ArticlePDF Available

A GSM/EDGE/WCDMA modulator with on-chip D/A converter for base stations

Authors:

Abstract and Figures

A global system for mobile communication (GSM)/enhanced data rates for GSM evolution (EDGE)/wideband code division multiple access (WCDMA) modulator with a 14-bit on-chip digital-to-analog (D/A) converter is presented. The modulator consists of several digital signal processing building blocks, including a programmable pulse shaping filter, interpolation filters, resampler, co-ordinate rotation digital computer (CORDIC) rotator, programmable output power level controller and ramping unit, and x/sinx filter. The precompensation filter, which compensates the sinc droop above the Nyquist frequency, makes it possible to use WCDMA signal images for up-conversion. The new programmable up/down unit allows power ramping on a time-slot basis as specified for GSM, EDGE and time division duplex (TDD)-WCDMA. The multistandard modulator meets the spectral, phase and error vector magnitude (EVM) specifications. The die area of the chip is 22.09 mm<sup>2</sup> in 0.35-μm CMOS technology. Power consumption is 1.7 W at 3.3 V with 110 MHz.
Content may be subject to copyright.
J. Vankka, J. Ketola, J. Sommarek, O. Väänänen, M. Kosunen and K. Halonen, A
GSM/EDGE/WCDMA Modulator with On-Chip D/A Converter for Base Stations,
IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal
Processing, Vol. 49, No. 10, pp. 645-655, Oct. 2002.
© 2002 IEEE
Reprinted with permission.
This material is posted here with permission of the IEEE. Such permission of the IEEE
does not in any way imply IEEE endorsement of any of Helsinki University of
Technology's products or services. Internal or personal use of this material is permitted.
However, permission to reprint/republish this material for advertising or promotional
purposes or for creating new collective works for resale or redistribution must be
obtained from the IEEE by writing to pubs-permissions@ieee.org.
By choosing to view this document, you agree to all provisions of the copyright laws
protecting it.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002 645
A GSM/EDGE/WCDMA Modulator With On-Chip
D/A Converter for Base Stations
Jouko Vankka, Member, IEEE, Jaakko Ketola, Student Member, IEEE, Johan Sommarek, Olli Väänänen,
Marko Kosunen, Student Member, IEEE, and Kari A. I. Halonen
Abstract—A global system for mobile communication
(GSM)/enhanced data rates for GSM evolution (EDGE)/wide-
band code division multiple access (WCDMA) modulator with a
14-bit on-chip digital-to-analog (D/A) converter is presented. The
modulator consists of several digital signal processing building
blocks, including a programmable pulse shaping filter, inter-
polation filters, resampler, cordinate rotation digital computer
(CORDIC) rotator, programmable output power level controller
and ramping unit, and x/sinx filter. The precompensation filter,
which compensates the sinc droop above the Nyquist frequency,
makes it possible to use WCDMA signal images for up-conversion.
The new programmable up/down unit allows power ramping on
a time-slot basis as specified for GSM, EDGE and time division
duplex (TDD)-WCDMA. The multistandard modulator meets
the spectral, phase and error vector magnitude (EVM) specifica-
tions. The die area of the chip is 22.09 mm
2
in 0.35- m CMOS
technology. Power consumption is 1.7 W at 3.3 V with 110 MHz.
Index Terms—Cordinate rotation digital computer (CORDIC),
current steering digital-to-analog (D/A) converter, multicarrier,
multistandard modulator, power control, power ramping, resam-
pler.
I. INTRODUCTION
THE global system for mobile communication (GSM) is a
second generation (2G) system that has rapidly gained ac-
ceptance and a worldwide market share. As the mobile commu-
nications market develops, interest is building up in data appli-
cations and higher data rate operations. Short message services
(SMS) were first added to the GSM system followed by high-
speed circuit switched data (HSCSD) and the general packet
radio service (GPRS). All of these services use the same modu-
lation format as the original GSM network [0.3 Gaussian min-
imum shift keying (GMSK)], and change the allocation of the
bits and/or packets to improve the basic GSM data rate. As a step
toward 3G, enhanced data rates for GSM evolution (EDGE) pro-
vides a higher data-rate enhancement of GSM. It uses the GSM
infrastructure with upgraded radio equipment to deliver signif-
icantly higher data rates. The primary objective of the EDGE
signal is to triple the on-air data rate while taking up essentially
the same bandwidth as the original 0.3 GMSK signal. The wide-
band code division multiple access (WCDMA) was selected by
the European Telecommunications Standards Institute (ETSI)
for wideband wireless access to support 3G services because of
Manuscript received April 4, 2002; revised November 2, 2002. This paper
was recommended by Associate Editor A. Petraglia.
The authors are with the Electronic Circuit Design Laboratory,
Helsinki University of Technology, Helsinki FIN-02015, Finland (e-mail:
jvankka@vipunen.hut.fi).
Digital Object Identifier 10.1109/TCSII.2002.807268
its resistance to multipath fading, and other advantages such as
increased capacity. This technology has a wider bandwidth and
different modulation format from GSM or EDGE.
The first generation of the 3G base station modulator should
include support for GSM, EDGE and WCDMA. The digital
IF modulator is designed using specifications related to those
standards [1]–[3]. The main requirements of the modulator are
shown in Table I. By programming the GSM/EDGE/WCDMA
modulator, different carrier spacings, modulation schemes,
power ramping, frequency hopping and symbol rates can be
achieved. By combining the outputs of multiple modulators,
multicarrier signals can be formed, or the modulator chips can
be used for steering a phased array antenna. The formation of
multicarrier signals in the modulator increases the base station
capacity. The major limiting factor of digital IF modulator
performance at base station applications is the digital-to-analog
(D/A) converter, because the development of D/A converters
does not keep up with the capabilities of digital signal pro-
cessing with faster technologies [4].
The paper is organized as follows. Section II provides a de-
scription of the multistandard modulator. The new ramp gener-
ator and output power level controller is described in Section III.
The up-conversion by using the images of the D/A converter is
described in Section IV. The on-chip D/A converter is described
in Section V. Finally, experimental results obtained from the
chip are presented in Section VI; these are followed by a few
concluding comments.
