Điện thoại di động vô tuyến điện - Tuyên truyền Channel P10 ppsx

Chapter 10 Mitigation of Multipath Eects 10.1 INTRODUCTION We have seen in Chapters 4 and 5 that buildings and other obstacles in built-up areas act as scatterers of the signal, and because of the interaction between the various incoming component waves, the resultant signal at the mobile antenna is subject to rapid and deep fading. The fading is most severe in heavily built-up areas such as city centres, and the signal envelope often follows a Rayleigh distribution over short distances in these heavily cluttered regions. As the degree of urbanisation decreases, the fading becomes less severe; in rural areas it is often only serious when there are obstacles such as trees close to the vehicle. A receiver moving through this spatially varying ®eld experiences a fading rate which is proportional to its speed and the frequency of transmission, and because the various component waves arrive from dierent directions there is a Doppler spread in the received spectrum. It has been pointed out that the fading and the Doppler spread are not separable, since they are both manifestations (one in the time domain and the other in the frequency domain) of the same phenomenon. In addition there is the delay spread which leads to frequency-selective fading. This causes distortion in wideband analogue signals and intersymbol interference (ISI) in digital signals. These multipath eects can cause severe problems and, particularly in urban areas, multipath is probably the single most destructive in¯uence on mobile radio systems. Much attention has been devoted to techniques aimed at mitigating the deleterious eects it causes and this chapter reviews some of the available approaches to the problem. 10.2 DIVERSITY RECEPTION One well-known method of reducing the eects of fading is to use diversity reception techniques. In principle they can be applied either at the base station or at the mobile, although dierent problems have to be solved. The basic idea underlying diversity reception has been outlined in Section 5.12 and relies on obtaining two or more samples (versions) of the incoming signal which have low, ideally zero, cross-correlation. It follows from elementary statistics that the probability of M independent samples of a random process all being simultaneously below a certain level is p M where p is the The Mobile Radio Propagation Channel. Second Edition. J. D. Parsons Copyright & 2000 John Wiley & Sons Ltd Print ISBN 0-471-98857-X Online ISBN 0-470-84152-4 probability that a single sample is below the level. It can be seen therefore that a signal composed of a suitable combination of the various versions will have fading properties much less severe than those of any individual version alone. Two questions must be answered. How can these independent samples (or versions) be obtained? Then how can they be processed to obtain the best results? Potentially there are several ways to obtain the samples; for example, we could use the fact that the electrical lengths of the scattered paths are a function of the carrier frequency to obtain independent versions of the signal from transmissions at dierent frequencies. However, frequency diversity, as it is called, is not a viable proposition for most mobile radio systems because the coherence bandwidth is quite large (from several tens of kilohertz to a few megahertz depending on the circumstances) and in any case the pressures on spectrum utilisation are such that multifrequency allocations cannot be made. Two other possibilities are polarisation diversity and ®eld diversity; polarisation diversity relies on the scatterers to depolarise the transmitted signal, and ®eld diversity uses the fact that the electric and magnetic components of the ®eld at any receiving point are uncorrelated, as shown in Chapter 5. Both these methods have their diculties, however, since there is not always sucient depolarisation along the transmission path for polarisation diversity to be successful, and there are diculties with the design of antennas suitable for ®eld diversity. Time diversity, i.e. repeating the message after a suitable time interval, has its attractions in digital systems where storage facilities are available at the receiver (see later). Automatic repeat request (ARQ) systems which use the same underlying principle have been available in conventional mobile radio systems for some years. It is space diversity (obtaining signals from two or more antennas physically separated from each other) that seems by far the most attractive and convenient method of diversity reception for mobile radio. The necessary antenna separation can easily be obtained at base stations and, assuming isotropic scattering at the mobile end of the link, the autocorrelation coecient of the envelope of the electric ®eld falls to a low value at distances greater than about a quarter-wavelength (Chapter 5). Almost independent samples can therefore be obtained from antennas sited this far apart. At VHF and above, the distance involved is less than a metre and this is easily obtained within the dimensions of a normal vehicle. At UHF it may be feasible even using hand-portable equipment; this will be discussed later. 