Telecommunications Engineering Topic 2: Modulation and FDMA

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Telecommunications EngineeringTopic 2
Modulation and FDMA

• James K Beard, Ph.D.
• [phone]
• jkbeard_at_temple.edu
• http//astro.temple.edu/jkbeard/

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Topics

• Homework
• Amplitude Modulation
• BPSK
• QPSK
• Summary
• Assignment
• References

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Modulation

• Text section 3.2
• Defined as encoding data onto a carrier
• Transmitter signal
• Single frequency, or carrier, without modulation
• Spectrum about carrier frequency with modulation

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Modulation Issues

• Spectrum
• Bandwidth of transmitted spectrum and bit rate
  are related
• Efficiency is a function of the modulation
• Multiple access
• Enables more than one user per channel
• Modulation concept is integrated with multiple
  access concept

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Linear and Nonlinear Modulation

• Linear
• Sum of two modulated transmitters is same as
  modulation from sum of signals
• Multiplying input by a constant results in the
  output of the modulator scaled by that constant
• Nonlinear when either condition does not hold

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Analog and Digital Modulation

• Analog modulation
• Signal is time-continuous
• Transmitted spectrum is, in general, a continuous
  spectrum
• Digital modulation
• Signal is discontinuous bit stream
• Transmitted spectrum falls off as 1/f or 1/f2

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Amplitude and Angle Modulation

• Amplitude modulation
• The transmit signal is the carrier multiplied by
  a linear function of the signal
• The phase of the transmitted signal is constant
• Angle modulation
• The phase or frequency of the carrier is varied
  in the modulation process
• The amplitude of the transmitted signal is
  constant

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Amplitude Modulation

• Text Section 3.3.1
• Definition
• Transmitted signal is product of
• Carrier signal unmodulated transmitter signal
• Data signal plus offset
• Offset is to make signal factor nonnegative
• Transmitted signal components
• Carrier from offset
• Sum and difference signals from data

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BPSK

• Text section 3.3.2
• BPSK Binary Phase-Shift Keying
• Modulation is phase inversions
• Spectrum is splattered quite a bit
• Spectral lines separated by bit rate frequency
• Shape of spectral lines follows sinc function
• The sinc function spectrum
• Parameterized for pi/2 increments
• Result is 1/f envelope on lines

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QPSK

• Text section 3.3.3
• QPSK Quadraphase-Shift Keying
• Similar to BPSK except four phases instead of two
• Variation Offset QPSK, or OQPSK
• Phase transitions confined to pi/4
• Elimination of pi/2 phase shifts improves
  spectrum
• Offset is related to mapping of code to waveform
• Chip rate doubles to implement code-waveform
  mapping

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Spectral Efficiency

• Spectral efficiency means
• High percentage of signal spectrum in band
• Better pulse shape reproduction in receivers
• More accurate decoding at a given SNR
• Less crosstalk and cross-interference
• Higher spectral efficiency
• The first goal of the waveform designer
• Gains in efficiency with little added complexity

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Improved Spectral Efficiency

• Baseline is square pulse
• Sinc function spectrum
• Rolloff is 1/f
• First cut is raised cosine
• Square spectrum with cosine transition
• Pulse is inverse Fourier transform
• Root raised cosine
• Square root of raised cosine in transmitter and
  receiver
• Transmitted pulse is inverse Fourier transform of
  square root of spectrum

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Raised-Cosine Spectra
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Raised-Cosine Pulses
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Root Raised-Cosine Spectra
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Root Raised-Cosine Pulses
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RRC for (0,1,1,0,0)
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Topics

• Continuous-phase modulation minimum shift
  keying (MSK)
• Power spectra of MSK signal
• Gaussian-filtered MSK
• Frequency division multiple access (FDMA)

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Continuous-Phase Modulation

• Also called Minimum Shift Keying
• FSK with phase continuity between pulses
• Allows rolloff of 1/f4 as opposed to 1/f
• Define the difference in the number of cycles
  between the two frequencies over a pulse time as
  the deviation ratio h

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Special Values of h

• When h is pi
• Phase is the same at the end of each pulse
• Starting phase is the same every time
• When h is pi/2
• Minimum for good spectral efficiency
• Starting phase can walk pi/2 per pulse
• Back to same phase every two pulses

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Power Spectra of MSK Signal

• Fourier transform of signal shows 1/f4 rolloff

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Gaussian-Filtered MSK

• Gaussian shape
• Represents a parabola on a dB plot
• Good first-order fit to many single-lobe curves
• Simple filters
• Main lobe of beam pattern
• Simple to work with
• Produces pulse as it would be transmitted
• Some spreading in time
• Good performance

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Frequency Division Multiple Access

• FDMA
• Closely-spaced frequency channels in transmission
  band
• Cross-channel modulation controlled
• Waveform design
• Guard band

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Summary

• Modulation
• Puts signal data on a carrier for transmission
• Linear or nonlinear
• Amplitude or angle
• Spectral efficiency
• Simple RC and RRC show first cut
• Gains are apparent using first principles
• MPSK provides good channel efficiency
• FDMA provides good multiplexing alternative

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Assignment

• Read Text 3.4.1, 3.7.3-3.7.5, 3.8
• Read Bit Error Rate (BER), section 3.12

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Bit Error Rates

• Examined here for simple receivers
• BPSK, QPSK, MSK, etc.
• No pulse shaping filters
• Purpose is to show
• Differences between fundamental modulation types
• The effect of the channel

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High SNR Bit Error Rate
General equations in Table 3.4 p. 159
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AWGN Bit Error Rates
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High SNR AWGN Bit Error Rates
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Rayleigh Fading Bit Error Rates
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BER Conclusions

• AWGN BER
• BPSK/QPSK/MSK provide best performance
• Others are close enough to be useful
• Select best spectral control for best achievable
  BER
• Fading
• Low SNR area of fading pdf drives BER
• Significant variable fading forces high BER
• Houston, we have a problem

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Study Problems and Reading Assignments

• Study examples and problems
• Problem 3.30, p. 177, Adjacent channel
  interference
• Problem 3.35 p. 178, look at part (a) part (b)
  was done in class
• Problem 3.36 p. 178, an intermediate difficulty
  problem in bit error rate using MSK
• Reading assignments
• Review Sections 4.1, 4.2 (EE300 material)
• Read Sections 4.3, 4.4

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Okumrua-Hata Empirical Model

• Chapter 2, Theme Example 1, p. 82
• Equation for propagation loss in urban
  environments
• Example of empirical model
• Look at measured data
• Estimate form that measurement variations might
  take
• Do RMS fits of different equations to the data
• Select the ones that seem to work best

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Parameters

• Range, valid from 1 km to 20 km
• Base station height, valid from 30 m to 200 m
• Receiver height, valid from 1 m to 10 m
• Operating frequency, valid from 150 MHz to 1 GHz

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Forms of equations

• Base equation is
• Fit is to A, B, C
• Note that B is 10 times the propagation exponent

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Results
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Practice Quiz

• What are the three layers and their functions?
• Problem 2.22 p. 81, Link Budget
• Example 2.21 p. 83, Base Station Antenna Height
  using Okumrua-Hata model
• Problem 3.17 p. 173