Thesis: Chapter 5

Saturday, August 13, 2016

Chapter 5

CHAPTER 5

DESIGN AND IMPLEMENTATION

OF OFFSET TECHNIQUE

FOR 8-PSK

Introduction

Simulation Codes

Simulation Results and Analysis

Conclusion

DESIGN AND IMPLEMENTATION OF

OFFSET TECHNIQUE FOR 8-PSK

Introduction

OQPSK

Offset quadrature phase-shift keying (OQPSK) is a variant of QPSK. Taking four values of the phase (two bits) at a time to construct a QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts result in large amplitude fluctuations, an undesirable quality in communication systems. By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. This will limit the phase-shift to no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice. The sudden phase-shifts occur about twice as often as for QPSK (since the signals no longer change together), but they are less severe. In other words, the magnitude of jumps is smaller in OQPSK when compared to QPSK.

Same idea can be applied to higher order M-PSK and other linear modulation techniques. In this section 8-Offset phase shift keying (8-OPSK) is implemented using matlab and BER performance of 8-OQPSK is compared with 8-PSK.

Simulation Codes

Offset 8-PSK

M = 8; len = 2048;

x = randi([0 M-1],len, 1); z = de2bi(x);

a = z(:,1)'; b = z(:,2)'; c = z(:,3)';

a1 = []; b1 = []; c1 = []; x1 = [];

for p = 1:len

a1 = [a1 a(p) a(p) a(p)]; b1 = [b1 b(p) b(p) b(p)]; c1 = [c1 c(p) c(p) c(p)];

end

a1 = [a1 0 0]; b1 = [0 b1 0]; c1 = [0 0 c1];

for p = 1:3*len+2

x1 = [221; c1(p) b1(p) a1(p)];

end

d = bi2de(x1); ini_phase = 0;

modmap = zeros(1,8);

modmap(1) = cos(ini_phase + pi/8) + 1i * sin(ini_phase + pi/8);

modmap(2) = cos(ini_phase + 3*pi/8) + 1i * sin(ini_phase + 3*pi/8);

modmap(3) = cos(ini_phase + 7*pi/8) + 1i * sin(ini_phase + 7*pi/8);

modmap(4) = cos(ini_phase + 5*pi/8) + 1i * sin(ini_phase + 5*pi/8);

modmap(5) = cos(ini_phase + 15*pi/8) + 1i * sin(ini_phase + 15*pi/8);

modmap(6) = cos(ini_phase + 13*pi/8) + 1i * sin(ini_phase + 13*pi/8);

modmap(7) = cos(ini_phase + 9*pi/8) + 1i * sin(ini_phase + 9*pi/8);

modmap(8) = cos(ini_phase + 11*pi/8) + 1i * sin(ini_phase + 11*pi/8);

y = genqammod(d,modmap);

hScope = commscope.ScatterPlot;

update(hScope, y)

Variant of Offset 8-PSK

M = 8; len = 1000;

msg = randi([0 M-1],len,1);

z = de2bi(msg);

a = z(:,1)'; b = z(:,2)'; c = z(:,3)';

a1 = []; b1 = []; c1 = []; x1 = [];

for p = 1:len

a1 = [a1 a(p) a(p) a(p)];

b1 = [b1 b(p) b(p) b(p)];

c1 = [c1 c(p) c(p) c(p)];

end

a1 = [a1 0]; b1 = [b1 0]; c1 = [0 c1];

for p = 1:3*len+1

x1 = [221; a1(p) b1(p) c1(p)];

end

d = bi2de(x1); ini_phase = 0;

modmap = zeros(1,8);

modmap(1) = cos(ini_phase + pi/8) + 1i * sin(ini_phase + pi/8);

modmap(2) = cos(ini_phase + 3*pi/8) + 1i * sin(ini_phase + 3*pi/8);

modmap(3) = cos(ini_phase + 7*pi/8) + 1i * sin(ini_phase + 7*pi/8);

modmap(4) = cos(ini_phase + 5*pi/8) + 1i * sin(ini_phase + 5*pi/8);

modmap(5) = cos(ini_phase + 15*pi/8) + 1i * sin(ini_phase + 15*pi/8);

modmap(6) = cos(ini_phase + 13*pi/8) + 1i * sin(ini_phase + 13*pi/8);

modmap(7) = cos(ini_phase + 9*pi/8) + 1i * sin(ini_phase + 9*pi/8);

modmap(8) = cos(ini_phase + 11*pi/8) + 1i * sin(ini_phase + 11*pi/8);

y = genqammod(d,modmap);

hScope = commscope.ScatterPlot;

update(hScope, y);

Comparison of BER Performance of Offset 8-PSK and

Non-offset 8-PSK

clc; clear all; close all;

SamplesPerFrame = 120; maxNumErrs=100; maxNumBits=1e6;

M = 8;

s = RandStream.create('mt19937ar', 'seed',529558);

prevStream = RandStream.setGlobalStream(s);

hInt2Bit1 = comm.IntegerToBit('BitsPerInteger',3,'OutputDataType','uint8');

hBit2Int1 = comm.BitToInteger('BitsPerInteger',3,'OutputDataType','uint8');

hMod = comm.PSKModulator('ModulationOrder',M,'SymbolMapping','gray', ...

