Digital Front-End Signal Processing - TUT · Digital Front-End Signal Processing Markku Renfors,...

Digital Front-End Signal Processing Markku Renfors, TUT/DCE

1. Review of multirate signal processing (mostly based on

lecture notes by T. Saramäki) • Motivation & basics • Efficient decimator/interpolator structures o Efficient implementation structure for basic FIR filters o Efficiency of multistage designs. o FIR Nth-band filters, especially halfband filters o CIC filter as an efficient multiplier-free structure for the

first stages of the decimation chain.

2. Frequency translation and multirate processing of bandpass I/Q signals

3. Multimode receivers • Main ideas • Examples

Why multirate signal processing is s good idea in advanced transceiver architectures?

1. A general approach to increase the flexibility of receiver implementations is to use wideband sampling in the receiver and select the desired channel among the many digitized ones using digital filtering, using a filter optimized for the particular transmission system in use.

o In case of wideband sampling, the initial sampling rate is much higher than symbol/chip rate used in baseband processing.

2. The commonly used delta-sigma AD-conversion principle is also based on heavy oversampling, even in the case of narrowband sampling.

Concerning the DSP implementation complexity and power consumption, it is very crucial to use the lowest possible sampling rate at each stage of the processing chain (good examples of this will be given later during the course).

o As a rule of thumb, for given (narrowband) selectivity requirements and given input sampling rate, the computational complexity (and power consumption) is, in a well-designed multirate system, directly proportional to the output sampling rate.

o Now think about the case where you could reduce the sampling rate by a factor of 300 (could really be the case in a wideband sampling receiver).

Similar ideas can be used also in the transmitter case: synthesizing a high-rate, possibly multi-channel signal using DSP would greatly improve the flexibility.

=> Reduction in implementation complexity, especially for small N!

(M+1)/4 multiplications per input sample needed for implementing a filter of length M+1. => A cascade of half-band filters is often a very efficient choice for multirate signal processing!

Receiver Architectures – Part 2 TLT-5806/RxArch2/1 M. 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 R is the decimation factor and N is the order of the CIC-filter.

A first-order CIC-filter takes the avarage of R consequtive input samples and decimates by R. It is also called moving average or running sum filter.

It is important to use modulo arithmetic (like 2's complement) in the implementation, because there will be inevitable internal overflows.

z-1 ↓32 z-1 z-1 z-1

( )NR

zzzH

−

−=

−

−

111

N

s

sFfRNj

Ffj

FfR

FRf

eeH ss

=

−

π

πππ

sin

sin)1(2



CIC-Filters In CIC filter, those frequencies aliasing to 0-frequency are heavily attenuated. For a relatively narrowband signal, low-order CIC-filters are sufficient; more wideband signals neede higher CIC-filter orders Example (for a GSM application): N=2, R=32.

Sampling and Multirate Techniques for Complex and Bandpass Signals TLT-5806/IQ/8 M. Renfors, TUT/DCE 21.9.2010


Frequency Translation One key operation in communications signal processing is the frequency translation of a signal spectrum from one center frequency to another. Conversions between baseband and bandpass representations (modulation and demodulation) are special cases of this. We consider two different ways to do the frequency translation: mixing and multirate operations, i.e., decimation and interpolation. In case of multirate operations, we assume for simplicity that the following two sampling rates are used: low sampling rate: 1sf

N N= T

high sampling rate: 1sf T=



Mixing for Complex Discrete-Time Signals 2( ) ( ) ( )LO LOj f kT j ky k e x k e x kπ ω= =

fc

f

f +fc LO

f

e j k ωLO

cos( )ωLok

sin( )ωLok

I I

I Q

Special case with real input signal:

This produces a pure frequency translation of the spectrum by . 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 without producing a complex result. Converts a lowpass signal to a highpass signal, and vice versa.

Tff sLO 414/ ==

in which case the multiplying sequence is +1, j, -1, -j, +1, j, ...



Complex Bandpass Filters Certain types of complex filters based on Hilbert transformers can be designed using standard filter design packages, like Parks-McClellan routine for FIR filters.

