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Telecommunications Engineering Topic 2: Modulation and FDMA. James K Beard, Ph.D. (215) 204-7932 jkbeard@temple.edu http://astro.temple.edu/~jkbeard/. Topics. Homework Amplitude Modulation BPSK QPSK Summary Assignment References. Modulation. Text section 3.2
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Telecommunications EngineeringTopic 2: Modulation and FDMA James K Beard, Ph.D. (215) 204-7932 jkbeard@temple.edu http://astro.temple.edu/~jkbeard/ Topic 2
Topics • Homework • Amplitude Modulation • BPSK • QPSK • Summary • Assignment • References Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
Raised-Cosine Spectra Topic 2
Raised-Cosine Pulses Topic 2
Root Raised-Cosine Spectra Topic 2
Root Raised-Cosine Pulses Topic 2
RRC for (0,1,1,0,0) Topic 2
Topics • Continuous-phase modulation – minimum shift keying (MSK) • Power spectra of MSK signal • Gaussian-filtered MSK • Frequency division multiple access (FDMA) Topic 2
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: Topic 2
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 Topic 2
Power Spectra of MSK Signal • Fourier transform of signal shows 1/f4 rolloff Topic 2
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 Topic 2
Frequency Division Multiple Access • FDMA • Closely-spaced frequency channels in transmission band • Cross-channel modulation controlled • Waveform design • Guard band Topic 2
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 Topic 2
Assignment • Read Text 3.4.1, 3.7.3-3.7.5, 3.8 • Read Bit Error Rate (BER), section 3.12 Topic 2
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 Topic 2
High SNR Bit Error Rate General equations in Table 3.4 p. 159 Topic 2
AWGN Bit Error Rates Topic 2
High SNR AWGN Bit Error Rates Topic 2
Rayleigh Fading Bit Error Rates Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
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 Topic 2
Forms of equations • Base equation is • Fit is to A, B, C • Note that B is 10 times the propagation exponent Topic 2
Results Topic 2
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 Topic 2