# ask help on viterbi equalization

Started by April 23, 2009
```Dear All,

I am learning how to use viterbi in GSM Channel Equalization. As a newer,

Q1, What I learn from textbook, viterbi can handle bit sequence with some
mistakes, and output correct bit sequence. How can it handle complex data
inputs? Because the received signal are complex.

Q2, Can you kindly introduce some papers with simple math derivations to
me or any key I need to focus on?I would like to chew them first, thanks a
lot!

Frankie
```
```On Apr 23, 10:02&#2013266080;pm, "Fan.Zhang" <zf...@sina.com> wrote:
> Dear All,
>
> I am learning how to use viterbi in GSM Channel Equalization. As a newer,
>
> Q1, What I learn from textbook, viterbi can handle bit sequence with some
> mistakes, and output correct bit sequence. How can it handle complex data
> inputs? Because the received signal are complex.
>

The purpose of a viterbi equalizer is to equalize channel or "reverse"
the channel effect rather than to correct error as a viterbi decoder.
Once you have estimated the channel, you can always calculate the
euclidean distance of receiving the channel output y given a certain
input
x based on the transition probability p(y|x). x and y could be real or
complex.

> Q2, Can you kindly introduce some papers with simple math derivations to
> me or any key I need to focus on?I would like to chew them first, thanks a
> lot!
>

The math derivation of a viterbi equalizer is the same as a viterbi
decoder. You probably can find such topics in proakis.

>
> Frankie

```
```"Fan.Zhang" <zf624@sina.com> wrote in message
news:g-qdnWDRE7MmgGzUnZ2dnUVZ_qidnZ2d@giganews.com...
> Dear All,
>
> I am learning how to use viterbi in GSM Channel Equalization. As a newer,
>
> Q1, What I learn from textbook, viterbi can handle bit sequence with some
> mistakes, and output correct bit sequence. How can it handle complex data
> inputs? Because the received signal are complex.
>
> Q2, Can you kindly introduce some papers with simple math derivations to
> me or any key I need to focus on?I would like to chew them first, thanks a
> lot!
>
>
>
> Frankie

```
```On Apr 23, 10:02&#2013266080;pm, "Fan.Zhang" <zf...@sina.com> wrote:
> Dear All,
>
> I am learning how to use viterbi in GSM Channel Equalization. As a newer,
>
> Q1, What I learn from textbook, viterbi can handle bit sequence with some
> mistakes, and output correct bit sequence. How can it handle complex data
> inputs? Because the received signal are complex.
>
> Q2, Can you kindly introduce some papers with simple math derivations to
> me or any key I need to focus on?I would like to chew them first, thanks a
> lot!
>
>
> Frankie

All you need for a Viterbi algorithm are:
1.  Some notion of distance or cost
2.  A description of the state-space
So it is not that mysterious.  The first one you get from computing
Eucliean
distance in the complex plane, and the second you get from your
channel
estimate.

Equalization using Viterbi (or more precisely, maximum-likelihood
sequence
estimation) is standard treatment in most intermediate communication
textbooks.  I don't know what level of math you find simple or not.

Julius
```
```On Apr 23, 10:02&#2013266080;pm, "Fan.Zhang" <zf...@sina.com> wrote:
> Dear All,
>
> I am learning how to use viterbi in GSM Channel Equalization. As a newer,
>
> Q1, What I learn from textbook, viterbi can handle bit sequence with some
> mistakes, and output correct bit sequence. How can it handle complex data
> inputs? Because the received signal are complex.
>
> Q2, Can you kindly introduce some papers with simple math derivations to
> me or any key I need to focus on?I would like to chew them first, thanks a
> lot!
>
>
> Frankie

There was a paper some years back in one of the IEEE magazines called
"How I Learned to Love the Trellis" by Bernard Sklar. I recommend it.

John
```
```>On Apr 23, 10:02=A0pm, "Fan.Zhang" <zf...@sina.com> wrote:
>> Dear All,
>>
>> I am learning how to use viterbi in GSM Channel Equalization. As a
>>
>> Q1, What I learn from textbook, viterbi can handle bit sequence with
some
>> mistakes, and output correct bit sequence. How can it handle complex
data
>> inputs? Because the received signal are complex.
>>
>> Q2, Can you kindly introduce some papers with simple math derivations
to
>> me or any key I need to focus on?I would like to chew them first,
thanks =
>a
>> lot!
>>
>>
>> Frankie
>
>There was a paper some years back in one of the IEEE magazines called
>"How I Learned to Love the Trellis" by Bernard Sklar. I recommend it.
>
>John
>

Frankie
```
```On Apr 24, 8:27&#2013266080;am, John <sampson...@gmail.com> wrote:
> On Apr 23, 10:02&#2013266080;pm, "Fan.Zhang" <zf...@sina.com> wrote:
>
>
>
>
>
> > Dear All,
>
> > I am learning how to use viterbi in GSM Channel Equalization. As a newer,
>
> > Q1, What I learn from textbook, viterbi can handle bit sequence with some
> > mistakes, and output correct bit sequence. How can it handle complex data
> > inputs? Because the received signal are complex.
>
> > Q2, Can you kindly introduce some papers with simple math derivations to
> > me or any key I need to focus on?I would like to chew them first, thanks a
> > lot!
>
>
> > Frankie
>
> There was a paper some years back in one of the IEEE magazines called
> "How I Learned to Love the Trellis" by Bernard Sklar. I recommend it.
>
> John- Hide quoted text -
>
> - Show quoted text -

That was a good article!

Clay
```