Another way to get complex bandpass filters is through frequency translations:

Real

0f

0f

fc

T T

e j f T2π c

⇒

prototype filter:

Complex bandpass filter: Transformation for frequency response and transfer function:

( ) ( )( ) ( ) ( )Tfjjj cc zeHzHeHeH πωωω 2−− →→ Generic transformation for block diagram:

If 1/T is an integer multiple of fc, this might be much easier than in the general case, see the special cases of the previous page.



Example of a Complex Bandpass Filters: Frequency Translated FIR

Frequency translation by fs/4 => Analytic bandpass filter with passband around fs/4.

0f

0f

fs/4 fs/2

fs/4 fs/2

Impulse response translated as:

h0, h1, h2, h3, h4, …, hN

⇓ h0, jh1, -h2, -jh3, h4, …, (j)NhN



FIR Filter with Frequency Translation by fs/4 (i) Real input signal

...

I

Q

h0 −h2 h4

h1 −h3 h5

T T T T T

(ii) Complex input signal ...

...

IQ

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 possible coefficient symmetry (of linear phase FIR) in both cases.


Sampling Theorem The sampling theorem says that a (real or complex) lowpass signal limited to the frequency band [-W, W] can represented completely by discrete-time samples if the sampling rate (1/T) is at least 2W.

In case of a complex signal, each sample is, of course, a complex number.

In general, discrete-time signals have periodic spectra, where the continuous-time spectrum is repeated around frequencies ± ± ±1 2 3


0f

fs 2fs−fs−2fs

T T T, , ,…

In case of complex signals, it is not required that the original signal is located symmetrically around 0.

Any part of the periodic signal can be considered as the useful part. This allows many possibilities for multirate processing of bandpass signals.

In general, the key criterion is that no destructive aliasing effect occur on top of the desired part of the spectrum.


Real vs. Complex Discrete-Time Signals

Real signal:

0f

fs−fs W

0f

−fs f =Ws

Here 2W real samples per second are sufficient to represent the signal.

Complex signal:

Here W complex samples per second are sufficient.

• The resulting rates of real-valued samples are the same.

• However, the quantization effects may be quite different. (Recall from the standard treatment of SSB that Hilbert-transformed signals may be difficult.)




Interpolation for Complex Signal Sampling rate increase produces a periodic spectrum, and the desired part of the spectrum is then separated by an (analytic) bandpass filter.

N

0f

1/NT

0f

n NT/n NT T/ 1/−

COMPLEXBP-FILTERRESPONSE

0f

1/NT

0f

n NT/

a)

b)



Decimation for Complex Signal Sampling rate decrease produces aliasing, such that the original band is at one of the image bands of the resulting final band. The signal has to be band-limited to a bandwidth of

NT/1 before this operation can be done without severe aliasing effects.

N

0f

1/NTn NT T/ 1/− n NT/

0f

COMPLEXBP-FILTERRESPONSE



Combined Multirate Operations for Complex Signal

Combining decimation and interpolation, a frequency shift by n N can be realized, where n is an arbitrary integer. T/

N M

0f

n f /N- f1 S S n f /N1 S

0f

0f

n f /N2 S It can be seen that the low sampling rate, limited to be higher than the signal bandwidth, determines the resolution of the frequency translations based on multirate operations.

If, for example, a bandpass signal is desired to be translated to the baseband form, this can be done using multirate operations if and only if the carrier frequency is a multiple of the low sampling rate.

Using also simple frequency translations (with coefficients +1, -1, +j, -j), the resolution is 1/(4NT).



Combining Mixing and Multirate Operations for Complex Signals

A general frequency shift of f nNT fO = + Δ can be done

in the following two ways: (1) Direct frequency conversion by fO using mixing. (2) Conversion using multirate operations by n NT followed by a mixing with fΔ (or vice versa). The differences in these two approaches are due to the possible filtering operations associated with the multirate operations, and aliasing/reconstruction filters in case of mixed continuous-time/discrete-time processing. Assuming ideal filtering, these two ways would be equivalent.



