M-ary phase shift keying (M-PSK) is a modulation technique where data bits select one of m phase-shifted carriers, resulting in m equally spaced signal points on a circle. The document discusses the error probability for M-PSK, emphasizing power and bandwidth efficiencies as critical factors for performance evaluation. It also highlights trade-offs in choosing digital modulation schemes, such as the impact of error control coding and the requirements for higher transmission power in M-ary schemes.

1. M-ary PSK Modulation
What is the M-ary PSK Modulation?
M-ary Phase Shift Keying - or MPSK - is a modulation where data bits select one of M phase
shifted versions of the carrier to transmit the data. Thus, the M possible waveforms all have the
same amplitude and frequency but different phases. The signal constellations consist of M
equally spaced points on a circle.
Note: M = 2n where n is integr No. 1,2,3,……

2. BPSK Vs. MPSK

3. An M-ary phase-shift keying (M-PSK) signal can be defined by:
for i = 0, 1, ..., M - 1. Here, A is a constant, fc is the carrier frequency, q' is the
initial phase angle, and T is the symbol duration.
So By sub. In s(t) Equation we get:
The signal has a power P = 𝐴2/2, so that A = √2P . Thus equation can be
written as:
where E = PT is the energy of s(t) contained in a symbol
duration for i = 0, 1, ...,
M - 1. For convenience, the arbitrary phase angle q' is taken
to be zero.

4. A possible mapping table for M-PSK coherent demodulation.

5. If we take:
as the orthonormal basis functions, the applicable signal constellation diagrams of the M-PSK and 4-PSK signals are shown
in Figure. All signal points lie on a circle of radius
signal constellation of m-ary PSK modulation

6. signal constellation of m-ary PSK modulation

7. How to get Probability of Error For M-PSK?
probability of error for M-PSK modulation technique calculated by:
𝑃𝑒𝑟𝑟𝑜𝑟 = 2𝑄
(
𝑑 𝑚𝑖𝑛
2
)
(
𝑁𝑜
2
)
From the previous signal constellation we noticed that:
So the probability of error will given by:

8. Performance of Error For Mpsk
The performance of symbol error probability for different values of M

9. Detection of MPSK

10. Conclusion
• The performance of a modulation scheme is often measured in terms of its power and
bandwidth efficiencies.
• Power efficiency:
– Problem: in order to increase noise immunity, it is necessary to increase the signal power.
The amount by which the signal power should be increased to maintain a certain BER
depends on the modulation scheme.
– Power efficiency describes the ability to preserve the fidelity of a digital message at low
power levels.
– The power efficiency expresses the "signal energy over the noise energy" ratio (Eb/No)
required at the receiver to guaranty a
certain BER.

11. • Bandwidth efficiency:
– Problem: increasing the data rate implies decreasing the pulse width of the digital symbol,
which increases the bandwidth of the signal.
– Bandwidth efficiency describes how efficiently the allocated bandwidth is used
– Defined as the ratio of the throughput data rate per Hertz (bps/
Hz)
– Fundamental upper bound:
C/B = log2(1+S/N)
where C is the channel capacity (bps), B the bandwidth (Hz) and S/N the signal-to-noise ratio.
Conclusion

12. Conclusion
• There are some Factors that influence the choice of Digital Modulation:
• Very often there is a trade-off:
– adding error control coding reduces the bandwidth efficiency (redundancy is transmitted
too) but increases the power efficiency (there remain fewer errors).
– M-ary schemes increase the bandwidth efficiency but require higher transmission power
to keep the same BER
- Other factors are important
– cost and the complexity of the receiver
– for wireless networks, the robustness under various types of channel impairments such as
Rayleigh fading and multipath dispersion is important