Communication Systems Introduction: Communication Systems

Biography Min-Goo Kang ’82-’86 B.S. ’87-’89 M.S. ’89-’94 Ph.D. in the Dept. of Electronic engineering, Yonsei University Professor in the Dept. of Inform. & Telecomm., Hanshin University, Osan, Korea, from 2000 ’85-’87 Researcher in Samsung ’97-’98 Post Doc. in Osaka University, Japan ’06-’07 Visiting Scholar in Queen’s University, Canada - Research interests Mobile Telecomm. & DTV. - E-mail : kangmg@hs.ac.kr

Contents Communication System Model Analog-to-Digital (A/D) Conversion : Sampling, Quantization,Coding Pulse-Code Modulation (PCM) : Line Coding(RZ, NRZ etc.) CODEC : Souce CODEC(JPEG, MPEG, H.264, MP3,…) Channel Coding(Viterbi, Turbo, …)  CH3,4,9 Filter : Lowpass Filter(LPF), Highpass Filter(HPF), Bandpass Filter(BPF) Fourier Series, Fourier Transform :FFT(Frequency Analysis) Modulation(MODEM) AM(ASK), FM(FM), PM(PSK)  CH11,14

Communication System Model Message signal m(t) analog or digital baseband signal Transmitter modifies the baseband signal for efficient transmission Channel Channel is a medium through which the transmitter output is sent example: wire, coaxial cable, optical fiber, radio link Receiver reprocesses the received signal by undoing the signal modifications made at the transmitter and the channel

Typical Digital Communication System

Analog-to-Digital (A/D) Conversion Sampling Sampling makes signal discrete in time Sampling theorem says that bandlimited signal can be sampled without introducing distortion The sample values are still not digital Quantization Quantizer makes signal discrete in amplitude Quantizer introduces some distortion (“quantization noise”) Good quantizers are able to use few bits and introduce small distortion Inherently digital information (e.g. computer files) do not require sampling or quantization.

Sampling

Quantization

Pulse-Code Modulation (PCM) Multi-amplitude pulse code

Channel Effects Distortion attenuation, noise, fading Simple channel model: additive white Gaussian noise (AWGN) transmitted signal received distorted signal (without noise) received distorted signal (with noise) regenerated signal (delayed)

Source Coding and Channel Coding Compression of digital data to eliminate redundant information Channel Coding Provides protection against transmission errors by selectively inserting redundant data

SNR, Bandwidth, Rate of Communication Fundamental parameters that control the rate and quality of information transmission are the channel bandwidth B and the signal power S. Channel Bandwidth B Range of frequencies that the channel can transmit with reasonable fidelity

SNR, Bandwidth, Rate of Communication Signal Power S Signal power is related to the quality of transmission Increasing S reduces the effects of channel noise, and the information is received with less uncertainty In any event, a certain minimum SNR is necessary for communication Channel bandwidth B and signal power S are exchangeable; - We can trade S for B, or vice versa. - One may reduce B if one is willing to increase S. Example: PCM with 16 quantization levels - multi-amplitude scheme - binary scheme

SNR, Bandwidth, Rate of Communication Rate of Information Transmission C Channel capacity : maximum number of bits that can be transmitted per second with a probability of error arbitrarily close to zero Shannon’s limit The channel capacity is related to channel bandwidth and signal power. It is impossible to transmit at a rate higher than channel capacity without incurring errors.

Modulation Converts digital data to a continuous waveform suitable for transmission over channel Baseband (usually square waveform): “line coding” Bandpass (usually sinusoidal waveform): “bandpass modulation” Carrier Modulation (bandpass modulation) Information is transmitted by varying one or more parameters of the carrier waveform: amplitude, frequency, phase A carrier is a sinusoid of high frequency, and one of its parameters (amplitude, frequency, phase) is varied in proportion to the baseband signal (message signal).

