SIMULATION OF PSK-BASED DIGITAL TRANSMISSION SCHEMES

Presented by:Group 2

PHASE-SHIFT KEYING (PSK) Two-level PSK (BPSK)

Uses two phases to represent binary digits

Where we can consider the above two functions to be multiplied by +1 and -1 for a binary 1 and binary 0 respectively

ts tfA c2cos tfA c2cos

1binary 0binary

tfA c2cos tfA c2cos

1binary 0binary

which equals

PHASE-SHIFT KEYING (PSK) Differential PSK (DPSK)

Phase shift with reference to previous bit▪ Binary 0 – signal burst of same phase as previous signal

burst▪ Binary 1 – signal burst of opposite phase to previous signal

burst The term differential is used because the phase shift

is with reference to the previous bit Doesn’t require an accurate receiver oscillator matched with

the transmitter for the phase information but obviously depends to the preceding phase (information bit) being received correctly.

PHASE-SHIFT KEYING (PSK) Four-level PSK (QPSK - quadrature PSK)

Each element represents more than one bit

ts

42cos tfA c 11

432cos tfA c

432cos tfA c

42cos tfA c

01

00

10

QPSK AND OQPSK MODULATORS

I stream (in-phase)

Q stream (quadrature data stream)

OQPSK (OFFSET QPSK) OQPSK has phase transitions between every half-

bit time that never exceeds 90 degrees (π/2 radians) Results in much less amplitude variation of the

bandwidth-limited carrier BER is the same as QPSK When amplified, QPSK results in significant

bandwidth expansion, whereas OQPSK has much less bandwidth expansion especially if the channel has non-linear components

MULTIPLE LEVEL PSK AMPLITUDE

AND PHASE

Multilevel PSK Using multiple phase angles with each angle having

more than one amplitude, multiple signals elements can be achieved

▪ D = modulation rate, baud▪ R = data rate, bps (note the difference in baud and bps)▪ M = number of different signal elements = 2L

▪ L = number of bits per signal element If L = 4 bits in each signal element using M = 16 combinations of

amplitude and phase, then if the data rate is 9600 bps,the line signaling speed/modulation rate is 2400 baud

MR

LRD

2log

QUADRATURE AMPLITUDE MODULATION

QAM is a combination of ASK and PSK Two different signals sent simultaneously on the same

carrier frequency

tftdtftdts cc 2sin2cos 21

BPSK TRANSMISSION SCHEME

0 5 10 15

10-1.8

10-1.7

10-1.6

10-1.5

10-1.4

10-1.3

10-1.2

Eb/N0 (dB)

BE

RBPSK transmission

BPSK TRANSMISSION SCHEME UNDER ONE PATH FADING

0 5 10 1510

-2

10-1

100

Eb/N0 (dB)

BE

R

BPSK transmission under one path fading

MATLAB RESUTLS Program 3.2 (bpsk_fading)

0 5 10 15 20 25 30 35 4010

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

BPSK performance

BPSK AWGN theoryBPSK AWGNBPSK Rayleigh theoryBPSK Rayleigh

OUTPUT – FLAT FADING CHANNEL(AMPLITUDE DISTORTION)ROLLOFF FACTOR = [0 0.5 1]

-10 -5 0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

BPSK In Flat Fading AWGN Channel - BER Vs SNR

SNR

BE

R

OUTPUT -- 16 QAM FLAT FADING

-10 -5 0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

16 QAM Flat Fading Channel Performance Comparison

SNR

BE

R

Amplitude Distortion Only

Amplitude & Phase Distortion

RECEIVED CONSTELLATION

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Qua

drat

ure

In-Phase

Received Constellation - 16 QAM Fading

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Qua

drat

ure

In-Phase

Received Constellation - 16 QAM Fading

Amplitude DistortionAmplitude + Phase Distortion

NYQUIST PULSESInput sr=256000.0; % Symbol rate ipoint=2^03; % Number of

oversamples ncc=1; %******************* Filter initialization

******************** irfn=21; % Number of filter taps

NYQUIST PULSES – IMPULSE RESPONSE

0 1 2 3 4 5 6 7 8 9

x 10-5

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time

Pul

se S

hape

Nyquist Pulses

Beta=0.5Beta=0Beta=1

NYQUIST PULSES – FREQUENCY RESPONSE

-1.5 -1 -0.5 0 0.5 1 1.5

x 106

0

1

2

3

4

5

6

7

8

9Frequency Response

TRANSMITTER AND RECEIVER FILTER COEFFICIENTS

0 20 40 60 80 100 120 140 160 180-0.2

0

0.2

0.4

0.6

0.8

1

1.2Transmitter and Receiver filter coefficients

Transmitter filter coefficientsReceiver filter coefficients

PLOT OF DATA1 Number of symbols (nd) = 10 data=rand(1,nd)>0.5 data1=data.*2-1

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1data1

PLOT OF DATA2 [data2] = oversamp( data1, nd , IPOINT)

