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,……

BPSK Vs. MPSK

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.

A possible mapping table for M-PSK coherent demodulation.

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

signal constellation of m-ary PSK modulation

How to get Probability of Error For M-PSK?

probability of error for M-PSK modulation technique calculated by:

𝑃𝑒𝑟𝑟𝑜𝑟 = 2𝑄(𝑑𝑚𝑖𝑛2

)

(𝑁𝑜2)

From the previous signal constellation we noticed that:

So the probability of error will given by:

Performance of Error For Mpsk

The performance of symbol error probability for different values of M

Detection of MPSK

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.

• 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

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