*2.3.1. Zero-forcing MIMO receiver*

BS

10 Selected Topics in WiMAX

**Figure 2.** Block Diagram of MU-MIMO System Configuration

**2.3. On MIMO receiver**

MU-MIMO-BC

*NT* 

MU-MIMO-MAC

be extracted by each mode of operation and specific configuration.

and optimal Maximum Likelihood Detections (MLD) [8, 10].

MU-MIMO single-cell configuration

Before returning to the general question like how to design the precoder, what is the best Precoder, and what we can gain by incorporating multi-user mode in the WiMAX standards, we summarize the different MIMO system configurations in figure 3. Basically, there are two main modes, SU-MIMO and MU-MIMO. Essentially MU-MIMO is a closed-loop transmission system which means that the channel-state information is required at the transmitter for any transmission. There are two modes of operation for SU-MIMO configurations – closed-loop where the CSI is required at the transmitter and open-loop where the CSI is not required to be used at the transmitter. Also the diagram indicates at each end the type of MIMO gain that can

MIMO receiver design is also one of the hot areas of wireless communication research and system development in the last decade. Many receiving techniques have been reported to decode these kinds of vector transmissions. For the linear transmission techniques, the decoders design complexities range from simple linear methods like Zero-Forcing (ZF) and Minimum Mean-Square-Error (MMSE) receivers to complex sphereical sub-optimal decoding

*MR1* 

*MRB* 

U1

UB

Zero-Forcing (ZF) decoder is a simple linear transformation of the received signal to remove the inter-channel interference by multiplying the received signal vector by the inverse of the channel matrix [38]. In fact, if perfect CSI is available at the receiver, the zero-forcing estimate of the transmitted symbol vector can be written as

$$\mathbf{\tilde{y}} = \mathbf{G}(\mathbf{H}\mathbf{s} + \mathbf{n}) = \mathbf{s} + \mathbf{G}\mathbf{n} \tag{18}$$

where the decoder is calculated from **G**=(**H**∗**H**) −1 **H**∗, which is also known as the pseudo inverse of the MIMO channel matrix. In ZF, the complexity reduction comes at the expense of noise enhancement which results in some performance losses compared to other MIMO receiving methods.
