*4.2.1. Scenario 1: Single cell MU-MIMO*

**Algorithm 2:** PA-SLNR MU-MIMO precoding based on FKT for multiple *B* independent MU-

*th* receive antenna covariance matrix **Π**1 using the FKT factor **P**to **Π˜** <sup>1</sup> and select the

<sup>1</sup> <sup>⋯</sup>**f***<sup>k</sup> Mk*

The algorithm takes the combined MU-MIMO channel matrix as well as the value of the noise variance as an input and outputs *B* users precoding matrices. It computes the FKT factor in step one and two and iterates *B* times (step three to six) to calculate the precoding matrices for *B* number of users. For each user, there are *Mk* sub-iteration operations (step four to five) to

In this section we will highlight the importance of Precoding for MU-MIMO and showcase the performance of the proposed PA-SLNR-FKT scheme in two scenarios – scenario 1, single cell MU-MIMO where there is no interference from other cell and scenario 2 of multi-cell process‐ ing (MCP) where there is multicell interference and the objective is to make use of multiple antennas in all basestation cooperatively to improve the overall system performance. We use both basic assumptions and a typical simplified WiMAX physical layer Standard discrete channel Models for the Monte-Carlo simulation. Firstly, with basic assumptions we provide comparative performance evaluation results of the proposed MU-MIMO Precoder and the PU-SLNR maximization techniques using GEVD and GSVD proposed in [34, 58]. The comparison is done in terms of average received BER and output received SINR outage performance metrics. In each simulation setup, the entries of *kth* user MIMO channel **H***k* is generated as complex white Gaussian random variables with zero mean and unit variance. The users data

*th*receive antenna at the *kth* user is: **f***<sup>k</sup>*

*<sup>j</sup>* <sup>=</sup>**Pν***<sup>k</sup> j*

• Input: Combined channel matrix for all *B*users and the input noise variance

• Output: Precoding matrices **F***k* for multiple *B*users such that, *k* =1, ⋯, *B*

*k <sup>j</sup>* **<sup>I</sup>***NT*

<sup>2</sup> from *SVD*(**Π**)

*j* of **Π˜** <sup>1</sup> ○ The precoding vector corresponding to the *j*

○ Synthesize the *kth* user precoding matrix is **F***<sup>k</sup>* = **f***<sup>k</sup>*

calculate each individual user precoding matrix in vector by vector basis.

\* **<sup>H</sup>**com <sup>+</sup> <sup>σ</sup> <sup>2</sup>

○ Transform the *j*

first eigenvector **ν***<sup>k</sup>*

MIMO users.

22 Selected Topics in WiMAX

1. Compute the sum **Π**=**H**com

2. Compute FKT factor **P**=**UD**<sup>−</sup> <sup>1</sup>

3. For *k*= 1 to *B* 4. For *j*=1 to *Mk*

**4.2. Performance evaluation**

End

End

**H***com* = **H**<sup>1</sup> *<sup>T</sup>* **<sup>H</sup>**<sup>2</sup> *<sup>T</sup>* <sup>⋯</sup>**H***<sup>B</sup> <sup>T</sup> <sup>T</sup>* , σ*<sup>k</sup>* 2

> In this scenario we consider single cell transmission where implicitly we assume that the multicell interference is zero. Figure 6. shows the average received BER performance of the proposed PA-SLNR-FKT and the reference methods of SLNR-GSVD and SLNR-GEVD precoding schemes for the MU-MIMO-BC system configurations of *NT* =14, *B* =3*Mk* =4. In this configu‐ ration, the numbers of the base station antennas are more than the sum of all receiving antennas which also signifies more degree of freedom in MU-MIMO transmission. In this simulation also, the base station utilizes 4-QAM modulation to modulate, spatially multiplexes and precodes a vector of length 4 symbols to each user. The average BER is calculated over 5000 MU-MIMO channel realization for each algorithm. The proposed method outperforms SLNR-GSVD and SLNR-GEVD. At BER equal to 10−<sup>4</sup> there is approximately 4dB performance gain over SLNR-GSVD.

> Figure 7 compares the received output SINR outage performance of the proposed PA-SLNR-FKT precoding and the reference SLNR-GSVD and SLNR-GEVD precoding methods. MU-MIMO system with full rate configuration of *B* =3, *Mk* =4, *NT* =12 and 2dB input SNR is considered in the simulation. The proposed method outperforms the SLNR-GSVD method by 1 dB gain at 10% received output SINR outage.

> Figure 8 compares the received output SINR outage performance of the proposed PA-SLNR-FKT precoding and the reference SLNR-GSVD and SLNR-GEVD precoding methods. MU-MIMO system with full rate configuration of *B* =3, *Mk* =4, *NT* =12 and 10dB input SNR are considered in the simulation. The proposed method outperforms the SLNR-GSVD method by approximately 1.5 dB gain at 10% received output SINR outage.

**Figure 6.** Shows The Compression of The Un-coded BER Performance for PA-SLNR-FKT, SLNR-GSVD and SLNR-GEVD Precoding Methods Under System Configuration of *B* =3, *Mk* =4, *NT* =14, 4QAM Modulated Signal.

*4.2.2. Scenario 2: MU-MIMO with Multi Cell Processing (MCP)*

Precoding Methods Under System Configuration of *B* =3, *Mk* =4, *NT* =12, and 10 dB Input SNR.

and slow fading discrete components as follows.

where **H ↔** *e <sup>k</sup>* ∈**C** *NRk* <sup>×</sup>*NT <sup>e</sup>*

To appreciate the importance of precoding to cancel inter-cell interference in the MCP configuration, geometrically we consider three cooperating BSs as illustrated in figure 9. Basically we consider micro-cellular setup of BS to BS distance equal to 1000 m. As shown in figure 9. we also consider a simplified as well as an extreme case where there are three users at the edges of the three cooperating cells, so that we just allow each user to uniformly position within the last 50 m of its anchor BS. In each transmission, a WiMAX standard channel model is used. Thus each entry of the *kth* user MIMO channel matrix is generated according to prespecified wireless communication channel model which include mean path loss, shadowing

**Figure 8.** Shows The Comparison of the Output SINR Outage Performance PA-SLNR-FKT, SLNR-GSVD and SLNR-GEVD

1/2 1 2 ( ) *k k e e* = f f

and the *eth* BS and in this system simulation we use the WiMAX discrete channel values as given in [72] and *ϕ*1 denotes the channel path loss component while *ϕ*2 is the lognormal shadowing fadingcomponent.Ineachstepofsimulationfixedleastsquarefilterisusedtodecodethereceived

data and unless specified otherwise, the following values listed in table 2. are used.

<sup>t</sup> **H H** (45)

On MU-MIMO Precoding Techniques for WiMAX

http://dx.doi.org/10.5772/56034

25

represent the fast fading channel discrete component between the *kth* user

**Figure 7.** Shows The Comparison of The Output SINR Outage Performance of The PA-SLNR-FKT, SLNR-GSVD and SLNR-GEVD Precoding Methods Under System Configuration of *B* =3, *Mk* =4, *NT* =12, and 2 dB Input SNR.

**Figure 8.** Shows The Comparison of the Output SINR Outage Performance PA-SLNR-FKT, SLNR-GSVD and SLNR-GEVD Precoding Methods Under System Configuration of *B* =3, *Mk* =4, *NT* =12, and 10 dB Input SNR.
