(a) Effect of shunt length on dispersion of the input function peak (first 5 min shown).
The samples were diluted and placed in the analysis chamber such that the laser beam passed through the entire length of the dispersions.
The fabrication process comprises three main steps: (1) synthesis of SWCNT forests of determined length; (2) dispersion of the SWCNTs; and (3) fabrication of the buckypaper.
Figure 5 shows an absorption spectrum (1-cm path length) of an alkaline dispersion (pH = 1) of RGO in the range 200 to 800 nm.
We shall assume a frequency-selective Rayleigh fading channel of dispersion length v having the CIR vector h = [h0, h1,..., hv-1] T. Then {h m, m = 0,1,...v} are uncorrelated and hence independent of each other.
For a frequency-selective channel of dispersion length v, let h = [h0, h1, ⋯, hv - 1] T be the channel impulse response (CIR) vector with {h m, m = 0, 1, … v - 1} being spatially uncorrelated and H = [H0, H1, ⋯, HN - 1] T be the channel frequency response (CFR) vector.
For a frequency-selective channel of dispersion length v, let h = [h0, h1, …, hv - 1] T be the CIR vector with {h m, m = 0, 1, …, v - 1} being spatially uncorrelated and H = [H0, H1, …, HN - 1] T be the CFR vector[29, 30].
These improvements will be demonstrated with performance comparisons by computer simulations in Section 4. Consider an OFDM system with DFT size N = 64 operated over a frequency-selective channel of dispersion length v = 9 having an exponential power profile αe-πm/10, m = 0, 1, …, v - 1, with unit power, where α is used to normalized the channel power[30].
For a frequency-selective channel of dispersion length v = 9, we choose a given exponential power profile with normalized channel power, i.e., ∑ m = 0 8 | h m | 2 = 1, Figure 1 gives the variance or MSE of the frequency offset estimator E [ 2 ] as a function of SNR γ for three values of L = 1,3,9 as obtained from Monte Carlo simulations as well as from the theoretical result of (24).
