Fundamentals ofCommunications

(XE37ZKT), Part I

Advanced Digital ModulationTechniques

Josef Dobes

7th

1

1 Outline

• Comparing the ASK, PSK, and FSK Spectra

– OOK and 4-ASK

– OOK Spectrum, derivation

– PSK Spectrum

– FSK Spectrum

• PSK and QAM

– 2-PSK and 4-PSK

– 8-PSK, 8-QAM, and 16-QAM

– Constellation diagrams

2

• MSK and GMSK

– Minimum shift keying rule

– Smoothing phase

– Phase trellis

– GMSK

• π/4 DQPSK

• Noise Properties

• Adaptive Modulation and Coding

3

2 Comparing ASK, PSK and FSK Spec-tra

2.1 OOK (On-Off Keying) and 4-ASK (Time)

2.2 OOK (Spectrum)

4

2.3 PSK (Time and Spectrum)

Highlights

• The main difference between the ASK and PSK modulationsconsists in nonexistence of carrier in PSK

• For the signal drawn above, the carrier has lesser magnitudethan the 1st harmonic component. Why?

• The even harmonic components (2, 4, 6, ...) are zero for bothASK and PSK.

5

OOK DC and 1st harmonic components Let assume the se-quence 1, 0, 1, 0, ... The DC component for such signal is

1

T

∫T

0

f(t)dt =1

T

∫ T2

0

dt =1

T

T

2=

1

2

The first harmonic component is (only the sine member of the Fourierseries is computed – the cosine member is zero on principle)

2

T

∫T

0

f(t) sin2π

Tt dt =

2

T

∫ T2

0

sin2π

Tt dt =

2

T

T

2π

[− cos

2π

Tt

]T2

0

=2

π>

1

2

Therefore, the magnitude of the 1st harmonic component is greaterthan the DC component for the most primitive OOK signal.

6

2.4 FSK (Time and Spectrum)

7

3 PSK and QAM

8

Signal constellation It is convenient to represent phases on a pha-sor diagram, known as the constellation, and each phase can be re-solved into cosine (I, In-phase) and sine (Q, Quadrature) components.

The modulated signal can be written as

f(t) = I cos ωct + Q sin ωct

showing that it is equivalent to a pair of DSB signals of the samecarrier frequency, but with the two carriers in quadrature – so themodulation is called QAM (Quadrature Amplitude Modulation).

9

4 MSK and GMSK

MSK (Minimum Shift Keying) is a variant of FSK with continuousphase.

Generally, the bandwidth can be saved if ω0 and ω1 are closetogether, but the closer they are the more difficult it is to distinguishbetween the binary values. The closest practical spacing is when thetwo frequencies differ by one half cycle in any bit period. If the timeper symbol is TB then the minimum frequency deviation is given by

∆f TB =1

2,

where ∆f = f0 − f1.

To produce the narrowest possible spectrum, the symbol transitionsare arranged to be phase-continuous, since any sudden change in awaveform will produce a wider spectrum.

10

However, a better way is to switch the frequencies at a maximum(or, alternatively, at a minimum) – the derivatives are zero at thesepoints and therefore the switching is smooth.

11

The phase can only take on one of two values, the values being 0

and π for t = 2kTb, and ±π/2 for t = (2k + 1)Tb (so called phasetrellis):

12

4.1 GMSK

If the data pulses are shaped by suitable filtering before being appliedto the voltage controlled oscillator, we can obtain a smooth transi-tion between the FSK frequencies, and this will reduce further thebandwidth requirement. The optimum shape for the pulses is that ofa Gaussian function, and this results in GMSK.

If BG is the bandwidth of the shaping filter, and TB is the pulsewidth, the parameter BGTB determines the bandwidth of the GMSKsignal. The “2G” or GSM mobile phone network uses GMSK modu-lation with BGTB = 0.3.

13

5 π/4 DQPSK

The signal constellation can be viewed as the superposition of twoQPSK signal constellations offset by 45 degrees relative to each other,resulting in eight phases.

Emphasize that none of the ways goes across the origin.

14

6 Noise Properties

The flexibility of digital modulation means that a modulation schemecan be chosen to suit most channels. For the limited bandwidth ofa telephone channel, a bandwidth efficient scheme such as QAM orQPSK is suitable. At the other extreme, m-FSK modulation can usethe wide bandwidth of the “space channel” to give good performanceat low signal-to-noise ratios approaching the Shannon limit of -1.6 dB

15

7 Adaptive Modulation and Coding

Both QAM and QPSK are modulation techniques used in IEEE 802.11(i.e., Wi-Fi), IEEE 802.16 (i.e., WiMAX) and 3G (i.e., WCDMA/HSDPA) wireless technologies. The modulated signals are then de-modulated at the receiver where the original message can be recov-ered. The use of adaptive modulation allows wireless technologiesto optimize, yielding higher throughputs while also covering long dis-tances.

16