Started by January 25, 2004
```Hi!

For an all digital BPSK receiver, If I place the Equalizer in
baseband, then what could be its exactloaction: Is the following
arrangement acceptable?

|PASS-BAND|--------------BASE-BAND----------------------|

fs  ------  fs ------  fs  fb ------  fb -------
r(nTs)--->|DEMOD|----|  MF  |---/---| EQUZ |---|SLICER |--->
------     ------    ^    --- |-     -------  |
^                 |        |               |
|                 |        `-----<---------`
------             ------
|  CR  |           | STR  |
------             ------

Where:
r(nTs)= Received pass-band Digital Samples at freq fs=1/Ts
fs = Sampling Frequency
fb = BPSK SYMBOL rate (bit rate) , fs >= 2.fb , fb=1/Tb , Tb=
symbol/bit rate
DMOD= Mix with recovered carrier and LPF, operating freq=fs
CR= COSTAS LOOP CARRIER RECOVERY
MF=Root Raised Cosine Filter, operating at fs
STR= Symbol Timing recovery
EQUZ= Symbol Spaced Equalizer, operating at fb
SLICER= Hard decisions +/-1 V

1) Is this arrangement acceptable as one possible form of a BPSK

2) Since Equalizer is operating at Bit/Symbol rate fb, it is called a
Symbol rate equalizer. What if I want to use a FSE (Fractionally
Spaced Equalizer)? Say Tb/2 spaced(that Equalizer will give output at
rate fb=1/Tb). Where should i place it? Before the MF ? What would the
position of STR in that case(The output of FSE would already have
deimated to fb, so how to implement the STR)? Do i have to move STR in
pass-band?

Regards
Rider
```
```
rider wrote:
>
> Hi!
>
> For an all digital BPSK receiver, If I place the Equalizer in
> baseband,

There is no practical need in EQ for BPSK.

> then what could be its exactloaction: Is the following
> arrangement acceptable?
>
>  |PASS-BAND|--------------BASE-BAND----------------------|
>
>         fs  ------  fs ------  fs  fb ------  fb -------
>  r(nTs)--->|DEMOD|----|  MF  |---/---| EQUZ |---|SLICER |--->
>             ------     ------    ^    --- |-     -------  |
>                ^                 |        |               |
>                |                 |        `-----<---------`
>            ------             ------
>           |  CR  |           | STR  |
>            ------             ------
>
> Where:
> r(nTs)= Received pass-band Digital Samples at freq fs=1/Ts
> fs = Sampling Frequency
> fb = BPSK SYMBOL rate (bit rate) , fs >= 2.fb , fb=1/Tb , Tb=
> symbol/bit rate
> DMOD= Mix with recovered carrier and LPF, operating freq=fs
> CR= COSTAS LOOP CARRIER RECOVERY
> MF=Root Raised Cosine Filter, operating at fs
> STR= Symbol Timing recovery
> EQUZ= Symbol Spaced Equalizer, operating at fb
> SLICER= Hard decisions +/-1 V

Since your BPSK is RRC filtered prior to transmission, you should remove
RRC filter from the receiver or use square root filters both in receiver
and transmitter.

> 1) Is this arrangement acceptable as one possible form of a BPSK

Why not? This arrangement is as good as any other.

> 2) Since Equalizer is operating at Bit/Symbol rate fb, it is called a
> Symbol rate equalizer. What if I want to use a FSE (Fractionally
> Spaced Equalizer)? Say Tb/2 spaced(that Equalizer will give output at
> rate fb=1/Tb). Where should i place it? Before the MF ?

Anywhere. It does not matter.

> What would the
> position of STR in that case(The output of FSE would already have
> deimated to fb, so how to implement the STR)?

In this case if the EQ is N-spaced then the STR should recover
N*Bitrate.

> Do i have to move STR in
> pass-band?

You don't have to. That is just the matter of convenience.

> Regards
> Rider

DSP Consultant

http://www.abvolt.com
```
```> >
> >  |PASS-BAND|--------------BASE-BAND----------------------|
> >
> >         fs  ------  fs ------  fs  fb ------  fb -------
> >  r(nTs)--->|DEMOD|----|  MF  |---/---| EQUZ |---|SLICER |--->
> >             ------     ------    ^    --- |-     -------  |
> >                ^                 |        |               |
> >                |                 |        `-----<---------`
> >            ------             ------
> >           |  CR  |           | STR  |
> >            ------             ------
> >
> >

Thanks for your reply. If I do use the above arrangement for my
receiver, What kind of STR technique should i use? I have heard of
various techniques, like Early/Late gate, Gardner etc. As far as i
understood, Gardner algorithm requires STR in passband(i.e. it tries
to lock to fs not fb) and it requires 2 samples per symbol ( i have
fs=8fb) and some interpolator.

1)Is Gardner algortihm applicable in base-band as shown in my figure?
2)If i can use Gardner algorithm as above, the I  already have fs=8fb,
so do i need to interpolate?
3)Where can i find a suitable resource for Gardner algorithm?

Regards
Rider

Thanks
```
```
rider wrote:
>
> > >
> > >  |PASS-BAND|--------------BASE-BAND----------------------|
> > >
> > >         fs  ------  fs ------  fs  fb ------  fb -------
> > >  r(nTs)--->|DEMOD|----|  MF  |---/---| EQUZ |---|SLICER |--->
> > >             ------     ------    ^    --- |-     -------  |
> > >                ^                 |        |               |
> > >                |                 |        `-----<---------`
> > >            ------             ------
> > >           |  CR  |           | STR  |
> > >            ------             ------
> > >
> > >
>
> Thanks for your reply. If I do use the above arrangement for my
> receiver, What kind of STR technique should i use? I have heard of
> various techniques, like Early/Late gate, Gardner etc.

I would use the simplest zero crossing STR for BPSK.

Here is a good book on CR/STR algorithms:

"Digital Communication Receivers : Synchronization, Channel Estimation"
Heinrich Meyr; Marc Moeneclaey; Stefan Fechtel