Ch13. Diversity
Instructor: • Mohammed Taha O. El Astal
LOGO 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.
deep fading (very low SNR)
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. 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: SNR BER-DFSK If Pnoise is 50 pW. Consider the following two cases : 0dB 0.5 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. 13dB 10−9 1. Compute BER for the case of AWGN channel. 13.5dB 10−10 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 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
Microdiversity Macrodiversity
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. original info. Alternatively, inf. is spread over a large BW, so that small parts of the inf. are conveyed by different frequency components. 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.
different antenna identical antenna
mutual coupling effect 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 .
w.ch . At RX. At TX. 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. 13.3 Macrodiversity
Shadowing
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. 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.
delay Synchronization
delay On frequency repeater Simulcast 13.4 Combination of Signals :
Methods of exploiting signals from diversity branches:
Selection diversity Combining 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
Performance gain
Array Gain Diversity Gain
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. 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. Equal Gain Combining :
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. 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 www.themegallery.com
LOGO