Post on 03-Jun-2018
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Digital Front-End Signal Processing
Markku Renfors, TUT/DCE
1.Review of multirate signal processing (mostly based onlecture notes by T. Saramki)
Motivation & basics
Efficient decimator/interpolator structures
oEfficient implementation structure for basic FIR filters
oEfficiency of multistage designs.
oFIR Nth-band filters, especially halfband filters
oCIC filter as an efficient multiplier-free structure for thefirst stages of the decimation chain.
2. Frequency translation and multirate processing of
bandpass I/Q signals3. Multimode receivers
Main ideas
Examples
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Why mult irate signal processing is s good idea inadvanced transceiver architectures?
1. A general approach to increase the flexibility of receiver
implementations is to use wideband sampling in the receiverand select the desired channel among the many digitizedones using digital filtering, using a filter optimized for theparticular transmission system in use.
o In case of wideband sampling, the initial sampling rate ismuch higher than symbol/chip rate used in basebandprocessing.
2. The commonly useddelta-sigma AD-conversion principle isalso based on heavy oversampling, even in the case ofnarrowband sampling.
Concerning the DSP implementation complexity and powerconsumption, it is very crucial to use the lowest possible sampling
rate at each stage of the processing chain (good examples of thiswill be given later during the course).
oAs a rule of thumb, for given (narrowband) selectivityrequirements and given input sampling rate, thecomputational complexity (and power consumption) is, in awell-designed multirate system, directly proportional to theoutput sampling rate.
oNow think about the case where you could reduce thesampling rate by a factor of 300 (could really be the casein a wideband sampling receiver).
Similar ideas can be used also in the transmitter case:synthesizing a high-rate, possibly multi-channel signal using DSPwould greatly improve the flexibility.
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Digital Front-End Signal Processing
Markku Renfors, TUT/DCE
1. Review of multirate signal processing (mostly based onlecture notes by T. Saramki)
Motivation & basics
Efficient decimator/interpolator structures
oEfficient implementation structure for basic FIR filters
oEfficiency of multistage designs.
oFIR Nth-band filters, especially halfband filters
oCIC filter as an efficient multiplier-free structure for thefirst stages of the decimation chain.
2. Frequency translation and multirate processing of
bandpass I/Q signals3. Multimode receivers
Main ideas
Examples
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=> Reduction in implementation complexity, especially forsmall N!
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(M+1)/4 multiplications per input sample needed for
implementing a filter of lengthM+1.
=> A cascade of half-band filters is often a very efficient
choice for multirate signal processing!
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Receiver Architectures Part 2 TLT-5806/RxArch2/1M. Renfors, TUT/DCE 10.10.11
DCE - Tampere University of Technology. All rights reserved.
CIC-Filters
CIC = Cascaded Integrator - Comb
Transfer function:
Frequency response:
Here Ris the decimation factor and Nis the order of theCIC-filter.
A first-order CIC-filter takes the avarage of Rconsequtiveinput samples and decimates by R. It is also called movingaverageor running sumfilter.
It is important to use modulo arithmetic (like 2'scomplement) in the implementation, because there will beinevitable internal overflows.
z-1 32z-1 z-1 z-1
( )
NR
z
zzH
=
11
1
N
s
sFfRNj
Ffj
F
fR
FRf
eeH ss
=
sin
sin)1(2
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Receiver Architectures Part 2 TLT-5806/RxArch2/2M. Renfors, TUT/DCE 10.10.11
DCE - Tampere University of Technology. All rights reserved.
CIC-Filters
In CIC filter, those frequencies aliasing to 0-frequency areheavily attenuated. For a relatively narrowband signal,low-order CIC-filters are sufficient; more wideband signalsneede higher CIC-filter orders
Example(for a GSM application):N=2, R=32.
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Digital Front-End Signal Processing
Markku Renfors, TUT/DCE
1. Review of multirate signal processing (mostly based onlecture notes by T. Saramki)
Motivation & basics
Efficient decimator/interpolator structures
oEfficient implementation structure for basic FIR filters
oEfficiency of multistage designs.
oFIR Nth-band filters, especially halfband filters
oCIC filter as an efficient multiplier-free structure for thefirst stages of the decimation chain.
2. Frequency translation and multirate processing ofbandpass I/Q signals
3. Multimode receivers
Main ideas
Examples
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/8M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Frequency Translation
One key operation in communications signalprocessing is the frequency translation of a signalspectrum from one center frequency to another.