II. GSM/EDGE/WCDMA MODULATOR
The block diagram of the modulator chip is shown in
Fig. 1. The use of different modulation formats requires
programmable pulse shaping filter coefficients. The recon-
figuration of new modulation formats can be done between
bursts (e.g., GSM/EDGE). The two half-band filters increase
preoversampling ratios, which reduce the complexity of the
resampler (the order of the polynomial interpolator). The
resampler circuit allows the sampling rate of the on-chip D/A
converter to have a variable noninteger relationship with the
input symbol rates [5]. This block is needed, because the
specified D/A converter sampling rates and input symbol rates
shown in Table I do not have integer frequency relationship.
The coordinate rotation digital computer (CORDIC) rotator
translates the baseband-centered spectrum to a programmable
carrier center frequency [6]. The IF signal is filtered by an
x/sinx filter for compensating the sample and hold response of
the on-chip 14 bit D/A converter [7]. The internal wordlengths
1057-7130/02$17.00 © 2002 IEEE
646 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002
TABLE I
GSM/EDGE/WCDMA MODULATOR SPECIFICATIONS
Fig. 1. GSM/EDGE/WCDMA modulator chip. The symbol rates (Fsym) are shown in Table I.
of the modulator are shown in Fig. 1. The wordlengths were
chosen such that the 14-bit D/A converter quantization noise
dominates the digital output noise.
A. Pulse Shaping and Half-Band Filters
The input symbols are filtered using Gaussian (BT
0.3)/linearized Gaussian/square root raised cosine ( )
pulse shaping filter in GSM/EDGE/WCDMA mode, respec-
tively [8], [3]. The square root raised cosine filter (excess
bandwidth ratio ) was designed to maximize the ratio
of the main channel power to the adjacent channels’ power
under the constraint that the error vector magnitude (EVM)
is below 2% [9]. In the GSM/EDGE systems a quarter of a
guard bit is inserted after each burst, resulting a burst length of
156.25 symbols [10]. Therefore, the input symbols to the pulse
shaping filter have to be oversampled by 4 in the GSM and
EDGE modes. The pulse shaping filter is implemented using
programmable canonic signed digit (CSD) coefficients [11].
The pulse shaping and the half-band filters are implemented
using a polyphase structure [12]. Taking advantage of the fact
that in the modulator data streams in the and paths are
processed with the same functional blocks, a further hardware
reduction can be achieved by pipeline interleaving techniques
[13]. The pulse shaping and the half-band filters are modified to
handle two channels by doubling the sampling rate and delay el-
ements between taps. This results in a more efficient layout with
a penalty in terms of increased power dissipation. The fixed co-
efficients of the half-band filters are implemented using CSD
numbers [14].
B. Resampler
The resampler consists of a resampling numerically con-
trolled oscillator (NCO) and a cubic Lagrange polynomial
interpolator shown in Fig. 2. The resampling NCO supplies
sampling clocks for resampler (clk1), half-band and pulse
shaping filters (clk1, clk1/2, clk1/4) as well as the trigger signal
for the input data symbols (clk1/8). The frequency control
word is calculated from the ratio of the input sampling
rate of the resampler (clk1) to output sampling rate (clk).
The trigger signals for different input symbol rates could be
achieved by altering the frequency control word. The output of
the resampling NCO ( ) may be considered to represent the
phase offset between the input sampling rate of the resampler
(clk1) to the output sampling rate (clk). Since the phase offset
changes on every output sample clock cycle, the interpolation
filter coefficients are time-varying. The time-varying filter
coefficients with long period can be easily implemented by
polynomial-based interpolation filters using so called Farrow
structure [15]. The cubic Lagrange polynomial interpolator was
found suitable for our application, because it fulfills spectral
and time domain (phase error and EVM) specifications [1]–[3].
The cubic Lagrange polynomial interpolator is implemented
with Farrow structure [5], where the number of unit delay
elements is minimized as in Fig. 2. Furthermore, the frequency
VANKKA et al.: GSM/EDGE/WCDMA MODULATOR WITH ON-CHIP D/A CONVERTER 647
Fig. 2. Resampler.
error term generated by the external digital phase locked loop
(DPLL) locking to an external symbol rate could be added to
the frequency control word .
C. CORDIC Rotator
The in-phase output of the CORDIC rotator is
(1)
where , are pulse shaped and interpolated quadrature
data symbols. The carrier frequency is
(2)
where is the -bit carrier frequency control word which can
range between , is the NCO word length,
and is the sampling frequency. The carrier frequency resolu-
tion is found by setting
(3)
The carrier frequency tuning resolution will be 0.0256 Hz by
(3), when is 110 MHz, and is 32. The frequency resolution
is better than the target frequency error specification in Table I.
The sign in (1) is controlled by the frequency control word.
The spectral inversion (modulation spectrum is reversed) in the
other up-conversion stages could be compensated by changing
the sign of the carrier frequency control word (the direction of
the vector rotation) in (1).
In the frequency modulation mode (GMSK modulation in
GSM [8]), the pulse shaped and interpolated frequency sam-
ples are added to the carrier frequency control word, and the
inputs of the CORDIC rotator are set constant [ is 1 and
is 0] as in Fig. 1, then the output is from (1)
(4)
where is the information-bearing component of the phase.
In the EDGE/WCDMA mode (quadrature amplitude modula-
tion [8], [3]), the input to the adder before the NCO is set zero
and samples are filtered by the pulse shaping filter and in-
terpolated prior to the CORDIC rotator.
The phase offset adds an offset to the NCO. This allows mul-
tiple modulators to be synchronized in order to produce carriers
with a known phase relationship. The phase offset allows intelli-
gent management of the relative phase of independent carriers.
This capability supports the requirements of phased array an-
tenna architectures [16].
III. RAMP GENERATOR AND OUTPUT POWER LEVEL
CONTROLLER
Summing the IF outputs from other devices allows the forma-
tion of a multicarrier signal in Fig. 1. This necessitates power
control to be implemented in the digital domain. Otherwise, it
would not be possible to adjust the relative power of a single
carrier with respect to the others. Therefore, a digital ramp gen-
erator and output power level controller is used as in Fig. 1. The
power control is realized by scaling the ramp curve [17].
