8

N= dimension of modulation(number of orthonormal function)

In general r=R/B = 2𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑁𝑁

APSK, PAM -- N=1; r=2𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)

QAM, MPSK -- N=2; r=𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)

FSK (coherent) ; r=2𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀

FSK (noncoherent) ; r=𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀

MFSK noncoherent orthogonal

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀

MPSK, QAM coherent

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)

MFSK noncoherent orthogonal

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀

MPSK, QAM coherent

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)

MFSK noncoherent orthogonal

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀

MPSK, QAM coherent

R/B = 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)

8

𝑃𝑃𝑏𝑏𝑏𝑏 = 𝑄𝑄 2𝐸𝐸𝑏𝑏𝑁𝑁0

Example 1:2 – PSK, PAM binary antipodal

Example 2:2 – PSK, PAM binary antipodal

𝑃𝑃𝑏𝑏𝑏𝑏 = 𝑄𝑄 2𝐸𝐸𝑏𝑏𝑁𝑁0

10−5 = 𝑄𝑄 4,2649Eb/N0 = (4,2649)^2/2Eb/N0 = 10log(Eb/N0)=9,5 dB

10−6 = 𝑄𝑄 4,7534Eb/N0 = (4,7534)^2/2Eb/N0 = 10log(Eb/N0)=10,5 dB

Krivka pre modulaciu sa pre lepsie 𝑷𝑷𝒃𝒃𝒃𝒃 posuva doprava (potvrdenie teorie)!!!

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25

4-QAM

16-QAM

8-QAM

32-QAM

64-QAM

256-QAMBER 10-4

BER 10-6

BPSK

QPSK

8-PSK

32-PSK

16-PSK

BER 10-4BER 10-6

BFSKQFSK8FSK16FSK

BER 10-4

BER 10-6

Eb/No [dB]

R/B

[bit/

s/Hz

]

BANDWIDTH-EFFICIENCY PLANE

Shannon limit-1,6 dB

Capacity bounderyR=C

coherent

noncoherent

M / T 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀FSKnoncoherent

For M-ary FSK, the frequency separation between adjacent frequencies is ∆f = 1/𝑇𝑇𝑠𝑠 for signal orthogonality.

The bandwidth required for M signals is B = M ∆f = M/𝑇𝑇𝑠𝑠.

noncoherentcoherent

M / T 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑀𝑀)/𝑀𝑀FSKnoncoherent

(a)(b)

(c)(d)

(e)50dB

(a) Half-power bandwidth. This is the interval between frequencies at which Gx(f ) has dropped to half-power, or 3 dB below the peak value. (c) Null-to-null bandwidth. The most popular measure of bandwidth for digital communications isthe width of the main spectral lobe, where most of the signal power is contained.

a) Half-power bandwidthb) Noise equivalent bandwidthc) Null-to-null bandwidth

d) Fractional power containment bandwidthe) Bounded power spectral densityf) Absolute bandwidth