In extreme cases, the structured LS estimator [9] which knows the location of nonzero taps (support) through an oracle, and estimates their corresponding values using LS estimation is the best estimator.
We consider LS estimation throughout.
By definition, the LS estimation assumes the deterministic unknown channels, i.e., the LS estimation is the classical estimation [10, 11, 16].
In order to overcome that, after performing the LS estimation, we set groups of virtual pilots uniformly spaced.
It should be noticed that the presence of a guard band with unmodulated subcarriers causes an ill conditioning problem in the LS estimation.
The estimation procedures including the design of training sequence and precoder are exactly the same as those presented from (17) to (23); add two groups, stack subgroups, and perform the LS estimation.
For two-hop relaying systems, the associated channel matrices can be estimated in separate LS estimation stages that operate sequentially at the destination [10].
Even one outlying observation can destroy an LS estimation, resulting in parameter estimates that do not provide useful information for the majority of the data.
When the allocation matrices Φ ( 1 ), Φ ( 2 ) and the input tensor are known, the matrix factors A ( 1 ), A ( 2 ) can be estimated through the LS estimation of their Kronecker product using the matrix unfolding (64).
These LS estimation problems can be solved alternately by estimating one channel matrix at each time, while fixing the other matrices to their values obtained in previous estimation steps.
We utilized the LS estimation approach to get the initial MIMO channel estimates at the pilot subcarriers, which was then further improved using a 2D DCT filtering technique in both time and frequency [30 32].