The programmable up/down unit allows power ramping on a
time-slot basis as specified for GSM, EDGE and time division
duplex WCDMA (TDD-WCDMA) [1], [2]. The ramp generator
is based on a recursive digital sine wave oscillator [17]. In pre-
vious work [17], the ramp duration was fixed and the ramp gen-
erator could only generate cosine windows that have only one
648 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002
Fig. 3. Ramp generator and output power level controller.
cosine term (e.g., a Hanning window). In Fig. 3, two digital os-
cillators are used; these allow the Blackman window generation
(two cosine terms). The Blackman window gives more attenua-
tion to the switching transients than the Hanning window.
Another method for implementing the ramp generator is to
use a look-up table LUT. Because the sampling frequency is
high, the size of the LUT becomes large. The size of the LUT
increases even more because of the high oversampling ratio re-
quired by the variable ramp duration (see Table I). Alternatively,
interpolation between the samples in the LUT can be used at the
expense of increased complexity. Furthermore, the multiplier is
needed to set the output power level. Therefore, the choice was
made in favor of the recursive digital oscillators.
A. Ramp Generator
The ramp generator shown in Fig. 3 has two recursive digital
sine wave oscillators. Their difference equation comprises one
multiplication operation and one subtraction
(5)
where
(6)
The angle represented by the oscillator coefficient is given
by
(7)
where is the desired frequency. Solving the one-sided trans-
form of (5) leads to
(8)
where (0) and (1) are the initial values of state variables.
Choosing the initial values of the state variables to be
and , we obtain from (8) a discrete-time si-
nusoidal function as the output signal
(9)
The equation has complex-conjugate poles at ,
and an impulse response
(10)
The impulse response of the second-order system with complex-
conjugate poles on the unit circle is a sinusoidal waveform. An
initial phase offset can be realized [18], namely
(11)
by choosing the initial values
(12)
(13)
The amplitude and phase is determined by the initial values (0)
and (1). The output frequency of the digital oscillator ( can
be altered by changing the coefficient in (5) and the initial
value in (12). The details and finite wordlength effects of the
digital ramp generator and output power level controller are de-
scribed in [17].
B. Initial Values of the Ramp Generator
The rising ramp of the Blackman window is given by
(14)
VANKKA et al.: GSM/EDGE/WCDMA MODULATOR WITH ON-CHIP D/A CONVERTER 649
Fig. 4. Parallel structure.
Fig. 5. Off-chip precompensation filter at baseband.
where is the ramp duration, is [0; ], and is the am-
plitude of the ramp. The falling ramp of the Blackman ramp
window is
(15)
The cosine terms are implemented with the digital sine wave
oscillators and the term 0.42 is added to their output. The
initial values for the falling Blackman ramp are
(16)
(17)
for the first oscillator. The initial values of the second oscillator
are
(18)
(19)
The constant is 0.42 . The initial values of the rising
Blackman ramp for the first oscillator are the negatives of the
falling ramp values. In the case of the Hanning window, the
Fig. 6. Precompensation filter structure.
initial values are the same as in the Blackman case for the first
oscillator, the values for the second oscillator are zero and the
constant is 0.5 . The ramp duration ( can be altered by
changing the output frequencies of the digital oscillators. The
value controls the amplitude of the ramp (output power
level). During the ramp period the signal sel is low in Fig. 3
and the multiplexer conducts the ramp signal to the multiplier
(Fig. 1). After the ramp duration ( the signal sel becomes
high; the output of the multiplexer is connected to the input of
the multiplexer; and the output power level is constant.
C. Parallel Structure
The recursive digital oscillator shown in Fig. 3 suffers from
two major drawbacks: the quantization noise accumulates in the
650 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002
Fig. 7. Measured second image of the WCDMA signal.
recursive structure and the maximum sampling rate of the dig-
ital oscillator is determined by its recursive parts. The oscillator
produces only one cycle of sine wave inthe Blackman ramp and
after that new initial values are updated, so the problem of the
accumulated noise is alleviated. The parallel structure is used to
reduce the sampling rate of the digital oscillators. Then the mul-
tipliers can be implemented with higher wordlengths but with a
reasonable area, as the speed requirement is not so stringent.
The idea of the implemented parallel structure is to generate the
desired sinusoidal oscillating signal with two oscillators, one of
which generates the odd samples, and the other the even sam-
ples. This means that four oscillators are needed to generate
Blackman ramps. The parallel structure is presented in Fig. 4,
where the sampling rate of the digital oscillator is halved. The
odd and even oscillator outputs are alternately selected with a
2-to-1 multiplexer (MUX), the select signal of which is the di-
vided clock. In order for the oscillators to generate correct sam-
ples to the multiplexer output, each oscillator must operate at
a double output frequency . A phase offset must be added
to the odd oscillator so that the outputs are not duplicated. The
initial values of the parallel ramp generator are calculated by
choosing first the same initial values as in the normal case and
calculating the next two values using the difference equation (5)
and choosing the odd samples for the odd oscillators and the
even samples for the even oscillators.
IV. UP-CONVERSION BY USING IMAGES OF THE D/A
CONVERTER
The output of the multistandard modulator can be hetero-
dyned up to the desired frequency by employing a mixer/local
oscillator/filter combination. An alternative method is to use im-
ages for up-conversion. To obtain frequencies above Nyquist
frequencies, the output of the D/A converter is bandpass-filtered
by an ‘image-selecting’ bandpass filter, rather than by the low-
pass filter. The output spectrum of the ideal D/A converter is
(20)
where is the sampling rate of the D/A converter. The images
exhibit significantly poorer signal to noise and distortion ratio
(SNDR) than the fundamental signal does, because of the sinc
attenuation. The amplitude of the image responses decreases
according to ; spurious responses due to the D/A-
converter clock feed-through noise and dynamic nonlinearities
generally roll off much more slowly with the frequency. Nev-
ertheless, the first and second image may still meet the system
SNDR requirements. If an odd-numbered image is used, any
modulation spectrum is inverted with respect to the fundamental
output. The output spectrum in (1) can be inverted by changing
the sign of the carrier frequency word.
