part 4. communications over wireless channelssdma/elec6040_2010/part 4-communications over... · p....

ELEC 6040 Mobile Radio Communications, Dept. of E.E.E., HKUp. 1

Part 4. Communications over Wireless Channels


Performance of a wireless communication system is basically limited by the wireless channel

How to get a wireless channel model– field measurement– statistical model

Wireless Channels

wired channel: stationary and predicable

wireless channel: random


Mobile Radio Propagation Characteristics


Large-Scale Propagation Characteristics

Large-scale propagation model– to predict the mean signal strength for arbitrary transmitter-receiver

separation– There is large variation of mean signal strength for different distances.

propagation loss for car 1 < propagation loss for car 2


Small-Scale Propagation Characteristics

Small-scale propagation model– to model signal variation within a small area or short time durations– over this small area, the mean signal strength is the same.– to model: multipath delay spread, signal variation due to fast fading

Multipath Propagation

Delay spread– Due to multipath propagation, the signal

via the direct path arrives at the earliest time whereas signals via reflected paths arrive with a delay relative to the one arrived via the direct path.

Fast fading– Due to constructive and destructive

addition of signals arrived from different paths, the signal strength varies when the mobile station moves.


Example of Propagation Measurement Result

Source: Rappaport’sWireless Communications, p. 71.

Measured Signal Power

Mean Signal Power(note: large-scale variation)

small-scalevariation


Large-Scale Path Loss


Free Space Propagation Model (1)

Is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed, line-of-sight path between them.– Example: Satellite communication

systems– Example: When the base

station is at the top of the mountain and the mobile station can view this base station.


Free Space Propagation Model (2)

Friis free space equation:

where Pt is the transmitted power, Pr(d) is the received power which is a function of the transmitter-receiver (T-R) separation, Gt is the transmitter antenna gain, Gr is the receiver antenna gain, d is the T-R separation in meters, and λ is the wavelength in meters, and L (≥ 1) is the system loss factor.

• Note: Received power is inversely proportional to the square of d.

Path loss (PL) in dB is given by

PL PP

G Gd

t

r

t r( ) log log( )

dB = = −LNM

OQP

10 10410 10

2

2 2λ

π

P d PG Gd Lr

t t r( )( )

=λ

π

2

2 24


Practical Aspects

The Friis equation is only useful for the far field. [Distance of interest to mobile communications is usually long enough to ensure that radiation falls onto the far field.]

With a reference received power Pr(d0) measured at a known reference distance d0, the received power at distance d is computed by

Notes:– The reference distance d0 is called the close-in distance.– The close-in distance is usually chosen to be 1m for indoor environments

and 100m or 1km in outdoor environments

P d P d ddr r( ) ( )= × FHIK0

02

inverse square law


P P d dP P d d

1 0 0 12

10 1 10 0 10 0 110 1 10 1 20=

⇒ = +( )

log ( ) log ( ) log ( ){inverse square law}

mW mW

Gt =1Gr =1

Example

Source: Rappaport’sWireless Communications, p. 74.


Two-Ray Ground Reflection ModelOne-ray communication seldom occurs.Ground reflection is a realistic phenomenon for mobile communications.A two-ray ground reflection model is useful.

Ground

Transmitter

Receiverht

hr

line-of-sight path

ground-reflected path

dIt is known that

where Pt is the transmitted power and Pr is the received power.

P PG G h hd

d h hr t t rt r

t r= >>2 2

4 ifa result from EM theory


Log-Distance Path-Loss Model

Usually, the path-loss model is deduced from experimental data.

The propagation characteristic can be described by the path lossexponent n and the path loss formula

where stands for the average path loss at a distance d away from the transmitter, and is the corresponding value in dB.

Note that knowledge of is required, which can be obtained by field measurement.

PL d PL d dd

PL d PL d n d d

n

( ) ( )

( ) ( ) log

= ×FHG

IKJ

= +

00

0 10 010dB dB {in dB domain}

PL d( )

PL d( )0

PL ddB( )


Path-Loss Exponent

Path-loss exponents are usually obtained through field measurement.