Conversions between baseband and bandpass
representations (modulation and demodulation) arespecial cases of this.
We consider two different ways to do the frequencytranslation: mixing and multirate operations, i.e.,decimation and interpolation.
In case of multirate operations, we assume forsimplicity that the following two sampling rates areused:
low sampling rate: 1sfN N
=T
high sampling rate: 1sf T=
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/9M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Mixing for Complex Discrete-Time Signals
2( ) ( ) ( )LO LO
j f kT j ky k e x k e x k
= =
fcf
f +fc LOf
ej k
LO
cos( )Lok
sin( )Lok
I I
I Q
Special case with
real input signal:
This produces a pure frequency translationof the spectrumby .LOf
Important special cases are:
Tff sLO 2
12/ ==
in which case the multiplying sequence is +1, -1, +1, -1, ...This case can be applied to a real signal withoutproducing a complex result. Converts a lowpass signalto a highpass signal, and vice versa.
Tff sLO 4
14/ ==
in which case the multiplying sequence is
+1, j, -1, -j, +1, j, ...
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/10M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Complex Bandpass Filters Certain types of complex filters based on Hilbert
transformers can be designed using standard filter designpackages, like Parks-McClellan routine for FIR filters.
Another way to get complex bandpass filters is throughfrequency translations:
Real
0f
0
f
fc
T T
ej f T2
c
prototypefilter:
Complexbandpassfilter:
Transformation for frequency response and transferfunction:
( ) ( ) Tfjjj cc zeHzHeHeH 2
Generic transformation for block diagram:
If 1/Tis an integer multiple offc, this might be much easierthan in the general case, see the special cases of the
previous page.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/11M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Example of a Complex Bandpass Filters:
Frequency Translated FIRFrequency translation byfs/4=> Analytic bandpassfilter with passband aroundfs/4.
0f
0
ff
s
/4 fs
/2
fs/4 fs/2
Impulse response translated as:
h0, h1, h2, h3, h4, , hN
h0, jh1, -h2, -jh3, h4, , (j)
NhN
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/12M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
FIR Filter with Frequency Translation byfs/4
(i) Real input signal
...
I
Q
h0 h2 h4
h1 h3 h5
T T T T T
(ii) Complex input signal
...
...
I
Q
I
Q
h0 h1 h2 h3 h4 h5
h0 h1 h2 h3 h4 h5
T T T T T
T T T T T
There are possibilities to exploit the possiblecoefficient symmetry (of linear phase FIR) in bothcases.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/14M. Renfors, TUT/DCE 21.9.2010
Sampling Theorem
The sampling theorem says that a (real or complex)lowpass signal limited to the frequency band [-W, W] canrepresented completely by discrete-time samples if thesampling rate (1/T)is at least 2W.
In case of a complex signal, each sample is, of course, acomplex number.
In general, discrete-time signals have periodic spectra,where the continuous-time spectrum is repeated aroundfrequencies 1 2 3
DCE - Tampere University of Technology. All rights reserved.
0f
fs 2fsfs2fs
T T T, , ,
In case of complex signals, it is not required that theoriginal signal is located symmetrically around 0.
Any part of the periodic signal can be considered as theuseful part. This allows many possibilities for multirateprocessing of bandpass signals.
In general, the key criterion is that no destructive aliasingeffect occur on top of the desired part of the spectrum.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/15M. Renfors, TUT/DCE 21.9.2010
Real vs. Complex Discrete-Time Signals
Real signal:
0f
fsfs W
0f
fs f =Ws
Here 2W real samples per second are sufficient torepresent the signal.
Complex signal:
Here Wcomplex samples per second are sufficient.The resulting rates of real-valued samples are the
same.
However, the quantization effects may be quitedifferent. (Recall from the standard treatment of
SSB that Hilbert-transformed signals may bedifficult.)
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/16M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Interpolation for Complex Signal
Sampling rate increase produces a periodicspectrum, and the desired part of the spectrum isthen separated by an (analytic) bandpass filter.
N
0f
1/NT
0 fn NT/n NT T / 1/
COMPLEX
BP-FILTER
RESPONSE
0 f1/NT
0f
n NT/
a)
b)
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/17M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Decimation for Complex SignalSampling rate decrease produces aliasing, such that
the original band is at one of the image bands of theresulting final band.
The signal has to be band-limited to a bandwidth ofNT/1 before this operation can be done without
severe aliasing effects.