The inverse filter shown in Fig. 1 compensates for roll
off in the first lobe of the frequency domain distor-
tion function of the D/A converter. The sinc effect introduces a
droop that is not acceptable when the bandwidth of the signal is
wide (e.g., WCDMA signal [3]). If the distortions of the images
are to be compensated, an additional precompensation filter is
needed. The precompensation filter could be before the D/A
converter. Locating the off-chip precompensation filter prior to
the resampling operation allows the precompensation filter to
run at a lower computational rate, as shown in Fig. 5.
In our case, the output signal of the D/A converter is prec-
ompensated so that the droop in the second image is canceled.
The D/A converter sampling frequency is 76.8 MHz, the signal
frequency is 19.2 MHz and the center frequency of the image
is located at 96 MHz (76.8 MHz 19.2 MHz). The peak error
target specification is 0.045 dB over the frequency band from
2.5 MHz through 2.5 MHz (WCDMA channel spacing). The
magnitude response of the precompensation filter is obtained
from inverse of (20), where is 76.8 MHz and is 96 MHz
2.5 MHz. The precompensation of this frequency band is done
at baseband (Fig. 5) and the inverse sinc filter in Fig. 1 is by-
passed. The complex precompensation filter requires five taps
with two CSD nonzero digits. These complex taps require a lot
of hardware. An alternative method is to up-convert the base-
band signal to . Then the up-converted and signals
are filtered by the two real filters and after that, down-converted
from to baseband. In this special case when the IF center
frequency is equal to a quarter of the sample rate, considerable
VANKKA et al.: GSM/EDGE/WCDMA MODULATOR WITH ON-CHIP D/A CONVERTER 651
Fig. 8. Block diagram of test system.
Fig. 9. Block diagram of the 14-b D/A converter.
Fig. 10. Typical INL and DNL.
simplification is achieved since the sine and cosine signals rep-
resenting the complex phasor degenerate into two simple se-
quences and , thus elimi-
nating the need for high-speed digital multipliers and adders to
implement the mixing functions. The block diagram of this pre-
compensation structure is shown in Fig. 6. The quadrature filter
requires seven taps with two nonzero CSD digits.
The precompensation filters were implemented with an
Altera FLEK 10KA-1 series device [19]. The complex filter
requires 456 (26% of the total) logic elements (LEs) in the
EPF10K30A device. The precompensation filter shown in
Fig. 6 requires 416 (24% of the total) LEs in the EPF10K3A
Fig. 11. SFDR as function of output frequency at full-scale (0 dBFS).
Fig. 12. Transmitted power level of the EDGE burst versus time. The carrier
frequency is 19.2 MHz.
device. The precompensation filters were implemented by
folded direct form structure [13]. Fig. 7 shows the second
image of the precompensated WCDMA signal. The adjacent
channel leakage power ratios are 50.43/55.09 dB, which meet
specifications (45/50 dB) [3].
V. D/A CONVERTER
As the multicarrier feature requires high dynamic range
requirements for the D/A converter, the wordlength was chosen
to be 14 bit. The 14-bit on-chip D/A converter is based on a
segmented current steering architecture [20]. It consists of a
6b-MSB matrix (2-b binary and 4-b thermometer coded), and
an 8-b binary coded LSB matrix (Fig. 9). The static linearity
is achieved by sizing the current sources for intrinsic matching
[20] and using layout techniques; this is a prerequisite for
obtaining a good dynamic linearity. The cascode structure
is used to increase the output impedance of the unit current
source, which improves the linearity of the D/A-converter. The
dynamic linearity is important in this IF modulator because
of the strongly varying signal. Therefore, a well-designed and
carefully laid out switch drivers and current switches are used.
A major function of the switch driver in Fig. 9 is to adjust the
652 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002
TABLE II
SPECTRUM DUE TO SWITCHING TRANSIENTS (PEAK–HOLD MEASUREMENT, 30 kHz FILTER BANDWIDTH,REFERENCE
300 kHz WITH ZERO OFFSET)
Fig. 13. Power spectrum of GSM signal.
cross point of the control voltages, and to limit their amplitude
at the gates of the current switches, in such a way that these
transistors are never simultaneously in the off state and that the
feedthrough is minimized. The crossing point of the control
signals is set by delaying the falling edge of the signal [21].
Dummy switch transistors are used to improve the synchro-
nization of the switch transistors control signals. Disturbances
connected to the external bias current are filtered out on-chip
with a simple one pole low-pass filter. The D/A-converter
is implemented with a differential design, which results in
reduced even-order distortions and provides a common-mode
rejection to disturbances.
VI. MEASUREMENT RESULTS
To evaluate the multistandard modulator, a test board was
built and a computer program was developed to control the mea-
surements. Fig. 8 illustrates the block diagram of the multi-
standard modulator test system. The on-chip D/A converter was
used in measurements. Measurements are performed with a 50
doubly terminated cable. The sampling rate of the D/A con-
verter was 76.8 MHz in the measurement. Fig. 10 shows that
typical integral linearity (INL) and differential linearity (DNL)
errors are 1.04/0.83 LSB, respectively. The spurious free dy-
namic range (SFDR) is shown as a function of the output fre-
quency in Fig. 11. The SFDR to Nyquist frequency is better than
Fig. 14. Power spectrum of EDGE signal.
Fig. 15. Power spectrum of WCDMA signal.
80 dBc at low synthesized frequencies, decreasing to 62 dBc
at high synthesized frequencies in the output frequency band
(single tone).
Fig. 12 shows the measured ramp up and down profiles of the
transmitted burst, which satisfy the EDGE base station masks.
VANKKA et al.: GSM/EDGE/WCDMA MODULATOR WITH ON-CHIP D/A CONVERTER 653
Fig. 16. Measured EVM errors in EDGE mode.
Fig. 17. Power spectrum of multicarrier WCDMA signal.
The allowed power of spurious responses originating from the
power ramping before and after the bursts is specified by the
switching transient limits. Some margin (3 dB) has been left
between the values in [1] and the values specified for this im-
plementation in Table II to take care of the other transmitter
stages that might degrade the spectral purity of the signal. The
power levels measured at the digital output and the D/A con-
verter output meet the limits shown in Table II.