10.3 BASIC DIVERSITY METHODS Having obtained the necessary versions of the signal, we must process them to obtain the best results. There are various possibilities, but what is `best' really amounts to deciding what method gives the optimum improvement, taking into account the complexity and cost involved. For most communication systems the possibilities reduce to methods which can be broadly classi®ed as linear combiners. In linear diversity combining, the various signal inputs are individually weighted and then added together. If addition takes place after detection the system is called a post-detection combiner; if it takes place before detection the system is called a predetection combiner. In the predetection 308 The Mobile Radio Propagation Channel combiner it is necessary to provide a method of cophasing the signals before addition. Assuming that any necessary processing of this kind has been done, we can express the output of a linear combiner consisting of M branches as sta 1 s 1 ta 2 s 2 t ::: a M s M t st  M k1 a k s k t10:1 where s k t is the envelope of the kth signal to which a weight a k is applied. The analysis of combiners is usually carried out in terms of CNR or SNR, with the following assumptions [1]: (a) The noise in each branch is independent of the signal and is additive. (b) The signals are locally coherent, implying that although their amplitudes change due to fading, the fading rate is much slower than the lowest modula- tion frequency present in the signal. (c) The noise components are locally incoherent and have zero means, with a constant local mean square (constant noise power). (d) The local mean square values of the signals are statistically independent. Dierent realisations and performances are obtained depending on the choice of a k , and this leads to three distinct types of combiners: scanning and selection combiners, equal-gain combiners and maximal ratio combiners. They are illustrated in Figure 10.1. In the scanning and selection combiners only one a k is equal to unity at any time; all others are zero. The method of choosing which a k is set to unity provides a distinction between scanning and selection diversity. In scanning diversity the system scans through the possible input signals until one greater than a preset threshold is found. The system then uses that signal until it drops below the threshold, when the scanning procedure restarts. In selection diversity the branch with the best short-term CNR is always selected. Equal-gain and maximal ratio combiners accept contributions from all branches simultaneously. In equal-gain combiners all a k are unity; in maximal ratio combiners a k is proportional to the root mean square signal and inversely proportional to the mean square noise in the kth branch. Scanning and selection diversity do not use assumptions (b) and (c), but equal-gain and maximal ratio combining rely on the coherent addition of the signals against the incoherent addition of noise. This means that both equal-gain and maximal ratio combining show a better performance than scanning or selection combining, provided the four assumptions hold. It can also be shown that in this case maximal ratio combiners give the maximum possible improvement in CNR; the output CNR being equal to the sum of the CNRs from the branches [2]. However, this is not true when either assumptions (b) or (c), or both, do not hold (as might be the case with ignition noise, which tends to be coherent in all branches), in which case selection or scanning can outperform maximal ratio and equal-gain combining, especially when the noises in the branches are highly correlated. In the remainder of this section we brie¯y review some of the fundamental results for dierent diversity schemes. The subject is fully treated by Jakes [3], so the detailed mathematical treatment is not reproduced here. Mitigation of Multipath Eects 309 310 The Mobile Radio Propagation Channel Figure 10.1 Diversity reception systems: (a) selection diversity, (b) maximal ratio combining (a k  r k =N), (c) equal-gain combining. 