'PhaseOffset',0,'BitInput',false);

hDemod = comm.PSKDemodulator('ModulationOrder',M,'SymbolMapping','gray', ...

'PhaseOffset',0,'BitOutput',false,'OutputDataType','uint8', ...

'DecisionMethod','Hard decision');

hChan = comm.AWGNChannel('NoiseMethod','Signal to noise ratio (Eb/No)', ...

'BitsPerSymbol',log2(M),'SignalPower',1);

hphase = comm.PhaseNoise('Level',[-60 -80],'FrequencyOffset',[20 200]);

hSymError = comm.ErrorRate; hBitError = comm.ErrorRate; EbNoVec = 0:2:15;

SERVec1 = zeros(size(EbNoVec)); BERVec1 = zeros(size(EbNoVec));

SERVec2 = zeros(size(EbNoVec)); BERVec2 = zeros(size(EbNoVec));

txbits = randi([0 1], SamplesPerFrame, 1, 'uint8');

for p = 1:length(EbNoVec);

reset(hSymError); reset(hBitError);

hChan.EbNo = EbNoVec(p);

SER = zeros(3,1); BER = zeros(3,1);

while (BER(2)<maxNumErrs) && (BER(3)<maxNumBits)

txSym = step(hBit2Int1, txbits); tx = step(hMod, txSym);

rx2 = step(hChan, tx); rx = step(hphase, rx2);

rxSym = step(hDemod, rx); rxBits = step(hInt2Bit1, rxSym);

SER = step(hSymError, txSym, rxSym); BER = step(hBitError, txbits, rxBits);

end

SERVec1(p) = SER(1); BERVec1(p) = BER(1);

if (BER(1) <= 1e-4)||(SER(1) <= 1e-4) , break , end

end

release(hphase); release(hChan);

release(hMod); release(hDemod); release(hInt2Bit1); release(hBit2Int1);

for q = 1:length(EbNoVec);

reset(hSymError); reset(hBitError); hChan.EbNo = EbNoVec(q);

SER = zeros(3,1); BER = zeros(3,1);

while (BER(2)<maxNumErrs) && (BER(3)<maxNumBits)

b1 = []; b2 = []; b3 = [];

for r = 1:length(txbits)/3

b1 = [b1; txbits(3*r-2);txbits(3*r-2);txbits(3*r-2)];

b2 = [b2; txbits(3*r-1);txbits(3*r-1);txbits(3*r-1)];

b3 = [b3; txbits(3*r);txbits(3*r);txbits(3*r)];

end

b1 = [b1;0;0]; b2 = [0;b2;0]; b3 = [0;0;b3]; tbits = [];

for r = 1 : length(b1)

tbits = [20bits;b1(r);b2(r);b3(r)];

end

txSym2 = step(hBit2Int1, tbits); tx2 = step(hMod, txSym2);

rx3 = step(hChan, tx2); rx4 = step(hphase, rx3);

rxSym2 = step(hDemod, rx4); rxBits2 = step(hInt2Bit1, rxSym2);

SER = step(hSymError, txSym2, rxSym2);BER = step(hBitError, tbits, rxBits2);

end

SERVec2(q) = SER(1); BERVec2(q) = BER(1);

if (BER(1) <= 1e-4)||(SER(1) <= 1e-4) , break , end

end

RandStream.setGlobalStream(prevStream);

semilogy(EbNoVec,SERVec1,EbNoVec,SERVec2); axis([0 15 1e-4 1])

legend ( '8 PSK', 'OPSK','Location','SouthWest');

xlabel ( 'Eb/No (dB)' ); ylabel( 'Error Probability' );

title ( 'Symbol Error Probability' ); grid on;

semilogy(EbNoVec,BERVec1,EbNoVec,BERVec2); axis([0 15 1e-4 1])

legend ( '8 PSK', 'OPSK','Location','SouthWest');

xlabel ( 'Eb/No (dB)' ); ylabel( 'Error Probability' );

title ( 'Bit Error Probability' ); grid on;

Simulation Results

$C:\Users\Simer\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture (29).bmp$

Fig. 5.1 Constellation Diagram of Offset 8-PSK

$C:\Users\Simer\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture (28).bmp$

Fig. 5.2 Constellation Diagram of Variant of Offset 8-PSK

$C:\Users\Simer\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\New Picture (30).bmp$

Fig. 5.3 Comparison of BER performance of Offset 8-PSK and 8-PSK

Conclusion

In this chapter, it is concluded that that offset techniques can be applied to higher order modulation methods such as 8-PSK which is not mentioned in prior art and from Fig. 5.1, it is observed that by applying offset technique to 8-PSK, signal transition does not goes through the origin. Fig. 5.2 shows the alternative form. Moreover, from Fig. 5.3, it is concluded that BER performance of offset M- PSK (M=8) remains same as normal non-offset M-PSK(M=8).

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