# Wireless Communication

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 ECE 461 Fall 26 Wireless Communication Channel Model for Mobile Communications PSfrag replacements s(t) h(ξ) y(t) r(t) w(t) Figure 1: Complex baseband point-to-point communications channel So far we studied the complex baseband model for point-to-point communications shown in Figure 1 Our goal now is to modify this channel model to incorporate the effects of the mobility We will focus on terrestrial mobile communications channels satellite channels are more well-behaved The following are points worth noting in making the transition to the mobile communication channel model The additive noise term w(t) is always present whether the channel is point-to-point or mobile, and usually w(t) is modelled as proper complex WGN For point-to-point communications the channel response is generally well modelled by a linear time invariant (LTI) system (h(ξ) may or may not be known at the receiver) For mobile communications, the channel response is time-varying, and we will see that it is well modelled as a linear time-varying (LTV) system To study the mobile communications channel, consider the situation where the mobile station (MS) is at location (x, y) or (d, ϕ) in a coordinate system with the base station (BS) at the origin as shown in Figure 2 A 3-d model may be more appropriate in some situations, but for simplicity we will consider a 2-d model Also, we restrict our attention now to the channel connecting one pair of transmit (Tx) and receive (Rx) antennas If the mobile is fixed at location (d, ϕ), the channel that it sees is time-invariant The response of this time-invariant channel is a function of the location, and is determined by all paths connecting the BS and the MS Thus we have the system shown in Figure 3, where h d,ϕ (ξ) is the impulse response of a causal LTI system, which is a function of the multipath profile between the BS and MS Referring to Figure 2, suppose the n-th path connecting the BS and MS has amplitude gain β n (d, ϕ) and delay τ n (d, ϕ) The delay of τ n (d, ϕ) introduces a carrier phase shift of φ n (d, ϕ) = 2πf c τ n (d, ϕ) + constant where the constant depends on the reflectivity of the surface(s) that reflect the path Then we can c VV Veeravalli, 26 1

2 Y MS PSfrag replacements d ϕ BS X Figure 2: Multipath channel seen at location (d, ϕ) for one Tx&Rx antenna pair PSfrag replacements s(t) h d,ϕ (ξ) y(t) Figure 3: Causal LTI system representing multipath profile at location (d, ϕ) write the output y(t) in terms of the input s(t) as y(t) = n β n (d, ϕ) e jφn(d,ϕ) s(t τ n (d, ϕ)) which implies that the impulse response is h d,ϕ (ξ) = n β n (d, ϕ) e jφn(d,ϕ) δ(ξ τ n (d, ϕ)) Scales of Variation As the MS moves, (d, ϕ) change with time and the linear system associated with the channel becomes LTV There are two scales of variation: The first is a small-scale variation due to rapid changes in the phase φ n as the mobile moves over distances of the order of a wavelength of the carrier λ c = c/f c, where c is the velocity of light This is because movements in space of the order of a wavelength cause changes in τ n of the order of 1/f c, which in turn cause changes in φ n of the order of 2π (Note that for a 9 MHz carrier, λ c 1/3 m) Modeling the phases φ n as independent Uniform[, 2π] random variables, we can see that the average power gain in the vicinity of (d, ϕ) is given by n β2 n(d, ϕ) We denote this average power gain by G(d, ϕ) c VV Veeravalli, 26 2

3 The second is a large-scale variation due to changes in {β n (d, ϕ)} and {τ n (d, ϕ)} both in the number of paths and their strengths These changes happen on the scale of the distance between objects in the environment To study these two scales of variation separately, we redraw Figure 3 in terms of two components as shown in Figure 4 PSfrag replacements s(t) x c d,ϕ (ξ) y(t) G(d, ϕ) Figure 4: Small-scale and large-scale variation components of channel Here c d,ϕ is normalized so that the average power gain introduced by c d,ϕ is 1, ie c d,ϕ (ξ) = n β n (d, ϕ)e jφn(d,ϕ) δ(ξ τ n (d, ϕ)) where {β n (d, ϕ)} is normalized so that n β2 n (d, ϕ) = 1 The large-scale variations in (average) amplitude gain are then lumped into the multiplicative term G(d, ϕ) The goal of wireless channel modeling is to find useful analytical models for the variations in the channel Models for the large scale variations are useful in cellular capacity-coverage optimization and analysis, and in radio resource management (handoff, admission control, and power control) Models for the small scale variations are more useful in the design of digital modulation and demodulation schemes (that are robust to these variations) We hence focus on the small scale variations in this class Small-scale Variations in Gain PSfrag replacements s(t) c d,ϕ (ξ) y(t) G Figure 5: Small-scale variations in the channel (with large-scale variations treated as constant) Recall that the small scale variations in the channel are captured in a linear system with response c d,ϕ (ξ) = n β n (d, ϕ)e jφn(d,ϕ) δ(ξ τ n (d, ϕ)), c VV Veeravalli, 26 3