10.3.1 Selection diversity Conceptually, and sometimes analytically, selection diversity is the simplest of all the diversity systems. In an ideal system of this kind the signal with the highest instantaneous CNR is used, so the output CNR is equal to that of the best incoming signal. In practice the system cannot function on a truly instantaneous basis, so to be successful it is essential that the internal time constants of a selection system are substantially shorter than the reciprocal of the signal fading rate. Whether this can be achieved depends on the bandwidth available in the receiving system. Practical systems of this type usually select the branch with the highest carrier-plus-noise, or utilise the scanning technique mentioned in the previous section. For the moment we examine the ideal selector (Figure 10.1(a)) and state the properties of the output signal. We assume that the signals in each diversity branch are uncorrelated narrow-band Gaussian processes of equal mean power; this means their envelopes are Rayleigh distributed and, following the analysis in Appendix B, the PDF of the CNR can be written as pg 1 g 0 expÀg=g 0  The probability of the CNR on any one branch being less than or equal to any speci®c value g s is Pg k 4g s   g s 0 pg k dg k  1 À expÀg s =g 0 10:2 and hence the probability that the CNRs in all branches are simultaneously less than or equal to g s is given by P M g s Pg 1 :::g M 4g s 1 ÀexpÀg s =g 0  M 10:3 This expression gives the cumulative probability distribution of the best signal taken from M branches. The mean CNR at the output of the selector is also of interest and can be obtained from the probability density function of g s :  g S   I 0 g S pg S dg S 10:4 where pg S  d dg S Pg S  M g 0 1 À expÀg S =g 0  MÀ1 expÀg S =g 0 10:5 and the upper case subscript S is used to denote selection. Substituting this into (10.4) gives  g S   I 0 g S M g 0 1 À expÀg S =g 0  MÀ1 expÀg S =g 0 dg  g 0  M k1 1 k 10:6 Mitigation of Multipath Eects 311 The cumulative probability distribution of the output SNR is plotted in Figure 10.2 for dierent orders of diversity. It is immediately apparent that there is a law of diminishing returns in the sense that the greatest gain is achieved by increasing the number of branches from 1 (no diversity) to 2. Moreover, the improvement is greatest where it is most needed, i.e. at low values of CNR. Increasing the number of branches from 2 to 3 produces some further improvement, and so on, but the increased gain becomes less for larger numbers of branches. Figure 10.2 shows a gain of 10 dB at the 99% reliability level for two-branch diversity and about 14 dB for three branches. 10.3.2 Maximal ratio combining In this method, each branch signal is weighted in proportion to its own signal voltage/noise power ratio before summation (Figure 10.1(b)). When this takes place before demodulation it is necessary to co-phase the signals before combining; various cophasing techniques are available [4, Ch. 6]. Assuming this has been done, the envelope of the combined signal is r R   M k1 a k r k 10:7 where a k is the appropriate branch weighting and the subscript R indicates maximal ratio. In a similar way we can write the sum of the branch noise powers as N tot  N  M k1 a 2 k 312 The Mobile Radio Propagation Channel Figure 10.2 Cumulative probability distribution of output CNR for selection diversity systems. 10 log(g/g 0 ) so that the resulting SNR is g R  r 2 R 2N tot Maximal ratio combining was ®rst proposed by Kahn [2], who showed that if the various branches are weighted in the ratio signal voltage/noise power (i.e. a k  r k =N then g R will be maximised and will have a value g R  À  r 2 k  N Á 2 2N  r 2 k =N 2   M k1 r 2 k 2N   M k1 g k 10:8 This shows that the output CNR is equal to the sum of the CNRs of the various branch signals, and this is the best that can be achieved by any linear combiner. The probability density function of g R is g R  g MÀ1 R expÀg R =g 0  g M 0 M À 1! g R 5010:9 and the cumulative probability distribution function is given by P M g R 1 À expÀg R =g 0   M k1 g R =g 0  kÀ1 k À1 ! 10:10 It is a simple matter to obtain the mean output CNR from (10.8) by writing  g R   M k1  g k   M k1 g 0  Mg 0 10:11 thus  g R varies linearly with M, the number of branches. Figure 10.3 shows the cumulative distributions for various orders of maximal ratio diversity, plotted from eqn. (10.10). 10.3.3 Equal-gain combining Equal-gain combining (Figure 10.1(c)) is similar to maximal ratio combining but there is no attempt at weighting the signals before addition. The envelope of the output signal is given by eqn. (10.7) with all a k  1; the subscript E indicates equal gain. We have r E   M k1 r k and the output SNR is therefore g E  r 2 E 2NM Of the diversity systems so far considered, equal-gain combining is analytically the most dicult to handle because the output r E is the sum of M Rayleigh-distributed variables. The probability density function of g E cannot be expressed in terms of tabulated functions for M > 2, but values have been obtained by numerical integration techniques. The curves lie in between the corresponding ones for Mitigation of Multipath Eects 313 maximal ratio and selection systems, and in general are only marginally below the maximal ratio curves. The mean value of the output SNR,  g E , can be obtained fairly easily as  g E  1 2NM   M k1 r k  2  1 2NM  M j, k1 r j r k 10:12 We have seen in Chapter 5 that r 2 k  E fr 2 k g2s 2 and r k  Efr k gs  p=2 p . Also, since we have assumed the various branch signals to be uncorrelated, r j r k  r j r k if j T k and in this case (10.12) becomes  g E  1 2NM  2Ms 2  MM À 1 ps 2 2   g 0  1 M À 1 p 4  10:13 314 The Mobile Radio Propagation Channel Figure 10.3 Cumulative probability distribution of output CNR for maximal ratio combining. 