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Lec 18

This lecture discusses Quadrature Phase Shift Keying (QPSK), a digital modulation scheme characterized by four possible waveforms, each differing by a phase shift of π/2. The waveforms can be represented using a phasor diagram and a 2-dimensional constellation diagram. Future lectures will cover matched filter design for QPSK and its Bit Error Rate (BER).

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9 views8 pages

Lec 18

This lecture discusses Quadrature Phase Shift Keying (QPSK), a digital modulation scheme characterized by four possible waveforms, each differing by a phase shift of π/2. The waveforms can be represented using a phasor diagram and a 2-dimensional constellation diagram. Future lectures will cover matched filter design for QPSK and its Bit Error Rate (BER).

Uploaded by

debjani goswami
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Principles of Communication Systems – Part II

Prof. Aditya K. Jagannatham


Department of Electrical Engineering
Indian Institute of Technology, Kanpur

Lecture - 18
Waveforms of Quadrature Phase Shift Keying (QPSK)

Hello. Welcome to another module in this massive open online course. So, we are looking
at a different digital modulation scheme that is Quadrature Phase Shift Keying.

(Refer Slide Time: 00:33)

In QPSK the signal is given by,

𝑥(𝑡) = 𝑎1 𝑝1 (𝑡) + 𝑎2 𝑝2 (𝑡)

Where 𝑎1 and 𝑎2 can both be ±𝐴.


(Refer Slide Time: 00:56)

Hence, there will be four possible waveforms,

𝐴𝑝1 (𝑡) + 𝐴𝑝2 (𝑡)


𝐴𝑝1 (𝑡) − 𝐴𝑝2 (𝑡)
𝑥(𝑡) =
−𝐴𝑝1 (𝑡) + 𝐴𝑝2 (𝑡)
{−𝐴𝑝1 (𝑡) − 𝐴𝑝2 (𝑡)

(Refer Slide Time: 01:52)

Consider the first waveform,


2 2
𝑥(𝑡) = 𝐴√ cos(2𝜋𝑓𝑐 𝑡) + 𝐴√ sin(2𝜋𝑓𝑐 𝑡)
𝑇 𝑇

2 1 1
=𝐴 { cos(2𝜋𝑓𝑐 𝑡) + sin⁡(2𝜋𝑓𝑐 𝑡)}
√𝑇 √2 √2

(Refer Slide Time: 02:56)

(Refer Slide Time: 03:29)

2𝐴 𝜋
= cos (2𝜋𝑓𝑐 𝑡 − )
√𝑇 4
(Refer Slide Time: 04:40)

Similarly the second waveform (𝐴𝑝1 (𝑡) − 𝐴𝑝2 (2)) we can write,

2𝐴 𝜋
= cos (2𝜋𝑓𝑐 𝑡 + )
√𝑇 4

(Refer Slide Time: 05:37)

The third waveform (−𝐴𝑝1 (𝑡) + 𝐴𝑝2 (𝑡)) can be written as,

2𝐴 3𝜋
= cos (2𝜋𝑓𝑐 𝑡 + )
√𝑇 4
And the fourth, (−𝐴𝑝1 (𝑡) − 𝐴𝑝2 (𝑡)),

2𝐴 3𝜋
= cos (2𝜋𝑓𝑐 𝑡 + )
√𝑇 4

(Refer Slide Time: 07:40)

Hence overall we can write,

2𝐴 𝜋
cos (2𝜋𝑓𝑐 𝑡 − )⁡
√𝑇 4
2𝐴 𝜋
cos (2𝜋𝑓𝑐 𝑡 + )
4
𝑥(𝑡) = √𝑇
2𝐴 3𝜋
cos (2𝜋𝑓𝑐 𝑡 + )
√𝑇 4
2𝐴 5𝜋
cos (2𝜋𝑓𝑐 𝑡 + )
{√𝑇 4
(Refer Slide Time: 08:53)

Note here that each consecutive waveform is shifted from the other by a phase difference
of 𝜋/2. Also the last waveform is shifted form the first with a phase shift of, 𝜋/2.⁡ Each
waveform is shifted form it’s neighbouring by a phase of 𝜋/2 or 90𝑜 or a quadrature. This
is the reason why, this scheme is known as Quadrature phase shift keying.

(Refer Slide Time: 12:06)


(Refer Slide Time: 13:01)

(Refer Slide Time: 14:19)

These different waveforms can be represented using a phasor diagram. The four signals
can be represented on a circle of radius 2𝐴/√𝑇 (see figure above.). Each is shifted from
its consecutive by a phase of 𝜋/2. The points at an angle of (from the positive x-axis),
𝜋/4, 3𝜋/4, 5𝜋/4 (-3𝜋/4) and 7𝜋/4 (−𝜋/4).

We can represent these waveforms using a 2-dimensional constellation diagram.


(Refer Slide Time: 16:35)

The four points will be, (A,A), (-A,A), (-A,-A) and (A,-A).

(Refer Slide Time: 18:47)

In the subsequent week, we will look into matched filter design for QPSK and its BER

Thank you very much.

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