Typical values of n: (source: Rappaport’s Wireless Communications)

Environment Path Loss Exponent, nFree space 2Urban area cellular radio 2.7 to 3.5Shadowed urban cellular radio 3 to 5In building line-of-sight 1.6 to 1.8Obstructed in building 4 to 6Obstructed in factories 2 to 3


ShadowingThe average power loss does not take into account the effects ofsurrounding environmental clutter, such as trees, and the movement of people and vehicles

These effects are summarized as shadowing.random effect on path loss

d d


Lognormal ShadowingLognormal distribution is widely used to model the signal power variation due to shadowing.

Lognormal shadowing:– The path loss in dB is distributed as a Gaussian random variable

The path loss in dB at a distance d is given by:

– where X is a standard normal random variable and σdB is the standard deviation of the power level in dB.

For example, σdB of 8dB is generally used.

( )dB dBdB dB 0 10 0 dB( ) ( ) ( ) 10 logPL d PL d X PL d n d d Xσ σ= + = + +


Overview of Propagation Models

Outdoor propagation models:– Longley-Rice model– Durkin’s model– Okumura model — important; empirical– Hata model — empirical model– PCS extension to Hata model– Wideband PCS microcell model

Indoor propagation models:– 1. Loss due to signal penetration into buildings – 2. Partition loss– 3. Floor attenuation

1 2

3


Small-Scale Fading


Characteristics of Small-Scale FadingRapid changes in signal strength over a small travel distance or time interval.Random frequency modulation due to variant Doppler shifts on different multipath signalsTime dispersion (echoes) caused by multipath propagation delays.

received signal:

( )( )0 0cos 2 ,c f tf t τπ⎡ ⎤+⎣ ⎦

( )( )1 1cos 2 ,c f tf t τπ⎡ ⎤+⎣ ⎦

( )( )1 1cos 2 ,c L Lf tf tπ τ− −⎡ ⎤+⎣ ⎦


Observations of Small-Scale Fading

The received signal is the sum of signals arrived via different paths. Constructive (destructive) summation of signals causes an enhancement (a reduction) of the received signal. Deep fading may occur.

A vehicle moving at high speed may experience several fades in a small period of time.

Due to relative motion between the mobile and base station, each path wave experiences a shift in frequency. Doppler shiftDoppler shift

( )( )( )1 1

0 0

0 1

0 1

0 1

0 1

received signal: cos 2

Constructive example: 2 cos 2 1.9 cos 2

cos 2

Destructive example: 2 cos 2 1.9 cos 2

3.9

L L

l l c ll l

c c

c

c c

lr f t

r f t r f t

r r f t

r f t r f t

r

f t

r

α π τ

π π

π

π π π

− −

= =

⎡ ⎤= + −⎣ ⎦

= × = ×⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦⇒ + = ⎡ ⎤⎣ ⎦= × = × +⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦

⇒ +

∑ ∑

0.1 deep fcos d2 a e: cf tπ= ⎡ ⎤⎣ ⎦


Doppler Shift

distance difference:

additional phase change:

Doppler shift:

cos cos

2 2 cos

1 cos2d

d v t

v t

vft

θ θ

π π θφλ λ

φ θπ λ

Δ = = Δ

Δ ΔΔ = =

Δ= ⋅ = ⋅

Δv = velocity of the vehicle

Approximations: Δl is the distance difference between SX and SY; the angle formed by SX and XY is the same as the angle formed by SY and XY

Holds if S is far enough


Example from Rappaport’s Wireless Communications

Higherobservedfrequency

Lowerobservedfrequency

θ=0

θ=π

cosdvf θλ

= ⋅


Factors Influencing Small-Scale FadingMultipath propagation– A result of the presence of reflecting objects and scatters in the channel.– Random amplitudes and phases of multipath components cause small-scale fading

and/or signal distortion.– Signal delay introduced by propagation via a longer reflected path causes smearing of

the signal, known as intersymbol interference.Speed of the mobile– Affects the Doppler shifts on each of the multipath components.

Speed of surrounding objects– Induces time-varying Doppler shift on multipath components.– Effects become dominant only if the surrounding objects move faster than the mobile

station.Signal bandwidth– If the transmitted signal has a bandwidth greater than the coherence bandwidth of the

channel, the received signal is distorted by the introduction of intersymbolinterference


Multipath Fading Channels (1)

Time varying multipath fading channels - an example of the discrete time impulse response model


Multipath Fading Channels (2)The channel can be regarded as a linear time-varying filter. The received signal is the convolution between the transmitted signal and the channel impulse response.

