5. Introduction
What is M- Ary Modulation?
In a M array modulation two or more bits are grouped together to form a symbol and an
assigned signal is transmitted during the symbol period Ts by changing one of the parameter
of the carrier (Amplitude, Frequency or Phase).
Number of possible symbols given by M= 2𝑁
.
Then the symbol period is given by 𝑇𝑠 = 𝑁𝑇𝑏.
If phase of the carrier is modulated it is known as MPSK.
𝜙𝑚 = 2𝑚 + 1
𝜋
𝑀
where m=0, 1, 2, ……., M-1
If frequency is modulated it is known as MFSK.
𝑓 = (𝑘 + 2𝑚)𝑓0 where m=0, 1, 2, ……., M-1
Modulation of amplitude as well as phase is know as MQAPSK.
6. 6
M-ary signaling scheme:
• In this signaling scheme 2 or more bits are grouped
together to form a symbol.
• One of the M possible signals
s1(t) ,s2(t),s3(t),……sM(t)
is transmitted during each symbol period
of duration Ts.
• The number of possible signals = M = 2n,
where n is an integer.
7. 7
n M = 2n Symbol
1 2 0, 1
2 4 00, 01, 10, 11
3 8 000, 001, 010,011,...
4 16 0000, 0001, 0010,0011,….
…. …… ……….
The symbol values of M for a given value of n:
8. 8
In M-ary PSK, the carrier phase takes on one of the M
possible values, namely i = 2 * (i - 1) / M
where i = 1, 2, 3, …..M.
The modulated waveform can be expressed as
where Es is energy per symbol = (log2 M) Eb
Ts is symbol period = (log2 M) Tb.
9. 9
The above equation in the Quadrature form is
By choosing orthogonal basis signals
defined over the interval 0 t Ts
10. 1
0
M-ary signal set can be expressed as
Since there are only two basis signals, the constellation of
M-ary PSK is two dimensional.
The M-ary message points are equally spaced on a circle
of radius Es, centered at the origin.
The constellation diagram of an 8-ary PSK signal set is
shown in fig.
13. 1
3
Noise Immunity:
Increasing M implies that the constellation is more densely
packed, and hence the distance between the two points
reduces, which leads to poor noise immunity.
Bandwidth Efficiency:
The first null bandwidth of M-ary PSK signals decrease as
M increases while Rb is held constant.
Therefore, as the value of M increases, the bandwidth
efficiency also increases.
14. 1
4
In M-ary FSK modulation the transmitted signals are
defined by:
where fc = nc/2Ts, for some fixed integer n.
The M transmitted signals are of equal energy and
equal duration, and the signal frequencies are
separated by 1/2Ts Hertz, making the signals
orthogonal to one another.
15. 1
5
The channel bandwidth of a noncohorent MFSK is :
This implies that the bandwidth efficiency of an M-ary
FSK signal decreases with increasing M. Therefore, unlike
M-PSK signals, M-FSK signals are bandwidth inefficient.
However, Noise Immunity of M-FSK is better as
compared to both M-PSK and M-QAPSK
16. 1
6
It’s a Hybrid modulation
As we allow the amplitude to also vary with the phase, a
new modulation scheme called quadrature amplitude
modulation (QAM) is obtained.
The constellation diagram of 16-ary QAM consists of a
square lattice of signal points.
17. Change both amplitude and phase
s(t)=Acos(2πfct+𝜙)
64-QAM: 64 constellation points, each with 8 bits
I
Q
‘1000’
‘1100’
‘0100’
‘0000’
‘1001’
‘1101’
‘0101’
‘0001’
‘1011’
‘1111’
‘0111’
‘0011’
‘1010’
‘1110’
‘0110’
‘0010’
Bits Symbols
‘1000’ s1=3a+3ai
’1001’ s2=3a+ai
‘1100’ s3=a+3ai
‘1101’ s4=a+ai
a 3a
16-QAM
18. 1
8
Noise Immunity and Bandwidth :
Noise Immunity of M-QAM is superior to M-ary
PSK.
Bandwidth efficiency of M-QAM is identical to
M-ary PSK.
