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If the test statistics indicate that one cointegrating vector exists, maximum likelihood estimates of this vector are given by the first column of ( beta ).

The data of this starting vector are given in the columns (tilde{lambda }_{text {start}}), (bar{k}_{text {start}}) and (tilde{c}_{text {start}}) in Table 2.

Details of the functions and their search space, where (n) is the dimension of the decision vector, are given in Table 1.

For the channel estimation task, one can view the received vector during one block length as φ [ t ] = [ ( y [ 1, t ] ) T, ( y [ 2, t ] ) T, …, ( y [ s ′, t ] ) T ] T. At the initialization, the mean and covariance matrix of this vector are given in Section 3.1.

Thus, by using (3.20), the components of the conserved vector are given by T 1 t = − u x ϕ − v x ψ, T 1 x = 12 v x ψ x u − 12 u x ϕ x u + u t ϕ + v t ψ ( t, x ) + 4 u x x ϕ x − 4 u x ϕ x x + 4 v x x ψ x − 4 v x ψ x x.

Thus, by using Ibragimov's theorem [33], the components of the conserved vector are given by T 1 t = − 6 p u x u + p u x x x − 6 p v x + 6 q u v x − 2 q v x x x, T 1 x = 6 p u u t − p u t x x + 6 p v t − 6 q u v t + 2 q v t x x − u t p x x + p x u t x + 2 v t q x x − 2 q x v t x.  .

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The vector is given by (40).

The measurement vector is given by (8).

Let satisfy (2.2), let matrices, vector be given, and let.

The receive beamforming vector is given by (58).

The received symbol vector is given as (4).

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