elementary question on channel equalization

Dear All,

I'm new to DSP and channel equalization topic and kindly ask you about some
fundamental questions:

-If I want to send a binary data on an AWGN channel with ISI, how do I know 
at the
receiver side, what was the sent information? Because it's easy to 
confuse -1 and 1..

-why it is good to send a training sequence at the beginning?

-What is theoretical BER and why we can't achive this?

-If I have SNR=30dB then what's the relationship between the signal and 
noise energy?

I'd be very happy if somebody could answer me, these are so fundamental 
issues that
I couldn't find them in the digital communication related books I have!
Tom 

On Sat, 5 Nov 2005 02:20:50 +0100, "Bill Thomas"
<anytime@anywhere.com> wrote:

>Dear All,
>
>I'm new to DSP and channel equalization topic and kindly ask you about some
>fundamental questions:
>
>-If I want to send a binary data on an AWGN channel with ISI, how do I know 
>at the
>receiver side, what was the sent information? Because it's easy to 
>confuse -1 and 1..

Assuming this isn't homework...

What sort of modulation are you assuming (assuming you are assuming a
modulation)?

For antipodal modulations like BPSK 1 and -1 are as different as you
can make them in order to minimize decision errors.   I'm not sure why
you think one would confuse 1 with -1.

>-why it is good to send a training sequence at the beginning?

Since you're asking about equalizers, the general idea is that you
want the equalizer trained and converged to a good solution before the
data arrives.   If you're training the equalizer during the data, the
information bits that go by during the training will be less reliable
than bits demodulated after the equalizer has converged.   For this
reason in many systems a preamble is used to provide time for signal
synchronization, channel estimation and equalizer training before the
data arrives.

>-What is theoretical BER and why we can't achive this?

There is more than one flavor of theoretical BER, so I'm not quite
sure how to answer this.   e.g., there is the so-called "matched
filter bound" which is the theoretical performance that can be
achieved without coding of any kind.  That one can be achieved within
a pretty slim margin without too much trouble.

If you're talking about the Shannon limit, or capacity, or some
theoretical maximum performance like that, then it, too, can be
approached pretty closely with current technology.   Practical
capacity-approaching codes have only existed for about ten years or
so, but they do exist.

>-If I have SNR=30dB then what's the relationship between the signal and 
>noise energy?

SNR is a power ratio, but it isn't hard to convert it to an energy
ratio like Eb/No.   These sorts of relationships are not difficult to
find in most comm texts.

>I'd be very happy if somebody could answer me, these are so fundamental 
>issues that
>I couldn't find them in the digital communication related books I have!

Most of these topic are covered in decent modern texts, but you may
just be having trouble finding them if you're unfamiliar with the
terminology, etc.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org