The output signal in Fig. 13 meets the GSM spectrum mask
requirements [1]. The output signal in Fig. 14 meets the EDGE
spectrum mask requirements [1]. Fig. 15 shows the WCDMA
output with a crest factor of 11.43 dB, where the adjacent
channel leakage powers (ACLR1/2) are 65.84 and 67.67,
respectively. Fig. 16 shows the error vector magnitude (EVM)
performance in EDGE mode, where the measured rms EVM is
0.37% with a maximum peak deviation of 1.55%. The signal
performance is summarized in Table III. The phase error, EVM
and spectral performance [3], measured at the digital output
and the D/A converter output, meet the specifications shown
in Table III. In the multistandard IF modulator, most of the
errors are generated less by quantization errors in the digital
domain and more by the D/A converter analog nonidealities, as
shown in Table III. There is some margin in the D/A converter
output for taking care of the other transmitter stages that might
degrade the signal quality. Combining a number of parallel
modulator outputs allows the formation of multicarrier signal
654 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 49, NO. 10, OCTOBER 2002
TABLE III
PERFORMANCE SUMMARY
Fig. 18. Chip micrograph.
in Fig. 1. Fig. 17 shows the multicarrier signal at the D/A
converter output. The firstadjacent channel leakage power ratio
is 57.19 dB, which meets the specification (45 dB) [3].
VII. CONCLUSION
A GSM/EDGE/WCDMA modulator with a 14-bit on-chip
D/A converter was implemented. The precompensation filter,
which compensates the droop above the Nyquist frequency,
makes it possible to use WCDMA signal images for up-con-
version. The new programmable up/down unit allows power
ramping on a time-slot basis as specified for GSM, EDGE and
TDD-WCDMA. The multistandard modulator meets the spec-
tral, phase, and EVM specifications. The die area of the chip is
22.09 mm in 0.35- m CMOS technology. Power consumption
is 1.7 W at 3.3 V with 110 MHz (maximum clock frequency).
The IC is in a 160-pin CQFP package. Fig. 18 displays the chip
micrograph.
REFERENCES
[1] GSM Recommendation 05.05, “Radio transmission and reception,”,
Dec. 1999.
[2] 3rd Generation Partnership Project; Technical Specification Group
Radio Access Networks; UTRA (BS) TDD, “Radio transmission and
reception,”, 3G TS 25.105, V3.3.0, June 2000.
[3] 3rd Generation Partnership Project; Technical Specification Group
Radio Access Networks; UTRA (BS) FDD, “Radio transmission and
reception,”, 3G TS 25.104, V3.3.0, June 2000.
[4] J. Vankka and K. Halonen, Direct Digital Synthesizers: Theory, Design
and Applications. Norwell, MA: Kluwer, 2001.
[5] L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital
modems—Part II: Implementation and performance,” IEEE Trans.
Commun., vol. COM-41, pp. 998–1008, June 1993.
[6] J. E. Volder, “The CORDIC trigonometric computing technique,” IRE
Trans. Electron. Comput., vol. EC-8, pp. 330–334, Sept. 1959.
[7] H. Samueli, “The design of multiplierless FIR filters for compensating
D/A converter frequency response distortion,” IEEE Trans. Circuits
Syst. II, vol. 35, pp. 1064–1066, Aug. 1988.
[8] GSM Recommendation 05.04, “Modulation,”, Dec. 1999.
[9] J. Vankka, M. Kosunen, I. Sanchis, and K. Halonen, “A multicarrier
QAM modulator,” IEEE Trans. Circuits Syst. II, vol. 47, pp. 1–10, Jan.
2000.
[10] GSM Recommendation 05.02, “Digital cellular telecommunications
system (Phase 2+); Multiplexing and multiple access on the radio
path,”, July 1999.
[11] J. C. Hausman, R. R. Harnden, E. G. Cohen, and H. G. Mills, “Pro-
grammable canonic signed digit filter chip,” U.S. Patent 5 262974, Nov.
16, 1993.
[12] N. J. Fliege, Multirate Digital Signal Processing. New York: Wiley,
1994.
[13] K. K. Parhi, VLSI Digital Signal Processing Systems: Design and Im-
plementation. New York: Wiley, 1999.
[14] H. Samueli, “An improved search algorithm for the design of multiplier-
less FIR filters with powers-of-two coefficients,” IEEE Trans. Circuits
Syst. II, vol. 36, no. 7, pp. 1044–1047, July 1989.
[15] C. W. Farrow, “A continuously variable digital delay element,” in
Proc. IEEE Int. Symp. Circuits and Systems (ISCAS), June 1988, pp.
2641–2645.
[16] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design.New
York: Wiley, 1981.
[17] J. Vankka, M. Honkanen, and K. Halonen, “A multicarrier GMSK mod-
ulator,” IEEE J. Select. Areas Commun., vol. 19, pp. 1070–1079, June
2001.
[18] N. J. Fliege and J. Wintermantel, “Complex digital oscillators and FSK
modulators,” IEEE Trans. Signal Processing, vol. SP-40, pp. 333–342,
Feb. 1992.
[19] “FLEK 10K embedded programmable logic family data sheet,” Altera
Corp., San Jose, CA, Oct. 1998.
[20] A. Van den Bosch, M. A. F. Borremans, M. S. J.Steyaert, and W. Sansen,
“A 10-bit 1-Gsample/s Nyquist current-steering CMOS D/A converter,”
IEEE J. Solid-State Circuits, vol. 36, pp. 315–324, Mar. 2001.
[21] H. Takakura, M. Yokoyama, and A. Yamaguchi, “A 10 bit 80MHz glitch-
less CMOS D/A converter,” in Proc. IEEE Custom Integrated Circuits
Conf., 1991, pp. 26.5.1–26.5.4.
Jouko Vankka (M’96) was born in Helsinki, Fin-
land, in 1965. He received the M.S. and Ph.D. degrees
in electrical engineering from Helsinki University of
Technology (HUT), in 1991 and 2000, respectively.
Since 1995, he has been with the Electronic Circuit
Design Laboratory, HUT. His research interests in-
clude VLSI architectures and mixed-signal integrated
circuits for communication applications.
VANKKA et al.: GSM/EDGE/WCDMA MODULATOR WITH ON-CHIP D/A CONVERTER 655
Jaakko Ketola (S’01) was born in Helsinki, Finland,
on January 1974. He received the M.S. degree in elec-
trical engineering from Helsinki University of Tech-
nology (HUT) in 2001, where he is currently working
toward the Ph.D. degree at the Electronic Circuit De-
sign Laboratory.
