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Signalling

Module by: Behnaam Aazhang. E-mail the author

Summary: (Blank Abstract)

Example 1

Data symbols are "1" or "0" and data rate is 1T 1 T Hertz.

Figure 1
Pulse amplitude modulation (PAM)
Pulse amplitude modulation (PAM) (Figure4-2_1.png)
Figure 2
Pulse position modulation
Pulse position modulation (Figure4-2_2.png)

Example 2: Example

Data symbols are "1" or "0" and the data rate is 2T 2 T Hertz.

Figure 3
Figure 3 (Figure4-3.png)

This strategy is an alternative to PAM with half the period, T2 T 2 .

Figure 4
Figure 4 (Figure4-4.png)

Relevant measures are energy of modulated signals

E m =0T s m 2td t   ,   m12M    E m m 1 2 M t 0 T s m t 2
(1)
and how different they are in terms of inner products.
s m , s n =0T s m t s n t*d t s m s n t 0 T s m t s n t
(2)
for m12M m 1 2 M and n12M n 1 2 M .

Definition 1: antipodal
Signals s 1 t s 1 t and s 2 t s 2 t are antipodal if s 2 t= s 1 t  ,   t 0 T    t t 0 T s 2 t s 1 t
Definition 2: orthogonal
Signals s 1 t s 1 t , s 2 t s 2 t ,…, s M t s M t are orthogonal if s m , s n =0 s m s n 0 for mn m n .
Definition 3: biorthogonal
Signals s 1 t s 1 t , s 2 t s 2 t ,…, s M t s M t are biorthogonal if s 1 t s 1 t ,…, s M 2 t s M 2 t are orthogonal and s m t= s M 2 + m t s m t s M 2 + m t for some m12M2 m 1 2 M 2 .

It is quite intuitive to expect that the smaller (the more negative) the inner products, s m , s n s m s n for all mn m n , the better the signal set.

Definition 4: Simplex signals
Let s 1 t s 2 t s M t s 1 t s 2 t s M t be a set of orthogonal signals with equal energy. The signals s 1 ˜ t s 1 ˜ t ,…, s M ˜ t s M ˜ t are simplex signals if
s m ˜ t= s m t1M k =1M s k t s m ˜ t s m t 1 M k 1 M s k t
(3)

If the energy of orthogonal signals is denoted by

E s =0T s m 2td t   ,   m12...M    m m 1 2 ... M E s t 0 T s m t 2
(4)
then the energy of simplex signals
E s ˜ =(11M) E s E s ˜ 1 1 M E s
(5)
and
s m ˜ , s n ˜ =-1M1 E s ˜   ,   mn    m n s m ˜ s n ˜ -1 M 1 E s ˜
(6)

It is conjectured that among all possible M M-ary signals with equal energy, the simplex signal set results in the smallest probability of error when used to transmit information through an additive white Gaussian noise channel.

The geometric representation of signals can provide a compact description of signals and can simplify performance analysis of communication systems using the signals.

Once signals have been modulated, the receiver must detect and demodulate the signals despite interference and noise and decide which of the set of possible transmitted signals was sent.

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

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| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks