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Viterbi Metric for a BFSK

Started by JAlbertoDJ 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. Vladimir Vassilevsky 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. Vladimir Vassilevsky 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. > > Vladimir Vassilevsky > > DSP and Mixed Signal Design Consultant > > http://www.abvolt.com
For the AWGN channel, the soft decoder uses the Euclidean distance as the metric. To reduce the complexity, only the cross-correlation between the received signal and the modulation constellation is used. For the BPSK system, (0,1) is mapped to (1, -1).