19. Comparison of 𝒅𝒎𝒊𝒏.
1. 𝑑𝑚𝑖𝑛 decreases in case of MPSK and MQAPSK with increase of M. Hence,
Noise Immunity also decreases.
2. Decrease in 𝑑𝑚𝑖𝑛 is more rapid in MPSK as compared to that of MQAPSK.
3. 𝑑𝑚𝑖𝑛 in MFSK increases with increase in M and hence the
Noise Immunity for M-ary FSK increases as M increases.
4. MFSK is most immune to noise or symbol probability error.
Theory Details
Table.1
20. Comparison of Spectral Efficiency of Modulation Schemes
M-PSK and QAPSK
image shows the average particle size of ~ 180 nm.
M-FSK
Theory Details
From the above table we notice that in M ary PSK as the values of M increases the
spectral efficiency also increases, a similar data is there in M ary QAPSK. In M ary FSK
spectral efficiency is constant for M=2 and M=4 and after that it decreases continuously.
Table.2
hs =
Data rate
BW
=
1
2
log2 M bits/sec/Hz
[ ]
hs =
Data rate
BW
=
2log2 M
M
bits/sec/Hz
[ ]
24. Implementation Complexity and Cost
While assuming the complexity and cost same for transmitter of the three schemes we
compared them only based on receiver complexity and cost.
M Ary PSK In this scheme we require N square law device, 2 multiplier, 1 bandpass filter, 2
integrator, 1 analog to digital converter and 1 parallel to serial converter.
M Ary FSK In this scheme for receiver we require M bandpass filter, M envelop detector, 1
decision device, 1 N bit analog to digital converter and 1 parallel to serial converter.
M Ary QAPSK In this scheme we require 2 square law device, 2 multiplier, 1 bandpass filter, 2
integrator, 2 analog to digital converter and 1 parallel to serial converter.
MODEL PRICES FOR COMPONENTS
MUX/ Switch = Rs 10
Integrator= Rs 20
Multiplier= Rs 200
Bandpass filter= Rs 15
25. Decision device= Rs 20
Analog to digital converter= Rs 10
Parallel to Serial converter = Rs 5× 𝑁 (where N is the no. of bits per symbol)
Envelop detector= Rs 15
Table.3
Implementation Complexity and Cost
Thus, from above table we see that complexity of M-Ary PSK and FSK increases with increase
in value of M whereas for QAPSK it remains same. Among PSK and FSK the latter shows rapid
increase in complexity and hence becomes costly as M increase. Therefore, in terms of
implementation QASK is best in terms of less complexity and cost.
M
Ary
No. of Components Price (Rs)
M=4 M=
8
M=1
6
M=3
2
M=6
4
M=4 M=
8
M=1
6
M=3
2
M=6
4
PSK 9 10 11 12 13 475 680 885 109
0
129
5
FSK 11 19 35 67 131 170 290 520 100
0
196
0
QAPS
K
10 10 10 10 10 885 890 895 900 905
26. SUMMARY
Table.4
S.NO
.
Parameter MPSK MFSK QAPSK
1 Modulation Phase Frequency Quadrature
amplitude and
Phase
2 Location of
Signal Points
On circle On M signal axis Signal points are
placed
symmetrically
about origin
3 Distance
between signal
points
4𝐸𝑆 sin(
𝜋
𝑀
) 2𝑁𝐸𝑏
6𝐸𝑏𝑁
𝑀 − 1
4 Error
probability
Highest Least Less than MPSK
but more than
MFSK for high
value of M
5 Noise immunity least Highest Better than MPSK
6 Bandwidth
required
Same as QAPSK Highest among
three
Same as MPSK
7 Complexity Shows increase
but less rapid
than MFSK
Increases with M Remains almost
same
8 Cost Increases with
M but less
rapid than
MFSK
Increases with M Least for high
value of M
27. References
Principle of Communication Systems by Taub and Schilling.
Channel Capacity Calculations For M–ary N-dimensional Signal sets
Philip Edward McIllree, B.Eng.
Communication Systems by S. Haykin.
Modern Digital and Analog Communication Systems by B.P Lathi.
