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### Transcript of Slide 1 Digital Communications Aspects of Physical Layer Radio Systems Michael Fitz fitz@ee.ucla.edu

• Slide 1
• Slide 1 Digital Communications Aspects of Physical Layer Radio Systems Michael Fitz fitz@ee.ucla.edu
• Slide 2
• Slide 2 UnWiReD Laboratory (http://www.ee.ucla.edu/~unwired/)
• Slide 3
• Slide 3 You control the flow of the class. If you ask no questions I will proceed linearly through the slides and the notes. Background Material Digital Modulations Wireless Channels Diversity Multiple Antennas Modems Radio ImpairmentsOverview
• Slide 4
• Slide 4 OSI Network Model
• Slide 5
• Slide 5 Physical Layer Abstraction
• Slide 6
• Slide 6 Bandpass Signals Two important characteristics of bandpass signals Non-zero center frequency Energy spectrum does not extend to DC
• Slide 7
• Slide 7 Bandpass Signal Representation I and Q form Amplitude and Phase form Transformations
• Slide 8
• Slide 8 Bandpass Signal Characteristics There are two degrees of freedom in bandpass signals Two low pass signals Communication engineers use two representations In-phase and quadrature Amplitude and phase
• Slide 9
• Slide 9 Complex Envelope Complex envelope Representing two signals as a complex vector
• Slide 10
• Slide 10 Analogous to Fourier Transform Complex valued analytical function Fourier transform is a function of frequency Complex envelope is a function of time Mathematical concepts are all the same Amplitude, phase, real, and imaginary for FT Amplitude, phase, in-phase, and quadrature for CE
• Slide 11
• Slide 11 Conversion
• Slide 12
• Slide 12 Visualizing and Testing The complex envelope is a three dimensional signal I-Q and time Amplitude, phase, and time
• Slide 13
• Slide 13Example
• Slide 14
• Slide 14 2D Representation of CE As humans we can absorb 2D information better I versus time - standard time plot Q versus time - standard time plot I versus Q - vector diagram
• Slide 15
• Slide 15 Time Plots
• Slide 16
• Slide 16 New Tool - Vector Diagram A plot of the in-phase signal versus the quadrature signal Originated in two channel oscilloscopes
• Slide 17
• Slide 17 Example Vector Diagram
• Slide 18
• Slide 18 Bandpass/Baseband Spectrum There is a simple mapping from baseband spectrum to bandpass spectrum
• Slide 19
• Slide 19Comparison
• Slide 20
• Slide 20Conclusions All wireless communications use bandpass signals The complex envelope is a two dimensional analytical representation of a bandpass signal All information about the bandpass signal is contained in the complex envelope except the carrier frequency A tool to characterize the complex envelope is the vector diagram
• Slide 21
• Slide 21 You control the flow of the class. If you ask no questions I will proceed linearly through the slides and the notes. Background Material Digital Modulations Wireless Channels Diversity Multiple Antennas Modems Radio ImpairmentsOverview
• Slide 22
• Slide 22 Digital Transmission Binary data source to be transmitted
• Slide 23
• Slide 23 Digital Modulation Convert bits into waveforms
• Slide 24
• Slide 24 Digital Demodulation
• Slide 25
• Slide 25 Limits on Performance of Digital Communications Shannon capacity of the AWGN channel Spectral efficiency
• Slide 26
• Slide 26 Our Benchmark Curve
• Slide 27
• Slide 27 Digital Communication Goals Achieve Shannons curve at a complexity that is linear in the number of bits to be sent
• Slide 28
• Slide 28 Transmitting K b Bits K b bits M=2 K b waveforms on [0, T p ] Bit rate W b =K b /T p
• Slide 29
• Slide 29 Examples- Frequency shift keying Signals
• Slide 30
• Slide 30 BFSK Vector Diagram
• Slide 31
• Slide 31 BFSK Bandpass Signals
• Slide 32
• Slide 32 Spectral Characteristics of BFSK
• Slide 33
• Slide 33 Example - Phase shift keying Signals
• Slide 34
• Slide 34 BPSK Vector Diagram
• Slide 35
• Slide 35 BPSK Bandpass Signal
• Slide 36
• Slide 36 Spectral Characteristics
• Slide 37
• Slide 37 Review of Binary Detection Problem formulation Statistics are the digital communication engineers friend
• Slide 38
• Slide 38 Maximum A Posterior Word Demodulation MAPWD
• Slide 39
• Slide 39 Block Diagram
• Slide 40
• Slide 40 Maximum Likelihood Word Demodulation Equal priors produce Matched filter and energy correction Complexity exponential in the number of bits being transmitted
• Slide 41
• Slide 41Performance
• Slide 42
• Slide 42 Where Are We With Respect to Shannon?
