Hence, sensing matrix should satisfy the conditions of incoherence and restricted isometry property (RIP) [5].
Since the transmission power at each antenna is equal to 1, the precoding matrix should satisfy: trace PP H ) ≤ N.
By differentiating this equation with respect to and setting the result equal to zero as well as using the constraint, we obtain that the optimal training matrix should satisfy (18).
It can be shown [5] that in order to minimize the variance of the MSE (when represented as a function of the channel fadings) the non-zero elements of the matrix should satisfy | a ij | = 1 N ; we shall employ the normalized Hadamard matrix, which satisfies this property.
Therefore, the pre-coding matrices of each user in cell 3 are used to eliminate the intra-cell interferences, so the pre-coding matrix should satisfy the following constraints left{begin{array}{c}hfill {mathbf{R}}_3^{1,3}{mathbf{V}}_{2,3}=0hfill hfill {mathbf{R}}_3^{2,3}{mathbf{V}}_{1,3}=0hfill end{array}right.
It is easy to see that, in general, the number of encoding steps equals the number of submatrices, M. The parity-check matrix H should satisfy the following three conditions: (A) The parity-check matrix H should contain an upper triangular pattern.
Moreover, to efficiently reconstruct f, the mapping matrix H should satisfy the restricted isometry property (RIP) [23] which requires that ( 1 - δ s ) ∥ f ∥ 2 2 ≤ ∥ H f ∥ 2 2 ≤ ( 1 + δ s ) ∥ f ∥ 2 2 (19).
In order to ensure that the user's receive signal is not interfered by MUI, relative matrices at each BS should satisfy the ZF criterion.
A constraint matrix C s which should satisfy (boldsymbol {C}_{s} dot {boldsymbol {x}}_{s} = boldsymbol {0}) is obtained from the constraint conditions.
A velocity transformation matrix A h which should satisfy (dot {tilde {boldsymbol {x}}}_{h}=boldsymbol {A}_{h}dot {boldsymbol {x}}_{h}) can thus be obtained from boldsymbol{A}_{h} = frac{partial tilde{boldsymbol{x}}_{h}}{partial boldsymbol{x}_{h}}, (31).
