Performance Analysis Of Different Digital Modulation Scheme

ASSIGNMENT

Performance Analysis Of Different Digital Modulation Scheme

Digital modulation techniques

ASK (Amplitude Shift Keying)Baseband

Data

ASK modulated

signal

1 10 0

Acos(t) Acos(t)

0,0

1),2cos()(

binary

binarytfAts c

Signal Space Representation for ASK

• Clearly, there is one basis function of unit energy

• Then,• Average energy per bit

• A binary ASK system is therefore characterized by having a signal space that is one-dimensional

Probability of Error for ASK

• Dependence of the error probability on the distance between two signal points. In general, is

• Thus, for ask Probability of Error is:

… Ref (1)

Concept of a constellation diagram

• A constellation diagram helps us to define the amplitude and phase of a signal when we are using two carriers…

Constellation Diagram of ASK

0,0

1),2cos()(

binary

binarytfAts c

Use of ASK

• The simplest and most common form of ASK operates as a switch. (OOK)

• Very high speeds over optical fiber.• Frequency Spectrum of ASK,

• Here, we can choose our fc so that the modulated signal

occupies available bandwidth.

Frequency Shift Keying (FSK)

Signal Space for FSK

• Unlike ASK, here two orthogonal basis functions are required to represent s1 (t) and s2 (t).

• Signal space representation,

Decision Regions of FSK • Signal space diagram for binary FSK

• The receiver decides in favor of s1 (t) if the received signal point represented by the observation vector r falls inside region R1. This occurs when r1 > r2

• When r1 < r2 , r falls inside region R2 and the receiver decides in favor of s2 (t).

Probability of Error for FSK

… Ref (1)Dependence of the error probability on the distance between two signal points. In general, is

Thus,

Identical to that of ASK

Binary Phase-Shift Keying (BPSK)• Modulation

0 ≤ t ≤ Tb , where Tb is bit duration

• Eb transmitted signal energy per bit, i.e.

• The pair of signals differ only in a relative phase shift of 180

degrees

Signal Space Representation for BPSK

• Clearly, there is one basis function of unit energy

• Then,

• A binary PSK system is therefore characterized by having a signal space that is in one-dimension.

Decision Rule of BPSK• Then the optimum decision boundary is the midpoint of the line

joining these two message points

Decision rule: • Guess signal s1 (t) (or binary 1) was transmitted if the received

signal point r falls in region R1 (r > 0)

• Guess signal s2 (t) (or binary 0) was transmitted otherwise (r ≤ 0)

• Since the signals s1(t) and s2(t) are equally likely to be transmitted, the average probability of error is

• Dependence of the error probability on the distance between two signal points. In general, is

Probability of Error for BPSK

Constellation Diagram and Advantages of PSK

• Noise can change the amplitude easier than it can change the phase. In other words, PSK is less susceptible to noise than ASK.

• PSK is superior to FSK because we do not need two carrier signals.

Probability of Error and the Distance Between Signals

… Ref (1)

Quadrature Phase Shift Keying (QPSK)

• In QPSK, we parallelize the bit stream so that every

two incoming bits are split up and PSK a carrier

frequency.

• One carrier frequency is phase shifted 90 from the

other - in quadrature.

• The two PSK signals are then added to produce one

of 4 signal elements.

Quadrature Phase Shift Keying (QPSK):• Also a type of linear modulation scheme

• The phase of the carrier takes on 1 of 4 equally spaced values, such as 0, /2, , and 3/2 where each value of phase corresponds to a unique pair of message bits.

• The QPSK signal for this set of symbol states may be defined as:

( ) cos(2 ( ))c cs t A f t t

Where, ϕ(t)= 0, 90, 180, 270

( ) cos ( ).cos(2 ) sin ( )sin(2 )c c c cS t A t f t A t f t

…(1)

Simplifying Equation 1

This Gives the Idea about Transmitter design

QPSK Waveform and Transmitter design

QPSK Constellation Diagram

• Quadrature Phase Shift Keying has twice the bandwidth efficiency of BPSK since 2 bits are transmitted in a single modulation symbol.

Carrier phases {0, /2, , 3/2}

Q

I

00011011

References:1) Meixia Tao, “Principles of Communications”, Shanghai Jiao

Tong University, Chapter 8: Digital Modulation Techniques , Textbook: Ch 8.4 – 8.5, Ch 10.1-10.5

http://iwct.sjtu.edu.cn/Personal/mxtao/course_comm/comm_ch08_digmod_en.pdf

2) BehrouzA. Forouzan , “Data Communications and Networking”, 4rdEdition, Chapter4, 2007

Thanks…

A special thanks to sir for guiding us…..