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Ch13. Diversity

Instructor:

• Mohammed Taha O. El Astal

13.1 Introduction

AWGN channels Rayleigh Fading

In AWGN, it may that a 10-dB SNR leads to BERs on the order of 10−4.

but in fading channels, we need an SNR on the order of 40 dB in order to

achieve a 10−4 BER, which is clearly unpractical.

CONT.

The reason ???

is the fading of the channel;

since the fading cause to have an attenuation being large, and thus of the

instantaneous SNR being low, so the BER be high.

deep fading

(very low SNR)

CONT.

The Solution!!!!

Make sure that the SNR at Rx. has a smaller probability of being low.

=make sure that the signal has a smaller probability to have a large attenuation

13.1.1 Principle of Diversity

The principle of diversity is to ensure that the same information reaches the

receiver (RX) on statistically independent channels.

Example:

If Pnoise is 50 pW. Consider the following two cases :

An AWGN channel with Psig,avg is 1 nW.

A fading channel where during 90% of the time the

received power is 1.11 nW, while for the remainder, it is

zero.

1. Compute BER for the case of AWGN channel.

2. Compute avg. BER with assuming it is selection diversity

in the following cases:

a. one received antenna.

b. two received antenna.

c. three received antenna

SNR BER-DFSK

0dB 0.5

.......

……

…...

……

13dB 10−9

13.5dB 10−10

13.1.2 Definition of the Correlation Coefficient

Any correlation between the fading of the channels decreases the

effectiveness of diversity, why??

The most important one is the correlation coefficient of signal envelopes x and

y:

For two statistically independent signals E{xy} = E{x}E{y} ρxy=0

Signals are often said to be “effectively” decorrelated if ρ is below a certain

threshold (typically 0.5 or 0.7).

Diversity

Diversity

MacrodiversityMicrodiversity

Microdiversity :The methods that can be used to combat small-scale fading.

Macrodiversity :The methods that can be used to combat shadowing effect.

13.2 Microdiversity:

Microdiversity :The methods that can be used to combat small-scale

fading.

Five common method to achieve that:

1. Spatial diversity.

2. Temporal diversity.

3. Frequency diversity.

4. Angular diversity.

5. Polarization diversity.

Correlation coefficient :

The following important equation will come in handy :

This equation can be applied to spatial, temporal, and frequency

diversity.

The following assumption must be hold :

1. Validity of the (WSSUS) model.

2. No existence of (LOS).

3. Exponential shape of the (PDP).

4. Isotropic distribution of incident power.

5. The Use of omnidirectional antennas.

13.2.1 Spatial Diversity

It is the oldest and simplest form of diversity.

Also known as antenna diversity

Its performance is influenced by correlation of the signals

between the antenna elements.

A large correlation between signals at antenna elements is

undesirable, as it decreases the effectiveness of diversity.

CONT.

An important factor in the designing process is the antenna displacement .

MS in cellular and cordless systems:

oAre spaced approximately λ/4, how??

oGSM8 cm,

ocordless and cellular (1,800MHz)4 cm.

oWLAN (2.4G, 5.8G)??

BS in cordless systems and WLANs.

oSame as previous.

BSs in cellular systems:

oThe required antenna spacing to obtain sufficient decorrelation increases.

o2–20 wavelengths for angular spreads between 1◦ and 5◦

CONT.

13.2.2 Temporal Diversity

Since the wireless propagation channel is time variant, signals that are

received at different times are uncorrelated.

For “sufficient” decorrelation, the temporal distance must be at least

1/(2fdmax), where fdmaxis the maximum Doppler frequency.

In a static channel, the channel state is the same at all times so ρ = 1 for

all time intervals, and temporal diversity is useless.

CONT.

Repetition coding:

Highly bandwidth inefficient.

Spectral efficiency decreases by a

factor that is equal to the number of

repetitions.

Automatic Repeat reQuest (ARQ):

Its spectral efficiency is better than that

of repetition coding.

But it requires a feedback channel.

Combination of interleaving and coding:

For more details, see Chapter 14.

13.2.3 Frequency Diversity

For two branch , if f1 < f2 by Bc, then their fading is approximately independent.

