Digital predistortion of wideband signals

based on power amplifier model with

memory
where M is the maximum delay in the unit of sample, and
J. Kim and K. Konstantinou
Memory effects in the power amplifier limit the performance of digital
predistortion for wideband signals. Novel algorithms that take into
account such effects are proposed. Measured results are presented for
single and multicarrier UMTS signals to demonstrate the effectiveness
of the new approach. where pm is the order of polynomial Bm(bm, xn–m). The components of
vector bm, {bm1, bm2, ..., bmpm}, are complex numbers.
Let b ≡ [b0b1...bM], then the estimation is obtaining the optimum b
Introduction: Digital predistortion (DPD) is one of the most promising
that best describes the characteristics of the PA. We use the minimum
linearisation techniques that could lead to more efficient and cost effec-
mean squared error (MMSE) criterion. Let the error function f(b) be
tive power amplifiers (PA). The linearisation method intentionally dis-
defined as
torts the input signal so that the nonlinearity of the PA can be
compensated. In effect, the predistorter has the ‘inverse’ characteristics
of the amplifier to be linearised.
Behaviour models for PA have traditionally been developed based on where E[z] is the mean of x. Then, bopt is the argument of the function f
the AM-AM and AM-PM curves [1, 2], and the PA gain is usually at its minimum. We used the Newton method [5] for the estimation.
approximated as a complex polynomial function of instantaneous input
power level [3, 4]. However, as the bandwidth of the signal increases,
memory effects in the transmitter distort this simplified picture. Memory
effects are attributed to filter group delays, the frequency response of
matching networks, nonlinear capacitances of the transistors and the
response of the bias networks. The performance of DPD algorithms that
do not take these memory effects into account is severely degraded as
the bandwidth of the input signal increases.
In this Letter, a relatively simple model that captures both memory
effects and nonlinear behaviour of a PA is proposed. Algorithms that
obtain the DPD function based on the estimated model parameters are
also described. Measured results are presented for single and multi-car-
rier universal mobile telecommunication systems (UMTS) input signals
to demonstrate the effectiveness of the new approach when compared to
memoryless DPD.

Fig. 2 Estimation errors for signals of different bandwidths

—u— 3 UMTS carriers (15 MHz)
—s— 1 UMTS carrier (5 MHz)

Let the estimation error ε be defined as

Fig. 1 Overview of proposed digital predistortion scheme

The estimation error is an indication of how close the PA model is to the

Overview of proposed predistortion scheme: The structure of the pro-
actual PA. Fig. 2 illustrates the effects of adding delay terms in the PA
posed DPD scheme is shown in Fig. 1. The complex baseband signal un
model. The PA tested was an LDMOS, class AB amplifier. A single-car-
and xn are the input and output of the DPD function, respectively, where
rier UMTS signal and a three-carrier UMTS signal were used as test
n is the time index. xn is up-converted and fed to the PA. A feedback
inputs. Peak limiting was applied so that the peak-to-average power
receiver is used to produce yn, which is the down-converted and normal-
ratio of the signal is 8 dB. The peak output power was near the 1 dB
ised output of the PA. yn is compared to xn for characterisation of the PA.
compression point of the PA. We used fifth-order polynomials for all the
The proposed approach is largely divided into two steps. First, the delay terms, i.e. pm = 5. In the case of narrowband signal, adding more
characteristics of PA are estimated, where proper modelling and param- delay terms does not reduce the estimation error much. On the contrary,
eter estimation based on that model are needed. Secondly, the DPD the estimation error for wideband signals is significantly reduced as the
function is obtained by ‘inverting’ the PA characteristics. number of delay term increases, indicating that a PA model with mem-
ory is essential for wideband systems.
Modelling and estimation of power amplifier: The baseband behaviour
of the PA can be described by using a complex polynomial in eqn. 1: Derivation of predistortion function and results: The ideal DPD func-
tion is the inverse function of the PA model in eqn. 2. In the case of the
memoryless model (M = 0), a good approximation of the inverse func-
tion can be obtained by polynomial fitting. In general, it is very difficult
to find analytical solutions for the inverse function of the polynomial in
where xn is the complex input of the PA, and ỹ n is the approximate out- eqn. 2. However, if the PA model has only one delay term (M = 1), a
put of the PA according to the model. p is the order of the polynomial. stable DPD function can be calculated by an easy iterative method. The
The above model has the same characteristics over the whole frequency PA model with one delay term is described as
band of operation, which is a good approximation for narrowband sig-
nals. However, a real PA has memory and its characteristics depend on
the signal frequencies. Having memory means that the output of the PA
xn can then be expressed in terms of yn and xn–1
is not only a function of the current input but also a function of the past
inputs and outputs. As the bandwidth of the signal increases, memory
effects in the PA become evident. A relatively simple baseband behav-
ioural model that accommodates memory as well as nonlinear behaviour
is introduced and described in eqn. 2: With ideal predistortion, the output yn of PA is the same as the input un

ELECTRONICS LETTERS 8th November 2001 Vol. 37 No. 23

of DPD. The DPD function is then described as The above algorithm converges after one or two iterations. This has
been verified after several tests on an experimental platform. Measured
results are shown in Fig. 3. When a single carrier UMTS signal is trans-
mitted, the memoryless DPD performs well. No significant performance
improvement (~ 1.5 to 3 dB) was measured by adding memory in the
Eqn. 8 describes the DPD function given that the PA characteristics (b0 DPD function. On the contrary, memoryless DPD does not perform as
and b1) are known. The problem is that |xn| is needed to calculate xn. well when three UMTS carriers are transmitted. A substantial amount
Thus, at the beginning, |un| is used instead of |xn| to obtain x̃ n that is the (~8 dB) of further ACP (adjacent channel power) reduction was meas-
approximation of xn. Then, | x̃ n| is used for the argument of β0(·) in ured using DPD with one delay term memory. Obtaining the DPD func-
eqn. 8 for a better approximation. The procedure is outlined as follows. tion for a PA model with multiple delay terms would be the next task for
Step 1. Calculate x̃ n by using β0(|un|) instead of β0(|xn|) in eqn. 8. further performance improvement.
Step 2. Calculate better x̃ n by using previously obtained | x̃ n| for the
argument of β0(·) in eqn. 8. © IEE 2001 8 August 2001
Electronics Letters Online No: 20010940
Step 3. Execute Step 2 by several iterations. The last x̃ n is the final xn. DOI: 10.1049/el:20010940
J. Kim and K. Konstantinou (Lucent Technologies, 67 Whippany Road,
Whippany, NJ 07981-0903, USA)
E-mail: kimj@lucent.com

References

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Fig. 3 Power spectrum of PA output for 1 UMTS carrier at 38 W output 3 HAN, J.H., CHUNG, T., and NAM, S.: ‘Adaptive predistorter for power
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ACP = (–55.3, –53) dBc with memoryless DPD. 4 CAVERS, J.K.: ‘Amplifier linearization using digital predistorter with fast
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ELECTRONICS LETTERS 8th November 2001 Vol. 37 No. 23