Channel impulse response:– Is used to characterize the channel.– Can be measured (though not conveniently) by sending a pulse to the channel

and recording the channel output by a receiver.– Is time-varying in nature for mobile communication channels.

D D D D

h(t,τ0) h(t,τ1) h(t,τ2) h(t,τ3) h(t,τL-1)


Channel Impulse Response

Measurement set-up(Source: S.-C. Kim, H. L. Bertoni and M. Stern, “Pulse propagation characteristics at 2.4GHz inside buildings,” IEEE Trans. Veh. Technol., vol. 45, pp. 579-592, Aug. 1996.)

Example: channel impulse responses(source: Proakis’s Digital Communications)


Characterization of Multipath Fading Channels (1)

The bandpass transmitted signal, sBP(t), at a carrier frequency fc is given by

where s(t) is the complex envelope of the signal (low-pass equivalent signal model).

The received bandpass signal, xBP(t), can be expressed in the form

where x(t) is the complex envelope of the received signal, cn(t) is the time-varying, complex-valued channel gain of the nth path and τn(t) is the nth-path delay, which can be assumed to be time-varying.

Thus, the low-pass equivalent channel impulse response, h(τ;t), is given by

where δ(.) is the Dirac delta function.

s t s t e j f tcBP( ) Re{ ( ) }= 2π

x t x t e e c t s t tj f t j f tn n

n

c cBP( ) Re ( ) Re ( ) ( ( ))= = −RST

UVW∑2 2π π τn s

h t c t t c t e tn nn

nj c t

nn

n( ; ) ( ) ( ( )) ( ) ( ( ))arg ( )τ δ τ τ δ τ τ= − = −∑ ∑



Denote the time-varying, low-pass equivalent channel impulse response as h(τ;t). The autocorrelation function of h(τ;t) is given by

Assume uncorrelated scattering, that is, different paths are statistically uncorrelated in properties such as gain and phase. Then

where φh(τ ; Δt) is the delay cross-power density function.

The special case that

is known as multipath intensity profile or delay power spectrum.

φ τ τ τ τh t E h t h t t( , ; ) ( ; ) ( ; )*1 2

12 1 2Δ Δ= +n s

φ τ τ φ τ δ τ τh ht t( , ; ) ( ; ) ( )1 2 1 2 1Δ Δ= −

φ τ φ τh h( ; ) ( )0 ≡



The delay power spectrum can be discrete or continuous.

Example 1: double-spike channel

where τd is the delay of the delayed path.

Example 2: exponentially dispersive channel

where τrms is the root-mean-square delay spread.

φ τ δ τ δ τ τh d( ) ( ) ( )= + −

φ τ τ τ τh ( ) exp( )= −−rms rms

1

τ

φ(τ)

0 τd

τ

φ(τ)

0


Characterization of Multipath Fading Channels (3a): Experimental Results regarding the Delay Power Spectrum

Source: S.-C. Kim, H. L. Bertoni and M. Stern, “Pulse propagation characteristics at 2.4GHz inside buildings,”IEEE Trans. Veh. Technol., vol. 45, pp. 579-592, Aug. 1996.


Characterization of Multipath Fading Channels (4)Taking the Fourier transform of h(τ;t) on the variable τ, we get

Assume that H(f;t) is wide-sense stationary. The autocorrelation function is

It follows that

so that ΦH(Δf ; Δt), known as the spaced-frequency, spaced-time correlation function, is the Fourier transform of the delay cross-power density function.