4 where the {β n (d, ϕ)} are normalized so that n β2 n(d, ϕ) = 1 As (d, ϕ) changes with t, the channel corresponding to the small-scale variations becomes time-varying and we get: c(t; ξ) := c d(t),ϕ(t) (ξ) = n β n (t) e jφn(t) δ(ξ τ n (t)) Treating the large scale variations G(d, ϕ) as roughly constant (see Figure 5), we obtain: y(t) = G c(t; ξ)s(t ξ)dξ Finally, we may absorb the scaling factor G into the signal s(t), with the understanding that the power of s(t) is the received signal power after passage through the channel Then y(t) = c(t; ξ)s(t ξ)dξ Doppler shifts in phase For movements of the order of a few wavelengths, {β n (t)} and {τ n (t)} are roughly constant, and the time variations in c(t; ξ) are mainly due to changes in {φ n (t)}, ie, c(t; ξ) n β n e jφn(t) δ(ξ τ n ) From this equation it is clear that the magnitude of the impulse response c(t; ξ) is roughly independent of t A typical plot of c(t; ξ) is shown in Figure 6 The width of the delay profile (delay spread) is of the order of tens of microseconds for outdoor channels, and of the order of hundreds of nanoseconds for indoor channels Note that the paths typically appear in clusters in the delay profile (why?) To study the phase variations φ n (t) in more detail, consider a mobile that is traveling with velocity v and suppose that the n-th path has an angle of arrival θ n (t) with respect to the velocity vector as shown in Figure 7 (Note that we may assume that θ n is roughly constant over the time horizon corresponding to a few wavelengths) Then for small t, φ n (t + t ) φ n (t) 2πf cv t cos θ n c = 2πv t λ c cos θ n, where λ c is the carrier wavelength and c is the velocity of light The frequency shift introduced by the movement of the mobile is hence given by φ n (t + t ) φ n (t) lim = v cos θ n = f max cos θ n, t 2π t λ c where f max = v/λ c is called the maximum Doppler frequency We will use this model for the variations in φ n (t) to characterize small-scale variations statistically in the following section Definition 1 The quantity τ ds = max τ n (d, ϕ) min τ n (d, ϕ) is called the delay spread of the channel c VV Veeravalli, 26 4

5 c(t; ξ) β (LOS) PSfrag replacements β n τ ds τ n ξ Figure 6: Typical delay profile of channel with LOS path having delay Without loss of generality, we may assume that the delay corresponding to the first path arriving at the receiver is Then min τ n (d, ϕ) =, τ ds = max τ n (d, ϕ), and: y(t) = τds c(t; ξ)s(t ξ)dξ PSfrag replacements v t cos θ n θ n v t v Figure 7: Doppler Shifts c VV Veeravalli, 26 5

6 Frequency Nonselective (Flat) Fading If the bandwidth of transmitted signal s(t) is much smaller than 1/τ ds, then s(t) does not change much over time intervals of the order of τ ds Thus y(t) s(t) τds c(t, ξ) = s(t) n β n e jφn(t) This implies that the multipath channel simply scales the transmitted signal without introducing significant frequency distortion The variations with time of this scale factor are referred to as frequency nonselective, or flat, fading Note that the distortions introduced by the channel depend on the relationship between the delay spread of the channel and the bandwidth of the signal The same channel may be frequency selective or flat, depending on the bandwidth of the input signal With a delay spread of 1 µs corresponding to a typical outdoor urban environment, an AMPS signal (3 khz) undergoes flat fading, whereas an IS-95 CDMA signal (125 MHz) undergoes frequency selective fading For flat fading, the channel model simplifies to y(t) = V (t)s(t) where V (t) = τds c(t, ξ)dξ = n β n e jφn(t) Purely Diffuse Scattering - Rayleigh Fading Our goal is to model {V (t)} statistically, but before we do that we distinguish between the cases where the multipath does or does not have a line-of-sight (LOS) component In the latter case, the multipath is produced only from reflections from objects in the environment This form of scattering is purely diffuse and can be assumed to form a continuum of paths, with no one path dominating the others in strength When there is a LOS component, it usually dominates all the diffuse components in signal strength To model {V (t)} statistically, we first fit a stochastic model to the phases {φ n (t)} n=1,2, Assumption 1 The phases {φ n (t)} n=1,2, are well modeled as independent stochastic processes, with φ n (t) being uniformly distributed on [, 2π] for each t and n Using this assumption, we get the following results: ➀ {V (t)} is a zero-mean process This is because E [V (t)] = n β n E [ e jφn(t)] = ➁ The process {v n (t)} defined by v n (t) = β n e jφn(t) is a proper complex random process c VV Veeravalli, 26 6

7 Proof We need to show that the pseudocovariance function of {v n (t)} equals zero C(t + τ, t) = E[v n (t)v n (t + τ)] = E[(β n e jφn(t) )(β n e jφn(t+τ) )] = βne[e 2 j(φn(t)+φn(t+τ)) ] βn 2 E[ej(2φn(t)+2πfmaxτ cos θn) ] = where the approximation on the last line follows from the Doppler equation ➂ If the number of paths is large, we may apply the Central Limit Theorem to conclude that {V (t)} is a proper complex Gaussian (PCG) random process First order statistics of {V (t)} for purely diffuse scattering For fixed t, V (t) = V I (t) + jv Q (t) is PCG random variable with [ E V (t) 2] = βn 2 = 1 n Since V (t) is proper, V I (t) and V Q (t) are uncorrelated and have the same variance, which equals half the variance of V (t) Since V (t) is also Gaussian, V I (t) and V Q (t) are independent as well Thus V I (t) and V Q (t) are independent N (, 1/2) random variables Envelope and Phase Processes The envelope process {α(t)} and the phase process {φ(t)} are defined by α(t) = V (t) = V 2 I (t) + V 2 Q (t), and φ(t) = tan 1 ( VQ (t) V I (t) ) We can write x(t) = V (t)s(t) in terms of α(t) and φ(t) as: x(t) = α(t)e jφ(t) s(t) This means that for flat fading, the channel is seen as a single path with gain α(t) and phase shift φ(t) Note that α and φ vary much more rapidly than the gain and phase of the individual paths β n and φ n (why?) For fixed t, using the fact that V I (t) and V Q (t) are independent N (, 1/2) random variables, it is easy to show that α(t) and φ(t) are independent random variables with α(t) having a Rayleigh pdf and φ(t) being uniform on [, 2π] The pdf of α(t) is given by p α (x) = 2xe x2 1 {x } It is easy to show that E[α] = [ π/4 and E[α 2 ] = E V (t) 2] = 1 Since the envelope has a Rayleigh pdf, purely diffuse fading is referred to as Rayleigh fading c VV Veeravalli, 26 7