• Slide 43
• Slide 43 Standard Modulation Conclusions One matched filter for each possible word Complexity scales exponentially with the number of bits to be transmitted This is not acceptable in practice Goal would be to have a complexity that is linear in the number of bits to be sent Spectral efficiency can be set at whatever value you need depending on modulation Performance can achieve a variety of levels depending on the modulation
• Slide 44
• Slide 44 Independent Bit Decisions The goal is to be able to design signals such that individual optimum bit decisions are independent of all the other bits that were transmitted Making optimal independent bit decisions gives linear complexity K b independent bit decisions
• Slide 45
• Slide 45 Orthogonal Modulation Demodulation Conditions for orthogonal modulations Orthogonality implies each bit is decoded independently
• Slide 46
• Slide 46 Orthogonal Modulations Examples Orthogonal in frequency Orthogonal in waveform (code) Orthogonal in time This orthogonality condition was first identified by Nyquist in 1928 Will assume each bit sent on a separate orthogonal waveform but generalizations are possible
• Slide 47
• Slide 47 Example - OFDM Orthogonal frequency division multiplexing Send each bit on an orthogonal subcarrier Signal model Orthogonality condition Used in wireless LANs (802.11a)
• Slide 48
• Slide 48 Temporal Characteristics of OFDM K=4 bits Vector DiagramAmplitude Plot
• Slide 49
• Slide 49 Demodulator for OFDM Fourier transform of the channel output evaluated at f_i
• Slide 50
• Slide 50 Spectrum Plots
• Slide 51
• Slide 51 Vector Diagram of Matched Filter Output Orthogonality ensures that each symbol can be decoded optimally and separately
• Slide 52
• Slide 52 Conclusions - OFDM Orthogonality gives linear complexity Same BEP performance as BPSK Spectral efficiency is about 1 bit/s/Hz with binary modulations per subcarrier OFDM has peak-to-average power issues Demodulator is implemented by using a Fourier transform to get the matched filter FFT is used in practice for implementation efficiency
• Slide 53
• Slide 53 Example - OCDM Orthogonal code division multiplexing Each bit sent on a different spreading waveform Signal model Orthogonality condition Used in cellular/mobile telephony
• Slide 54
• Slide 54 Example Spreading Waveforms
• Slide 55
• Slide 55 Temporal Characteristics of OCDM K=4 bits
• Slide 56
• Slide 56 Demodulator for OCDM
• Slide 57
• Slide 57 Spectrum Plots
• Slide 58
• Slide 58 Conclusions - OCDM Orthogonality gives linear complexity OCDM is most general form of orthogonal modulation Same BEP performance as BPSK Spectral efficiency is about 1 bit/s/Hz Transmitted signal has peak to average power issues
• Slide 59
• Slide 59 Example - OTDM Orthogonal time division multiplexing Bits modulated on time shifted pulses Stream modulation Signal model Orthogonality condition Used in all wireless systems
• Slide 60
• Slide 60 Temporal Characteristics of Stream Modulations K=4 bits
• Slide 61
• Slide 61Demodulator
• Slide 62
• Slide 62 Matched Filter Output
• Slide 63
• Slide 63 Spectrum Plots
• Slide 64
• Slide 64 Conclusions - Stream Orthogonality gives linear complexity Same performance as bits sent in isolation Spectral efficiency is about 1 bit/s/Hz Stream modulations give better control on peak to average power of the transmitted signal Almost all communications systems use the idea of time orthogonality and stream bits in time
• Slide 65
• Slide 65 Where Are We With Respect to Shannon? With linear complexity we can now achieve
• Slide 66
• Slide 66 Can we get closer to Shannon? Orthogonal modulations Orthogonal modulations with memory