TELE4652 Mobile and Satellite Communications


 Hollie Robinson
 3 months ago
 Views:
Transcription
1 Mobile and Satellite Communications Lecture 7 Modulation Modulation he process of inserting our information signal onto a carrier wave he carrier wave is better suited to propagation over the channel Systematically vary a parameter of the carrier wave: s( t) Ac cos( π f ct + θc) Frequency, Amplitude, or Phase
2 Basic ASK, PSK, & FSK Good Modulation Scheme ASK, PSK, & FSK are basic modulation techniques We wish to perform modulation such that robust to receiver noise bandwidth efficient robust to fading easy to detect and recover
3 Marymodulation ransmit one of M possible symbols per symbol period Each symbol carries Symbol rate relates to bit rate: bits Signal bandwidth is fundamentally proportional to the symbol rate Spectral Efficiency η k log R b BW M R k s R b BWαRs s Example  QASK ransmitted signal is s( t) [ a gt n cos πf t a gt n sin πf t ] n [ n] ( ) ( c ) Q[ n] ( ) ( c ) I I and Q components each have one of four possible levels (transmitting bits each)
4 Example 6QASK ransmit 4bits per symbol Increased bit rate for the same signal bandwidth his comes at a cost of signalling power (higher voltage amplitudes ±3V) Recall, our communication resources: S C B log + N Optimal Receivers Consider simple binary ASK over AWGN channel A single symbol, the received signal will be r ( t) a g( t) n( t) m m + where g(t)is the shape of the transmitted waveform at the receiver (after the channel) Our aim is to detect the transmitted amplitude ± a m
5 Optimal Receivers A linear receiver could always be modelled by an impulse response, h(t): Output of the receiver is: Aim to maximise the signal part over the noise part of the output Maximise: y ( τ t) g( τ) dτ h ( t) am h( τ t) g( τ) dτ + h( τ t) n( τ) dτ Optimal Receivers Maximise this with the constraint of fixed receiver power: h ( t) dt Simple mathematical problem: what function, when multiplied by our given function g(t), when integrated, will give the largest result? max f ( x) f α ( x) g( x) dx g( x)
6 Optimal Receivers Optimal solution is always a scaled version of the function itself (it will agree in all places) For our receiver, the impulse response should be a scaled version of the received pulse shape  > Matched filter h( t) g( t) α Equivalent correlator form of the receiver (more suited to digital systems) Received signal r( t) am g( t) + n( t) ψ ( t) g( t) Eg dt Discriminator input, r Matched filter h( t) g( t) Eg Discriminator input, r Generalised Optimal Receiver ransmitted symbol must be one of M possible signals { s ( t )} M m m Can construct a basis for the space spanned by these signals (the signal basis): { ψ ( t )} N k k Signal vector: ( t) smkψk( t) k Symbol Energy must satisfy: s m s m N ( s, s,, s ) m m K mn E N m sm( t) dt k s mk
7 Generalised Optimal Receiver Optimal receiver should correlate received signal against the signal basis: his determines the received signal vector: k rm( t) ψk( t) dt smk nk r + ψ ( t) ( r K, r ) ( s, K, s ) + ( n,, n ) s n r +, N m mn K N m Received signal r ( t) s( t) + n( t) ψ ( t ) dt dt r r Discriminator inputs, r k ψ K (t) dt r K Symbol Discrimination he received signal vector is then the sent symbol vector plus a Ndimensional AWGN noise vector Detection method choose symbol closest to received signal vector in the Euclidean sense: arg min{ d( r, s )} arg min{ r s } m m m m m his is called Maximum Likelihood detection (ML) If we know the probability distribution of sent symbols we could do a bit better > Maximum Apriori detection (MAP)
8 Example  QASK Consider 4QASK (same as 4QPSK) Signal constellation (set of possible sent signals) { s ( ) ( ) cos( ) m t aig t πfct aqg ( t) sin( πfct) ai ± ; aq ± } An appropriate basis: g ( ) ( t) g ( ) ( ) ( t) ψ t cos πfct, ψ t sin( πfct) Eg Eg Every symbol can be expressed as a linear combination of basis signals { s ( t) a E ψ ( t) + a E ψ ( t) a ± ; a } m I g i Q g I Q ± Bandwidth Efficiency Recall basic Fourier theory, fort x ( t) X( f), his basic example gives our fundamental result in communications theory Bandwidth otherwise sin πf ( πf) usedα α Symbol rate Symbol duration
9 Bandwidth Efficiency We wish to minimise signal bandwidth: So more users can share the channel (say FDMA) o allow greater data rates to be communicated o reduce out of band power (and so minimise adjacent channel interference) Reduce distortion due to ISI (Intersymbol Interference) Nyquist Criterion For a communication channel channel bandwidth will limit data rate that can be achieved r( t) akg t k + Received signal must be: k Use a matched correlator receiver, to recover symbol when k, he receiver output is: r [ ] r( t), ψ ( t) a[ ] g ( t), ψ ( t) + a[ k] g ( t k ), ψ ( t) + n( t), ψ ( t) k [ ] ( ) n( t) ψ ( t ) g ( t) Eg
10 Nyquist ISI For no intersymbol interference, we require the second term to be zero: g ( t k), ψ ( t) g ( t) g ( t k) dt for allk An obvious choice would be to have the symbol waveforms in different symbol periods nonoverlapping > but after passage through a bandlimited channel, this is not trivial to obtain Eg Nyquist ISI Rearrange the condition for noisi on the channel to give: g tg ~ τ t dt g g ~ t κ t k where g ~ ( t) g( t ) ( ) ( ) ( )( ) δ( k) τ k his looks like a sampled version of the convolution of the shaping pulse with its timereversed copy Fourier transform to express in the frequency domain: G ( f + kr) κ k
11 Nyquist Criterion Using the sampling theorem (that the Fourier of a sampled signal consist of spectral copies of the spectrum of the original signal, spaced at multiples of the sampling frequency G(f)is the spectrum of the received pulse his is the condition for there to be noisi in the communication system, when expressed in the frequency domain k G ( f + kr) κ his is an important result > allows us to construct systems that satisfy this condition Nyquist Criterion Demonstrates the importance of channel on achievable data rates Case I: (R > B) ISI is inevitable G(f) B X(f) f 3R/ R/ R R/ 3R/ f
