*2.3.5. MIMO in the current WiMAX standard*

where . *<sup>F</sup>*

12 Selected Topics in WiMAX

2 denotes the matrix/or vector Frobenius norm. The complexity of this decoder

**Multi-user MIMO (MU-MIMO)** 

**Multi-User MIMO Multi-access Channel (MU-MIMO-MAC)** 

**closed loop (CSIT)** 

**Multi-user MIMO Broadcast channel** 

increases exponentially as the number of transmit and receive antennas increases. In spite of

**Multi-elements Antennas** 

**Spatial Diversity with space time/or space frequency coding** 

**(MU-MIMO-BC)** 

Sphere Decoding (SD) families are the new decoding techniques that aim to reduce the computational complexity of the ML decoding technique. In the sphere decoder, the received signal is compared to the closest lattice point, since each codeword is represented by a lattice point. The number of lattice points scanned in a sphere decoder depends on the initial radius

**(STC/SFC)** 

**Spatial Multiplexing** 

**Figure 3.** Different forms of Multi-element Antennas Channel Configuration

its good BER performance, ML decoding is however not used in any practical system.

**Single user MIMO channel (SU-MIMO)** 

**CSIT)** 

**Spatial Multiplexing with Precoding** 

**forming** 

**Spatial diversity or Beam** 

*2.3.4. Sphere decoding MIMO receiver*

**Closed Loop SU-MIMO (using CSIT) Channel** 

**Open Loop SU-MIMO Channel (NO need for** 

MIMO techniques have been incorporated in all recent wireless standards including IEEE 802.16e, IEEE 802.16m, IEEE 802.11n, and the Long-Term Evaluation (LTE). The WiMAX profile IEEE 802.16e defines three different single user open loop transmission schemes in both uplink and downlink channel summarized as below:


In addition to the basic MIMO techniques supported by the IEEE 802.16e, the profile of IEEE 801.16m also supports several advanced MIMO techniques including more complex configu‐ rations of SU-MIMO and MU-MIMO (spatial Multiplexing and beam-forming) as well as a number of advanced transmit diversity [43, 44]. The profile also defines multi-mode capability to adapt between SU-MIMO and MU-MIMO in a predefined and flexible manner. Further‐ more, flexible receiver decoding mode selection is also supported. Unitary precoding or beamforming with code-book is also defined for both SU-MIMO and MU-MIMO configurations [45]. Cade-book based MU-MIMO precoding techniques found to be effective for the FDD mode of operation because of the great amount of reduction on feedback channel provided, while they are ineffective in the TDD mode of operation [24]. In the next section, we will introduce non-unitary MU-MIMO precoding method to the area of WiMAX. It can be shown that the non-unitary precoding like our proposed method will be applicable and suitable to the TDD mode of operation as accurate CSI is available at the transmitter for the precoding design. In the next section, we will review the most recent researched precoding methods and extend them by proposing our new method.
