Part 4-Communications over wireless channels

ELEC 6040 Mobile Radio Communications, Dept. of E.E.E., HKUp. 3

About HomeworkThe 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 the course materials learned in the class and we will have a test (close-book, 10 minutes) in next class.

Six classes left. Five tests. Five scores. The best three out of the five scores will be taken as the final score of your homework.

Answers of all tests and the homework of part 1 to 4 will be revealed in the final class (tutorial) on Nov. 29.


Part 4. Communications over Wireless Channels (Con't)


System Performance over Radio Links


Modulation: Review (1)Modulation: The transformation of a sequence of digital data into an analog waveform appropriate for transmission.– Digital communications, information needed 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. bits:

01

Amp. of the carrier:0Α

2FSKInfo. bits:

01

Freq. of the carrier:f2f1

BPSKInfo. bits:

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/2π3π/2

00

01

11

10

QPSK

Signal Constellation Diagram


Examples of combined ASK-PSK signal const. diagram

Examples of rectangular ASK-PSK (QAM) signal const. diagram

4QAM 8QAM

16QAM


Modulation: Review (2)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: four symbols, two bits constitute a symbol, and this symbol is used to control

the phase shift of the carrier frequency– M-ary PSK/QAM: M symbols, log2M bits form a symbol.– In M-ary signaling, when the bit transmission rate is 1/Tb bits per second, the symbol

rate is 1/Tb/log2M symbols per second.

Question: How many bits are transmitted by one symbol if 16QAM (or 64QAM) is employed?


Es/N0: signal to noise ratio per symbol

(in AWGN channel)


Modulation: Review (3)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 (4)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 (=π)

Transmission time: t'

Phase of the carrier frequency

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, estimate the additional phase shift caused by carrier freq. φfc, thus ϕi can be obtained by subtracting φfc from (ϕi+φfc)

Nocoherent detection: The transmitted symbol is detected without a 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 rec. pilot: π/2

What is known to the rec.:the trans. pilot has a initial phase of zero

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

=π/2

phase of rec. data sym: (ϕi+φfc+2πfcTs) =3π/2

phase carrying info. 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 diff.:0 0 1 0Detected bits:


Error Probabilities for AWGN Channels (Comparison)

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

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


Comparison between Coherent and Noncoherent Detection Performances 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)

Bit

Erro

r Pro

babi

lity

Coherentdetection

Noncoherentdetection

Performances for BPSK and DBPSK using coherentand 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 freq.

―coherent detection always provides better performance than noncoherent detection


Diversity Techniques (Motivation)

Observation: Performance of communications over a Rayleighfading 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.

Performances for BPSK systems using coherent detection andoperating 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)

Bit

Erro

r Pro

babi

lity

Rayleigh-fadingchannels

AWGNchannels


Repetition

One single info. data

Rayleigh Fading Channel

Interleaving

Easy to be corrupted by the channel and detection error occurs

Simplest way to enhance the perf.

Likely to experience deep fading concurrently

The probability that all copies experience deep fading is greatly reduced

Amp.

t

Further enhance by time diversity

Illustration of Time Diversity

∆t


Diversity Techniques (Principle)

Diversity ≈ Redundancy in transmission or reception.

Principle: Consider the case that the same signal is transmitted two times. 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 able to 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 inside the signal 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

∆t


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

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

Method to exploit– Previous examples: repetition code– More power 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 with sufficient

time separation. 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 signals at different frequencies. Condition to obtain freq. diversity: ∆f > (∆f )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

freq. separation

∆f


Diversity Techniques (3)Multipath diversity:– Freq. domain: freq. selective channel: fsig>(∆f)c

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

Method to exploit: direct-sequence spread-spectrum techniques (i.e., CDMA techniques) plus RAKE receiverSummary– Advantage: Efficient utilization of the implicit freq. 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. While diversity can be exploited, only one

receive antenna is required.– 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.

ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 30

Example of Diversity CombiningReceive Diversity (SIMO)– receive antennas: sufficiently spaced, independent fading– channel is known – 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 order 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


What is the purpose of modulation?Three basic types of modulation schemes according to the parameters of the carrier adjusted to transmit digital information.Familiar with popular modulation schemes like BPSK, DBPSK, QPSK, 16QAM.How to represent a modulation scheme using signal constellation diagram?Concepts of bit and symbol.How to do Gray encoding and differential encoding?What are coherent detection and noncoherent detection? What are their advantages and disadvantages, respectively?Understand the principle of diversity.What are time diversity, frequency diversity and space diversity?Understand the operation of selection combining and maximal ratio combining.

Summary

Part 4-Communications over wireless channels

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Transcript of Part 4-Communications over wireless channels