12 Nyquist Criterion Case II: (R B) theoretically possible by G(f) taking f G( f) κπ R B f Not physically realisable 3R/ R/ R R/ 3R/ (infinite support) Case III: (R < B) can satisfy criteria. Only if Ris less than Bcan we communicate G(f) without ISI B f X(f) X(f) f 3R/ R/ R R/ 3R/ f G ( f) Nyquist Pulses A common, practical pulse shape that satisfies the Nyquist criterion Known as rootraised cosine (RRC) pulses Frequency response is: R if f ( β) f π β β R R ( β) ( + + cos β) + if f R R if f ( + β) heir bandwidth is thus: ( βis the rolloff factor) R B ( +β)
13 Signal Bandwidth Consider QASK/QPSK for illustration A transmitted signal can be expressed as: s( t) ai[ n] g( t n) cos( πfct) aq[ n] g( t n) sin( πfct) n Under the assumptions that symbol sequence { a I[ n], aq[ n] } is uncorrelated and uniformly distributed Can easily show, by Fourier transforming the timeaveraged autocorrelation function, that the power spectral density of the signal is: S (( f) R ( E E ) G( f f ) + G( f + f ) S [ ] s g { c c } Pulse shaping he important point is that the bandwidth of the shaping pulse determines the signal bandwidth rue for all modulation schemes (FSK), but analysis and expression is more complicated Shaping pulse determines spectral characteristics
14 Basic Fourier theory results Signal with discontinuities PSD decays as (db per decade) Example: square pulse: Continuous signal with discontinuous first 4 derivative PSD decays as f (4dB/decade) Example: triangular pulse: t, for t Continuous signal with continuous first 6 derivative decays at least as fast as f (6dB/decade) ( t) x, for t, otherwise X ( f) x ( t) X( f) sinc ( πf), otherwise f sin πf ( πf) Pulse Shaping Illustrations of the results for square and triangular pulse below o minimise bandwidth we want to make the signal as smooth as possible Digital modulation the more marked the discontinuities, the easier it is for the receiver to recover the data
15 ime domain: Square Pulse g( t) u ( t) ift (, ) otherwise PSD: G( f ) sin c 9% Bandwidth: ( πf) Rolloff: db/decade B Halfsinusoid Pulse ime domain: g( t) u ( t) πt sin PSD: G( f ) 9% bandwidth: 4 π cos ( πf) ( f) [ ] B Halfsinusoid pulse 4dB/decade rolloff
16 Raised Cosine pulse ime domain: g( t) u ( t) πt cos 3 PSD: G( f ) 6 sin c ( πf) ( f) ( ) Raisedcosine pulse 9% bandwidth: B dB/decade rolloff Gaussian Pulse Shapes ime domain: Pulse spectrum: Spectrally efficient but violates the Nyquist criterion t g( t) erfc π B3 erfc π B3 log log H ( f) e log f B 3 Degree of ISI introduced is quantified by the 3dB bandwidthsymbol period product B 3 Effectively this is the ratio between the symbol period and the Gaussian pulse width GSM uses this with B 3.3 ( t )
17 Pulse Shaping  example Pulse shaping can smooth out signal discontinuities, reducing bandwidth FSK  comments Can be generated in a way to have continuous phase (but discontinuous frequency) waveform: E b ( t) u ( t) cos[ π f t+ θ( t) ] s he instantaneous frequency carries the information symbols: fi( t) fc + h ang( t n) Instantaneous carrier phase is the integral of the instantaneous frequency: t Note that carrier phase is continuous, which means the signal is continuous too c n ( t) π fi( τ) dτ πfct + πh anq( t n) θ i n
18 he signal derivative is: FSK  comments If can smooth the frequency waveform, the signal derivative will be continuous too Gradual frequency transitions (freq. shaping pulse) ( t) ds dt dθi Ac π fc+ c + dt sin Produces a signal with a rolloff of at least 4dB/decade FSK with the continuous phase property have inherently good spectral performance ( πft θ ( t) ) i Carrier Synchronisation he receiver will always need to recover the carrier s phase and frequency Inaccuracies result in a reduction of receiver performance > increased BER Carrier phase must be tracked in realtime: Unknown/changing xrx distance Oscillator drift wo options: Pilot assisted transmit a reference carrier (pilot tone) Nonpilot assisted use the information signal itself to lock
19 Carrier Synchronisation Pilot tone transmitted stable carrier for the receiver to synchronise to. Uses available signalling power Can be efficient if multiple receivers can share the same pilot tone (on the cellular Downlink) Use a simple PLL to lock receiver Local Oscillator onto this pilot tone Noncoherent Receiver For the uplink, it is inefficient to have each MS transmitting its own pilot and the BS running a separate PLL for each MS Use a noncoherent detection scheme
20 Noncoherent Detection  QPSK Noncoherent detection removes the need for a pilot tone, at the cost of reduced SNR performance he above structure works for FSK (or really any orthogonal signalling scheme) QPSK requires a different methodology Differential Encoding can be used for QPSK Differential Encoding map the transmitted symbol to the change in the carrier phase, and not the actual carrier phase Differential Encoding ransmitted carrier phase is determined by: where symbol m θ + mn m[ n] m[ n ] [ ] M [ n] {,, KM } is the transmitted Receiver then only needs to track carrier phase changes (and not the precise carrier phase) Can easily be implemented with a detector with memory θ π
21 r(t) DPSK Receiver phase Shift, 9 º g( t) ( ) dt E g cos( π f c t+φ) local oscillator sin( π t+φ) f c g( t) ( ) dt E g r I [n] [ n ] he decisions are made according to: ri ri[ n] ri[ n ] + rq[ n] rq[ n ] rq rq[ n] ri[ n ] ri[ n] rq[ n ] he matched filter outputs are: ri [ n] Es cos( θm[ n] φ) + ni[ n] rq [ n] Es sinθ ( m[ n] φ) + nq[ n] So, detector outputs: r I Es cos( θm[ n] θm[ n ]) + n I r Q Es sin( θm n θmn ) + n Q [ ] [ ] delay mixer delay r I r Q [n] [ n ] r Q r I r Q phase detector DQPSK  Example Consider a QPSK system with differential encoding, and signal mapping as shown Input data stream: Carrier phase change(δθ): π/ π π/ π ransmitted phase: π/ π/ π Noncoherent detector outputs: Decision points: θ(n) (x(n),y(n)) Output bits (+, ) π/ (, +) π (, ) π/ (, ) x ( n) E s cos( θm[ n] θm[ n ] ) [ n] E s sin( θm[ n] θm[ n ] ) y