8 Figure 8: Rayleigh pdf Scattering with a LOS component Ricean Fading If there is a LOS (specular) path with parameters θ, β and φ (t) in addition to the diffuse components, then V (t) = β e jφ(t) + 1 β 2 ˇV (t) where { ˇV (t)} is a zero mean PCG, Rayleigh fading process with variance E [ ˇV (t) 2] = 1 Note: {V (t)} is also a zero-mean process, but it is not Gaussian since the LOS component {β e jφ (t) } dominates the diffuse components in power However, conditioned on {φ (t)}, {V (t)} is a PCG process with mean {β e jφ (t) } Rice Factor: The Rice factor κ is defined by κ = From the definition of κ it follows that β = power in the LOS component total power in diffuse components = β2 1 β 2 κ κ + 1, and 1 β2 = 1 (κ + 1) For fixed t, the pdf of the envelope α(t) can be found by first computing the joint pdf of α(t) and φ(t), conditioned on φ (t) This is straightforward since, conditioned on φ (t), V (t) is a PCG random variable with mean β e jφ (t) We can then show that the pdf of α(t) conditioned on φ (t) is not a function of φ (t), and we get: p α φ (x) = 2x ( ) [ 2xβ 1 β 2 I 1 β 2 exp x2 + β 2 ] 1 β 2 1 {x } = p α (x) This pdf is called a Ricean pdf and it can be rewritten in terms of κ as: p α (x) = 2x(κ + 1) I (2x ) κ(κ + 1) exp [ x 2 (κ + 1) κ ] 1 {x } where I ( ) is the zeroth order modified Bessel function of 1st kind, ie, I (y) = 1 2π π π exp(y cos φ)dφ c VV Veeravalli, 26 8

9 It is easy to see that when κ =, p α (x) reduces to a Rayleigh pdf The pdf of α 2 (t) is easily computed as: p α 2(x) = p α( x) ( 2 x = (κ + 1) I 2 ) xκ(κ + 1) exp [ x(κ + 1) κ] 1 {x } Rayleigh Ricean κ=1 Ricean κ=5 Ricean κ= Figure 9: Ricean pdf for various Rice factors Signaling Through Slow Flat Fading Channels We assume that the long-term variations in the channel are absorbed into E m Then E m represents the average received symbol energy (for symbol m) over the time frame for which the multipath profile may be assumed to be constant Then the received signal is given by: where E[α 2 (t)] = 1 r(t) = V (t)s(t) + w(t) = α(t)e jφ(t) s(t) + w(t) For slow fading, α(t) and φ(t) may be assumed to be constant over each symbol period Thus, for memorlyless modulation and symbol-by-symbol demodulation, y(t) for demodulation over symbol period [, T s ] may be written as r(t) = αe jφ s m (t) + w(t) (conditioned on symbol m being transmitted) Average probability of error for slow, flat fading The error probability is a function of the received signal-to-noise ratio (SNR), ie, the received symbol energy divided by the noise power spectral density We denote the symbol SNR by γ s, and the corresponding bit SNR by γ b, where γ b = γ/ν and ν = log 2 M c VV Veeravalli, 26 9

10 For slow, flat fading, the received SNR is γ s = α2 E s N The average SNR (averaging over α 2 ) is given by The corresponding bit SNR s are given by γ s = E[α 2 ] E s N = E s N γ b = γ ν, and γ b = E s N ν = E b N Suppose the symbol error probability with SNR γ s is denoted by P e (γ s ) Then the average error probability (averaged over the fading) is where p γs (x) is the pdf of γ s P e = P e (x)p γs (x)dx For Rayleigh fading, α 2 is exponential with mean 1; hence γ s is exponential with mean γ s, ie, p γs (x) = 1 ] exp [ xγs 1 γ {x } s For Ricean fading, γ s has pdf ( p γs (x) = κ + 1 I 2 γ s ) xκ(κ + 1) γ s [ ] x(κ + 1) exp κ γ s 1 {x } P e for Rayleigh Fading Useful result (see problem 1 of HW#1): Q( x ) e x/γ dx = 1 [ γ 1 γ γ ] BPSK P b (γ b ) = Q( 2γ b ) Thus we get [ P b = Q( 2x )p γb (x)dx = γ b 1 + γ b ] 1 4γ b (for largeγ b ) c VV Veeravalli, 26 1

11 Binary coherent orthogonal modulation (eg FSK) P b (γ b ) = Q( γ b ) Here P b is the same as that for BPSK with γ b replaced by γ b /2, ie, [ ] P b = 1 γ 1 b 1 (for large γ γ b 2γ b ) b Binary DPSK P b (γ b ) = 1 2 e γ b In this we case we may integrate directly to get P b = 1 e x/γb e x dx = 2 γ b Binary noncoherent orthogonal modulation (FSK) 1 2(1 + γ b ) 1 2γ b (for large γ b ) P b (γ b ) = 1 2 e γ b/2 Here P b is the same as that for DPSK with γ b replaced by γ b /2, ie, P b = γ b 1 γ b (for large γ b ) Similar expressions may be derived for other M-ary modulation schemes Note that without fading the error probabilities decrease exponentially with SNR, whereas with fading the error probabilities decrease much more slowly with SNR (inverse linear in case of Rayleigh fading) P e for Ricean Fading Direct approach: Compute P e by direct integration of P e (γ s ) wrt p γs This is cumbersome except in some special cases Binary DPSK [ ] κ + 1 P b = 2(κ γ b ) exp κγ b κ γ b as done in class Again, it is easy to check that we get the Rayleigh result when κ = and the AWGN result as κ Binary noncoherent FSK Same as DPSK with γ b replaced by γ b /2 There are other approaches for computing expressions for the error probability for Ricean fading channels, which are beyond the scope of this class c VV Veeravalli, 26 11

