Real and Complex Modulation

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1 Real and Complex Modulation TIPL 4708 Presented by Matt Guibord Prepared by Matt Guibord 1

2 What is modulation? Modulation is the act of changing a carrier signal s properties (amplitude, phase, frequency) in a controlled way in order to transmit data across a channel or to obtain desired signal properties 2

3 Types of Digital Modulation Pulse Amplitude Modulation (PAM) Phase Shift Keying (PSK) Quadrature Amplitude Modulation (QAM) Frequency Modulation (FM) 3

4 Phase and Amplitude Modulation A phase and amplitude modulated carrier signal can be represented as: cos 2 Where: is the amplitude modulation function is the phase modulation function is the carrier frequency Which can be decomposed using the angle sum trigonometric identity into: cos cos 2 sin sin 2 cos 2 sin 2 Where: is the in phase modulation function is the quadrature phase modulation function This is a bandpass signal since the I and Q functions Often are modulating called I and a carrier Q 4

5 Analytical Equivalent and Baseband Equivalent The bandpass signal can be decomposed into a lowpass modulation function multiplied by a complex exponential (carrier) by using Euler s formula and defining a new baseband equivalent modulation function, X bb (t): Baseband equivalent Recall Euler s formula: cos sin Then: cos 2 sin 2 Analytic equivalent 0 Hz (DC) Baseband or Lowpass f C RF or Bandpass 5

6 Real Modulation Example (Real Mixing) As an example of real modulation, consider the case of mixing a low frequency sine wave to a higher frequency, such that X bb (t) is simply a cosine wave: The resulting modulated signal is: cos From Euler s Desired signal cos cos 2 Undesired Image signal 6

7 Complex Modulation Example (Complex Mixing) Define X bb (t) to be a complex exponential at the same frequency as the cosine in the previous example: cos [ 2 ] sin [ 2 ] The resulting modulated signal is: X I (t) X Q (t) cos 2 sin 2 From Euler s cos 2 Desired signal only 7

Real vs Complex Example Visualized Real signals have equivalent (mirrored) positive and negative frequency spectrums: Lower sideband Upper sideband Complex signals have independent positive and

8 Real vs Complex Example Visualized Real signals have equivalent (mirrored) positive and negative frequency spectrums: Lower sideband Upper sideband Complex signals have independent positive and negative frequency spectrums: Lower sideband Upper sideband -f IF f IF f IF 0 Hz (DC) Baseband or Low pass f C RF or Band pass 0 Hz (DC) Baseband or Low pass f C RF or Band pass This type of transmission is called double sideband (DSB) transmission since the same information is transmitted in both sidebands This type of transmission is called single sideband (SSB) transmission since each sideband can transmit unique information 8

9 Applications of Complex Modulation Image reject mixing uses the concept of complex modulation, exactly as shown in the complex modulation example, to reject the image signal in order to relax filtering requirements Image Real Reject Mixing Mixing Relaxed Image Image Reject Reject Filter Filter 0 Hz (DC) Baseband or Low pass f C RF or Band pass Digital communications uses complex modulation to double the data rate for a given signal bandwidth, ultimately using sine and cosine as an orthogonal basis in order to transmit independently on the in-phase and quadrature-phase signals cos 2 sin 2 Transmit independent information on both I and Q 9

10 Digital Communications and Constellation Plots Constellation plots are used to visualize the complex baseband modulation function, X bb (t), by mapping the complex values onto the complex plane Amplitude of the carrier is the distance from the origin: Phase of the carrier is the angle measured relative to the positive I axis: X Q (t) Quadrature-Phase Component (Q) a(t) 16-QAM Constellation Plot θ(t) tan Symbols In-Phase Component (I) X I (t) Example bit mapping 10

11 Find Transmitted Signal from Constellation Plot We want to transmit 0011 across the channel using the 16-QAM plot on the previous slide To send 0011, choose I = 1, Q = -3: 1 3 Carrier amplitude: Carrier phase: tan Resulting signal, X(t): 3 tan 1 10 cos cos 2 3sin X Q (t) Quadrature-Phase Component (Q) Easier to implement in digital hardware 16-QAM Constellation Plot In-Phase Component (I) a(t) θ(t) X I (t) 11

12 Example Constellation Plots QPSK Constellation Plot 8-PSK Constellation Plot 32-QAM Constellation Plot 1024-QAM Constellation Plot Quadrature-Phase Component (Q) Quadrature-Phase Component (Q) Quadrature-Phase Component (Q) Quadrature-Phase Component (Q) In-Phase Component (I) In-Phase Component (I) In-Phase Component (I) In-Phase Component (I) More challenging noise and distortion requirements Lower data rate (fewer bits per symbol) 12

13 Thanks for your time! 13

14 Copyright 2017 Texas Instruments Incorporated. All rights reserved. This material is provided strictly as-is, for informational purposes only, and without any warranty. Use of this material is subject to TI s, viewable at TI.com

Outline. EECS 3213 Fall Sebastian Magierowski York University. Review Passband Modulation. Constellations ASK, FSK, PSK.

Outline. EECS 3213 Fall Sebastian Magierowski York University. Review Passband Modulation. Constellations ASK, FSK, PSK. EECS 3213 Fall 2014 L12: Modulation Sebastian Magierowski York University 1 Outline Review Passband Modulation ASK, FSK, PSK Constellations 2 1 Underlying Idea Attempting to send a sequence of digits through