H f t h t e dj f( ; ) ( ; )= −−∞∞z τ τπ τ2

Φ Δ ΔH f f t E H f t H f t t( , ; ) ( ; ) ( ; )*1 2

12 1 2= +n s

Φ Δ Δ

Δ

Δ

Δ Φ Δ Δ ΔΔ

Hj f f

hj f f

hj f f

hj f

H

f f t E h t h t t e d d

t e d d

t e d

t e d f t f f

( , ; ) ( ; ) ( ; )

( ; ) ( )

( ; )

( ; ) ( ; )

* ( )

( )

( )

( )

1 212 1 2

21 2

1 2 12

1 2

12

1

12

1 2

1 1 2 2

1 1 2 2

1 2 1

1

= +

= −

=

= ≡ =

−−∞∞

−∞∞

−−∞∞

−∞∞

−−∞∞

−−∞∞

zzzz

zz

τ τ τ τ

φ τ δ τ τ τ τ

φ τ τ

φ τ τ

π τ τ

π τ τ

π τ

π τ

n s

with − f1

Based on the assumption of uncorrelated scattering


Characterization of Multipath Fading Channels (5)Let

Then we have

Φ Δ Φ ΔH Hf f( ; ) ( )0 ≡

Φ Δ ΔH h

j ff e d( ) ( ) ( )= −−∞∞z φ τ τπ τ2

Source: Proakis’s Digital Communications

H

H

h

h

H h



Significance of ΦH(Δf): Since ΦH(Δf) is an autocorrelation function in the frequency domain, it provides us with a measure of the frequency coherence of the channel, i.e., the correlation of the frequency components separated by Δf (Hz) in frequency.

Coherence bandwidth of the channel: The reciprocal of the multipath spread is a measure of the coherence bandwidth of the channel, (Δf)c, i.e.,

where Tm is the multipath spread.

Note 1. If the coherence bandwidth is small compared to the signal bandwidth, the channel is said to be frequency-selective; otherwise it is frequency-nonselective.

Note 2. A frequency-selective fading channel introduces intersymbol interference (ISI), which distorts the signal, but ISI can be utilized by spread-spectrum transmission to exploit multipath diversity to combat the adverse effects due to fading.

( )Δf Tc m≈1



Taking the Fourier transform of ΦH(Δf ; Δt) on the variable Δt, we have

The special case that

is known as the Doppler power spectrum of the channel.

S f f t e d tH Hj t( ; ) ( ; ) ( )Δ Φ Δ Δ ΔΔλ πλ= −

−∞∞z 2

S SH H( ; ) ( )0 λ λ≡

Source: Proakis’s Digital Communications

H H

H H

H H



Doppler spread: The range of λ over which SH(λ) is essentially non-zero is called the Doppler spread Bd of the channel.

Coherence time of the channel: The coherence time of the channel, (Δt)c, is just the reciprocal of the Doppler spread. That is,

Note. If the coherence time is small compared to the symbol duration, the channel is said to be time-selective. Time selectivity complicates the receiver design because the signal is varying so fast that it is difficult to establish frequency and time synchronization at the received signal.

fast fading

( )Δt Bc d≈1


Characterization of Multipath Fading Channels (9)The scattering function is given by

It follows that

and

Note: The scattering function is the most commonly used function to describe a multipath fading channel.A simplifying assumption: Sometimes the scattering function is assumed to be decomposable into a product of the delay power spectrum and the Doppler power spectrum, i.e.,

S t e d th hj t( ; ) ( ; ) ( )τ λ φ τ πλ= −

−∞∞z Δ ΔΔ2

2 ( )( ; ) ( ; ) j fh HS S f e d fπττ λ λ

∞ Δ

−∞= Δ Δ∫

S f t e e d t d fh Hj t j f( ; ) ( ; ) ( ) ( )( ) ( )τ λ πλ πτ= −

−∞∞

−∞∞ zz Φ Δ Δ Δ ΔΔ Δ2 2

S Sh h H( , ) ( ) ( )τ λ φ τ λ=


Characterization of Multipath Fading Channels (Summary)

φ τh t( ; )Δ

Φ Δ ΔH f t( ; )

Taking Fouriertransform in the

variable τ


variable Δt

Sh ( ; )τ λ

S fH ( ; )Δ λ


variable Δt


variable τ

Delay cross-powerdensity function

Spaced-frequency,spaced-time

correlation functionScattering function

Δt=0φh(τ): Multipath intensity profile

Δf=0

ΦH(Δt): Spaced-time correlation function

Δf=0 SH(λ): Doppler power spectrum

Δt=0

ΦH(Δf): Spaced-freq. correlation function


Mathematical model for the channel response in each path

Consider an example multipath intensity profile with discrete paths:

where cn(t) is a zero-mean complex-Gaussian WSS random process and all cn(t)’s are statistically uncorrelated. Note that uncorrelated Gaussian processes are statistically independent. Assume that the processes are ergodic, so that the time average equals the ensemble average. Then the ensemble average of the magnitude square of cn(t) is the power gain of the nth multipath of the channel.

