Telecommunications Engineering Topic 2: Modulation and FDMA James K Beard, Ph.D. (215) 204-7932 jkbeard@temple.edu http://astro.temple.edu/~jkbeard/ 11/30/2018 Topic 2

Topics Homework Amplitude Modulation BPSK QPSK Summary Assignment References 11/30/2018 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 11/30/2018 Topic 2

Modulation Issues Spectrum Multiple access 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 11/30/2018 Topic 2

Linear and Nonlinear Modulation 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 Topic 2

Raised-Cosine Spectra 11/30/2018 Topic 2

Raised-Cosine Pulses 11/30/2018 Topic 2

Root Raised-Cosine Spectra 11/30/2018 Topic 2

Root Raised-Cosine Pulses 11/30/2018 Topic 2

RRC for (0,1,1,0,0) 11/30/2018 Topic 2

Topics Continuous-phase modulation – minimum shift keying (MSK) Power spectra of MSK signal Gaussian-filtered MSK Frequency division multiple access (FDMA) 11/30/2018 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: 11/30/2018 Topic 2

Special Values of h When h is pi When h is pi/2 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 11/30/2018 Topic 2

Power Spectra of MSK Signal Fourier transform of signal shows 1/f4 rolloff 11/30/2018 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 11/30/2018 Topic 2

Frequency Division Multiple Access FDMA Closely-spaced frequency channels in transmission band Cross-channel modulation controlled Waveform design Guard band 11/30/2018 Topic 2

Summary Modulation Spectral efficiency 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 11/30/2018 Topic 2

Assignment Read Text 3.4.1, 3.7.3-3.7.5, 3.8 Read Bit Error Rate (BER), section 3.12 11/30/2018 Topic 2

Bit Error Rates Examined here for simple receivers Purpose is to show BPSK, QPSK, MSK, etc. No pulse shaping filters Purpose is to show Differences between fundamental modulation types The effect of the channel 11/30/2018 Topic 2

High SNR Bit Error Rate General equations in Table 3.4 p. 159 11/30/2018 Topic 2

AWGN Bit Error Rates 11/30/2018 Topic 2

High SNR AWGN Bit Error Rates 11/30/2018 Topic 2

Rayleigh Fading Bit Error Rates 11/30/2018 Topic 2

BER Conclusions AWGN BER Fading 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 11/30/2018 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 11/30/2018 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 11/30/2018 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 11/30/2018 Topic 2

Forms of equations Base equation is Fit is to A, B, C Note that B is 10 times the propagation exponent 11/30/2018 Topic 2

Results 11/30/2018 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 11/30/2018 Topic 2