22 Bit Clock Synchronisation If there is a long sequence of bits that don t change, it is difficult to detect when bits begin and end A clever solution in DQPSK is π/4dqpsk Rotate the constellation every symbol period by π/4 Ensures the carrier phase changes every symbol Input Bit Pair Phase change of carrier π/4 3π/43π/4 π/4 Bit Clock Synchronisation Can be determined similar to carrier phase synchronisation (effectively using a PLL) Performed at the baseband Often can be implemented digitally (on a sampled waveform) Other techniques exist such as EarlyLate Gate Estimation
23 Error Performance Measured as the Bit Error Rate (BER) probability of a bit error Noise robustness of the signalling scheme Depends on the model of noise adopted he simplest is AWGN: Noise is additive Gaussian distribution White spectrum Autocorrelation S N ( f ) r(t) s(t) + n(t) P( n) N e πσ N N R N ( τ ) F n σ δ( τ) Binary Signalling Ultimately, noise performance is determined by how far apart points are in the signal constellation For example, binary PSK with coherent detection Per symbol is: Pr Error probability: { error } Pr{ n> d / } Pr { error} Pr{ n> d / } Bit Error Rate: since, E b g d / Q Q σ n P e Q E N b d N
24 BER Example QPSK QPSK with coherent detection Can assume that noise effects each component independently. Probability a symbol is detected in error:  a Q a I Pr { symbol} Q d N nn Nearest neighbour distance: here are two bits per symbol: d nn g E Es b Map symbols such that neighbours differ by a single bit: P eb P es > BER for QPSK with coherent detection g P e Q E N b BER General Constellation A general constellation, expressed in terms of its signal basis Correlator output: Received signal r ( t) s( t) + n( t) rm( t) ψk( t) dt smk nk Received signal vector: r ( r K, r ) ( s, K, s ) + ( n,, n ) s + n k r +, N m mn K N m ψ ( t ) ψ ( t ) ψ K (t) dt dt dt r r r K Discriminator inputs, r k Noise vector is an iid Gaussian random vector. Each component is independent
25 BER General Constellation ML decision thresholds regions closest to each symbol point Error probability prob. that the mdimensional noise vector causes received signal vector to be closer to M another symbol. Pes Pr does not lie in Zi mi sent M ( ) ( r m ) dr he exact BER can be a quite complex integral over an mdimensional region M  i M M M P( r lies in Zi mi sent) i i Zi P i BER General Constellation Nearestneighbour approximation accurate for large SNR values Assume if symbol is detected in error it will be detected as one of its nearest neighbours only: Forms an upper bound: P e ( m ) i P UAij P( Aij) j i j i Pairwise error probabilities: P ( ) ij A ij Q N d Assuming symbols are all equally likely: Pe M M Q d ij N i j n.n i
26 BER General Constellation Can relate symbol error rate to BER in several ways:.hierarchical constellation some points are closer to others Use a Gray code (eg. QASK) hen, for Mary scheme log M eb P e.nonhierarchical distances between points are uniform Example an orthogonal constellation (FSK) Every other symbol is equally likely Note: as M gets large > Peb P e P P eb M Pe K M K Pe BER Results for Common Signalling Schemes Some common signalling schemes (all with coherent detection) BPSK binary FSK QPSK Eb P e Q N E b P e Q N Eb P e Q N Mary PSK Mary FSK P eb Q log M P eb log M E sin N b π ( ) M E log M ( ) b M Q N Note: all involve Qfunction  asymptotic Peb Q E N κ b κeb e N
27 Noncoherent Detection Much more complex Usually involve (noise)^ terms no longer Gaussian Often analytic expressions can t be obtained Some useful results: Binary FSK P eb e Eb N Binary PSK P eb e Eb N BER Key Results he exact expression for the BER of a signalling scheme is determined by: Modulation scheme Detection method/receiver structure General trends Will always be a function of energy to noise PSD per bit, E b N As E b N increases, BER decreases Asymptotic behaviour > exponential (large SNR) Peb Q κeb κeb N e N
28 Rayleigh Channel Model For channels other than the AWGN the analysis is more involved he next simplest is the slow, flatfading Rayleigh channel Slow, flat Rayleigh Model At any instant the channel is AWGN he channel SNR varies (slowly changes much slower than a symbol period), and follows an exponential distribution (this models fading), Pγ e Γ γ Γ ( ) BER for Rayleigh Model the average BER over this channel can be calculated as: Often this integral must be evaluated numerically Analytical results for some common modulation schemes Coherent BPSK: e Γ γ Γ Coherent binaryfsk: Noncoherent BPSK: P ray eb P P eb AWGN eb P eb ( γ) dγ Γ +Γ P eb ( +Γ ) Γ +Γ Asymptotic behaviour > P eb E N b
29 Nonlinear Effects in Modulation Variations in xrx distance, and fading events, imply variable amplification is needed Difficult to build amplifiers that are linear over a wide voltage range (not to mention tuneable too) Recall WA CONSAN AMPLIUDE MODULAION Seek modulation schemes that feature a constant amplitude envelope Signal information is not associated with amplitude of waveform envelope Constant Amplitude Modulation FSK inherently has the constant amplitude property BPSK with a smooth amplitude pulse (to improve bandwidth performance) does not have this g(t) property P(t) t t
30 Offset  QPSK A variation of QPSK to achieve a constant amplitude waveform o combat the effects of fading and nonlinear distortion in amplifiers Offset the I and Q phases by half a symbol period Offset QPSK When the halfsinusoid shaping pulse is used, the resulting waveform will have constant amplitude OQPSK signal: ( ) st ai g( t n ) ( ) ( ( + ) ) ( )] [ ] b cos πfct aq gt n [ ] b sin πfct m n m n [ n Power profile: ( t) g ( t nb) + g ( t ( n+ ) b) P n n If use halfsinusoid pulse: Resulting profile: g πt ( t) u ( t) sin ( ) ( ) ( ( ) ) π t n b + + π t n b Pt sin sin n b b ( ) ( ) π t nb π t nb sin + cos n b b [ ] n 