Rayleigh fading is a widely used fading model for statistically characterizing small-scale fading experienced by channels without line-of-sight paths.

Rician fading occurs when there is a line-of-sight (LOS) path.

φ τ δ τ τh n nn

Lc t( ) ( ) ( )= −

=

−∑

0

1


Origin of Rayleigh Fading

Assume that the mobile station isotropically receives the diffused signals arrived from all 360° in the angle. The addition of all diffused signals gives rise to one resultant signal, whose signal amplitude and phase are random rather than deterministic. The amplitude and phase are distinguished by correlating the received signal with the sine and cosine components of the carrier frequency. By the central-limit theorem, the resultant distributions of the sine and cosine components are Gaussian with zero mean. It is reasonable to assume that the two components are uncorrelated and hence statistically independent.

Mobilestation

diffused signals arrivedfrom all directions, with

equal signal strength

cosine direction

sine d

irecti

on

Sig

nal d

istri

butio

n


Mathematics of Rayleigh Fading

The PDFs of amplitude and phase:

2

2 2( ) exp , 02

1( ) , 0 22

r rp r r

p

σ σ

θ θ ππ

⎡ ⎤= − ≥⎢ ⎥

⎣ ⎦

= ≤ <

Rayleigh distribution uniform distribution

Channel response at each path: jc re θ=


Rician FadingRayleigh fading occurs frequently when there is no line-of-sight (LOS) path. When there is a LOS path, the mean of the complex-valued signal strength is not zero. The resultant distribution is known as the Rician distribution (or Nakagami-Rice distribution in some references).

Let r exp(jθ) = x + jy where x and y are Gaussian distributions with means mx and my, repectively, and a common standard deviation σ. The random variable r follows a Rician distribution with (see Proakis’s Digital Communications)

where s2 = mx2 + my

2 and I0(x) is the 0th order modified bessel function of the first kind

The Rician factor K is the ratio of the LOS-path power to the power of diffused components, given by

p r r e I rs rr s( ) ,( )= FH

IK ≥− +

σ σσ

22

0 22 2 2

0

K s=

2

22σ


Statistical Modeling of Mobile Radio Channels for Outdoor and Indoor Scenarios

Outdoor environments:– Macrocells, having a coverage radius in the order of 10km, are likely not to have LOS

paths. Rayleigh fading can be assumed.– Microcells, having a coverage radius in the order of 1km, may or may not have LOS

paths, depending on the distance between the base station and the mobile station. In the presence (absence) of a LOS path, Rician (Rayleigh) fading can be assumed.

Indoor environments:– Picocells, having a coverage in the order of 100m or 10m in radius, may or may not

have LOS paths. Rician and Rayleigh distributions can be assumed for, respectively, the channels with and without LOS paths.

– Temporal variation. It is possible that the mobile station is a portable communication equipment, wherein the equipment does not move when making communications. In this case, the channel is relatively stable and can be modeled by a Rician-fading channel. See R. J. C. Bultitude, “Measurement, characterization and modeling of indoor 800/900 MHz radio channels for digital communications,” IEEE Communications Magazine, vol. 25, no. 6, pp. 5-12, Jun. 1987.


Other Aspects of Wireless Communications


Modulation: Review (1)Modulation: The transformation of a sequence of digital data into an analog waveform appropriate for transmission.– Digital communications, information to be transmitted: discrete bit sequences– Signal suitable for radio transmission: usually a continuous sinusoidal wave

– Digital information is transmitted by varying one or more parameters of the transmitted signal or waveform:• Amplitude – Amplitude Shift Keying (ASK)• Frequency – Frequency Shift Keying (FSK)• Phase – Phase Shift Keying (PSK)

( ) ( )sin 2 cs t A f tπ ϕ= ⋅ +

amplitude frequency phase


( ) ( )sin 2 cs t A f tπ ϕ= ⋅ +

2ASKInfo. bit:

