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DATA COMMUNICATION 2-dimensional transmissionPowerPoint Presentation

DATA COMMUNICATION 2-dimensional transmission

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„orthogonal“ binary signaling

2 signals S1 (t) S2 (t) in time T

Example:

Property: orthogonal

energy E

T

T

QAM receiver

1/0

+/-

r(t)

1/0

+/-

r(t) = S(t) + n(t)

Note: sin(x)sin(x) = ½ (1 – cos (2x) )

sin(x)cos(x) = ½ sin (2x)

about the noise

Conclusion: n1 and n2 are Gaussian Random Variables

zero mean

uncorrelated (and thus statistically independent (f(x,y) =f(x)f(y) )

with variance 2.

performance

From Chapter 1: P(error) =

Geometric presentation (2)

1

equal density

transmitted

2

noise vector n

received

The noise vector n has length |n| = ( 12+22) ½

n has a spherically symmetric distribution!

Error probability for coded transmission

The error probabiltiy is similar to the 1-dimensional situation:

We have to determine

the minimum d2Euclidean between any two codewords

Example:

C

d2Euclidean =

C‘

Error probability

The two-code word error probability is then given by:

modulation schemes

On-off

FSK

8-PSK

3 bits/s

1 bit/symbol

1 bit/symbol

4-QAM 2 bits

16-QAM

4 bits/s

Coding with same symbol speed

In k symbol transmissions, we transmit k information bits. We use a rate ½ code

In k symbol transmissions, we transmit k bits

ML receiver:

Famous Ungerböck coding

In k symbol transmissions transmit

We can transmit

2k information bits

and k redundant digits

In k symbol transmissions transmit 2k digits

Hence, we can use a code with rate 2/3 with the same energy per info bit!

example

transmit

00

00

00

10

10

01

Parity even

Parity odd

11

11

11

or

00

01

00

01

10

11

10

11

Decoder:

1) first detect whether the parity is odd or even

2) do ML decoding given the parity from 1)

Homework: estimate the coding gain

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