31 Sophisticated Modulation Schemes wo good examples of modulation schemes that combine the ideas we ve discussed:.π/4 ODQPSK π/4 Offset Differential Quadrature Phase Shift Keying Used in the USDC (G Cellular standard in the US).GMSK Gaussian Minimum Shift Keying Used in GSM Features: π/4odqpsk π/4 offset in the symbol constellation, to improve symbol synchronisation performance Offset I and Q phases, to smooth power profile > robustness to fading and nonlinear amplification Differential encoding, to allow noncoherent detection (say for the uplink). Also could be employed with a pilot tone and coherent detection (would improve BER performance)
32 π/4odqpsk ransmitter structure Receiver Structure (Coherent) θ Gaussian Minimum Shift Keying Form of FSK with continuous phase he continuous phase property is an example of a modulation scheme with memory Phase waveform πh ( t) θ( ) ± t, for t Additional Gaussian filter employed to smooth out the phase transitions
33 GMSK Gaussian filter response log f B 3 ( ) H f e h( t) π 3 π B log B t 3e log 3dB bandwidth is B 3 t g( t) erfc π B3 erfc π B 3 log log ( t ) Reduces bandwidth but introduces ISI he smaller the bandwidth, the wider the pulses Symbol period 3dB bandwidth product quantifies the level of ISI introduced into the modulation scheme GMSK Symbol period3db bandwidth product B 3 he smaller the value the more significant the ISI GSM uses GMSK with B 3.5 Minimum Shift Keying binary FSK where the frequency separation is chosen so as to be minimum that makes the symbol waveforms orthogonal
34 MSK Consider two frequency signals hey will be orthogonal if: s o minimise the frequency separation: Recall modulation index of FM: > h cos s E b ( t) u ( t) cos( πft) for i, i ( πft) cos( πf t) dt sinc( π ( f f )) k f s, k,,3,k f f ( ) h f f f i s s MSK Modulation with memory Can show that it is equivalent to OffsetQPSK with the halfsinusoid shaping pulse: E his implies an easy structure to generate GMSK E 3π / π π / t  3π / π π /   3π /   π π /  3π / π π / t t t 3 b b ( t) cos( θ( t) ) cos( πf t) sin( θ( t) ) sin( πf t) s c c
35 GMSK GMSK can be recovered using either Coherent or Noncoherent techniques: GMSK Noise performance is slightly worse than BPSK/QPSK his is due to the ISI introduced by the Gaussian filter For Coherent detection: for B 3.5 ρ.68 Q ρe N ρ.85 for pure MSK, Spectral performance is superior to QPSK (6dB rolloff performance) P eb b B 3
36 3G Standards Employ basic BPSK or QPSK oo difficult to employ more sophisticated modulation scheme at that chip rate and over that bandwidth Signal processing: CDMA BER Performance Recall SNR expression for CDMA SINR N B Implies BER, if assume coherent BPSK/QPSK: CDMA is interference limited P G SNR SNR G s ( K ) + ( K ) > even as improve SNR, the BER will never improve beyond P eb > Q P s data+ G K P Q E b K + N G eb
Digital Modulation Schemes
Digital Modulation Schemes 1. In binary data transmission DPSK is preferred to PSK because (a) a coherent carrier is not required to be generated at the receiver (b) for a given energy per bit, the probability
More informationDIGITAL COMMUNICATIONS SYSTEMS. MSc in Electronic Technologies and Communications
DIGITAL COMMUNICATIONS SYSTEMS MSc in Electronic Technologies and Communications Bandpass binary signalling The common techniques of bandpass binary signalling are:  Onoff keying (OOK), also known as
More informationDigital Modulators & Line Codes
Digital Modulators & Line Codes Professor A. Manikas Imperial College London EE303  Communication Systems An Overview of Fundamental Prof. A. Manikas (Imperial College) EE303: Dig. Mod. and Line Codes
More informationDigital modulation techniques
Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband channels Signal space representation Optimal
More informationDigital Communication System
Digital Communication System Purpose: communicate information at required rate between geographically separated locations reliably (quality) Important point: rate, quality spectral bandwidth, power requirements
More informationRevision of Wireless Channel
Revision of Wireless Channel Quick recap system block diagram CODEC MODEM Wireless Channel Previous three lectures looked into wireless mobile channels To understand mobile communication technologies,
More informationQUESTION BANK SUBJECT: DIGITAL COMMUNICATION (15EC61)
QUESTION BANK SUBJECT: DIGITAL COMMUNICATION (15EC61) Module 1 1. Explain Digital communication system with a neat block diagram. 2. What are the differences between digital and analog communication systems?
More informationObjectives. Presentation Outline. Digital Modulation Revision
Digital Modulation Revision Professor Richard Harris Objectives To identify the key points from the lecture material presented in the Digital Modulation section of this paper. What is in the examination
More informationMobile Radio Propagation: SmallScale Fading and Multipath
Mobile Radio Propagation: SmallScale Fading and Multipath 1 EE/TE 4365, UT Dallas 2 Smallscale Fading Smallscale fading, or simply fading describes the rapid fluctuation of the amplitude of a radio
More informationDownloaded from 1
VII SEMESTER FINAL EXAMINATION2004 Attempt ALL questions. Q. [1] How does Digital communication System differ from Analog systems? Draw functional block diagram of DCS and explain the significance of
More informationDigital Communication System
Digital Communication System Purpose: communicate information at certain rate between geographically separated locations reliably (quality) Important point: rate, quality spectral bandwidth requirement
More informationMSK has three important properties. However, the PSD of the MSK only drops by 10log 10 9 = 9.54 db below its midband value at ft b = 0.