Line Coding

Modulation

Modulation Examples of Digital Modulation 1) Amplitude Shift Keying (ASK) or ON/OFF Keying (OOK): 2) Phase Shift Keying (PSK): 3) Frequency Shift Keying (FSK):

Bit Error Probability for Binary Systems

Good Communication System Large data rate (measured in bits/sec), R Small bandwidth (measured in Hertz), B Small required signal power (measured in Watts or dBW), or equivalently small required Eb/N0 Low distortion (measured in S/N or probability of bit error) Large system utilization: large number of users with small delay Low system complexity, computational load, and system cost With digital communications, high complexity does not always result in high cost In practice, there are tradeoffs made in achieving these goals

Data Rate vs. Bandwidth Data rate R ↑  data pulse width ↓  bandwidth B ↑ This tradeoff cannot be avoided - however, some systems use bandwidth more efficiently than others. Define Bandwidth Efficiency as the ratio of data rate R to bandwidth B: hB = R / B We want large bandwidth efficiency hB

BER vs. Signal Power One way to get low probability of error would be to use large signal power to overcome the effect of noise. Some types of modulation achieve low probability of error at lower power than others. Define hE for Energy Efficiency : We want small

Tradeoff in System Design Tradeoff between bandwidth efficiency and energy efficiency M-ary modulation Binary modulation sends only one bit per use of the channel. M-ary modulation sends multiple bits, but is more vulnerable to noise. Error correction coding Inserting redundant bits improves BER performance, but increases bandwidth

Why Digital Communication? Any noise introduces distortion to an analog signal. Since a digital receiver needs only distinguish between two waveforms it is possible to exactly recover digital information. Many signal processing techniques are available to improve system performance: source coding, channel coding, equalization, encryption. Digital ICs are inexpensive to manufacture: a single chip can be mass produced at low cost, no matter how complex. Digital communication allows integration of voice, video, and data on a single system. Digital communication systems provide a better tradeoff of bandwidth efficiency and energy efficiency than analog systems.

Fourier Series Example (pulse train)  Line spectrum

Fourier Series

Fourier Series Example (pulse train): in terms of frequency  Line spectrum

Fourier Series

Fourier Series Sampling function and sinc function

Fourier Series

Fourier Series Sampling function and sinc function

Fourier Series Pulse Signals

Fourier Series

Fourier Series impulse train

Linear System & Fourier Series System Analysis For periodic input: h

Fourier Transform :FFT (Fast Fourier Transform :Frequency Analysis)

Fourier Transform As the fundamental period of the time waveform increases, the fundamental frequency of the Fourier series components making up the waveform decreases and the harmonics become more closely spaced. In the limit, as the time between pulses approaches infinity, the harmonic spacing becomes infinitely small and the spectrum is in fact continuous and bounded by the sinc function as shown.

Fourier Transform

Fourier Transform

Fourier Transform Fourier transform pair

Fourier Transform Example 1: rectangular pulse A smaller  produces a wider main lobe (broad bandwidth)

Fourier Transform Example 2: exponential function

Fourier Transform Example 2: exponential function

Properties of Fourier Transform Linearity Time shifting; shifting in time changes only the phase

Properties of Fourier Transform Time scaling expanding in time (|a|<1) leads to slow variation (deemphasizing high frequency components) a fast replay (|a|>1) of man’s voice may be heard like girl’s voice

Properties of Fourier Transform Time scaling

Properties of Fourier Transform Frequency shifting and modulation Example:

Properties of Fourier Transform Frequency shifting and modulation

Properties of Fourier Transform Duality Example:

Properties of Fourier Transform Duality

Properties of Fourier Transform Differentiation Example: Integration

Properties of Fourier Transform Example : triangular pulse

Properties of Fourier Transform Parseval’s Theorem Energy Spectral Density (ESD) : the frequency distribution of total energy

Properties of Fourier Transform Convolution (in time)

Properties of Fourier Transform Multiplication (in time) : dual of convolution property

Application of Fourier Transform Communication system : modulation and demodulation Modulation

Application of Fourier Transform Communication system : modulation and demodulation Demodulation

Application of Fourier Transform Multiplexing (frequency division multiplexing)

Useful Fourier Transform Pairs Unit impulse Constant Unit step function Exponential

Useful Fourier Transform Pairs Complex exponential Sinusoidal functions

Useful Fourier Transform Pairs Rectangular pulse Triangular pulse Impulse train

Fourier Transform of Periodic Signals Impulse train i) Fourier series ...

Energy Spectral Density (ESD) Energy transmission through LTI system

Power Spectral Density (PSD) Power Spectral Density (PSD) function Average power Power Spectral Density Sx(f)

Power Spectral Density (PSD) Power transmission through LTI system

Filter Ideal Lowpass Filter (LPF)

Filter Ideal Highpass Filter (HPF) and Bandpass Filter (BPF)