Exact(3)
Then, for a given pilot placement obtained by the CE algorithm, a closed form expression to obtain optimal pilot power distribution is employed.
This allows us to derive optimal pilot positioning for a given pilot sequence that meets some other constrains (e.g., constant envelope signals, low peak-to-average ratio, etc).
For a given pilot set, the optimal pilot power λi,1,…, λ i, N p that minimizes the channel MSE η i can be found numerically by resorting to convex optimization technique[11].
Similar(57)
We, however, select known pilot patterns (e.g., Barker sequences) so that we keep constant envelope signals and optimize the positioning for this given pilot pattern.
From Equation (25), for a given set of pilot symbols in frequency domain, the corresponding time domain representation of the pilot symbols with phase information can be written as x p i = Γ p i diag ( X p i ) e j ϕ i, (26).
For a given set of pilot subcarriers, Equation (15) requires O ( N d N p L ) operations to compute the power of the pilot symbol.
For a given number of pilot symbols, the CRB slightly increases with the guard interval length.
Sufficient conditions for minimum and maximum aperiodic ACF sidelobe energy for a given number of pilot tones are presented.
The analytical solution for optimal pilot power distribution in[13] can also be adopted, for a given set of arbitrary pilot placement,[13] is a prominent candidate for OFDM systems with large number of subcarriers.
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It is obvious that { P k } k = 0 N - 1 is a partition for P. We denote P ¯ k = { ( n, k ) | ∀ n } - P as the subset of time-frequency pair indexes which are not pilot for a given frequency index k.
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