01

Amp. of the carrier:0Α

2FSKInfo. bit:

01

Freq. of the carrier:f2f1

BPSKInfo. bit:

01

Phase of the carrier:π0


Modulation: Review (2)

Signal Constellation Diagram

( ) ( )sin 2 cs t A f tπ ϕ= ⋅ +

QPSK

Information bits:

00011110

Phase of the sine wave:

0π/2π

3π/2

Signal Constellation Diagram


Examples of combined ASK-PSK signal constellation diagram

Examples of rectangular ASK-PSK (QAM) signal constellation diagram

4QAM 8QAM

16QAM


Modulation: Review (3)Modulation techniques commonly used in mobile communications: GMSK (GSM), BPSK and QPSK (IS-95, WCDMA), 8-PSK (EDGE), 16QAM (HSPA), 64QAM (HSPA+, LTE)

Bit and symbol: A symbol is the fundamental unit that is used to modulate the carrier waveform. – QPSK: two bits constitute a symbol, and this symbol is used to control the phase shift

of the carrier frequency (four symbols)– M-ary PSK/QAM: log2M bits form a symbol (M symbols) – In M-ary modulation, when the bit transmission rate is 1/Tb bits per second, the

symbol rate is 1/Tb/log2M symbols per second.


Es/N0: signal to noise ratio per symbol

(in AWGN channel)


Modulation: Review (4)Gray Encoding: Two adjacent symbols each consisting of m bits have exactly one bit position where the bits in the two symbols are different.– Advantage: minimization of bit error when a symbol is incorrectly decoded as an

adjacent symbol.– Examples:

Natural encoding Gray encoding Gray encoding


Modulation: Review (5)Differential encoding: For example, in differential PSK (DPSK), the carrier phase shift depends not only on the symbols transmitted at the current instant but also on the carrier phase shift at the previous time instant.

Original info. bits bi

Bits after diff. encoding di=di-1+bi

Carrier

Advantage: easy to detect


Tx Rx

Wireless Channel

t0 t0

Ts Ts

t'

( ) ( )2 'ci c i ff tϕ π ϕ φ+ = +

what we get at the receiver:( ) ( )sin 2i c is t A f tπ ϕ= ⋅ +

BPSK signal:

Data info. is carried in ϕi (=0, π)

Transmission time: t'

Phase of the carrier frequency: unknown

Detection Methods (1)Transmitter Receiver


Detection Methods (2)

Problem: how to get ϕi from (ϕi+φfc)

Coherent detection: With the help of a pilot tone or a sequence of pilot symbols, the additional phase shift caused by carrier freq. φfc is estimated, thus ϕi can be obtained by subtracting φfc from (ϕi+φfc)

Nocoherent detection: The transmitted symbol is detected without knowledge of the phase of the carrier frequency. Differential encoding is required.


t0

data sym.pilot sym.

Example of coherent detectionTransmitter

Pilot symbol is a known symbol to the receiver

t0 t'

Receiver

data sym.pilot sym.

phase of received pilot: π/2

What is known to the receiver:the transmitted pilot has a initial phase of zero

Phase of the carrier frequency 2πfct'=φfc=π/2-0

=π/2

phase of received data symbol: (ϕi+φfc+2πfcTs) =3π/2

phase carrying information bit: ϕi =3π/2-π/2=π

Ts Ts t’+Ts

2π


Example of noncoherent detection

t0

t0 t'

Transmitter Receiver

Original bits:1 0 0 1 0

Differentially encoded bits:

1 1 1 0 0

0 2 'cf tϕ π+ ( )1 2 'c sf T tϕ π+ +

( ) [ ]1 0

1 0

known: 2

Phase difference:

2 ' 2 '

2c s c

c s

f T t f t

f Tπ

ϕ π ϕ π

ϕ ϕ π

+ + − +⎡ ⎤⎣ ⎦= − +

DBPSK: original bit 0: no phase change original bit 1: phase change

0 0 π 0Phase difference:

0 0 1 0Detected bits:


Error Probabilities for AWGN Channels

The SNR difference required to achieve the same Pb of 10–5 :

Is a fraction of dB only: between 2-phase PSK and 2-phase DPSK.Is more than 2dB: between 4-phase PSK and 4-phase DPSK.