For frequency diversity , equation 3.14 become as follow :

Also this equation lead to same result that the frequency diversity required Bc

CONT.

CONT.

Example 2:

Compute the correlation coefficient of two frequencies with separation

(i) 30 kHz.

(ii) 200 kHz.

(iii) 5MHz.

in the “typical urban” environment, as defined in COST 207 channel

models(σ= 0.977μsec)

CONT.

Traditional frequency diversity would greatly

decrease spectral efficiency.

Alternatively, inf. is spread over a large BW,

so that small parts of the inf. are conveyed by

different frequency components.

original info.

Spreaded Info.

The Rx. can then sum over the different frequencies to recover the original

information.

These methods allow the transmission of information without wasting

bandwidth.

i.e.

oCDMA

oDSSS and FHSS

oOFDM

13.2.4 Angle Diversity

Angle diversity principle : Since the MPCs are usually come from different

directions, the collocated antennas with different patterns “see” differently

weighted MPCs (so that the MPCs interfere differently for the two antennas).

Also known as pattern diversity

It is usually used in conjunction with spatial diversity; it enhances the

decorrelation of signals at closely spaced antennas.

CONT.

mutual coupling effect

identical antennadifferent antenna

13.2.5 Polarization Diversity

H and V polarized copies propagate differently in a wireless channel,

why?

The fading of signals with different polarizations is stat. independent,

thus, receiving both polarizations, offers diversity.

CONT.

The prop. effects lead to depolarization .

Thus, receiving both polarizations using a dual-polarized antenna, and

processing the signals separately, offers diversity.

But the average Rx. signal strength in the two diversity branches is not

identical, this lead to decrease the effectiveness this scheme.

Various antenna arrangements have been proposed in order to mitigate

this problem.

w.ch

.

At TX.At RX.

13.3 Macrodiversity

Spatial and Temporal Diversity can be used.

Freq. and Polarization Diversity can not be used. why?

since the shadowing is almost independent of TX. frequency and

polarization, so they are not effective.

Shadowing

CONT.

Spatial Diversity for large scale fading :

1.Simplest approach / On frequency repeater :

It just retransmit an amplified version of the signal.

CONT.

Spatial Diversity for large scale fading :

2.Simulcast:

The same signal is transmitted simultaneously from different BSs.

CONT.

Comparison:

In simulcast , a large amount of signaling info. that has to be carried

on T1/Microwave, but after usage of fiber it is not a problem.

it need synchronization whereas on frequency repeater does not.

It does not introduce delay as on frequency repeater.

On frequency repeater Simulcast

delay

Synchronizationdelay

13.4 Combination of Signals :

Methods of exploiting

signals from diversity

branches:

Combining diversitySelection diversity

In selection methods:

Choose the best diversity branch signal and ignore the other , then

process the signal( Demod. + Decoding).

There are many criteria to determine the best signal.

In Combining methods:

Not choose or select but combine all signal copies then decode.

there are different approaches to combine.

CONT.

since it exploits all signal copies , it will be has better performance

than selection methods, but it will require more complex systems.

It is complex due to :

it require Nr antennas and Nr down conversion chains since most

Rx. process the signal in the baseband.

Performance parameters

The Array gain results from the coherent combining of multiple Rx.

signal. even in the absence of fading, this can lead to an increase in

avg. Rx. SNR.

It equal : , is defined as the increased in avg. combined SNR

over the avg. branch SNR.

Maximum array gain is N, for diversity scheme have N branchs.

Array gain occurs for all diversity combining techniques.

Performance gain

Diversity GainArray Gain

CONT.

In particular, for some diversity systems their avg. BER can be

expressed in the form :

where : C is constant depend on the type of modulation and coding.

is avg SNR per branch.

M is the diversity order.

The diversity order indicates how the slope of the avg. BER as a

function of avg. SNR changes with diversity.

Maximum diversity order is N, for diversity scheme have N

branches.

13.4.1 Selection Diversity

1. RSSI Driven Diversity:

in this scheme, the Rx. will choose signal which have a largest int.

power or largest RSSI, then it processed it(demod.+decoding)

what is RSSI?

This scheme require: Nr of antennas.

