Adaptive Modeling and Identification of Nonlinear MIMO Channels Using Neural Networks - Adaptive Signal Processing in Wireless Communications - page 140

Table 5.1

Sigmoid
Transforms Parameters Multiplications Additions

Proposed NN M(3N + L) MN M(2N + L) M(2N + L + 1)

MLP MN(M + L + 1) MN MN(M + L) MN(M + L + 1)

The number of sigmoid transforms is the same, since we have the same number of
neurons in the two structures. However, the MLP requires much more multiplications
and additions. This is because in the MLP structure, all inputs are connected to all first-
layer neurons ( MN neurons in total), whereas in the block structure, each input is con-
nected to one block that is composed of N neurons only.

5.3 Applications and Simulation Results

5.3.1 Modeling and Identification of MIMO Transmitters with
Nonlinear Amplifiers and RF Coupling Interference
In this section, we apply the proposed NN for modeling and identification of MIMO
RF transmitters that are equipped with nonlinear HPAs. Figure 5.5 shows the coupling
terms generated by RF interference [10, 16]. In this application, the unknown nonlinear
HPA transfer functions to be identified are taken from a family of nonlinear functions
of the form

 

β 2
2

− x

gx () = α x exp  

i

  ,

i i

 

where α i and β i are positive constants.
For the simulations presented in this section, we have taken the following parameters:
M = L = 2, α 1 = α 2 = 1, β 1 = 1, β 2 = 2. For each output, the noise is taken as white Gauss-
ian with variance σ i 2 . For the simulation, the inputs were zero-mean white Gaussian
processes with unit variance.

I/Q
data stream

HPA

Local
oscilator

Coupling matrix

I/Q
data stream

HPA

FIgure 5.5 Example of a two-dimensional MIMO RF transmitter, including the coupling
matrix between antennas.