New mobile radio communication systems (e.g., 3G, HSPA) turn to use coherent detection rather than noncoherent detection. A pilot signal (for both uplink and downlink) is used to contain the phase information.

Copied from Proakis’s Digital Communications


Performance Comparison between Coherent and NoncoherentDetections in Rayleigh Fading

A 3dB loss in Eb/N0 is incurred by using noncoherent detection over coherent detection, even though binary signaling is considered.

Another piece of evidence showing that coherent detection is preferred for mobile radio communications.

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

Coherent detection

Noncoherent detection

Performances for BPSK and DBPSK using coherent and noncoherent detection techniques, respectively


Detection Methods (3)

Summary of coherent and noncoherent detection―noncoherent detection is easy to implement; no need for pilot, higher

transmission efficiency

―coherent detection is more complicated than noncoherent detection because it needs pilot to track the phase of carrier frequency

―coherent detection always provides better performance than noncoherent detection


Diversity Techniques (Motivation)

Observation: Performance of communications over a Rayleigh fading is very poor in comparison to the one over an unfaded AWGN channel.

Motivation: The need to enhance the performance.

Diversity: One method to enhance the performance is the use of diversity techniques.

Performance for BPSK systems using coherent detection and operating on AWGN channels or Rayleigh-fading channels

0 5 10 15 20 25 30 35 4010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

Eb/N0 (dB)

Rayleigh-fading channels

AWGN channels


Repetition

One single information data

Rayleigh Fading Channel

Interleaving

Easy to be corrupted by the channel and detection error occurs

Simplest way to enhance the performance

Likely to experience deep fading concurrently

The probability that all copies experience deep fading is greatly reduced

Amplitude

t

Further enhance by time diversity

Illustration of Time Diversity

Δt


Diversity Techniques (Principle)

Diversity ≈ Redundancy in transmission or reception.

Principle: Consider the case that the same signal is transmitted twice. When the first replica of the signal is transmitted on a channel that is in deep fade, the information contained in the signal can hardly be recovered. In the next time instant, the second replica of the signal is transmitted. At that time, the channel is in good condition, the information can be recovered with low/acceptable bit error probability.

1st time oftransmission

Channel in deep fade,signal very weak

2nd time oftransmission

Channel in good condition, signal verystrong

time diversity

Δt


Diversity Techniques (1)Condition to obtain time diversity: Δt > (Δt )c

– Reason: The fading characteristics of a channel at two time instants separated by more than the coherence time are slightly correlated. By transmitting the same signal on multiple discrete time instants mutually separated by more than the coherence time, diversity can be obtained.

Method to exploit– Previous example: repetition code– More powerful error-correcting codes: convolutional code, turbo code, LDPC code

Summary– Advantage: Easy to implement.– Disadvantage 1: Need to ensure that two successive bits are separated by sufficient

time. Interleaving is required.– Disadvantage 2: If the channel is very slowly varying, time diversity is ineffective.– Relevance to mobile communications: Error-correcting coding is always implemented

in mobile communication systems. It is already implicitly used to exploit time diversity.


Diversity Techniques (2)Frequency diversity: At the transmitter, the same information is transmitted via two or multiple waveforms at different frequencies. Condition to obtain frequency diversity: Δf > (Δf )c

Summary– Disadvantage: More transmit power is required. Signal bandwidth is expanded.– Relevance to mobile communications: Another form frequency diversity, known as

multipath diversity, is frequently employed in CDMA mobile communication systems.

ej2πf0t

ej2πfnt

f0 f1 fn

signal spectrum

frequency separation

Δf


Diversity Techniques (3)Multipath diversity:– Frequency domain: frequency selective channel: fsig>(Δf)c

– Time domain: Multipath channel. Multipath components are independently faded. By combining these components, deep fading can be avoided.

Method to exploit: direct-sequence spread-spectrum techniques (i.e., CDMA techniques) plus RAKE receiverSummary– Advantage: Efficient utilization of the implicit frequency diversity offered by the

wideband signal.– Disadvantage: Wideband signals are generally more difficult to handle.– Relevance to mobile communications: cdmaOne, WCDMA and cdma2000

signal spectrum fsig

coherence bandwidth

f

t


Diversity Techniques (4)Receive diversity: At the receiver, two or more antennas separated sufficiently are used for signal reception. The separation is such that the correlation of signals received at different antennas is small.– Advantage: Transmit power does not need to be increased.– Disadvantage: More antennas are needed. May not be possible at mobile stations.– Relevance to mobile communications: Very popular for use at base stations.