His current research interests are in the area of
high-speed digital CMOS circuits for communica-
tions applications.
Johan Sommarek was born in Kervo, Finland, in
1974. He received the M.Sc. degree from the Helsinki
University of Technology, in 2000 where he is cur-
rently working toward the D.Sc. degree in electrical
and telecommunications engineering.
His research interests are in the areas of VLSI for
signal processing in telecommunications and high-
speed CMOS integrated circuit design.
Olli Väänänen was born in Kajaani, Finland, on
July 1977. He received the M.S. degree in electrical
engineering from Helsinki University of Technology
(HUT) in 2001, where he is currently working
toward the Ph.D. degree at the Electronic Circuit
Design Laboratory.
His current research interests are in the area of
signal processing in telecommunications systems.
Marko Kosunen (S’97) was born in Helsinki, Fin-
land, in 1974. He received the M.S. and the Lic.Tech.
degrees in electrical engineering from Helsinki Uni-
versity of Technology (HUT) in 1998 and 2001, re-
spectively, where he is currently working toward the
Ph.D. degree at the Electronic Circuit Design Labo-
ratory.
Since 1996, he has been a Research Scientist with
the Electronic Circuit Design Laboratory at HUT. His
current research interests include DSP for wireless
communication systems, and D/A converters.
Kari A. I. Halonen was born in Helsinki, Finland, on
May 23, 1958. He received the M.Sc. degree in elec-
trical engineering from Helsinki University of Tech-
nology (HUT) in 1982, and the Ph.D. degree in elec-
trical engineering from the Katholieke Universiteit
Leuven, Heverlee, Belgium, in 1987.
From 1982 to 1984, he was an Assistant at HUT
and a Research Assistant at the Technical Research
Center of Finland. From 1984 to 1987, he was
a Research Assistant at the E.S.A.T. Laboratory,
Katholieke Universiteit Leuven, enjoying also a
temporary grant from the Academy of Finland. From 1988 to 1990, he was
a Senior Assistant with the Electronic Circuit Design Laboratory, HUT, and
from 1990 to 1993, he was the Director of the Integrated Circuit Design
Unit at the Microelectronics Center, HUT. From 1992 to 1993, he was on
academic leave of absence and was the Research and Development Manager
at Fincitec, Inc., Finland. From 1993 to 1996, he was an Associate Professor,
and since 1997, a Full Professor at the Faculty of Electrical Engineering
and Telecommunications, HUT. In 1998, he became the Head of Electronic
Circuit Design Laborator at HUT. He is author or coauthor over a hundred and
fifty international and national conference and journal publications on analog
integrated circuits. He has several patents on analog integrated circuits. His
research interests include CMOS and BiCMOS analog integrated circuits,
particularly for telecommunication applications.
Dr. Halonen received the Beatrice Winner Award at the International
Solid-State Circuits Conference in 2002. He was an Associate Editor of IEEE
TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND
APPLICATIONS from 1997 to 1999. He has been a Guest Editor for the IEEE
JOURNAL OF SOLID-STATE CIRCUITS and the Technical Program Committee
Chairman for the European Solid-State Circuits Conference in 2000.
... A traditional way of transmitting these data is depicted in Fig. 1, using oversampled digital-to-analog converters followed by low-pass filters to reject the image replicas and respect the required transmission masks. To address multistandard within the same hardware, a direct-digital RF modulator was proposed in [3] programmable sample rate converters, as proposed in [4] and [5], to adapt to the appropriate radio channel. ...
Article
This paper presents a novel transmitter architecture which is tailored for low power, all-digital, and high speed implementation. It is based on two-path parallel digital-to-analog converters (DAC) which are driven by 180 ° phase-shifted clocks. The architecture operates in high pass mode and extends the output carrier frequency up to half the DAC clock rate. To decrease the number of analog unit current cells in the converter, a low-pass ΔΣ-modulator is used. Since the modulator also converts the input resolution to 1-bit, an inherently-linear digital-to-analog conversion is realized by embedding filtering in the DAC. Furthermore, the finite impulse response DAC transfer function is designed to cancel the ΔΣ-modulator quantization noise. Simulation results at system level demonstrate the robustness of the architecture against random coefficient mismatches, and its suitability for broadband transmissions. The error vector magnitude of the quadrature output is simulated for up to 15% random coefficient mismatch and it maintains a value below -22 dB even when the input signal bandwidths vary from 20 MHz (64-subcarrier OFDM) to 160 MHz (512-subcarrier OFDM). Experimental results are presented to discuss the validity of the proposed all-digital transmitter architecture and to highlight the challenges of implementing it in advanced CMOS nodes. IEEE
... A traditional way of transmitting these data is depicted in Fig. 1, using oversampled digital-to-analog converters followed by low-pass filters to reject the image replicas and respect the required transmission masks. To address multistandard within the same hardware, a direct-digital RF modulator was proposed in [3] programmable sample rate converters, as proposed in [4] and [5], to adapt to the appropriate radio channel. ...
Article
IEEE 802.11ac (WiFi) and IEEE 802.11ad (60-GHz WiGig) are emerging gigabit-per-second standards providing complementary services but different nature of signals. The 802.11ac targets high-resolution and narrow-to-medium bandwidth channels, while 802.11ad aims to provide broadband communications with simple modulation schemes. This work proposes a single-physical-layer transmitter baseband architecture for both 11ac and 11ad standards. The core of the proposed transmitter is a configurable mixed-signal digital-to-analog converter (DAC), which has an embedded semidigital filtering tailored for four WiFi modes (20, 40, 80, and 160 MHz) and the 1.76-GHz bandwidth of the 60-GHz WiGig standard. The DAC operates on the oversampled WiFi and raw WiGig data at a common 3.52-GHz clock frequency. System-level simulations of the finite impulse response DAC-based architecture show that the requirements of the standards can be met with maximum hardware sharing and reduced area penalty.
... The digital quadrature modulator is fed by two digital complex modulators, shown in Fig. 2, which modulate the baseband in-phase (I) and quadrature (Q) channels into orthogonal carriers (X, Y ) at the first IF frequency. One example of such a complex modulator suitable for this purpose is presented in [1]. These complex modulators can be operated at a much lower sampling frequency than the quadrature modulator. ...
