Adaptive Compensation of Frequency Response
Mismatches in High-Resolution Time-Interleaved
ADCs using a Low-Resolution ADC and a
Time-Varying Filter
Shahzad Saleem
Signal Processing and
Speech Communication Laboratory
Graz University of Technology, Austria
Email: ssaleem@tugraz.at
Christian Vogel
Signal Processing and
Speech Communication Laboratory
Graz University of Technology, Austria
Email: c.vogel@ieee.org
Abstract— This paper investigates the adaptive compensa-
tion of frequency response mismatches in an M -channel time-
interleaved analog-to-digital converter (TI-ADC) using an extra
low-resolution ADC and a time-varying FIR filter. The introduced
compensation structure may be used to compensate any linear
frequency response mismatches including time skew mismatches.
The coefficients of the time-varying filter are adapted using
the least-mean square (LMS) algorithm. The performance of
the proposed compensation structure is demonstrated through
numerical simulations.
I. INTRODUCTION
As the functionality of communication systems is moving
more and more into the digital domain in order to provide
increased flexibility and more precision [1], the requirements
on the data converters increase in terms of higher speed and
larger bandwidth. In this regard, a TI-ADC can be a reasonable
solution to achieve higher sampling rates for medium-to-high
resolution applications. By using a TI-ADC one can increase
the throughput of a data converter by using several ADCs in
parallel and sampling the data in a time-interleaved manner.
AsshowninFig.1,inanM-channel TI-ADC each individual
ADC with an analog frequency response
ˆ
H
m
(jΩ), m =
0, 1, ..., M − 1 operates with a sampling rate of f
s
/M , thus
the overall sampling frequency is f
s
.
The performance of a TI-ADC however, suffers from mis-
match errors among the subconverters [2]. These mismatch
errors uncover the time-varying behavior of a TI-ADC and
cause modulated spurious images of the input spectrum in
the output spectrum leading to a significant decrease in the
performance.
Beside the calibration of gain and timing mismatches [3]–
[6], the calibration of frequency response mismatches can lead
to a further improvement in the overall performance of a TI-
ADC. A hybrid filter-bank model of a two-channel TI-ADC for
semi-blind calibration of bandwidth mismatches is presented
in [7]. In [8] a compensation technique for frequency response
mismatches using a least-square design for an M -periodic
output
ˆ
H
0
(jΩ)
Q
H
(nM +0)T
s
ˆ
H
m
(jΩ)
(nM + m)T
s
Q
H
MUX
ADC
m
(nM +(M − 1))T
s
ˆ
H
M−1
(jΩ)
ADC
M−1
TI-ADC
nT
s
R(jΩ)
Q
L
ADC
R
reference
f
s
f
s
=
1
T
s
y[n]
digital
output
d[n]
ADC
0
Q
H
x(t)
Fig. 1: Model of a TI-ADC comprising M linear high-
resolution time-invariant channels
ˆ
H
m
(jΩ), m =0, 1, ..., M −
1 with quantizers Q
H
and an extra low-resolution ADC R(jΩ)
with quantizer Q
L
.
time-varying filter is presented. A flexible and scalable struc-
ture to compensate frequency response mismatches in TI-
ADCs using an M-periodic time-varying compensation filter
is presented in [9]. An adaptive technique for an all-digital
communication receiver using feed-forward equalizer (FFE)
to correct mismatches in a TI-ADC is presented in [10].
In this paper, we present a structure comprising an M-
channel high resolution TI-ADC and an extra low-resolution
ADC. The extra ADC and the time-varying FIR filter are used
to calibrate frequency response mismatches introduced by the
TI-ADC, where output of the extra ADC acts as reference
input for the M -periodic least-mean square (LMS) algorithm
that estimates the coefficients sets for the M-periodic time-