Example of Combining Mixing and Multirate Operations

Conversion from bandpass to baseband representation and decimation to symbol rate, i.e., I/Q-demodulation.

Assume that - N=6, f0=4/(6T)+fΔ. - The required complex bandpass filter is obtained from an FIR filter of length 50 by frequency translation.

(ii)(iN

e −j k0

N

e −j k0

N

e −j kΔ

)

The following three ways are equivalent but lead to different computational requirements (the required real multiplication rates at input rate are shown, not exploiting possible coefficient symmetry):

LPF BPF

(iii) BPF

Case (i) Case (ii) Case (iii) Filter 100 100/6 100/6 Mixer 4 2 4/6 Total 104 18.7 17.3



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 the filter. Utilizing coefficient symmetry is easiest in this case.

(iii) As (i) but decimation can be included efficiently with the filter.

- Mixing and LO generation done at lower rate and thus easier to implement.

Here we have not taken use of the possible coefficient symmetry, which may reduce the multiplication rates by 1/2 in all cases. In general, mixing is a memoryless operation, so up-sampling and down-sampling operations can be commuted with it in block diagram manipulations.



Frequency Translation for Real Signals Mixing and multirate operations can be done in similar way for real signals. The difference is that the two parts of the spectrum, on the positive and negative frequency axis, and their 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( )ωLOt

Mixing produces two translated spectral components (note that cos( ) ( ) / 2j t j tt e eω ωω −= + ). The image band appearing on top of the desired band after mixing must be suppressed before mixing. (2) Multirate operations

In case of decimation, to avoid destructive aliasing effects, the signal to be translated must be within one of the intervals

1 1, or ,2 2n n n n

NT NT NT NT NT NT⎡ ⎤ ⎡+ −⎣ ⎦ ⎣

⎤⎦

Otherwise destructive aliasing will occur. In the latter case, the spectrum will be inverted.



Interpolation for Real Bandpass Signal

X f ( )

0 fsfs/2−fs/2−fs

f

W f( )

0f

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



Decimation for Real Bandpass Signal

x n( ) y m( )x nBP( )

fs fs/N

0f

X f BP( )

0f

Y f( )

0f

0f

f Ns/ 3 /(2f N)s−f Ns/−3 /(2f N)s

3 /(2f N)s−3 /(2f N)s 2 /f Ns−2 /f Ns

N

−f /Ns

X f BP( )

Y f( )

0f

f Ns/−f Ns/

k=3 k=2 k=1 k=0 k=0 k=1 k=2 k=3

f Ns/



Analytic Filtering and Taking Real Part as Multirate Operations

The transformations between real and complex signal formats can be seen as multirate operations:

• Taking the real part effectively reduces the rate of real-valued samples by two. It produces mirror images, in contrast to the periodic images produced by decimation by two. In both cases, the new spectral components may fall on top of the existing spectral components.

If this operation follows, e.g., an FIR filter, considerable computational simplifications can be made by combining the real part- operation with the filter in a cleaver way. There is no sense to compute samples that are thrown away by the real part –operation!!.

• Analytic filtering (in any form – baseband, bandpass, filter bank) increases the rate of real-valued samples by two. Mirror images are removed form the spectrum, in contrast to the periodic images that are removed in interpolation.



Example of Down-Conversion: I/Q-Demodulation

N4

PHASESPLITTER 2 MATCHED

FILTER 2I

Q

0

0

2/T

f

f

0 1/Tf

It is usually a good idea to keep the signal as a real signal as long as possible, because after converting to complex form, all subsequent signal processing operations require (at least) double computational capacity compared to the corresponding real algorithms.



Digital Channel Selection & Down-Conversion Digital Down-Conversion 1. Desired channel centered at fixed IF

=> Fixed down-conversion Special choices of fIF and fs make things easy. Especially when fIF=(2k+1) fs/4, the signal aliases to fs/4 and down-conversion is very easy.

2. Wideband sampling case => Tunable down-conversion and NCO (numerically controlled oscillator) needed.

3. Multistage decimation => Tunable digital down-conversion is possible also without NCO, using a configurable multistage decimation chain.