Article
Full-text available
A digital quadrature modulator with a bandpass ΔΣ-modulator is presented that interpolates orthogonal input carriers by 16 and performs a digital quadrature modulation at carrier frequencies f s /4, −f s /4 (f s is the sampling frequency). After quadrature modulation, the signal is converted into an analogue IF signal using a bandpass ΔΣ modulator and a 1-bit D/A converter. The die area of the chip is 5.2 mm2 (0.13 μm CMOS technology). The total power consumption is 139 mW at 1.5 V with a clock frequency of 700 MHz (D/A converter full-scale output current 11.5 mA).
Article
In this research, we present the architecture and implementation of a Full-digital transmitter with radio frequency output targeting a System on Chip FPGA device. SoC FPGA devices have been widely adopted in the applications of digital signal processing (DSP) and digital communication. They are typically well suited for the evolving technology of software defined radios (SDR) due to their reconfigurability and programmability. However, SoC FPGA devices are mostly used to implement digital baseband and intermediate frequency (IF) functionalities. Therefore, significant analog and RF components are still needed to fulfill the radio communication requirements. The Full-digital transmitter presented in this paper directly synthesizes RF signal in the digital domain, therefore eliminates the need for most of the analog and RF components. The Full-digital transmitter consists of one QAM modulator and one RF pulse width modulator (RF PWM). The binary output waveform from RF PWM is centered at 800MHz with 256-QAM signaling format. The entire transmitter is implemented using Altera Cyclone V SoC device with on chip Multi-Gigabit Transceiver (MGT). The adjacent channel leakage ratio (ACLR) measured in the 20 MHz passband is (-46dB). Our work extends the digital implementation of communication applications on a SoC FPGA platform to radio frequency, therefore making a significant evolution towards an ideal SDR. Keywords: SDR system, Pulse Width Modulation, 256-QAM, Implementation via System on Chip FPGA.
Article
This paper describes the first purely digital approach to reduce the receive band noise in digitally-intensive RF transmitters. The proposed solution applies bandpass delta-sigma modulation and dynamic element matching (DEM) to the receive band (RX-band) instead of the transmit band. This enables selective attenuation of the noise originating from amplitude quantization and static mismatches of the digital-to-analog converter (DAC), which would otherwise reach the transmitter output almost unattenuated. A highly configurable 4th-order noise transfer function is designed to achieve optimum attenuation in the programmable RX-band, while ensuring negligible degradation of the transmitted signal quality as well as stable operation of the tree structure DEM encoder. A general validation of DEM, independent from the duration of the DAC impulse response, is also presented. The proposed solution is verified through system-level simulations with LTE signals. In the presence of typical amplitude and timing mismatches, the RX-band noise can be reduced below -160 dBc/Hz without filtering after the DAC, thus potentially enabling SAW-less operation of all-digital transmitters.
Article
Full-text available
The approach adopted in Digital Synthesizers and Transmitters for Software Radio will provide an understanding of key areas in the field of digital synthesizers and transmitters. It is easy to include different digital techniques in the digital synthesizers and transmitters by using digital signal processing methods, because the signal is in digital form. By programming the digital synthesizers and transmitters, adaptive channel bandwidths, modulation formats, frequency hopping and data rates are easily achieved. Techniques such as digital predistortion for power amplifier linearization, digital compensation methods for analog I/Q modulator nonlinearities and digital power control and ramping are presented in this book. The flexibility of the digital synthesizers and transmitters makes them ideal as signal generators for software radio. Software radios represent a major change in the design paradigm for radios in which a large portion of the functionality is implemented through programmable signal processing devices, giving the radio the ability to change its operating parameters to accommodate new features and capabilities. A software radio approach reduces the content of radio frequency (RF) and other analog components of traditional radios and emphasizes digital signal processing to enhance overall transmitter flexibility. Software radios are emerging in commercial and military infrastructure.
Article
Full-text available
software radio basically refers to an ensemble of techniques that permit the reconfiguration of a communication system without the need to change any hardware system element. That goal is to produce communication devices capable of supporting several different services, applications, and standards. In particular one can imagine a given devices that should support several digital mobile telephony standards, service and function by just changing its software. Current devices can provide only one type of standards due to limitations mainly imposed by their analogue technology parts. The software radio as a promising solution for the future of 4G wireless communications, because of its ability to provide flexible architecture, was enabling multi-mode, multi-band, multi-services, and multi-standards devices. This paper presents a multi-modes modulator/demodulator conception for a software radio. For it the modulator design is based to the multi-modes mapper and DDS bloc. The multi-mode mapper generate symbol mapping using a constellation diagram to implement a variety of mapping schemes for multi-mode modulator design. This bloc is used by many modulation schemes. Example includes quadrature amplitude modulation (QAM), phase shift keying (PSK), and orthogonal frequency division multiplexing (OFDM). The demodulator is based to algorithm for automatic modulation recognition that exploits the flexibility of a software radio. Our algorithm is based to calculate several parameters and used a threshold metric. A purposed approach can be exploited a flexibility for software radio. Copyright © 2007 Praise Worthy Prize S.r.l. -All rights reserved.