10 log(g/g 0 ) 10.4 IMPROVEMENTS FROM DIVERSITY There are various ways of expressing the improvements obtainable from diversity techniques. Most of the theoretical results have been obtained for the case when the branches have signals with independent Rayleigh fading envelopes and equal mean CNR. One useful way of obtaining an overall ideal of the relative merits of the various diversity methods is to evaluate the improvement in average output CNR relative to the single-branch CNR. For Rayleigh fading conditions this quantity,  D, is easily obtained in terms of M, the number of branches, using eqns (10.6), (10.11) and (10.13). The results are: Selection SC:  DM  M k1 1 k 10:14 Maximal ratio MRC:  DMM 10:15 Equal gain EGC:  DM1  p 4 M À 110:16 These functions have been plotted in the literature [3, Ch. 5] and show that selection has the poorest performance and maximal ratio the best. The performance of equal- gain combining is only marginally inferior to maximal ratio; the dierence between the two is always less than 1.05 dB (this is the dierence when M 3I). The incremental improvement also decreases as the number of branches is increased; it is a maximum when going from a single branch to dual diversity. Equations (10.14) to (10.16) show that the average improvements in CNR obtain- able from the three techniques do not dier greatly, especially in systems using low orders of diversity, and the extra cost and complexity of the combining methods cannot be justi®ed on this basis alone. Looking back at Section 10.3, we see that with selection diversity the output CNR is always equal to the best of the incoming CNRs, whereas with the combining methods, an output with an acceptable CNR can be produced even if none of the inputs on the individual branches are themselves acceptable. This is a major factor in favour of the combining methods. 10.4.1 Envelope probability distributions The few decibels increase in average CNR (or output SNR) which diversity provides is relatively unimportant as far as mobile radio is concerned. If this were all it did, the same eect could be achieved by increasing the transmitter power. Of far greater signi®cance is the ability of diversity to reduce the number of deep fades in the output signal. In statistical terms, diversity changes the distribution of the output CNR ± it no longer has an exponential distribution. This cannot be achieved just by increasing the transmitter power. To show this eect, we examine the ®rst-order envelope statistics of the signal, i.e. the way the signal behaves as a function of time. Cumulative probability distributions of the composite signal have been calculated for Rayleigh-distributed individual branches with equal mean CNR in the previous paragraphs. For two-branch selection and maximal ratio systems the appropriate cumulative distributions can be obtained from (10.3) and (10.10), and for M  2 an expression for equal-gain combining can be written in terms of tabulated functions. The normalised results have the form: Mitigation of Multipath Eects 315 Selection SC: pg n 1 ÀexpÀg n  2 10:17 Maximal ratio MRC: pg n 1 À1  g n  expÀg n 10:18 Equal gain EGC: pg n 1 ÀexpÀ 2g n À  pg n p expÀg n erf  g n p 10:19 where g n is the chosen output CNR relative to the single-branch mean and erf :  is the error function. Figure 10.4 shows these functions plotted on Rayleigh graph paper with the single- branch median CNR taken as reference; the single-branch distribution is shown for comparison. It is immediately obvious that the diversity curves are much ¯atter than the single-branch curve, indicating the lower probability of fading. To gain a quan- titative measure of the improvement, we note that the predicted reliability for two- branch selection is 99% in circumstances where a single-branch system would be only about 88% reliable. This means that the coverage area of the transmitter is far more `solid' and there are fewer areas in which signal ¯utter causes problems. This may be a very signi®cant improvement, especially when data transmissions are being considered. To achieve a comparable result by altering the transmitter power would involve an increase of about 12 dB. Apart from the cost involved, such a step would be undesirable since it would approximately double the range of the transmitter and hence make interference problems much worse. Nor would it change the statistical characteristics of the signal, which would remain Rayleigh. We have already seen that there is a law of diminishing returns when increasing the number of diversity branches. In equal-gain combiners the use of two-branch diversity increases reliability at the À8 dB level from 88% to 99%; three-branch 316 The Mobile Radio Propagation Channel Figure 10.4 Cumulative probability distributions of output CNR for two-branch diversity systems. 