Transmitter

Receiver

Com

bine

r

large enough


Diversity Techniques (5)Transmit diversity: At the transmitter, multiple antennas are used to transmit thesame information signal. The antennas are sufficiently separated to ensure low correlation in fading. The carrier phases of all the signals are adjusted such that the signals are coherently added at the receive antenna.– Advantage: Can be used at base station. Diversity can be exploited with only one

receive antenna.– Disadvantage: Phase adjustment is required. Closed-loop control is required.– Relevance to mobile communications: The benefit of capacity enhancement outweighs

the implementation difficulty. WCDMA has approved the use of transmit diversity.

Transmitter

Receiver

Phas

e A

djus

tmen

t

large enough


Diversity CombiningOrder of diversity– It is the number of replicas of the same signal available in a diversity system.– When the order of diversity is one, the system is a non-diversity system.– The higher the order, the better the system performance

Selection combining (SC)– The replicas are compared and the largest one in magnitude or SNR is selected for

demodulation or detection.Maximal ratio combining (MRC)– The replicas are weighted and coherently added together so that the resultant SNR is

maximized.Equal-gain combining (EGC)– The replicas are coherently added to form an estimate that is used for demodulation of

detection.


Example of Diversity CombiningReceive Diversity (SIMO)

– receive antennas: sufficiently spaced, independent fading– channel is known from channel estimation – how to obtain receive diversity: selection combining, gain combining

Tx

SIMO

RxSingle Input Single Output (SISO)

Tx Rx

s hs+nhs r=hs+n

{ } { } { } { }{ }{ }

2 22

22

22

0, 0, 1, 1, 0.5 :

signal-to-noise ratio (SNR) at receiver: SNR= 0.25

sig

sig

E s E n P E s E n h

E hs h P

E n

σ

σ

= = = = = = =

⋅= =


Receive Diversity (2)Selection combining

Tx Rx

{ } { } { } { }2 2 2 221 2 31, 1 : sigP E s E n E n E nσ= = = = = =

h1=0.5h2=1.1

h3=-0.2

{ }{ }

22

1 11 22

1

SNR at receiver 1: SNR = 0.25sigE h s h P

E n σ⋅

= =

{ }{ }

22

2 22 22

2


E n σ⋅

= =

{ }{ }

22

3 33 22

3


E n σ⋅

= =

Choose the largest SNR!Received signal

from antenna 2 is retained!

r1=h1s+n1

r2=h2s+n2

r3=h3s+n3


Receive Diversity (3)Maximal Ratio Combining (Gain combining)

Tx Rx

h1=0.5h2=1.1

h3=-0.2

– make use of all received signals– weighting: the one with higher SNR should have a more important role in

the final signal

( ) ( )

* * *1 1 2 2 3 3 1 1 2 2 3 3

2 2 2 * * *1 2 3 1 1 2 2 3 3

signal after weighting:

y w r w r w r h r h r h r

h h h s h n h n h n

= + + = + +

= + + + + +

r1=h1s+n1

r2=h2s+n2

r3=h3s+n3

( ){ }

( )( )

( )

22 2 2 22 2 21 2 3 1 2 3

2 2 2 2 2* * *1 2 31 1 2 2 3 3

2 2 21 2 3

2

SNR after weighting: SNR=

1.50

sig

sig

E h h h s h h h P

h h hE h n h n h n

h h h P

σ

σ

⎧ ⎫+ +⎨ ⎬ + + ⋅⎩ ⎭ =+ ++ +

+ + ⋅= =

Maximal ratio

combining (MRC)


Bit Error Probability for MRC Systems

A higher order of diversity gives a better performance.

A higher diversity system yields a BER curve that has a steeper slope of BER reduction.

The advantage of Eb/N0reduction for a higher order diversity system diminishes. That is, diminishing return is observed.

Copied from Proakis’s Digital Communications

Non-diversitysystems

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