Finally the covariance matrix is estimated by summing terms, where represents the appropriate manifold.
The oscillation of the summed terms about the sawtooth is called the Gibbs phenomenon.
Hence, all contributions from the sum term are undesirable and will contaminate the CSI.
Second, an auxiliary vector-valued function is introduced to establish a novel finite-sum inequality, which can provide a tighter bound than some existing ones for some finite-sum term.
where ω n =2πn/T p (n is the integer number); n = 0 in the sum term corresponding to the averaged intensity distribution for one period has been omitted.
The second sum term on the right hand side represents a geometric series, so that similarly to (10) the si-function can be used to obtain an approximation, which is given as (A.3).
Consequently, the undesirable part of the pilot signal, i.e., the sum term in (2), varies rapidly between time slots compared to the variation caused by the mobility of a single contaminator in a fixed schedule.
Here, only signals leading to contamination are included in the sum term since any (h^{ij}_{n} boldsymbol {x}^{ij}_{n}) ∀ i,jnotin mathcal {C}_{n}^{kell }) are removed when correlating with the applied pilot sequence.
The reason why both a Coulomb term and a bond valence sum term were needed is discussed in section 22.3.
The first sum term in Equation (2) with can be considered a unary potential or data term, in which we want to match the intensity between two volumes.
