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.