Article
Full-text available
Traditional designs of high bandwidth frequency synthesizers employ the use of a phase-locked-loop (PLL). A direct digital synthesizer (DDS) provides many significant advantages over the PLL approaches. Fast settling time, sub-Hertz frequency resolution, continuous-phase switching response and low phase noise are features easily obtainable in the DDS systems. Although the principle of the DDS has been known for many years, the DDS did not play a dominant role in wideband frequency generation until recent years. Earlier DDSs were limited to produce narrow bands of closely spaced frequencies, due to limitations of digital logic and D/A-converter technologies. Recent advantages in integrated circuit (IC) technologies have brought about remarkable progress in this area. By programming the DDS, adaptive channel bandwidths, modulation formats, frequency hopping and data rates are easily achieved. This is an important step towards a "software-radio" which can be used in various systems. The DDS could be applied in the modulator or demodulator in the communication systems. The applications of DDS are restricted to the modulator in the base station. The aim of this research was to find an optimal front-end for a transmitter by focusing on the circuit implementations of the DDS, but the research also includes the interface to baseband circuitry and system level design aspects of digital communication systems. The theoretical analysis gives an overview of the functioning of DDS, especially with respect to noise and spurs. Different spur reduction techniques are studied in detail. Four ICs, which were the circuit implementations of the DDS, were designed. One programmable logic device implementation of the CORDIC based quadrature amplitude modulation (QAM) modulator was designed with a separate D/A converter IC. For the realization of these designs some new building blocks, e.g. a new tunable error feedback structure and a novel and more cost-effective digital power ramp generator, were developed. Report / Helsinki University of Technology, Department of Electrical and Communications Engineering, Electronic Circuit Design Laboratory, ISSN 1455-8440; 32
Article
Full-text available
A multicarrier quadrature amplitude modulation (QAM) modulator has been developed and implemented with programmable logic devices. The multicarrier QAM modulator contains four CORDIC-based QAM modulators. A conventional QAM modulator needs two multipliers, one adder, and sine/cosine ROM's. The designed CORDIC-based QAM modulator has about the same logic complexity as the two multipliers and the adder with the same word sizes. Each QAM modulator accepts 13-bit in-phase and quadrature data streams, interpolates them by 16, and upconverts the baseband signal to a selected center frequency. The frequencies of the four carriers can be independently adjusted. The proposed multicarrier QAM modulator does not use an analog I/Q modulator, and therefore, the difficulties of adjusting the dc offset, phasing, and the amplitude levels between the in-phase and quadrature-phase signal paths are avoided. The multicarrier QAM modulator is designed to fulfil the spectrum and error vector magnitude (EVM) specifications of the wideband code-division multiple-access (WCDMA) system. The simulated EVM is 1.06% root mean square (rms), well below the specified 12.5% rms for WCDMA. The measured ratio of the integrated first/second/third adjacent channel power (4.096-MHz bandwidth) to the integrated channel power (4.096-MHz bandwidth) is -68.16/-68.24/-66.17 dB versus the specified -45/-55/-55 dB
Article
Antenna fundamentals and definitions are examined, taking into account electromagnetic fundamentals, the solution of Maxwell's equations for radiation problems, the ideal dipole, the radiation pattern, directivity and gain, reciprocity and antenna pattern measurements, antenna impedance and radiation efficiency, antenna polarization, antennas in communication links and radar, and the receiving properties of antennas. Some simple radiating systems are considered along with arrays, line sources, wire antennas, broadband antennas, moment methods, and aperture antennas. High-frequency methods and aspects of antenna synthesis are discussed, giving attention to geometrical optics, physical optics, wedge diffraction theory, the ray-fixed coordinate system, the cylindrical parabolic antenna, and linear array methods.
Conference Paper
The author describes an FIR (finite-impulse-response) filter which synthesizes a controllable delay. By changing the delay the filter has the ability to interpolate between samples in the data stream of a band-limited signal. Because high sampling rates are not required, the filter is especially suited for implementation in a digital signal processor (DSP), and has been implemented in a real-time DSP. The interpolator can be used as a practical way to reconstruct an original band limited signal from samples taken at the Nyquist rate. The variable delay filter can also be used as a more general computational element. Performance results are presented
Article
The COordinate Rotation DIgital Computer(CORDIC) is a special-purpose digital computer for real-time airborne computation. In this computer, a unique computing technique is employed which is especially suitable for solving the trigonometric relationships involved in plane coordinate rotation and conversion from rectangular to polar coordinates. CORDIC is an entire-transfer computer; it contains a special serial arithmetic unit consisting of three shift registers, three adder-subtractors, and special interconnections. By use of a prescribed sequence of conditional additions or subtractions, the CORDIC arithmetic unit can be controlled to solve either set of the following equations: Y' = K(Y cos¿ + X sin¿) X' = K(X cos¿ - Y sin¿), or R = K¿X2 + Y2 ¿ = tan-1 Y/X, where K is an invariable constant. This special arithmetic unit is also suitable for other computations such as multiplication, division, and the conversion between binary and mixed radix number systems. However, only the trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.
Conference Paper
In this paper, a 10 bit 1 GS/s current-steering CMOS D/A converter is presented. The measured INL is better than +/-0.2 LSB. The 1 GS/s conversion rate has been obtained by a fully custom designed thermometer decoder. The dynamic limitations have been solved, resulting in more than 61 dB measured SFDR in the interval from DC to Nyquist at all conversion rates up to 1 GS/s. At this conversion rate, the power consumption equals 110 mW. The chip has been processed in a standard 0.35 μm CMOS technology and has an active area of only 0.35 mm<sup>2 </sup>
Conference Paper
A multicarrier QAM modulator has been developed and simulated. The multicarrier QAM modulator contains four upconversion circuits. Each upconverting circuit accepts 12 b in-phase and quadrature data streams, interpolates those by 16 and upconverts the baseband signal to a selected center frequency. The outputs of these upconverting circuits are combined together in the digital domain. The multicarrier QAM modulator was designed to fulfil the spectrum and error vector magnitude (EVM) specification of the wideband code division multiple access (WCDMA) system
Conference Paper
A high-accuracy (10-b) and high-speed (80-MHz) glitchless D/A (digital-to-analog) converter has been realized. The device is based on the following circuit techniques: 1023 new cells with a clocked AND-NOR gate for data-latch function; a new current source circuit for reduction of switching noise; and a current source arrangement independent of current variation. The LSI has been fabricated by a 1.0-μm double-metal CMOS process
Article
The authors present complex-valued free running oscillators derived from digital filter structures. Four alternative approaches of complex direct-form and coupled-form oscillator structures are discussed leading to a multiple-output direct-form oscillator as the best solution from the viewpoint of computational efficiency. Two inherent advantages of direct-form structures can be avoided by appropriate means. The problem of poor frequency resolution at low frequencies is solved by a method called two's complement improvement (TCI). An oscillator frequency displacement is discovered which is caused by correlation between one state variable and the quantization error using finite arithmetic. This frequency error can be substantially reduced by appropriate error noise shaping. Some telecommunication applications like fixed-frequency complex oscillators for baseband signal processing, complex baseband frequency shift keying (FSK) modulators, and multiple-phase oscillators for multipath filters are discussed