1 S Modulation and Coding Methods Introduction / Overview into linear system analysis

2 S Modulation and Coding Methods: Practical arrangements (2 cr) n Lectures: Timo Korhonen, Otakaari 8, room 209, 2. Floor, phone , n Tutorials: Jahangir Sarker, Otakaari 5, phone , n Lectures on Mondays, 14-16, hall S1. Tutorials on Thursdays, 12-14, hall S5 (Exercises carry bonus points!) n Text books : –A.B. Carlson: Communication Systems, IV ed –B.P. Lathi: Digital and Analog Communication Systems –Reference: J. G. Proakis: Digital Communications n Homepage

3 Course outline, fall 2001 Introduction Linear modulation Exponential modulation Carrier wave systems Noise in carrier wave systems Revision I Sampling and pulse coded modulation I Sampling and pulse coded modulation II Baseband digital transmission Error control coding I Error control coding II Bandpass digital transmission Revision II

4 Introduction n Electrical systems utilize varying currents, voltages (eg. varying electromagnetic fields) to store and convey information n Telecommunication systems are dedicated to transporting information from point to point using links or networks n Telecommunication messages are transmitted via different media as copper wire, microwave or optical fiber n Signal is adapted to the transmission and media by modulation and coding

5 Motivation for applying modulation and coding n Modulation is done to enable to use the media for the intended message. Thus the modulation scheme is selected based on Message to be transmitted as –voice –data –continuous / bursty traffic Allowed delay Media that is to be used; compare –Note that for instance in wireless networks a different modulation method can be more appetizing than in wire- line local area networks (LANs) or in public switched telephone network (PSTN)

6 Motivation for applying modulation and coding (cont.) n Coding is done... –For detection and/or correction of errors produced by the channel (as block and convolutional coding) by noise interference distortion –linear –nonlinear –To alleviate synchronization problems (as Manchester coding) –To alleviate detection problems (as differential coding) –To enable secrecy (as scrambling or ciphering) n Channel coding principles: –ARQ (Automatic Repeat Request) –FEC (Forward Error Correction)

7 A classification of communication systems n Communication systems balance between different efficiencies n With respect of markets, systems is a failure if anyone of these efficiencies criteria is not met for a particular application platform:

8 System efficiencies, examples n Microwave links: –good bandwidth efficiency, low error rate required –power efficiency and cost not so important n Wireless mobile systems: –power, bandwidth and cost efficiency very important –earlier bandwidth efficiency was easiest to compromise –nowadays signaling rates increase and bandwidth efficiency is becoming more and more important issue n It is most important that a system designer should recognize communication system relationship to these basic qualifiers:

9 Telecommunication research areas 2001

10 n The sinusoidal wave is parameterized by constant amplitude, frequency and phase: n All parameters known, thus: convoys no information! n Mathematically and experimentally convenient basic formulation whose parameterization by variables enables presenting all the modulation formats: Unmodulated sinusoidal

11 Practical signals n A set of voice tones: –Several tones superimposed –Tones can not be separated from the time domain representation –Frequency components can be separated from a frequency domain representation n “This is some speech” –Bursts –Amplitude varies –Frequency (phase) varies –Many other practical sources are bursty as video signals data packets (for instance in Ethernet)

12 Time domain representation can only seldom reveal small superimposed signals

13 Frequency domain representation of the same signal reveals more!

14 Examples of other signals’ spectra n All finite signals have spectra that can be computed via Fourier transformations or Fourier series

15 Noise and interference n In practical communication systems signals are blurred by noise and interference: Time DomainFrequency Domain

16 A short review to signals and systems n (A) Signals and spectra –Line spectra, Fourier series Phasors and line spectra Periodic signals - average power Parseval’s power theorem –Fourier transform and continuous spectra Fourier transforms Rayleigh’s energy theorem Duality –Time and frequency transformations

17 Signal classification n Deterministic signals n Random signals; purely and pseudo-random n Energy signals; pulses n Power signal; periodic n Also: n Continuous time - discrete time: n Analog - digital n Real - complex

18 Deterministic signals n Deterministic signals are signals which are completely specified as a function of time. n Examples of deterministic signals: n Some properties for delta function

19 Example n Verify that n Proof is based on equivalence property, e.g. two functions f 1 and f 2 are equal only if where  (t) is any function. Consider thus now an integral and thus

20 Random signals n Random signals are signals that take a random value at any given instance of time n These signals must be modeled probabilistically (e.g. using distribution functions as PDF and CDF) n The discrete and continuous mean (e. g. mean for a discrete variable) is defined by where A is the span where p(x) exists. n The variance (AC power) is defined by n The RMS value is

21 Using MathCad for calculating averages and variances

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23 Energy and power signals n The normalized energy of a signal (pulse) is n Examples of energy signals n For periodic signals average power is defined instead of energy n Note that some signals are not energy or power signals as: Wiener-Kinchine theorem defines an important relationship between PSD P(  ) and autocorrelation R xx

24 Correlation and convolution n Correlation between signals x and y is defined by n Convolution is defined by n The Fourier transform of an autocorrelation yields the PSD n Signal energy (or power) can be calculated in time domain or in frequency domain n Correlation is often used to find out PSD for random signals n Convolution is used for determining output of linear systems

25 Fourier transform and Fourier series n F-transforms are used to analyze pulses, F-series for analyzing periodical signals n Definitions, Fourier transform: n Fourier series: n Total signal power (Parseval’s theory):

26 Some Fourier transforms

27 Some Fourier transforms (cont.)

28 Inspecting Fourier series using Mathcad

29 Inspecting Fourier series by Mathcad (cont.)

30 Inspecting Fourier series by Mathcad (cont.)