Gaussian MSK MSK has three important properties Constant envelope (why?) Relatively narrow bandwidth Coherent detection performance equivalent to that of QPSK However, the PSD of the MSK only drops by
More informationPrinciples of Communications
Principles of Communications Meixia Tao Shanghai Jiao Tong University Chapter 8: Digital Modulation Techniques Textbook: Ch 8.4 8.5, Ch 10.110.5 1 Topics to be Covered data baseband Digital modulator
More informationChannel. Muhammad Ali Jinnah University, Islamabad Campus, Pakistan. MultiPath Fading. Dr. Noor M Khan EE, MAJU
Instructor: Prof. Dr. Noor M. Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111878787, Ext. 19 (Office), 186 (Lab) Fax: +9
More informationAbout Homework. The rest parts of the course: focus on popular standards like GSM, WCDMA, etc.
About Homework The rest parts of the course: focus on popular standards like GSM, WCDMA, etc. Good news: No complicated mathematics and calculations! Concepts: Understanding and remember! Homework: review
More informationEE3723 : Digital Communications
EE3723 : Digital Communications Week 11, 12: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and RaisedCosine Filter Eye Pattern Equalization (On Board) 01Jun15 Muhammad Ali Jinnah
More informationMuhammad Ali Jinnah University, Islamabad Campus, Pakistan. Fading Channel. Base Station
Fading Lecturer: Assoc. Prof. Dr. Noor M Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111878787, Ext. 19 (Office), 186 (ARWiC
More informationWireless Communication Fading Modulation
EC744 Wireless Communication Fall 2008 Mohamed Essam Khedr Department of Electronics and Communications Wireless Communication Fading Modulation Syllabus Tentatively Week 1 Week 2 Week 3 Week 4 Week 5
More informationWireless Communication: Concepts, Techniques, and Models. Hongwei Zhang
Wireless Communication: Concepts, Techniques, and Models Hongwei Zhang http://www.cs.wayne.edu/~hzhang Outline Digital communication over radio channels Channel capacity MIMO: diversity and parallel channels
More informationLecture 3: Wireless Physical Layer: Modulation Techniques. Mythili Vutukuru CS 653 Spring 2014 Jan 13, Monday
Lecture 3: Wireless Physical Layer: Modulation Techniques Mythili Vutukuru CS 653 Spring 2014 Jan 13, Monday Modulation We saw a simple example of amplitude modulation in the last lecture Modulation how
More informationUniversity of Manchester. CS3282: Digital Communications 06. Section 9: Multilevel digital modulation & demodulation
University of Manchester CS3282: Digital Communications 06 Section 9: Multilevel digital modulation & demodulation 2/05/06 CS3282 Sectn 9 1 9.1. Introduction: So far, mainly binary signalling using ASK,
More informationRevision of Previous Six Lectures
Revision of Previous Six Lectures Previous six lectures have concentrated on Modem, under ideal AWGN or flat fading channel condition multiplexing multiple access CODEC MODEM Wireless Channel Important
More informationChapter 4. Part 2(a) Digital Modulation Techniques
Chapter 4 Part 2(a) Digital Modulation Techniques Overview Digital Modulation techniques Bandpass data transmission Amplitude Shift Keying (ASK) Phase Shift Keying (PSK) Frequency Shift Keying (FSK) Quadrature
More informationDepartment of Electronics and Communication Engineering 1
UNIT I SAMPLING AND QUANTIZATION Pulse Modulation 1. Explain in detail the generation of PWM and PPM signals (16) (M/J 2011) 2. Explain in detail the concept of PWM and PAM (16) (N/D 2012) 3. What is the
More informationCSE4214 Digital Communications. Bandpass Modulation and Demodulation/Detection. Bandpass Modulation. Page 1
CSE414 Digital Communications Chapter 4 Bandpass Modulation and Demodulation/Detection Bandpass Modulation Page 1 1 Bandpass Modulation n Baseband transmission is conducted at low frequencies n Passband
More information= = (1) Denote the noise signal in the i th branch as n i, assume without loss of generality that the noise is zero mean and unit variance. i.e.
Performance of Diversity Schemes & Spread Spectrum Systems* 6:33:546 Wireless Communication echnologies, Spring 5 Department of Electrical Engineering, Rutgers University, Piscataway, NJ 894 Vivek Vadakkuppattu
More informationMultiPath Fading Channel
Instructor: Prof. Dr. Noor M. Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111878787, Ext. 19 (Office), 186 (Lab) Fax: +9
More informationCommunication Channels
Communication Channels wires (PCB trace or conductor on IC) optical fiber (attenuation 4dB/km) broadcast TV (50 kw transmit) voice telephone line (under 9 dbm or 110 µw) walkietalkie: 500 mw, 467 MHz
More informationQUESTION BANK EC 1351 DIGITAL COMMUNICATION YEAR / SEM : III / VI UNIT I PULSE MODULATION PARTA (2 Marks) 1. What is the purpose of sample and hold
QUESTION BANK EC 1351 DIGITAL COMMUNICATION YEAR / SEM : III / VI UNIT I PULSE MODULATION PARTA (2 Marks) 1. What is the purpose of sample and hold circuit 2. What is the difference between natural sampling
More informationMobile Radio Systems OPAM: Understanding OFDM and Spread Spectrum
Mobile Radio Systems OPAM: Understanding OFDM and Spread Spectrum Klaus Witrisal witrisal@tugraz.at Signal Processing and Speech Communication Laboratory www.spsc.tugraz.at Graz University of Technology
More informationRevision of Previous Six Lectures
Revision of Previous Six Lectures Previous six lectures have concentrated on Modem, under ideal AWGN or flat fading channel condition Important issues discussed need to be revised, and they are summarised
More informationCommunication Theory
Communication Theory Adnan Aziz Abstract We review the basic elements of communications systems, our goal being to motivate our study of filter implementation in VLSI. Specifically, we review some basic
More informationProblem Sheet 1 Probability, random processes, and noise
Problem Sheet 1 Probability, random processes, and noise 1. If F X (x) is the distribution function of a random variable X and x 1 x 2, show that F X (x 1 ) F X (x 2 ). 2. Use the definition of the cumulative
