Simulation of Base-band System in AWGN Channel using MATLAB

- Gaurav Kulkarni

BPSK systemSimplest form of Phase shift keying.Uses 2 signal which are 180 degree out of

phaseBPSK signal can be defined as

Where b(t)=+1 or -1, fc is the carrier frequency, t is the bit duration

• Theoretical Bit Error Rate(BER) Formula for BPSK is Pb= Q(√(2Eb/N0)) = 0.5*erfc(√(Eb/N0))

Where Eb= bit energy N0/2= double sides noise spectrum density

mapDetect

or

DelayCompar

e

Input data

Output data

BER

SIMULATION MODEL

AWGN NOISE

BER of BPSK system

We can observe that at BER= 10^-5 , Eb/N0= 9.6 dB

ISI effect using eye-diagram

Eb/N0= 5dB

Eb/N0= 10dB

Eb/N0= 20dB

QPSK SYSTEM• QPSK are often used for their Bandwidth efficiency and data rate as compared to BPSK• Each symbol determines the shift of carrier wave

Symbol Phase shift (in degrees )

00 0

01 90

10 180

11 360

Simulation model of QPSK

Map Detector

DelayCompar

e

Input

AWGN NOISE

AWGN NOISE

BER

BER of QPSK

We can observe that at BER= 10^-5 , Eb/N0= 9.6 dB, same as BPSK

Effect of noise on constellation diagram

No noise

Eb/N0= 5dB

Eb/N0= 20 dB

BPSK with SQRC filter• SQRC filter is usually used as a pulse shaping filter• SQRC filter is often implemented as FIR filter• Impulse response of SQRC filter is

Where β= roll off factor , 0 <β<1

Simulation model of BPSK-SQRC system

map X 4SQRCFilter

MatchFilter 4 Detect

or

DelayCompar

eBER

AWGN NoiseInp

ut

BER of BPSK-SQRC system

At NC= 25, BER=10^-5, Eb/N0= 9.8 dBAt NC= 33, BER=10^-5, Eb/N0= 9.55 dBAt NC= 41, BER=10^-5, Eb/N0= 9.5 dB

Thank you