Channel Selection Filtering - After down-conversion, efficient lowpass decimator structure

is 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 decimation

chain.



NCO-Based Arbitrary Digital Down-

Conversion Dedicated processors implementing the following kind of down-conversion and channel selection structure are available for several vendors (like Harris).

Sampling rates in the 50 ... 100 MHz range are possible. However, the power consumption is still too high for terminal applications.



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 kHz

Frequency responses of the filter stages:



Example (continued) Overall frequency response and the effects of different stages:



Multimode Receivers

In flexible multi-mode receivers, the target is to use common blocks for different systems as much as possible.

A long-term target is to make the transceiver configurable for any system. However, presently a combination of a few 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 IF

frequency & sampling rate to make the down-conversion simple. Typically, fIF=(2k+1) fs/4.

- Digital channel selection filtering optimized for the different systems.

IF1

LO

filter S&HI

LNA DSP

0,1,0,-1

1,0,-1,0

QDSPIF2

ADC

AGC



Case Study: GSM/WCDMA dual-mode receiver

* This part is based on the diploma thesis work of Vesa Lehtinen carried out at TUT/DCE during years 2001-03.



Case Study on Wideband IF Sampling in

GSM Receivers*

• Sampling and Quantization Requirements as Functions of Analog Filter Bandwidth

* This part is based on the diploma thesis work of Juho Pirskanen carried out at TUT/ICE during years 1999-2000.



GSM Case: Wideband Receiver

Receiver with wideband front-end and wideband AD-conversion

– Analog front-end can be simplified – One AD-converter can be used for different

systems – Performance requirements of the ADC are

increased

Channelization filtering must be done in digital domain to obtain desired system characteristics



GSM Case: Interference Mask

• Obtained from the GSM specifications • Includes interference signals from

– Adjacent channel – Out of band blocking – Intermodulation test

–



GSM Case: Attenuation Requirement

• Attenuation requirements for GSM can be found by

• PI is the interference signal • Psign is the desired signal • C/Ic is the carrier to interference ratio • Am is the extra noise margin

( )( ) ( ) /s I sign c mA f P f P C I A= − − −



GSM Case: ADC Dynamic Requirements

ADC dynamic range requirement can be calculated as

• As is the attenuation requirement • H(f) is the amplitude response of the analog filter

Fourth-order Chebyshev type two filters :

The red squares mark the critical points where the dynamic range requirement is maximized for each filter bandwidth.

( ) ( ){ }maxdynamic sfSNR A f H f= +



GSM Case: ADC Dynamic Requirements

• By combining equations, the number of bits can be found by

• Used sampling rates – Multiples of GSM symbol rate 17.33 MHz, 34.66

MHz and 69.33 MHz

• Studied filter types – Butterworth and Chebyshev type two filters

• Used filter orders – Fourth and sixth order filters

• Filter bandwidth – From 100 kHz to 2.5 MHz

101.76 10log 26.02

sdynamic

fSNR Bb

− − =



GSM Case: Number of Bits Required in ADC

Fourth-order Butterworth filters: Sixth-order Chebyshev type two filters:

Notice that in practice the minimum number of bits is higher than the lowest values indicated here, in order to be able to carry out the channel equalization properly.



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 timing error is given by:

( ) ( ){ }maxADC IfP P f H f= +

2 2max

24

ssig m

cA

ADC

F CP AB IT

f Pπ

⋅ − − =



GSM Case: Jitter Requirements for fIF=156 MHz The timing jitter requirements when using fourth-order Butterworth filters: The timing jitter requirements when using sixth-order Chebyshev type two filters:



GSM Case: Conclusions

• Dynamic requirement of the ADC – Highly effected by the analog filter bandwidth – Analog filter order and type has only one bit effect

on ADC requirement (together 2 bits in some cases)

• Standard deviation of timing jitter

– Highly 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 MHz – Fractional decimation has to be done

Digital Front-End Signal Processing - TUT · Digital Front-End Signal Processing Markku Renfors,...

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