N
0f
1/NTn NT T / 1/ n NT/
0f
COMPLEX
BP-FILTER
RESPONSE
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/18M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Combined Multirate Operations for
Complex SignalCombining decimation and interpolation, a frequency shiftby n N can be realized, where nis an arbitrary integer.T/
N M
0f
n f /N- f 1 S S n f /N 1 S
0f
0f
n f /N 2 S
It can be seen that the low sampling rate, limited to behigher than the signal bandwidth, determines the resolutionof the frequency translations based on multirate
operations.
If, for example, a bandpass signal is desired to betranslated to the baseband form, this can be done usingmultirate operations if and only if the carrier frequency is amultiple of the low sampling rate.
Using also simple frequency translations (with coefficients+1, -1, +j, -j), the resolution is 1/(4NT).
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/19M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Combining Mixing and Multirate Operations
for Complex SignalsA general frequency shift of f nNT fO= + can be done
in the following two ways:
(1) Direct frequency conversion by fOusing mixing.
(2) Conversion using multirate operations by nNT
followed by a mixing with f (or vice versa).
The differences in these two approaches are due tothe possible filtering operations associated with the
multirate operations, and aliasing/reconstructionfilters in case of mixed continuous-time/discrete-timeprocessing.
Assuming ideal filtering, these two ways would beequivalent.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/20M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Example of Combining Mixing and Multirate
OperationsConversion from bandpass to baseband representationand decimation to symbol rate, i.e., I/Q-demodulation.
Assume that
- N=6, f0=4/(6T)+f.- The required complex bandpass filter is obtained from
an FIR filter of length 50by frequency translation.
(ii)(i
N
e j k0
N
e j k0
N
e j k
)
The following three ways are equivalent but lead todifferent computational requirements (the required realmultiplication rates at input rate are shown, not exploitingpossible coefficient symmetry):
LPFBPF
(iii) BPF
Case (i) Case (ii) Case (iii)Fil ter 100 100/6 100/6
Mixer 4 2 4/6Total 104 18.7 17.3
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/21M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Example of Combining Mixing and Multirate
Operations (continued)Notes:
(i) Complex bandpass filter, real inputs=> 100 real multipliers needed for filter
(ii) Real lowpass filter, complex input to filter
=>100 real multipliers needed for filter
- Decimation can be combined efficiently with thefilter. Utilizing coefficient symmetry is easiest inthis case.
(iii) As (i) but decimation can be included efficientlywith the filter.
- Mixing and LO generation done at lower rateand thus easier to implement.
Here we have not taken use of the possible
coefficient symmetry, which may reduce themultiplication rates by 1/2 in all cases.
In general, mixing is a memoryless operation, so up-sampling and down-sampling operations can becommuted with it in block diagram manipulations.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/22M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Frequency Translation for Real Signals
Mixing and multirate operations can be done in similar wayfor real signals. The difference is that the two parts of thespectrum, on the positive and negative frequency axis, andtheir images, must be accommodated in the spectrum.
(1) Mixing
0
0
fc fc
f fc LO +f fc LO f fc LO f fc LO+
f
fcos( )LOt
Mixing produces two translated spectral components (notethat cos( ) ( ) / 2j t j tt e e = + ). The image band appearing
on top of the desired band after mixing must besuppressed before mixing.
(2) Multirate operations
In case of decimation, to avoid destructive aliasing effects,the signal to be translated must be within one of theintervals
1 1, or ,2 2
n n n nNT NT NT NT NT NT
+
Otherwise destructive aliasing will occur. In the latter case,the spectrum will be inverted.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/23M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Interpolation for Real Bandpass Signal
X f( )
0 fsfs/2fs/2fsf
W f( )
0
f
Y f( )| k=2
0f
0f
Y f( )| k=3
k=3 k=2 k=1 k=0 k=0 k=1 k=2 k=3
k=2 k=2
k=3 k=3
Nx n( ) y m( )w m
( )
fs Nfs
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/24M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Decimation for Real Bandpass Signal
x n( ) y m( )x nBP( )
fs fs/N
0f
X fBP( )
0f
Y f( )
0f
0f
f Ns/ 3 /(2f N)sf Ns/3 /(2f N)s
3 /(2f N)s3 /(2f N)s 2 /f Ns2 /f Ns
N
f /Ns
X fBP( )
Y f( )
0
ff N
s
/f Ns/
k=3 k=2 k=1 k=0 k=0 k=1 k=2 k=3
f Ns/
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/25M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Analytic Filtering and Taking Real Part as
Multirate OperationsThe transformations between real and complex signalformats can be seen as multirate operations:
Taking the real part effectively reduces the rate of real-valued samples by two. It produces mirror images, incontrast to the periodic images produced by
decimation by two. In both cases, the new spectralcomponents may fall on top of the existing spectralcomponents.
