digital front end

8/12/2019 Digital Front End

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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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1. Review of multirate signal processing (mostly based onlecture notes by T. Saramki)

Motivation & basics






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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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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Motivation & basics






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


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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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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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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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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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 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


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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Example (continued)

Overall frequency response and the effects of different

stages:


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Motivation & basics






2. Frequency translation and multirate processing ofbandpass I/Q signals

3. Multimode receivers

Main ideas

Examples


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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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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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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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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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GSM Case: Interference Mask

Obtained from the GSM specifications

Includes interference signals fromAdjacent channelOut of band blockingIntermodulation test


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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

digital front end

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