Analog Devices ADRV9029 User Manual page 8

The mathematical representation of the DPD coefficient estimation is shown in Figure 9. The DPD engine observes N samples of
PA input samples (X) and PA output samples (Y), and computes M-coefficients (c) corresponding to the inverse PA function F(x).
The coefficient set (c) is estimated through a least squares approximation as described in matrix multiplication equations (1) to
(3).
DPD direct learning involves using the pre-DPD actuator Tx signal (U) as reference to minimize the error between the observed
DPD Direct Learning
(Y) and reference data (U).
The mathematical representation of the DPD coefficient estimation via direct learning is described as follows. An error E is
defined as the difference between observed (Y) and pre-DPD actuator data (U).
The PA is modeled as the function Fx multiplied by adaptive coefficients C through the error matrix E as shown in Figure 11.
Y
f1(x1)
y1
f1(x2)
=
y2
f1(x3)
y3
f1(x4)
y4
.
.
.
yN
f1(xN)
Figure 9. DPD Indirect Learning Coefficient Computation
Y = F x C
H H
F Y = (F F)C
H -1 H
(F F) (F Y) = C
Auto- Cross-
correlation correlation
Figure 10. DPD Direct Learning Architecture
F(x)
f2(x1) f3(x1) f4(x1) ..... fM(x1)
f2(x2) f3(x2) f4(x2) ..... fM(x2)
f2(x3) f3(x3) f4(x3) ..... fM(x3)
f2(x4) f3(x4) f4(x4) ..... fM(x4)
.
.
.
f2(xN) f3(xN) f4(xN) ..... fM(xN)
(1)
(2)
Multiply by complex conjugate of F on both sides
Take the inverse of the auto-correlation function to
(3)
E = Y – U
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Preliminary Technical
c
c1
c2
c3
c4
.
.
.
cM
obtain C
Data