EE303 Lesson 20:Digital Modulation 2

Digital modulation schemes

We’ve discussed these types of digitalmodulation

OOK signal

FSK signal

BPSK signal

QPSK signal

In order to increase the data rate withoutincreasing bandwidth, we can further increasethe number of bits per symbol.

In the 8-PSK constellation below, 8 possiblephase shifts allow 3 bits to be transmitted byeach symbol.

M-ary PSK

0˚180˚

90˚

270˚

0˚ = binary 000

45˚ = binary 001

90˚ = binary 011

315˚ = binary 100

270˚ = binary 101

135˚ = binary 010

180˚ = binary 110

225˚ = binary 111

8-PSK

Consider the bit stream below and the resulting8-PSK signal.

unmodulatedcarrier

8-PSKsignal

000(0˚)

010(135˚)

111(225˚)

100(315˚)

001(45˚)

101(270˚)

011(90˚)

100(315˚)

bit stream

We could further increase to 4 bits/symbol using16-PSK.

To demodulate 16-PSK, the receiver mustdetermine the phase within 11.25˚.

16-PSK

0˚180˚

90˚

270˚

Noise effects

Like all transmissions, the received signal will bedegraded by noise.

This can be depicted in the phasor domain asfollows.

BPSK signal

BPSK signalwith noise

0˚180˚

90˚

270˚

demodulationerrors causedby noise

Noise effects

0˚180˚

90˚

270˚

10 dB SNR

0˚180˚

90˚

270˚

0˚180˚

90˚

270˚

20 dB SNR

2 dB SNR

Noise effects

A BPSK receiver must make a decision todetermine the phase of a received signal todetermine the corresponding binary signal.

Now consider the same noise in the presence ofa QPSK or 8-PSK signal.

Noise effects (8-PSK)

What is the relative likelihood of an error?

0˚180˚

90˚

270˚

10 dB SNR

Quadrature Amplitude Modulation

In order to increase the distance between pointsin the signal constellation, another option is tomodulate both the amplitude and the phase.

This is called quadrature amplitude modulation.

Consider the 8-QAM constellation below.

0˚180˚

90˚

270˚

101 101

110100

000 010

011001

8-QAM

Consider the bit stream below and the resulting8-QAM signal.

unmodulatedcarrier

8-QAMsignal

000 001 010 011 100 101 110 111 bit stream

Higher level QAM signals

QAM signals can be extended to much higher bitrates as depicted.

64-QAM and 256-QAM are common in cablemodems, satellites, and high-speed fixedbroadband wireless.

0˚180˚

90˚

270˚

64-QAM

256-QAM

0˚180˚

270˚

90˚

Spectral Efficiency

Spectral efficiency is a measure of how fast datacan be transmitted over a given bandwidth.

It is measured in bits per second per hertz(bps/Hz).

2QPSK

416-QAM

38-PSK

1BPSK

1.35MSK

<1FSK

Spectral efficiency(bps/Hz)

Modulation

Based on the spectral efficiency of the various digitalmodulation schemes, what is the minimum bandwidthrequired to transmit at a rate of 9600 bps using:

a. MSK (or GMSK)

b. BPSK

c. 8-PSK

d. 16-QAM

Example Problem 1

Bit errors

Another factor that influences spectral efficiencyis channel signal-to-noise (S/N) ratio.

The larger the amount noise present (lower S/Nratio), the greater the number of bit errors.

The ratio of the number of bit errors to thenumber of bits transmitted is the bit error rate(BER).

For example, if 5 bit errors occur every milliontransmitted bits, the BER is

6number of errors 55 10

number of transmitted bits 1,000,000BER

BER vs. C/N for digital modulation

BER vs. C/N for digital modulation

The bit error rates of various modulationschemes have been calculated versus carriersignal-to-noise ratios.

The plot shows that the more basic modulationschemes (BPSK, QPSK) have a higher immunityto noise that the more complex constellations.

This plot does not take signal bandwidth intoconsideration (noise increases with bandwidth)

Also, the plot does not take into account the bitrates of the various formats.

What is the required carrier signal-to-noise (C/N) ratiorequired to achieve a BER of 10-6 for each of the followingmodulation schemes?

a. BPSK

b. QPSK

c. 16-PSK

d. 256-QAM

Example Problem 2

Eb/N0

A better measure of signal to noise ratio is tocompared the energy per bit (Eb) versus thenoise power density (N0) given by

Eb/N0 takes into account the bandwidthrequirements and bit rates of the variousformats.

0

b

b

E C B

N N f

BER vs. Eb/N0 for digital modulation

Consider transmitting 10,000,000 bits over a channel witha S/N ratio (expressed in Eb/N0) of 10 dB. Roughly howmany bits errors would you expect to experience for eachof the following modulation schemes?

a. BPSK

b. Coherent OOK

c. FSK

d. 16-QAM

Example Problem 3