If this operation follows, e.g., an FIR filter, considerablecomputational simplifications can be made bycombining the real part- operation with the filter in a
cleaver way. There is no sense to compute samplesthat are thrown away by the real part operation!!.
Analytic filtering (in any form baseband, bandpass,filter bank) increases the rate of real-valued samplesby two. Mirror images are removed form the spectrum,in contrast to the periodic images that are removed ininterpolation.
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Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/26M. Renfors, TUT/DCE 21.9.2010
DCE - Tampere University of Technology. All rights reserved.
Example of Down-Conversion:
I/Q-Demodulation
N4
PHASE
SPLITTER 2 MATCHED
FILTER 2
I
Q
0
0
2/T
f
f
0 1/Tf
It is usually a good idea to keep the signal as a real signalas long as possible, because after converting to complex
form, all subsequent signal processing operations require(at least) double computational capacity compared to thecorresponding real algorithms.
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Receiver Architectures Part 2 TLT-5806/RxArch2/3M. Renfors, TUT/DCE 10.10.11
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Digital Channel Selection & Down-Conversion
Digital Down-Conversion
1. Desired channel centered at fixed IF
=> Fixed down-conversion
Special choices offIFandfsmake things easy.
Especially whenfIF=(2k+1)fs/4, the signalaliases tofs/4 anddown-conversion is very easy.
2. Wideband sampling case=> Tunable down-conversion and NCO (numericallycontrolled oscillator) needed.
3. Multistage decimation
=> Tunable digital down-conversion is possible also withoutNCO, using a configurable multistage decimation chain.
Channel Selection Filtering
- After down-conversion, efficient lowpass decimator structureis needed.
- CIC-filters are commonly used in the first decimation stages,FIR-filters and the last stages. Nth-band IIR filters also an
efficient solution.Adjusting Symbol Rates
- Different systems use different symbol/chip rates.
- Common sampling clock frequency is preferred.
=> Decimaton by a fractional factor is needed.
- This can be done at baseband or earlier in the decimationchain.
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Receiver Architectures Part 2 TLT-5806/RxArch2/4M. Renfors, TUT/DCE 10.10.11
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NCO-Based Arbitrary Digital Down-
Conversion
Dedicated processors implementing the following kind ofdown-conversion and channel selection structure areavailable for several vendors (like Harris).
Sampling rates in the 50 ... 100 MHz range are possible.However, the power consumption is still too high forterminal applications.
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Receiver Architectures Part 2 TLT-5806/RxArch2/5M. Renfors, TUT/DCE 10.10.11
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Example
Using Harris HSP50214 for GSM channel selection
filtering.- Input sample rate: 39 MHz- CIC-filter: decimation by 18, order=5- Two pre-designed FIR half-band filters are used for
the next decimation stages.- The final filter stage is an FIR design.
- Output sample rate: 541.667 kHzFrequency responses of the filter stages:
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Receiver Architectures Part 2 TLT-5806/RxArch2/6M. Renfors, TUT/DCE 10.10.11
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Example (continued)
Overall frequency response and the effects of different
stages:
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Digital Front-End Signal Processing
Markku Renfors, TUT/DCE
1. Review of multirate signal processing (mostly based onlecture notes by T. Saramki)
Motivation & basics
Efficient decimator/interpolator structures
oEfficient implementation structure for basic FIR filters
oEfficiency of multistage designs.
oFIR Nth-band filters, especially halfband filters
oCIC filter as an efficient multiplier-free structure for thefirst stages of the decimation chain.
2. Frequency translation and multirate processing ofbandpass I/Q signals
3. Multimode receivers
Main ideas
Examples
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Receiver Architectures Part 2 TLT-5806/RxArch2/7M. Renfors, TUT/DCE 10.10.11
DCE - Tampere University of Technology. All rights reserved.
Multimode Receivers
In flexible multi-mode receivers, the target is to usecommon blocks for different systems as much aspossible.
A long-term target is to make the transceiver configurablefor any system. However, presently a combination of afew predetermined systems is more realistic, e.g.,
GSM/WCDMA/WLAN.
