# Viterbi Metric for a BFSK

Started by February 16, 2007
```
In the hard decsion case, if I receive [0,1] say, then the metric
compared to [0,0] is 1. Suppose I received [0.9,1.1] in the soft
decision case. Is the metric compared to [0,1]...

(0.9)^2 + (1.1)^2 ???  or 0.9 + 1.1 ?????

Note: 0.9 is the correlation for a symbol 0
Note: 1.1 is the correlation for a symbol 1

Both correlations have been calculated by Quadrature Receiver (nocoherent
detection)

```
```On Feb 16, 9:53 am, "JAlbertoDJ" <nietoro...@yahoo.es> wrote:
> In the hard decsion case, if I receive [0,1] say, then the metric
> compared to [0,0] is 1. Suppose I received [0.9,1.1] in the soft
> decision case. Is the metric compared to [0,1]...
>
>  (0.9)^2 + (1.1)^2 ???  or 0.9 + 1.1 ?????

Soft decoders are typically designed to use Euclidean distance as the
metric; therefore it is correct to square each difference component.

Therefore, the metric for [0.9, 1.1] vs. [0, 1] is:

(0.9 - 0)^2 + (1.1 - 1)^2

--
Oli

```
```
JAlbertoDJ wrote:

> In the hard decsion case, if I receive [0,1] say, then the metric
> compared to [0,0] is 1.

It depends.

Suppose I received [0.9,1.1] in the soft
> decision case. Is the metric compared to [0,1]...
>
>  (0.9)^2 + (1.1)^2 ???  or 0.9 + 1.1 ?????

It depends.

>
> Note: 0.9 is the correlation for a symbol 0
> Note: 1.1 is the correlation for a symbol 1
>
> Both correlations have been calculated by Quadrature Receiver (nocoherent
> detection)

The metric is the generalized distance between the reference vectors and
the received vector. It depends on what signal vectors corresponds to
[0,1], [0,0] and such.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```
Oli Charlesworth wrote:

>
> Soft decoders are typically designed to use Euclidean distance as the
> metric; therefore it is correct to square each difference component.

No, this is not a correct statement.
It depends on what is the channel and what are the signals.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```On Feb 16, 6:45 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> Oli Charlesworth wrote:
>
> > Soft decoders are typically designed to use Euclidean distance as the
> > metric; therefore it is correct to square each difference component.
>
> No, this is not a correct statement.
> It depends on what is the channel and what are the signals.
>