More informationAmplitude Frequency Phase
Chapter 4 (part 2) Digital Modulation Techniques Chapter 4 (part 2) Overview Digital Modulation techniques (part 2) Bandpass data transmission Amplitude Shift Keying (ASK) Phase Shift Keying (PSK) Frequency
More informationPrinciples of Communications
Principles of Communications Weiyao Lin Shanghai Jiao Tong University Chapter 8: Digital Modulation Techniques Textbook: Ch 8.4.8.7 2009/2010 Meixia Tao @ SJTU 1 Topics to be Covered data baseband Digital
More informationFund. of Digital Communications Ch. 3: Digital Modulation
Fund. of Digital Communications Ch. 3: Digital Modulation Klaus Witrisal witrisal@tugraz.at Signal Processing and Speech Communication Laboratory www.spsc.tugraz.at Graz University of Technology November
More informationModulation and Coding Tradeoffs
0 Modulation and Coding Tradeoffs Contents 1 1. Design Goals 2. Error Probability Plane 3. Nyquist Minimum Bandwidth 4. Shannon Hartley Capacity Theorem 5. Bandwidth Efficiency Plane 6. Modulation and
More informationECE5713 : Advanced Digital Communications
ECE5713 : Advanced Digital Communications Bandpass Modulation MPSK MASK, OOK MFSK 04May15 Advanced Digital Communications, Spring2015, Week8 1 Inphase and Quadrature (I&Q) Representation Any bandpass
More informationChapter 6 Passband Data Transmission
Chapter 6 Passband Data Transmission Passband Data Transmission concerns the Transmission of the Digital Data over the real Passband channel. 6.1 Introduction Categories of digital communications (ASK/PSK/FSK)
More informationWIRELESS COMMUNICATIONS PRELIMINARIES
WIRELESS COMMUNICATIONS Preliminaries Radio Environment Modulation Performance PRELIMINARIES db s and dbm s Frequency/Time Relationship Bandwidth, Symbol Rate, and Bit Rate 1 DECIBELS Relative signal strengths
More informationLecture 3 Digital Modulation, Detection and Performance Analysis
MIMO Communication Systems Lecture 3 Digital Modulation, Detection and Performance Analysis Prof. ChunHung Liu Dept. of Electrical and Computer Engineering National Chiao Tung University Spring 2017 2017/3/26
More informationEXPERIMENT WISE VIVA QUESTIONS
EXPERIMENT WISE VIVA QUESTIONS Pulse Code Modulation: 1. Draw the block diagram of basic digital communication system. How it is different from analog communication system. 2. What are the advantages of
More informationSpread Spectrum Techniques
0 Spread Spectrum Techniques Contents 1 1. Overview 2. Pseudonoise Sequences 3. Direct Sequence Spread Spectrum Systems 4. Frequency Hopping Systems 5. Synchronization 6. Applications 2 1. Overview Basic
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON ELEC6014W1 SEMESTER II EXAMINATIONS 2007/08 RADIO COMMUNICATION NETWORKS AND SYSTEMS Duration: 120 mins Answer THREE questions out of FIVE. University approved calculators may
More informationChapter 14 MODULATION INTRODUCTION
Chapter 14 MODULATION INTRODUCTION As we have seen in previous three chapters, different types of media need different types of electromagnetic signals to carry information from the source to the destination.
More informationLecture 9: Spread Spectrum Modulation Techniques
Lecture 9: Spread Spectrum Modulation Techniques Spread spectrum (SS) modulation techniques employ a transmission bandwidth which is several orders of magnitude greater than the minimum required bandwidth
More informationSpread Spectrum (SS) is a means of transmission in which the signal occupies a
SPREADSPECTRUM SPECTRUM TECHNIQUES: A BRIEF OVERVIEW SS: AN OVERVIEW Spread Spectrum (SS) is a means of transmission in which the signal occupies a bandwidth in excess of the minimum necessary to send
More informationDigital Communication Digital Modulation Schemes
Digital Communication Digital Modulation Schemes Yabo Li Fall, 2013 Chapter Outline Representation of Digitally Modulated Signals Linear Modulation PAM PSK QAM MultiDimensional Signal Nonlinear Modulation
More informationDigital Communications over Fading Channel s
over Fading Channel s Instructor: Prof. Dr. Noor M Khan Department of Electronic Engineering, Muhammad Ali Jinnah University, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (51) 111878787, Ext. 19 (Office),
More informationNarrow and wideband channels
RADIO SYSTEMS ETIN15 Lecture no: 3 Narrow and wideband channels Ove Edfors, Department of Electrical and Information technology Ove.Edfors@eit.lth.se 20120319 Ove Edfors  ETIN15 1 Contents Short review
More informationSwedish College of Engineering and Technology Rahim Yar Khan
PRACTICAL WORK BOOK Telecommunication Systems and Applications (TL424) Name: Roll No.: Batch: Semester: Department: Swedish College of Engineering and Technology Rahim Yar Khan Introduction Telecommunication
More informationEE3723 : Digital Communications
EE3723 : Digital Communications Week 89: Bandpass Modulation MPSK MASK, OOK MFSK 04May15 Muhammad Ali Jinnah University, Islamabad  Digital Communications  EE3723 1 Inphase and Quadrature (I&Q) Representation
More informationUNIT I Source Coding Systems
SIDDHARTH GROUP OF INSTITUTIONS: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code: DC (16EC421) Year & Sem: IIIB. Tech & IISem Course & Branch: B. Tech
More informationDigital Signal Processing for Communication Systems
Digital Signal Processing for Communication Systems 1999. 7. 5. Prof. YONG HOON LEE DEPARTMENT OF ELECTRICAL ENGINEERING KAIST Contents 1. DSP for TDMA (IS136) Mobile Communication 2. DSP for CDMA (IS95)
More informationMobile & Wireless Networking. Lecture 2: Wireless Transmission (2/2)
192620010 Mobile & Wireless Networking Lecture 2: Wireless Transmission (2/2) [Schiller, Section 2.6 & 2.7] [Reader Part 1: OFDM: An architecture for the fourth generation] Geert Heijenk Outline of Lecture
More information3/26/18. Lecture 3 EITN STRUCTURE OF A WIRELESS COMMUNICATION LINK
Lecture 3 EITN75 208 STRUCTURE OF A WIRELESS COMMUNICATION LINK 2 A simple structure Speech Data A/D Speech encoder Encrypt. Chann. encoding Modulation Key Speech D/A Speech decoder Decrypt. Chann. decoding
