Real and Complex Modulation TIPL 4708 Presented by Matt Guibord Prepared by Matt Guibord 1 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 Types of Digital Modulation Pulse Amplitude Modulation (PAM) Phase Shift Keying (PSK) Quadrature Amplitude Modulation (QAM) Frequency Modulation (FM) 3 Phase and Amplitude Modulation • A phase and amplitude modulated carrier signal can be represented as: cos2 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 cos2sin sin2 This is a “bandpass” signal cos 2 sin 2 Where: since the I and Q functions Oftenare modulating called “I” and a carrier “Q” is the “in‐phase” modulation function is the “quadrature‐phase” modulation function 4 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, Xbb(t): Recall Euler’s formula: Baseband equivalent cossin Then: Analytic equivalent cos 2 sin 2 0 Hz (DC) fC “Baseband” or “Lowpass” “RF” or “Bandpass” 5 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 Xbb(t) is simply a cosine wave: From Euler’s cos2 2 • The resulting modulated signal is: 2 1 1 2 2 1 1 Desired signal 2 2 Undesired 1 1 cos 2 cos 2 Image signal 2 2 6 Complex Modulation Example (Complex Mixing) • Define Xbb(t) to be a complex exponential at the same frequency as the cosine in the previous example: cos[ 2 sin ] [ 2 ] XI(t) XQ(t) • The resulting modulated signal is: From Euler’s cos 2 sin2 cos2 Desired signal only 7 Real vs Complex Example Visualized Real signals have equivalent (mirrored) Complex signals have independent positive and positive and negative frequency spectrums: negative frequency spectrums: Lower Upper Lower Upper sideband sideband sideband sideband -fIF fIF fIF 0 Hz (DC) fC 0 Hz (DC) fC “Baseband” or “Low pass” “RF” or “Band pass” “Baseband” or “Low pass” “RF” or “Band pass” This type of transmission is called “double This type of transmission is called “single sideband” (DSB) transmission since the same sideband” (SSB) transmission since each information is transmitted in both sidebands sideband can transmit unique information 8 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 ImageReal Reject Mixing Mixing Relaxed Image ImageReject Reject Filter Filter 0 Hz (DC) fC “Baseband” or “Low pass” “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 Digital Communications and Constellation Plots • Constellation plots are used to visualize the complex baseband modulation function, Xbb(t), by mapping the complex values onto the complex plane • Amplitude of the carrier is the distance 16-QAM Constellation Plot from the origin: θ(t) XQ(t) a(t) 0111 1111 • Phase of the carrier is the angle measured Quadrature-Phase Component (Q) Component Quadrature-Phase relative to the positive I axis: 0011 1011 In-Phase Component (I) XI(t) tan Symbols Example bit mapping 10 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: 16-QAM Constellation Plot 13 X (t) 1 • Carrier amplitude: Q 2 1 3 10 3 -3 -2 -1 1 2 3 • Carrier phase: 0111 1111 -1 3 a(t) θ(t) tan tan 71.6° 1.25 -2 Quadrature-Phase Component (Q) Component Quadrature-Phase 1 0011 1011 -3 • Resulting signal, X(t): In-Phase Component (I) XI(t) 10 cos 2 1.25 Easier to implement in cos23sin2 digital hardware 11 Example Constellation Plots QPSK Constellation Plot 8-PSK Constellation Plot 32-QAM Constellation Plot 1024-QAM Constellation Plot Quadrature-Phase Component (Q) Component Quadrature-Phase Quadrature-Phase Component (Q) Component Quadrature-Phase Quadrature-Phase Component (Q) Component Quadrature-Phase Quadrature-Phase Component (Q) Component Quadrature-Phase 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 Thanks for your time! 13 © Copyright 2017 Texas Instruments Incorporated. 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