10 log(g/g 0 ) [...]... 3 parity bits Table 10.1 Block encoding lookup table Single-error codewords at receiver Double-error codewords at receiver 11 000 00010 00111 01110 10110 00010 00000 10100 01100 01111 01001 00101 11101 10101 00001 10001 10010 10111 11011 00011 11111 01011 11001 11010 11100 10000 01000 - - - - - 10 011 - - - - - 01 101 - - - - - 00 110 - - - - - Tx codewords ... mitigate the e€ects of fading If a stream of digits (a data stream) from a single source is sent via a Rayleigh fading channel then there will be two observable e€ects Firstly, the overall error rate will be higher in the fading channel than it would be in a channel having a constant CNR equal to the mean CNR in the fading channel Secondly, whereas errors in the non-fading channel occur randomly throughout... non-Rayleigh fading The performance of selection and equal-gain systems depends on the signal distribution; the less disperse the distribution (e.g Rician with large signal-torandom-component ratio), the nearer equal-gain combining approaches maximal ratio combining In these conditions selection becomes relatively poorer For more disperse distributions, selection diversity can perform marginally better than equal... interleavers, which have a di erent structure, are well matched to convolutional codes [18] 10.13 CHANNEL EQUALISATION Equalisation is a very important anti-multipath technique in wideband systems and has received much attention in recent years Generally, fading in mobile radio channels is space (or time) selective and frequency selective; both have been discussed earlier Frequency-selective fading arises whenever... combining is used 10.8 POST-DETECTION DIVERSITY Postdetection diversity is probably the most straightforward if not the most economical technique among the well-known diversity systems The cophasing function is no longer needed since after demodulation only baseband signals are present The earliest diversity systems were of the post-detection type where an 326 The Mobile Radio Propagation Channel operator manually... Secondly, whereas errors in the non-fading channel occur randomly throughout the bitstream, the fading causes errors to occur in bursts coinciding with the rapid reductions in short-term CNR resulting from that fading 336 The Mobile Radio Propagation Channel Interleaving is used to introduce some time diversity into a digital communication system so that data bits which are generated consecutively are not... as a ®ve-repeat simple majority voting scheme, and it has the potential to improve channel utilisation considerably 10.10 DIVERSITY ON HAND-PORTABLE EQUIPMENT Space diversity is implemented in a number of operational cellular radio systems In most cases the diversity system exists at the base station where antenna separations of tens of Mitigation of Multipath E€ects 331 wavelengths are readily available... fades to occur in the channel transfer function, and in the absence of any suitable signal processing in the receiver this leads to signi®cant distortion of the signal and hence to intersymbol interference (ISI) ISI is the major barrier to high-speed digital transmissions over mobile radio channels but it is possible to exploit the diversity implicit in the various echo paths if the radio receiver can constructively... average fade duration (AFD) in wavelengths for two-branch diversity systems is sucient To give some idea of the magnitude of the quantities involved, a two-branch selection diversity system has an output random FM about 13 dB lower than that of a single-branch system The use of three-branch diversity further improves this to about 16 dB Selection diversity therefore provides a signi®cant reduction... that two-branch post-detection systems are only about 0.9 dB inferior to predetection combiners 10.9 TIME DIVERSITY In order to make diversity e€ective, two or more samples of the received signal which fade in a fairly uncorrelated manner are needed As an alternative to space diversity, these independent samples can be obtained from two or more transmissions sent over the mobile radio link at di erent . is the The Mobile Radio Propagation Channel. Second Edition. J. D. Parsons Copyright & 2000 John Wiley & Sons Ltd Print ISBN 0-4 7 1-9 8857-X Online ISBN 0-4 7 0-8 415 2-4 probability that a. signal distribution; the less disperse the distribution (e.g. Rician with large signal-to- random-component ratio), the nearer equal-gain combining approaches maximal ratio combining. In these conditions selection. for comparison. It is immediately obvious that the diversity curves are much ¯atter than the single-branch curve, indicating the lower probability of fading. To gain a quan- titative measure of the