In amultiple Precodedantenna MIMOdownlink BCsystems systemwhich withcomprises a <math>N_t</math> transmittertransmit antennasantenna access atpoint (AP) and a<math>K</math> receiversingle receive antenna forusers, the received signal eachof user <math>k</math>, theinput-output relationship can beis described as
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>y_k</math> and <math>n_k</math> areis the received symbol and noise respectivelysignal, <math>\mathbf{h}_k</math> is the <math>N_t \times 1</math> vector of channel coefficientsvector and <math>\mathbf{w}_i</math> is the <math>N_t \times 1</math> linear precoding vector.
For the comparison purpose, we describe the mathematicalreceived descriptionsignal ofmodel MIMOfor multiple antenna uplink MACsystems. In a MIMOthe MACuplink system with a <math>N_r</math> receiver antennas atantenna AP and a transmit antenna for each user <math>kK</math> whereK <math>k=1,2,single \ldots,transmit K</math>antenna user, the input-outputreceived relationshipsignal canat the AP beis described as
where <math>s_i</math> is the transmitted symbolsignal forof user <math>i</math>, <math>\mathbf{y}</math> and <math>\mathbf{n}</math> areis the <math>N_r \times 1</math> vector of received symbols and noise respectivelyvector, <math>\mathbf{h}_k</math> is the <math>N_r \times 1</math> vector of channel coefficientsvector.