Nr of RSSI sensors.

single Max switch.

CONT.

For an exact performance assessment , it is important to obtain the

SNR distribution of the output of the selector:

Assume that the instantaneous signal amplitude is Rayleigh distributed,

As the RX selects the branch with the largest SNR, the probability

that the chosen signal lies below the threshold is the product of the

probabilities that the SNR at each branch is below the threshold.

CONT.

Example 13.3:

Compute the probability that the output power of a selection

diversity system is 5 dB lower than the mean power of each

branch, when using Nr = 1, 2, 4 antennas.

Example 13.4:

Consider now the case that Nr = 2, and that the mean powers

in the branches are 1.5γ and 0.5γ , respectively. How does the

result change?

RSSI driven diversity is suitable for Noise limited systems but not

Interference (co-channel) systems, why?

13.4.1 Selection Diversity

2. BER Driven Diversity:

Firstly, transmit known sequence, then demod. every sequence from

all antennas , then compare them with TX sequence, finally select

the branch for the subsequent reception of data signal.

Repeat this process at regular time period and update the decision.

The necessary repetition rate depend on the coherence time Tc

CONT.

BER driven diversity drawbacks :

Rx. requires Nr of demod & RF. chain complex system.

send Tx. sequence Nr times decrease spec. eff.

Since the duration of the training sequence is finite, the selection

criterion – i.e., bit error probability – cannot be determined exactly.

If the RX has only one demodulator, then it is not possible to

continuously monitor the selection criterion (i.e., the BER) of all

diversity branches. This is especially critical if the channel changes

quickly.

13.4.2 Switched Diversity:

The major drawback of Selection diversity schemes which is the

requirement to monitors all branches continually (this leads to

Complex hardware or low spectral eff.).

To avoid that’s drawback : Switched Diversity have been proposed.

Also known as Threshold Div. or Switched and Stay Div.

Switching only depends on the quality of the active diversity branch;

it does not matter whether the other branch actually provides a better

signal quality or not.

CONT.

Switched diversity have a great problems when both branches have

signal quality below the threshold: in that case, the RX just switches

back and forth between the branches.

This problem can be avoided by introducing a hysteresis or hold

time, so that the new diversity branch is used for a certain amount of

time, independent of the actual signal quality.

We thus have two parameters to be optimized : switching threshold

and hysteresis time. These parameters have to be selected very

carefully

why?

CONT.

if threshold is too high it becomes probable that the branch the

RX switches to actually offers lower signal quality than the

currently active one.

if threshold is too low then a diversity branch is used even when

the other antenna might offer better quality

if holding time is too long then a “bad” diversity branch can be

used for a long time

if holding time is too short then the RX spends all the time

switching between two antennas.

13.4.3 Combining Diversity

Basic Principle :

Selection and switched Diversity wastes signal energy by

discarding Nr-1 copies of the Rx. signal.

This drawback can be avoid by using combining diversity which

exploits all available signal copies.

Each copies is multiplied by a complex weight and then add up.

Phase correction.

Amplitude weight.

MRC

1. Compensate the phases.

2. weight the signal according to their SNR.

This is the optimum way of combining diversity branch if several

assumption are fulfilled.

CONT.

1. The channel is slow fading

2. The channel is flat fading

3. Only disturbance is AWGN

if they are fulfilled, then

then correct the phases and weight the amplitude through wn , the SNR

of output become as follow :

CONT.

By optimization or cauchy-schwartz inequality ,

if the phase are corrected.

this result lead to have a combined SNR equal to :

and to have a pdf for the output of combiner as follow :

and the mean SNZ of the combiner output equal to :

CONT.

If all branches suffer from Rayleigh fading with the same mean SNR γ .

It is quite remarkable that EGC performs worse than MRC by only a

factor π/4 (in terms of mean SNR).

The performance difference between EGC and MRC becomes

bigger when mean branch SNRs are also different.

Equal Gain Combining :

13.5 Error Probability in fading channels with diversity reception:

we will deal with just with error probability of flat fading channel by

classical computation method.

It can be done through :

As an example , let us consider the performance of BPSK with Nr

diversity branches with MRC:

For large value of SNR

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