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:<math>y_k = \mathbf{h}_k^T\mathbf{x}+n_k, \quad k=1,2, \ldots, K</math>
where <math>\mathbf{x} = \sum_{i=1}^K s_i P_i \mathbf{w}_i</math> is the <math>N_t \times 1</math> vector of transmitted symbols, <math>n_k</math> is the noise signal, <math>\mathbf{h}_k</math> is the <math>N_t \times 1</math> channel vector and <math>\mathbf{w}_i</math> is the <math>N_t \times 1</math> linear precoding vector. From the fact that each Beam generated by ZF-precoding is orthogonal to all the other user channel vectors, we can rewrite the received signal as
:<math>y_k = \mathbf{h}_k^T \sum_{i=1}^K s_i P_i \mathbf{w}_i+n_k = \mathbf{h}_k^T s_k P_k \mathbf{w}_k +n_k, \quad k=1,2, \ldots, K</math>
For comparison purpose, we describe the received signal model for multiple antenna uplink systems. In the uplink system with a <math>N_r</math> receiver antenna AP and <math>K</math> K single transmit antenna user, the received signal at the AP is described as
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