fading taps with an exponentially decaying power delay profile (41).
The R-rays are random, with Rayleigh-distributed amplitudes and random phases, with exponentially decaying power delay profile.
Two channel models with exponentially decaying power delay profile (PDP) were used to simulate indoor (50 nanoseconds rms delay spread) and outdoor environments (250 nanoseconds rms delay spread).
The multipath channel has been modeled to consist of 17 independent Rayleigh fading taps h(l) with an exponentially decaying power delay profile.
We have also simulated channels with less severe ISI (that is, decaying power profiles), and the advantage of using was even larger, as could be expected.
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More specifically the realization of doubly selective channels h l, n, m ( r u, p ) is generated by using the exponentially decaying power-delay profile of λ l 2 = e - l ∕ 4 ∑ l ′ = 0 L - 1 e - l ′ ∕ 4 [10].
With the number of channel tap gains L = 5 and the exponentially decaying power-delay profile [10], the time-variant multipath channels are first generated by the modified Jakes' model [12], and then fitted (approximated) by the DPS-BEM [10] using Q basis functions.
The random vectors h j are assumed to be independent zero-mean complex Gaussian with two choices of power-delay profile: Uniform power-delay profile with variance 1/(L + 1), and exponentially decaying power-delay profile θ ( τ k ) = C e - τ k ∕ τ r m s with delays τ k that are uniformly and independently distributed [24].
For intermediate degrees of connectivity, where the data are sufficient to reveal a trend, the distributions show decaying power-law tails, similarly to previous observations [ 10, 11].
For example, in both Saccharomyces cerevisiae and Escherichia coli, the number of regulatory proteins binding a gene is exponentially distributed, whilst the number of genes a transcription factor can bind follows a decaying power-law [ 6].
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