More informationEE5713 : Advanced Digital Communications
EE573 : Advanced Digital Communications Week 4, 5: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and RaisedCosine Filter Eye Pattern Error Performance Degradation (On Board) Demodulation
More informationPerformance Evaluation Of Digital Modulation Techniques In Awgn Communication Channel
Performance Evaluation Of Digital Modulation Techniques In Awgn Communication Channel Oyetunji S. A 1 and Akinninranye A. A 2 1 Federal University of Technology Akure, Nigeria 2 MTN Nigeria Abstract The
More informationMultipath Path. Direct Path
Chapter Fading Channels. Channel Models In this chapter we examine models of fading channels and the performance of coding and modulation for fading channels. Fading occurs due to multiple paths between
More informationObjectives. Presentation Outline. Digital Modulation Lecture 03
Digital Modulation Lecture 03 InterSymbol Interference Power Spectral Density Richard Harris Objectives To be able to discuss InterSymbol Interference (ISI), its causes and possible remedies. To be able
More informationEENG473 Mobile Communications Module 3 : Week # (12) Mobile Radio Propagation: SmallScale Path Loss
EENG473 Mobile Communications Module 3 : Week # (12) Mobile Radio Propagation: SmallScale Path Loss Introduction Smallscale fading is used to describe the rapid fluctuation of the amplitude of a radio
More informationExercises for chapter 2
Exercises for chapter Digital Communications A baseband PAM system uses as receiver filter f(t) a matched filter, f(t) = g( t), having two choices for transmission filter g(t) g a (t) = ( ) { t Π =, t,
More informationCALIFORNIA STATE UNIVERSITY, NORTHRIDGE FADING CHANNEL CHARACTERIZATION AND MODELING
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE FADING CHANNEL CHARACTERIZATION AND MODELING A graduate project submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical
More informationModern Quadrature Amplitude Modulation Principles and Applications for Fixed and Wireless Channels
1 Modern Quadrature Amplitude Modulation Principles and Applications for Fixed and Wireless Channels W.T. Webb, L.Hanzo Contents PART I: Background to QAM 1 Introduction and Background 1 1.1 Modulation
More informationMobile Communications
Mobile Communications WenShen Wuen Trans. Wireless Technology Laboratory National Chiao Tung University WS Wuen Mobile Communications 1 Outline Outline 1 Structure of Wireless Communication Link 2 Analog
More information8.1 Geometric Representation of Signal Waveforms
Haberlesme Sistemlerine Giris (ELE 361) 30 Ekim 2017 TOBB Ekonomi ve Teknoloji Universitesi, GÃ 1 4 z 201718 Dr. A. Melda Yuksel Turgut & Tolga Girici Lecture Notes Chapter 8 Digital Modulation Methods
More informationPhysical Layer: Modulation, FEC. Wireless Networks: Guevara Noubir. S2001, COM3525 Wireless Networks Lecture 3, 1
Wireless Networks: Physical Layer: Modulation, FEC Guevara Noubir Noubir@ccsneuedu S, COM355 Wireless Networks Lecture 3, Lecture focus Modulation techniques Bit Error Rate Reducing the BER Forward Error
More informationECEn 665: Antennas and Propagation for Wireless Communications 131. s(t) = A c [1 + αm(t)] cos (ω c t) (9.27)
ECEn 665: Antennas and Propagation for Wireless Communications 131 9. Modulation Modulation is a way to vary the amplitude and phase of a sinusoidal carrier waveform in order to transmit information. When
More informationOutline Chapter 3: Principles of Digital Communications
Outline Chapter 3: Principles of Digital Communications Structure of a Data Transmission System Up and DownConversion LowpasstoBandpass Conversion Baseband Presentation of Communication System Basic
More informationChapter 7. Multiple Division Techniques
Chapter 7 Multiple Division Techniques 1 Outline Frequency Division Multiple Access (FDMA) Division Multiple Access (TDMA) Code Division Multiple Access (CDMA) Comparison of FDMA, TDMA, and CDMA Walsh
More informationRevision of Lecture 3
Revision of Lecture 3 Modulator/demodulator Basic operations of modulation and demodulation Complex notations for modulation and demodulation Carrier recovery and timing recovery This lecture: bits map
More informationFundamentals of Digital Communication
Fundamentals of Digital Communication Network Infrastructures A.A. 2017/18 Digital communication system Analog Digital Input Signal Analog/ Digital Low Pass Filter Sampler Quantizer Source Encoder Channel
More informationTSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY
TSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY 2 Basic Definitions Time and Frequency db conversion Power and dbm Filter Basics 3 Filter Filter is a component with frequency
More informationENSC327 Communication Systems 27: Digital Bandpass Modulation. (Ch. 7) Jie Liang School of Engineering Science Simon Fraser University
ENSC37 Communication Systems 7: Digital Bandpass Modulation (Ch. 7) Jie Liang School of Engineering Science Simon Fraser University 1 Outline 7.1 Preliminaries 7. Binary AmplitudeShift Keying (BASK) 7.3
More informationISHIK UNIVERSITY Faculty of Science Department of Information Technology Fall Course Name: Wireless Networks
ISHIK UNIVERSITY Faculty of Science Department of Information Technology 20172018 Fall Course Name: Wireless Networks Agenda Lecture 4 Multiple Access Techniques: FDMA, TDMA, SDMA and CDMA 1. Frequency
More informationLecture #11 Overview. Vector representation of signal waveforms. Twodimensional signal waveforms. 1 ENGN3226: Digital Communications L#
Lecture #11 Overview Vector representation of signal waveforms Twodimensional signal waveforms 1 ENGN3226: Digital Communications L#11 00101011 Geometric Representation of Signals We shall develop a geometric
More informationTSTE17 System Design, CDIO. General project hints. Behavioral Model. General project hints, cont. Lecture 5. Required documents Modulation, cont.