13 The MPE (ML) decision rule is the same as without diversity except that the constellation is scaled in amplitude based on the fading on the channels Special Case: BPSK with diversity The sufficient statistic in this case takes the form R = ± where W = L α l Eb,l W l is PCG with L α 2 l E b,l + W, E[ W 2 ] = N L E b,l α 2 l The MPE decision rule for equal priors (or the ML decision rule)is to decide +1 (symbol 1) if R I >, and 1 (symbol 2) if R I < For fixed {α l }, P b = P({R I > } {symbol 2 sent}) = P = Q L 2 α 2 l E b,l N = Q L 2 { γ b,l W I > } L α 2 l E b,l ( ) = Q 2γb where γ b,l is the received bit SNR on the l-th channel, and γ b = L γ b,l is the total received bit SNR The average BER is given by P b = ( ) Q 2x p γb (x)dx Thus, we may evaluate P b by first finding the pdf p γb (x) Special case: Rayleigh fading If the fading is Rayleigh on all channels, then Case 1: γ b,l s are distinct for l = 1, 2,, L P b = L C l 2 [ 1 γb,l 1 + γ b,l ] where C l = i l γ b,l γ b,l γ b,i c VV Veeravalli, 26 13

14 Case 2: γ b,l s are identical, ie γ b,l = γ b /L for all l P b = [ ( γb A L )] L L 1 ( L 1 + l l l= )[ 1 A ( )] l γb L with A ( ) [ γb = 1 γ 1 b L 2 L + γ b ] For large γ b, Thus A ( ) γb L L 4γ b and 1 A ( ) γb 1 L ( ) L L L ( ) ( ) L 1 + l L L ( ) 2L 1 P b = 4γ b l 4γ b L Note that with diversity P b decreases at (γ b ) L which is a significant improvement over the inverse linear performance obtained without diversity (See Figure 1) 1 1 Performance of BPSK with diversity on Rayleigh fading channel 1 2 Average Probability of Bit Error L=8 L=4 L=2 L= Average Bit SNR Figure 1: BPSK with diversity on Rayleigh fading channels c VV Veeravalli, 26 14

### Digital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System

Digital Modulation David Tipper Associate Professor Department of Information Science and Telecommunications University of Pittsburgh http://www.tele.pitt.edu/tipper.html Typical Communication System Source

### PHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUMBER OF REFERENCE SYMBOLS

PHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUM OF REFERENCE SYMBOLS Benjamin R. Wiederholt The MITRE Corporation Bedford, MA and Mario A. Blanco The MITRE

### Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur

Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 3 Rayleigh Fading and BER of Wired Communication

### Wireless Channel Models 8-1

Wireless Channel Models 8-1 Why do we need models? Help analyze the performance of large systems Ask fundamental questions about a system E.g. what is the best I can do with a given system? Allows comparison

### ABHELSINKI UNIVERSITY OF TECHNOLOGY

Fading Models S-72.333 Physical Layer Methods in Wireless Communication Systems Fabio Belloni Helsinki University of Technology Signal Processing Laboratory fbelloni@wooster.hut.fi 23 November 2004 Belloni,F.;

### Errata Introduction to Wireless Systems P. Mohana Shankar. Page numbers are shown in blue Corrections are shown in red.

Errata Introduction to Wireless Systems P. Mohana Shankar Page numbers are shown in blue Corrections are shown in red February 25 Page 11 below Figure 2.4 The power detected by a typical receiver is shown

### 3.5.1 CORRELATION MODELS FOR FREQUENCY SELECTIVE FADING

Environment Spread Flat Rural.5 µs Urban 5 µs Hilly 2 µs Mall.3 µs Indoors.1 µs able 3.1: ypical delay spreads for various environments. If W > 1 τ ds, then the fading is said to be frequency selective,

### Principles of Digital Modulation. Dr Mike Fitton, Telecommunications Research Lab Toshiba Research Europe Limited

Principles of Digital Modulation Dr Mike Fitton, mike.fitton@toshiba-trel.com Telecommunications Research Lab Toshiba Research Europe Limited 1 Principles of Digital Modulation: Outline of Lectures Introduction

### FUNDAMENTALS OF WIRELESS COMMUNICATIONS

Objectives: 1) basic channel models 2) factors that determines throughput/bit error rate in wireless communication Readings: 1. Rappaport, Wireless Communications: Principles and Practice, Pearson (chap

### Unit 3 Spread Spectrum Modulation

Unit 3 Spread Spectrum Modulation Instructor: Sau-Hsuan Wu Dept. of Electrical and Computer Eng., NCTU 1 What is spread spectrum modulation? A means of transmission in which data sequences occupy a bandwidth

### Probability and Random Variables. Generation of random variables (r.v.)

Probability and Random Variables Method for generating random variables with a specified probability distribution function. Gaussian And Markov Processes Characterization of Stationary Random Process Linearly

### WiMAX Performance Analysis under the Effect of Doppler s Shift

WiMAX Performance Analysis under the Effect of Doppler s Shift Navgeet Singh 1, Amita Soni 2 1, 2 Department of Electronics and Electrical Engineering, PEC University of Technology, Chandigarh, India Abstract:

### 2 The wireless channel

CHAPTER The wireless channel A good understanding of the wireless channel, its key physical parameters and the modeling issues, lays the foundation for the rest of the book. This is the goal of this chapter.

### Wireless Communication Technologies

1 Wireless Communication Technologies Lin DAI Requirement 2 Prerequisite: Principles of Communications A certain math background Probability, Linear Algebra, Matrix Be interactive in class! Think independently!

### EE4367 Telecom. Switching & Transmission. Prof. Murat Torlak

Path Loss Radio Wave Propagation The wireless radio channel puts fundamental limitations to the performance of wireless communications systems Radio channels are extremely random, and are not easily analyzed

### Contents. A Error probability for PAM Signals in AWGN 17. B Error probability for PSK Signals in AWGN 18

Contents 5 Signal Constellations 3 5.1 Pulse-amplitude Modulation (PAM).................. 3 5.1.1 Performance of PAM in Additive White Gaussian Noise... 4 5.2 Phase-shift Keying............................

