*8.1.2. MU-MIMO with Zero Forcing precoding*

16 Recent Trends in Multiuser MIMO Communications

channel matrix.

such that:

achievable throughput.

(*Mk* × <sup>1</sup>) is expressed as :

**8.1. Zero Forcing and Block Diagonalization methods**

*8.1.1. MU-MIMO with Block Diagonalization precoding*

Popular low-complexity techniques include both Zero Forcing (ZF) and Block Diagonalization (BD)[27][28] methods. Algorithms for the ZF as well as BD methods are presented in [29]. The aim of these solutions is to improve the sum rate capacity of the communication system under a given power constraint. These performances could be achieved by canceling inter-user interference. Zero Forcing Dirty Paper Coding (DPC) [30] represents a famous technique for data precoding where the channel is subject to interference which is assumed to be known at the transmitter. The precoding matrix is equal to the conjugate transpose of the upper triangular matrix obtained via the QR decomposition of the

We consider a communication system model with a broadcast MIMO channel where the transmitter is a base station equipped with *N* antennas and the receiver consists of *K* users *Uk*; *k* = 1... *K* (See figure 6(b)). The received signal at user *Uk*; *k* = 1... *K* with dimension

We assume in the following that users *U*1,... *UK* have the same number of antennas which will be denoted by *M*. Block Diagonalization strategy defines a set of precoding matrices *VBD*(*k*)(*<sup>N</sup>* × *<sup>M</sup>*) associated to users *<sup>U</sup>*1,..., *UK*. These matrices form an orthonormal basis

The aim of these conditions is to eliminate multi-user interference so that to maximize the

The performance of downlink communication scenarios with precoding techniques depends on the SNR level. In fact, it has been shown in [27] that SU-MIMO achieves better performances than MU-MIMO at low SNRs. However, the BD MU-MIMO achieves better performances at high SNRs. As such, switching between SU-MIMO and MU-MIMO is

• *Hk*(*Mk* × *<sup>N</sup>*) is the channel matrix between user *Uk* and the base station

• *VBD*(*k*)(*<sup>N</sup>* × *Mk*) is the BD precoding matrix for user *Uk*

[*VBD*(*k*) ] ∗

• *Xk* is the transmit signal for user *Uk*

• *Bk*(*Mk* × <sup>1</sup>) is the additive noise signal vector

and the Block Diagonalization algorithm achieves :

optimal for obtaining better total rates over users.

*Yk* = *Hk* · *VBD*(*k*) · *Xk* + *Bk* ; *<sup>k</sup>* = 1, . . . , *<sup>K</sup>* (23)

· *VBD*(*k*) = *IM* ; *<sup>k</sup>* = 1... *<sup>K</sup>* (24)

*Hk* · *VBD*(*j*) = 0 ; ∀ *<sup>j</sup>* �= *<sup>K</sup>* (25)

Case of Zero Forcing strategy, each transmitted symbol to the *l* − *th* antenna (among *M* antennas of user *Uk*) is precoded by a vector which is orthogonal to the columns of *Hj*, *<sup>j</sup>* �= *<sup>k</sup>* but not orthogonal to the *<sup>l</sup>* − *th* column of *Hk* [26].