TSTE17 System Design, CDIO Lecture 5 1 General project hints 2 Project hints and deadline suggestions Required documents Modulation, cont. Requirement specification Channel coding Design specification
More informationLecture 10. Digital Modulation
Digital Modulation Lecture 10 OnOff keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary PSK (BPSK) Frequency shift keying Typical spectra Modulation/demodulation
More informationMicrowave Seminar. Noise and Bit Error Ratio. J. Richie. Spring 2013
Microwave Seminar Noise and Bit Error Ratio J. Richie Spring 2013 Outline Noise Noise and Equivalent Temperature Noise Figure Small Scale Fade and Multipath Impulse Response Model Types of Fading Modulation
More informationOnoff keying, which consists of keying a sinusoidal carrier on and off with a unipolar binary signal
Bandpass signalling Thus far only baseband signalling has been considered: an information source is usually a baseband signal. Some communication channels have a bandpass characteristic, and will not propagate
More informationMobile Radio Propagation Channel Models
Wireless Information Transmission System Lab. Mobile Radio Propagation Channel Models Institute of Communications Engineering National Sun Yatsen University Table of Contents Introduction Propagation
More informationChapter 2 Channel Equalization
Chapter 2 Channel Equalization 2.1 Introduction In wireless communication systems signal experiences distortion due to fading [17]. As signal propagates, it follows multiple paths between transmitter and
More informationChapter 1 INTRODUCTION
Chapter 1 INTRODUCTION 1.1 Motivation An increasing demand for high data rates in wireless communications has made it essential to investigate methods of achieving high spectral efficiency which would
More informationChapter 2 DirectSequence Systems
Chapter 2 DirectSequence Systems A spreadspectrum signal is one with an extra modulation that expands the signal bandwidth greatly beyond what is required by the underlying codeddata modulation. Spreadspectrum
More informationChapter 3 Communication Concepts
Chapter 3 Communication Concepts 1 Sections to be covered 3.1 General Considerations 3.2 Analog Modulation 3.3 Digital Modulation 3.4 Spectral Regrowth 3.7 Wireless Standards 2 Chapter Outline Modulation
More informationTSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY
TSEK02: Radio Electronics Lecture 2: Modulation (I) Ted Johansson, EKS, ISY An Overview of Modulation Techniques: chapter 3.1 3.3.1 2 Introduction (3.1) Analog Modulation Amplitude Modulation Phase and
More informationcomparasion to BPSK, to distinguish those symbols, therefore, the error performance is degraded. Fig 2 QPSK signal constellation
Study of Digital Modulation Schemes using DDS 1. Introduction Phase shift keying(psk) is a simple form of data modulation scheme in which the phase of the transmitted signal is varied to convey information.
More informationEXAMINATION FOR THE DEGREE OF B.E. Semester 1 June COMMUNICATIONS IV (ELEC ENG 4035)
EXAMINATION FOR THE DEGREE OF B.E. Semester 1 June 2007 101902 COMMUNICATIONS IV (ELEC ENG 4035) Official Reading Time: Writing Time: Total Duration: 10 mins 120 mins 130 mins Instructions: This is a closed
More informationLab 3.0. Pulse Shaping and Rayleigh Channel. Faculty of Information Engineering & Technology. The Communications Department
Faculty of Information Engineering & Technology The Communications Department Course: Advanced Communication Lab [COMM 1005] Lab 3.0 Pulse Shaping and Rayleigh Channel 1 TABLE OF CONTENTS 2 Summary...
More informationWireless Channel Propagation Model Smallscale Fading
Wireless Channel Propagation Model Smallscale Fading Basic Questions T x What will happen if the transmitter  changes transmit power?  changes frequency?  operates at higher speed? Transmit power,
More informationObjectives. Presentation Outline. Digital Modulation Lecture 01
Digital Modulation Lecture 01 Review of Analogue Modulation Introduction to Digital Modulation Techniques Richard Harris Objectives You will be able to: Classify the various approaches to Analogue Modulation
More informationDigital Modulation Lecture 01. Review of Analogue Modulation Introduction to Digital Modulation Techniques Richard Harris
Digital Modulation Lecture 01 Review of Analogue Modulation Introduction to Digital Modulation Techniques Richard Harris Objectives You will be able to: Classify the various approaches to Analogue Modulation
More informationThus there are three basic modulation techniques: 1) AMPLITUDE SHIFT KEYING 2) FREQUENCY SHIFT KEYING 3) PHASE SHIFT KEYING
CHAPTER 5 Syllabus 1) Digital modulation formats 2) Coherent binary modulation techniques 3) Coherent Quadrature modulation techniques 4) Non coherent binary modulation techniques. Digital modulation formats:
More informationAN INTRODUCTION OF ANALOG AND DIGITAL MODULATION TECHNIQUES IN COMMUNICATION SYSTEM
AN INTRODUCTION OF ANALOG AND DIGITAL MODULATION TECHNIQUES IN COMMUNICATION SYSTEM Rashmi Pandey Vedica Institute of Technology, Bhopal Department of Electronics & Communication rashmipandey07@rediffmail.com
More informationEC6501 Digital Communication
EC6501 Digital Communication UNIT 1 DIGITAL COMMUNICATION SYSTEMS Digital Communication system 1) Write the advantages and disadvantages of digital communication. [A/M 11] The advantages of digital communication
More informationChapter 6 Passband Data Transmission
Chapter 6 Passband Data ransmission Different methods of digital modulation Outline PSK(Phaseshift keying), QAM(Quad. amp. mod), FSK(Phaseshift keying) Coherent detection of modulated signals in AWGN
More informationEE390 Final Exam Fall Term 2002 Friday, December 13, 2002
Name Page 1 of 11 EE390 Final Exam Fall Term 2002 Friday, December 13, 2002 Notes 1. This is a 2 hour exam, starting at 9:00 am and ending at 11:00 am. The exam is worth a total of 50 marks, broken down
More informationANALOGUE TRANSMISSION OVER FADING CHANNELS
J.P. Linnartz EECS 290i handouts Spring 1993 ANALOGUE TRANSMISSION OVER FADING CHANNELS Amplitude modulation Various methods exist to transmit a baseband message m(t) using an RF carrier signal c(t) =
More informationPerformance measurement of different MAry phase signalling schemes in AWGN channel
Research Journal of Engineering Sciences ISSN 2278 9472 Performance measurement of different MAry phase signalling schemes in AWGN channel Abstract Awadhesh Kumar Singh * and Nar Singh Department of Electronics
More informationTheory of Telecommunications Networks
TT S KE M T Theory of Telecommunications Networks Anton Čižmár Ján Papaj Department of electronics and multimedia telecommunications CONTENTS Preface... 5 1 Introduction... 6 1.1 Mathematical models for
More information