Fading multipath radio channels Narrowband channel modelling Wideband channel modelling Wideband WSSUS channel (functions, variables & distributions) Low-pass equivalent (LPE) signal ( ) = Re ( ) s t RF

### Chapter 2 Mobile Communication

Page 77 Chapter 2 Mobile Communication 2.1 Characteristics of Mobile Computing 2.2 Wireless Communication Basics 2.3 Wireless Communication Technologies PANs (Bluetooth, ZigBee) Wireless LAN (IEEE 802.11)

### Antennas & Propagation. CS 6710 Spring 2010 Rajmohan Rajaraman

Antennas & Propagation CS 6710 Spring 2010 Rajmohan Rajaraman Introduction An antenna is an electrical conductor or system of conductors o Transmission - radiates electromagnetic energy into space o Reception

### MODULATION Systems (part 1)

Technologies and Services on Digital Broadcasting (8) MODULATION Systems (part ) "Technologies and Services of Digital Broadcasting" (in Japanese, ISBN4-339-62-2) is published by CORONA publishing co.,

### EE4512 Analog and Digital Communications Chapter 5. Chapter 5 Digital Bandpass Modulation and Demodulation Techniques

Chapter 5 Digital Bandpass Modulation and Demodulation Techniques Chapter 5 Digital Bandpass Modulation and Demodulation Techniques Binary Amplitude Shift Keying Pages 212-219 219 The analytical signal

### Appendix D Digital Modulation and GMSK

D1 Appendix D Digital Modulation and GMSK A brief introduction to digital modulation schemes is given, showing the logical development of GMSK from simpler schemes. GMSK is of interest since it is used

### Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network

Recent Advances in Electrical Engineering and Electronic Devices Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network Ahmed El-Mahdy and Ahmed Walid Faculty of Information Engineering

### Index Terms: 8 PSK modulation, LMS Linear equalizer, Rayleigh fading, Doppler effect, constellation diagram. Fig.1 A constellation diagram for 8-PSK.

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 3 Issue. 3 Equalization of Doppler Effect Using Constellation Diagram of 8- PSK Modulation Vinay Negi 1, Sanjeev Kumar

### Modulation methods. S-72. 333 Physical layer methods in wireless communication systems. Sylvain Ranvier / Radio Laboratory / TKK 16 November 2004

Modulation methods S-72. 333 Physical layer methods in wireless communication systems Sylvain Ranvier / Radio Laboratory / TKK 16 November 2004 sylvain.ranvier@hut.fi SMARAD / Radio Laboratory 1 Line out

### 5 Signal Design for Bandlimited Channels

225 5 Signal Design for Bandlimited Channels So far, we have not imposed any bandwidth constraints on the transmitted passband signal, or equivalently, on the transmitted baseband signal s b (t) I[k]g

### I. Wireless Channel Modeling

I. Wireless Channel Modeling April 29, 2008 Qinghai Yang School of Telecom. Engineering qhyang@xidian.edu.cn Qinghai Yang Wireless Communication Series 1 Contents Free space signal propagation Pass-Loss

### Introduction. Antennas and Propagation. Types of Antennas. Radiation Patterns. Antenna Gain. Antenna Gain

Introduction Antennas and Propagation Chapter 5 An antenna is an electrical conductor or system of conductors Transmission - radiates electromagnetic energy into space Reception - collects electromagnetic

Benha Faculty of Engineering Electrical Engineering Department 5 th Year Telecommunication Final Exam: 26 May 2012 Examiner: Dr. Hatem ZAKARIA Time allowed: 3 Hours Radio and Television (E522) Answer All

### CDMA Performance under Fading Channel

CDMA Performance under Fading Channel Ashwini Dyahadray 05307901 Under the guidance of: Prof Girish P Saraph Department of Electrical Engineering Overview Wireless channel fading characteristics Large

### Indoor Propagation Models

Indoor Propagation Models Outdoor models are not accurate for indoor scenarios. Examples of indoor scenario: home, shopping mall, office building, factory. Ceiling structure, walls, furniture and people

### TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS

TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of

### Signal Encoding Techniques

Signal Encoding Techniques Guevara Noubir noubir@ccs.neu.edu 1 Reasons for Choosing Encoding Techniques Digital data, digital signal Equipment less complex and expensive than digital-to-analog modulation

### Department of Electrical and Computer Engineering Ben-Gurion University of the Negev. LAB 1 - Introduction to USRP

Department of Electrical and Computer Engineering Ben-Gurion University of the Negev LAB 1 - Introduction to USRP - 1-1 Introduction In this lab you will use software reconfigurable RF hardware from National

### IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 1, JANUARY 2007 341

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 1, JANUARY 2007 341 Multinode Cooperative Communications in Wireless Networks Ahmed K. Sadek, Student Member, IEEE, Weifeng Su, Member, IEEE, and K.

### ABHELSINKI UNIVERSITY OF TECHNOLOGY

Basic of Propagation Theory S-72.333 Physical Layer Methods in Wireless Communication Systems Fabio Belloni Helsinki University of Technology Signal Processing Laboratory fbelloni@wooster.hut.fi 23 November

### CS263: Wireless Communications and Sensor Networks

CS263: Wireless Communications and Sensor Networks Matt Welsh Lecture 2: RF Basics and Signal Encoding September 22, 2005 2005 Matt Welsh Harvard University 1 Today's Lecture Basics of wireless communications

### Lecture 1: Introduction

Mobile Data Networks Lecturer: Victor O.K. Li EEE Department Room: CYC601D Tel.: 857 845 Email: vli@eee.hku.hk Course home page: http://www.eee.hku.hk/courses.msc/ 1 Lecture 1: Introduction Mobile data

### A SIMULATION STUDY ON SPACE-TIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT

A SIMULATION STUDY ON SPACE-TIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT U. Trautwein, G. Sommerkorn, R. S. Thomä FG EMT, Ilmenau University of Technology P.O.B.