A realistic approach has the following elements:- Separate RF stages for different systems.- Common IF/baseband analog parts; bandwidth
according to the most wideband system.- Common ADC at IF or baseband; fixed sampling rate.
- Especially in the terminal side: careful choice of IFfrequency & sampling rate to make the down-conversion simple. Typically,fIF=(2k+1)fs/4.
- Digital channel selection filtering optimized for thedifferent systems.
IF1
LO
filter S&HILNA DSP
0,1,0,-1
1,0,-1,0
QDSPIF2
ADC
AGC
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Receiver Architectures Part 2 TLT-5806/RxArch2/8M. Renfors, TUT/DCE 10.10.11
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Case Study: GSM/WCDMA dual-mode
receiver
* This part is based on the diploma thesis work of Vesa Lehtinencarried out at TUT/DCE during years 2001-03.
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Receiver Architectures Part 2 TLT-5806/RxArch2/9M. Renfors, TUT/DCE 10.10.11
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Receiver Architectures Part 2 TLT-5806/RxArch2/10M. Renfors, TUT/DCE 10.10.11
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Case Study on Wideband IF Sampling in
GSM Receivers*
Sampling and Quantization Requirements asFunctions of Analog Filter Bandwidth
* This part is based on the diploma thesis work of JuhoPirskanen carried out at TUT/ICE during years 1999-2000.
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Receiver Architectures Part 2 TLT-5806/RxArch2/11M. Renfors, TUT/DCE 10.10.11
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GSM Case: Wideband Receiver
Receiver with wideband front-end and wideband AD-conversion
Analog front-end can be simplifiedOne AD-converter can be used for different
systems
Performance requirements of the ADC areincreased
Channelization filtering must be done in digital domain toobtain desired system characteristics
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Receiver Architectures Part 2 TLT-5806/RxArch2/12M. Renfors, TUT/DCE 10.10.11
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GSM Case: Interference Mask
Obtained from the GSM specifications
Includes interference signals fromAdjacent channelOut of band blockingIntermodulation test
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Receiver Architectures Part 2 TLT-5806/RxArch2/13M. Renfors, TUT/DCE 10.10.11
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GSM Case: Attenuation Requirement
Attenuation requirements for GSM can be found by
PI is the interference signalPsignis the desired signal
C/Ic is the carrier to interference ratioAm is the extra noise margin
( )( ) ( ) /s I sign c mA f P f P C I A=
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GSM Case: ADC Dynamic Requirements
ADC dynamic range requirement can be calculated as
As is the attenuation requirementH(f)is the amplitude response of the analog filter
Fourth-order Chebyshev type two filters :
The red squares mark the critical points where thedynamic range requirement is maximized for each filterbandwidth.
( ) ( ){ }maxdynamic sf
SNR A f H f = +
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GSM Case: ADC Dynamic Requirements
By combining equations, the number of bits can befound by
Used sampling ratesMultiples of GSM symbol rate 17.33 MHz, 34.66
MHz and 69.33 MHz
Studied filter typesButterworth and Chebyshev type two filters
Used filter ordersFourth and sixth order filters
Filter bandwidth
From 100 kHz to 2.5 MHz
101.76 10log 2
6.02
sdynamic
fSNR
Bb
=
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GSM Case: Number of Bits Required in ADC
Fourth-orderButterworth filters:
Sixth-orderChebyshevtype twofilters:
Notice that in practice the minimum number of bits ishigher than the lowest values indicated here, in order to
be able to carry out the channel equalization properly.
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GSM Case: Jitter Noise
The maximum signal power to be sampled is:
Using the standard white-noise model for the jitter effects,the maximum allowed standard deviation of the timingerror is given by:
( ) ( ){ }maxADC If
P P f H f = +
2 2
max
2
4
ssig m
c
A
ADC
F CP AB I
Tf P
=
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GSM Case: Jitter Requirements for fIF=156 MHz
The timing jitter requirements when using fourth-orderButterworth filters:
The timing jitter requirements when using sixth-orderChebyshev type two filters:
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GSM Case: Conclusions
Dynamic requirement of the ADCHighly effected by the analog filter bandwidthAnalog filter order and type has only one bit effect
on ADC requirement (together 2 bits in somecases)
Standard deviation of timing jitterHighly effected by the analog filter bandwidth and
used IF frequency (IF sampling)Analog filter order and type has only slight effect
When considering GSM/WCDMA receivers
The analog bandwidth should be about 2 MHzFractional decimation has to be done