0 10 20 30 40 50 60 70 80-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1data2

PLOT OF DATA3 data3 = conv(data2,xh)

0 50 100 150 200 250-1.5

-1

-0.5

0

0.5

1

1.5data3

PLOT OF A SAMPLE OF THE RANDOM AWGN

0 50 100 150 200 250-5

-4

-3

-2

-1

0

1

2

3

4

5inoise=randn(1,length(data3)).*attn

PLOT OF DATA4

0 50 100 150 200 250-5

-4

-3

-2

-1

0

1

2

3

4

5data4=data3+inoise

PLOT OF DATA5

0 50 100 150 200 250 300 350 400 450-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2data5=conv(data4,xh2)

PLOT OF DATA6

1 2 3 4 5 6 7 8 9 10-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2data6 = data5(sampl:8:8*nd+sampl-1)

BPSK DEMODULATION demodata=data6 > 0

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1demodata=data6 > 0

EYE DIAGRAM

Graphical eye pattern showing an example of two power levels in an OOK modulation scheme. Constant binary 1 and 0 levels are shown, as well as transistions from 0 to 1, 1 to 0, 0 to 1 to 0, and 1 to 0 to 1

Source: Wikipedia

PLOT OF THE INPHASE AND QUADRATURE PHASE CHANNELS

0 50 100 150 200 250 300 350 400 450-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2I-Channel (ich4)

0 50 100 150 200 250 300 350 400 450-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5Q-Channel (qch4)

MSK – MINIMUM SHIFT KEYING MSK is a continuous phase FSK (CPFSK)

where the frequency changes occur at the carrier zero crossings.

MSK is unique due to the relationship between the frequency of a logic 0 and 1.The difference between the frequencies is

always ½ the data rate.This is the minimum frequency spacing that

allows 2 FSK signals to be coherently orthogonal.

MSK – HOW IT WORKS The baseband modulation starts with a

bitstream of 0’s and 1’s and a bit-clock. The baseband signal is generated by first

transforming the 0/1 encoded bits into -1/1 using an NRZ filter.

This signal is then frequency modulated to produce the complete MSK signal.

The amount of overlap that occurs between bits will contribute to the inter-symbol interference (ISI).

EXAMPLE OF MSK 1200 bits/sec baseband MSK data signal Frequency spacing = 600Hz

a) NRZ data b) MSK signal

PROS OF MSK Since the MSK signals are orthogonal and

minimal distance, the spectrum can be more compact.

The detection scheme can take advantage of the orthogonal characteristics.

Low ISI (compared to GMSK)

CONS OF MSK The fundamental problem with MSK is that

the spectrum has side-lobes extending well above the data rate (See figure on next slide).

For wireless systems which require more efficient use of RF channel BW, it is necessary to reduce the energy of the upper side-lobes.

Solution – use a pre-modulation filter:Straight-forward Approach: Low-Pass FilterMore Efficient/Realistic Approach: Gaussian Filter

THE NEED FOR GMSK Gaussian Filter

Impulse response defined by a Gaussian Distribution – no overshoot or ringing (see lower figure)

BT – refers to the filter’s -3dB BW and data rate by:

Notice that a bit is spread over more than 1 bit period. This gives rise to ISI.

For BT=0.3, adjacent symbols will interfere with each other more than for BT=0.5

GMSK with BT=∞ is equivalent to MSK.

Trade-off between ISI and side-lobe suppression (top and bottom figures)

The higher the ISI, the more difficult the detection will become.

BitRatefBT dB3

GMSK – APPLICATIONS An important application of GMSK is GSM,

which is a time-division multiple-access system.

For this application, the BT is standardized at 0.3, which provides the best compromise between increased bandwidth occupancy and resistance to ISI.

Ninety-nine percent of the RF power of GMSK signals is specified to confine to 250kHz (+/- 25kHz margin from the signal), which means that the sidelobes need to be virtually zero outside this frequency band and the ISI should be negligible.

COMMENTS The program bpsk.m prints the BER in

each simulation loop, and this causes the program to run slowly, therefore, I stopped printing those results. Instead, I plotted the BER vs. EbN0 with a counter that displays the current value of EbN0.

I tried to plot the eye diagram for QPSK, but I didn’t succeed in that.

REFERENCES Wikepedia.com Haykin, S. 2001: “Communication Systems”.

4th ed. New York, NY. John Wiley & Sons. Introduction to GMSKwww.eecs.tufts.edu/~gcolan01 GMSK: Practical GMSK Data Transmissionhttp

://www.eetchina.com/ARTICLES/2003AUG/PDF/2003AUG29_NTEK_AN.PDF

Minimum Shift Keying: A Spectrally Effiecient Modulation

http://www.elet.polimi.it/upload/levantin/SistemiIntegrati/msk_pasupathy_1979.pdf