### Nonparametric adaptive age replacement with a one-cycle criterion

Nonparametric adaptive age replacement with a one-cycle criterion P. Coolen-Schrijner, F.P.A. Coolen Department of Mathematical Sciences University of Durham, Durham, DH1 3LE, UK e-mail: Pauline.Schrijner@durham.ac.uk

### Principles of Digital Communication

Principles of Digital Communication Robert G. Gallager January 5, 2008 ii Preface: introduction and objectives The digital communication industry is an enormous and rapidly growing industry, roughly comparable

### Lezione 6 Communications Blockset

Corso di Tecniche CAD per le Telecomunicazioni A.A. 2007-2008 Lezione 6 Communications Blockset Ing. Marco GALEAZZI 1 What Is Communications Blockset? Communications Blockset extends Simulink with a comprehensive

### Multiple Access Techniques

Multiple Access Techniques Dr. Francis LAU Dr. Francis CM Lau, Associate Professor, EIE, PolyU Content Introduction Frequency Division Multiple Access Time Division Multiple Access Code Division Multiple

Symbol interval T=1/(2B); symbol rate = 1/T=2B transmissions/sec (The transmitted baseband signal is assumed to be real here) Noise power = (N_0/2)(2B)=N_0B \Gamma is no smaller than 1 The encoded PAM

### Outlines. LECTURE 3: Wireless Transmission Technologies. Wireless Transmission on Unguided Media

LECTURE 3: Wireless Transmission Technologies CIS 472 Wireless Communications and Networks Winter 2016 Instructor: Dr. Song Xing Outlines Wireless Data Transmission Modulation Spread Spectrum Department

### Noise Terminology: An Overview of Noise Terminology and Applications Author: Bob Muro, Applications Engineer

Noise Terminology: An Overview of Noise Terminology and Applications Author: Bob Muro, Applications Engineer Today s Webinar Important noise characteristics Technologies effected by noise Noise applications

### ISI Mitigation in Image Data for Wireless Wideband Communications Receivers using Adjustment of Estimated Flat Fading Errors

International Journal of Engineering and Management Research, Volume-3, Issue-3, June 2013 ISSN No.: 2250-0758 Pages: 24-29 www.ijemr.net ISI Mitigation in Image Data for Wireless Wideband Communications

### Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur

Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 1 Introduction to 3G/4G Standards (Refer Slide

### Implementation of Digital Signal Processing: Some Background on GFSK Modulation

Implementation of Digital Signal Processing: Some Background on GFSK Modulation Sabih H. Gerez University of Twente, Department of Electrical Engineering s.h.gerez@utwente.nl Version 4 (February 7, 2013)

### Unit 1 Digital Data transmission

Unit 1 Digital Data transmission Digital Transmission Digital data needs to be carried on an analog signal. A carrier signal (frequency f c ) performs the function of transporting the digital data in an

### QAM Demodulation. Performance Conclusion. o o o o o. (Nyquist shaping, Clock & Carrier Recovery, AGC, Adaptive Equaliser) o o. Wireless Communications

0 QAM Demodulation o o o o o Application area What is QAM? What are QAM Demodulation Functions? General block diagram of QAM demodulator Explanation of the main function (Nyquist shaping, Clock & Carrier

### PART 5D TECHNICAL AND OPERATING CHARACTERISTICS OF MOBILE-SATELLITE SERVICES RECOMMENDATION ITU-R M.1188

Rec. ITU-R M.1188 1 PART 5D TECHNICAL AND OPERATING CHARACTERISTICS OF MOBILE-SATELLITE SERVICES Rec. ITU-R M.1188 RECOMMENDATION ITU-R M.1188 IMPACT OF PROPAGATION ON THE DESIGN OF NON-GSO MOBILE-SATELLITE

### Capacity Limits of MIMO Channels

Tutorial and 4G Systems Capacity Limits of MIMO Channels Markku Juntti Contents 1. Introduction. Review of information theory 3. Fixed MIMO channels 4. Fading MIMO channels 5. Summary and Conclusions References

### Environmental Effects On Phase Coherent Underwater Acoustic Communications: A Perspective From Several Experimental Measurements

Environmental Effects On Phase Coherent Underwater Acoustic Communications: A Perspective From Several Experimental Measurements T. C. Yang, Naval Research Lab., Washington DC 20375 Abstract. This paper

### PERFORMANCE ANALYSIS OF MC-CDMA OVER DIFFERENT FADING CHANNELS

PERFORMANCE ANALYSIS OF MC-CDMA OVER DIFFERENT FADING CHANNELS Vinita 1, Amita Soni 2 1M.Tech. Student, Electronics & Communication, PEC University of Technology, Chandigarh, India 2Assistant Professor,

### Lecture 1 Wireless Channel

Leture 1 Wireless Channel I-Hsiang Wang ihwang@ntu.edu.tw 2/20, 2014 Wireless hannels vary at two sales Channel quality Time Large-sale fading: path loss, shadowing, et. Small-sale fading: onstrutive/destrutive

### Performance of Quasi-Constant Envelope Phase Modulation through Nonlinear Radio Channels

Performance of Quasi-Constant Envelope Phase Modulation through Nonlinear Radio Channels Qi Lu, Qingchong Liu Electrical and Systems Engineering Department Oakland University Rochester, MI 48309 USA E-mail:

### EE2/ISE2 Communications II

EE2/ISE2 Communications II Part I Communications Principles Dr. Darren Ward Chapter 1 Introduction 1.1 Background Communication involves the transfer of information from one point to another. In general,

### P(a X b) = f X (x)dx. A p.d.f. must integrate to one: f X (x)dx = 1. Z b

Continuous Random Variables The probability that a continuous random variable, X, has a value between a and b is computed by integrating its probability density function (p.d.f.) over the interval [a,b]:

### Rayleigh Fading Channels in Mobile Digital Communication Systems Part I: Characterization Bernard Sklar, Communications Engineering Services

ABSTRACT When the mechanisms of channels were first modeled in the 95s and 96s, the ideas were primarily applied to over-thehorizon communications covering a wide range of frequency bands. The 3 3 MHz

### Example/ an analog signal f ( t) ) is sample by f s = 5000 Hz draw the sampling signal spectrum. Calculate min. sampling frequency.

1 2 3 4 Example/ an analog signal f ( t) = 1+ cos(4000πt ) is sample by f s = 5000 Hz draw the sampling signal spectrum. Calculate min. sampling frequency. Sol/ H(f) -7KHz -5KHz -3KHz -2KHz 0 2KHz 3KHz

### Non-Data Aided Carrier Offset Compensation for SDR Implementation

Non-Data Aided Carrier Offset Compensation for SDR Implementation Anders Riis Jensen 1, Niels Terp Kjeldgaard Jørgensen 1 Kim Laugesen 1, Yannick Le Moullec 1,2 1 Department of Electronic Systems, 2 Center

### HD Radio FM Transmission System Specifications Rev. F August 24, 2011

HD Radio FM Transmission System Specifications Rev. F August 24, 2011 SY_SSS_1026s TRADEMARKS HD Radio and the HD, HD Radio, and Arc logos are proprietary trademarks of ibiquity Digital Corporation. ibiquity,

### The Vertical Handoff Algorithm using Fuzzy Decisions in Cellular Phone Networks

International Journal of Electronics Engineering, 2(), 200, pp. 29-34 The Vertical Handoff Algorithm using Fuzzy Decisions in Cellular Phone Networks Chandrashekhar G.Patil & R.D.Kharadkar 2 Department

### 3GPP FDD Base Station Tests with Signal Generators and Analyzers

3GPP FDD Base Station Tests with Signal Generators and Analyzers 1GPP-Dq 04/02 1 3GPP tests with SMIQ Agenda to TS 25.141 Adjacent channel selectivity 1GPP-Dq 04/02 2 Base stations Multi standard base

### Revision 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

### Some stability results of parameter identification in a jump diffusion model

Some stability results of parameter identification in a jump diffusion model D. Düvelmeyer Technische Universität Chemnitz, Fakultät für Mathematik, 09107 Chemnitz, Germany Abstract In this paper we discuss

### DVB-T. The echo performance of. receivers. Theory of echo tolerance. Ranulph Poole BBC Research and Development

The echo performance of DVB-T Ranulph Poole BBC Research and Development receivers This article introduces a model to describe the way in which a single echo gives rise to an equivalent noise floor (ENF)

### T-79.7001 Postgraduate Course in Theoretical Computer Science T-79.5401 Special Course in Mobility Management: Ad hoc networks (2-10 cr) P V

T-79.7001 Postgraduate Course in Theoretical Computer Science T-79.5401 Special Course in Mobility Management: Ad hoc networks (2-10 cr) P V professor Hannu H. Kari Laboratory for Theoretical Computer

### CDMA Technology : Pr. S. Flament www.greyc.fr/user/99. Pr. Dr. W. Skupin www.htwg-konstanz.de. On line Course on CDMA Technology

CDMA Technology : Pr. Dr. W. Skupin www.htwg-konstanz.de Pr. S. Flament www.greyc.fr/user/99 On line Course on CDMA Technology CDMA Technology : Introduction to Spread Spectrum Technology CDMA / DS : Principle

### A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails

12th International Congress on Insurance: Mathematics and Economics July 16-18, 2008 A Uniform Asymptotic Estimate for Discounted Aggregate Claims with Subexponential Tails XUEMIAO HAO (Based on a joint

### Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics. Indian Institute of Technology, Delhi

Basic Quantum Mechanics Prof. Ajoy Ghatak Department of Physics. Indian Institute of Technology, Delhi Module No. # 02 Simple Solutions of the 1 Dimensional Schrodinger Equation Lecture No. # 7. The Free

Direct Sequence Spreading Gene W. Marsh I. A General Description of Direct Sequence Spreading A. The standard view of a communication syste m Channel Encoder Modulator Channel Demodulator Channel Decoder

### TTT4110 Information and Signal Theory Solution to exam

Norwegian University of Science and Technology Department of Electronics and Telecommunications TTT4 Information and Signal Theory Solution to exam Problem I (a The frequency response is found by taking

### communication over wireless link handling mobile user who changes point of attachment to network

Wireless Networks Background: # wireless (mobile) phone subscribers now exceeds # wired phone subscribers! computer nets: laptops, palmtops, PDAs, Internet-enabled phone promise anytime untethered Internet

### ADVANCED APPLICATIONS OF ELECTRICAL ENGINEERING

Development of a Software Tool for Performance Evaluation of MIMO OFDM Alamouti using a didactical Approach as a Educational and Research support in Wireless Communications JOSE CORDOVA, REBECA ESTRADA

### Chapter 8 - Power Density Spectrum

EE385 Class Notes 8/8/03 John Stensby Chapter 8 - Power Density Spectrum Let X(t) be a WSS random process. X(t) has an average power, given in watts, of E[X(t) ], a constant. his total average power is

### Greens functions - solution for earthʼs surface movement due to a slipping patch at depth

Greens functions - solution for earthʼs surface movement due to a slipping patch at depth Need to know slip distribution along the fault as a function of time No closed-form solution for Greens functions

### Performance analysis of bandwidth efficient coherent modulation schemes with L-fold MRC and SC in Nakagami-m fading channels

Title Performance analysis of bandwidth efficient coherent modulation schemes with L-fold MRC and SC in Nakagami-m fading channels Author(s) Lo, CM; Lam, WH Citation Ieee International Symposium On Personal,

### PROTECTION OF THE BROADCASTING SERVICE FROM BROADCASTING SATELLITE SERVICE TRANSMISSIONS IN THE BAND 620 790 MHz

Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT) PROTECTION OF THE BROADCASTING SERVICE FROM BROADCASTING SATELLITE SERVICE

### Performance Improvement of DS-CDMA Wireless Communication Network with Convolutionally Encoded OQPSK Modulation Scheme

International Journal of Advances in Engineering & Technology, Mar 0. IJAET ISSN: 3-963 Performance Improvement of DS-CDMA Wireless Communication Networ with Convolutionally Encoded OQPSK Modulation Scheme

### Wireless digital communication

Chapter 9 Wireless digital communication 9.1 Introduction This chapter provides a brief treatment of wireless digital communication systems. More extensive treatments are found in many texts, particularly

### ANALOG VS DIGITAL. Copyright 1998, Professor John T.Gorgone

ANALOG VS DIGITAL 1 BASICS OF DATA COMMUNICATIONS Data Transport System Analog Data Digital Data The transport of data through a telecommunications network can be classified into two overall transport

### Supplement to Call Centers with Delay Information: Models and Insights

Supplement to Call Centers with Delay Information: Models and Insights Oualid Jouini 1 Zeynep Akşin 2 Yves Dallery 1 1 Laboratoire Genie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92290

### 1 Sufficient statistics

1 Sufficient statistics A statistic is a function T = rx 1, X 2,, X n of the random sample X 1, X 2,, X n. Examples are X n = 1 n s 2 = = X i, 1 n 1 the sample mean X i X n 2, the sample variance T 1 =

### THE NEXT-generation wireless systems are required to

IEEE JOURNAL ON SELECT AREAS IN COMMUNICATIONS, VOL. 16, NO. 8, OCTOBER 1998 1451 A Simple Transmit Diversity Technique for Wireless Communications Siavash M. Alamouti Abstract This paper presents a simple

### Proposal of Adaptive Downlink Modulation Using OFDM and MC-CDMA for Future Mobile Communications System

Proposal of Adaptive Downlink Modulation Using and MC-CDMA for Future Mobile Communications System Masato FURUDATE, Takeo OHSEKI, Hiroyasu ISHIKAWA, and Hideyuki SHINONAGA YRP Research Center, KDDI R&D

### 22. Amplitude-Shift Keying (ASK) Modulation

. mplitude-shift Keying (SK) Modulation Introduction he transmission of digital signals is increasing at a rapid rate. Low-frequency analogue signals are often converted to digital format (PM) before transmission.

### Characterization of Ultra Wideband Channel in Data Centers

Characterization of Ultra Wideband Channel in Data Centers N. Udar 1,K.Kant 2,R.Viswanathan 1, and D. Cheung 2 1 Southern Illinois University, Carbondale, IL 2 Intel Corporation, Hillsboro, OR Abstract.

### Statistics and System Performance Metrics for the Two Wave With Diffuse Power Fading Model

1 Statistics and System Performance Metrics for the Two Wave With Diffuse Power Fading Model Milind Rao, F. Javier Lopez-Martinez and Andrea Goldsmith Wireless Systems Lab, Electrical Engineering Department

### Coding and decoding with convolutional codes. The Viterbi Algor

Coding and decoding with convolutional codes. The Viterbi Algorithm. 8 Block codes: main ideas Principles st point of view: infinite length block code nd point of view: convolutions Some examples Repetition

### Microwave Antennas and Radar. Maria Leonora Guico Tcom 126 2 nd Sem Lecture 8

Microwave Antennas and Radar Maria Leonora Guico Tcom 126 2 nd Sem Lecture 8 G P P directional isotropic Antenna Basics Isotropic Dipole High gain directional 0 db i 2.2 db i 14 db i Antenna performance

### 1 Prior Probability and Posterior Probability

Math 541: Statistical Theory II Bayesian Approach to Parameter Estimation Lecturer: Songfeng Zheng 1 Prior Probability and Posterior Probability Consider now a problem of statistical inference in which

### Digital vs. Analog Transmission Nyquist and Shannon Laws

1 Digital vs. Analog Transmission Nyquist and Shannon Laws Required reading: Garcia 3.1 to 3.5 CSE 3213, Fall 2010 Instructor: N. Vlajic Transmission Impairments 2 Transmission / Signal Impairments caused

### Sampling Theorem Notes. Recall: That a time sampled signal is like taking a snap shot or picture of signal periodically.

Sampling Theorem We will show that a band limited signal can be reconstructed exactly from its discrete time samples. Recall: That a time sampled signal is like taking a snap shot or picture of signal

### Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 2, FEBRUARY 2002 359 Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel Lizhong Zheng, Student

### ECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015

ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1

### Mini-project in TSRT04: Cell Phone Coverage

Mini-project in TSRT04: Cell hone Coverage 19 August 2015 1 roblem Formulation According to the study Swedes and Internet 2013 (Stiftelsen för Internetinfrastruktur), 99% of all Swedes in the age 12-45

### WHITEPAPER. Improving recovered signal quality in TETRA Systems

Improving recovered signal quality in TETRA Systems To ensure the reliable recovery of transmitted digital signals, modern communication systems must overcome a number of factors affecting the signal s

### Iterative Channel Estimation for MIMO MC-CDMA

Iterative Channel Estimation for MIMO MC-CDMA Stephan Sand, Ronald Raulefs, and Armin Dammann (DLR) 2 nd COST 289 Workshop, Antalya, Turkey, 6 th July Outline System model Frame structure Pilot aided channel