1IntroductionThe potential of communicating with moving vehicles without theuse of wire was soon recognized following the invention of radioequipment by the end of the nineteenth century and its developmentin the beginning of the twentieth century [1.1, 1.2]. However, it is onlythe availability of compact and relatively cheap radio equipmentwhich has led to the rapid expansion in the use of land mobile radiosystems. Land mobile radio systems are now becoming so popular,for both business and domestic use, that the available frequencybands are becoming saturated without meeting even a fraction ofthe increasing demand. To give an example, the estimated numberof mobile radios in use in 1984 was about 540 000 with a growth rate ofabout 10% per annum in the UK; estimates of growth rates up to 20%have been made for other European countries [1.3]. Using thesefigures leads to estimates of approximately 2.5 million UK users bythe end of this century. A growth rate of 20% annually would lead tomore than 13 million users worldwide by the year 2 000. Such a figureis comparable to the 11 million business and 18 million residentialfixed telephone in use at present [1.3]. Introduction Solutions to spectral congestion in the land mobile radio environ-ment can be envisaged in the following ways.(a) The Cellular ConceptIn cellular systems, spectral efficiency is achieved by employingspatial frequency re-use techniques on an interference-limited basis.Frequency re-use refers to the use of radio channels on the samecarrier frequency to cover different areas which are separated fromone another by a sufficient distance so that co-channel interference isnot objectionable [1.4]. This is achieved by dividing the service areainto smaller `cells, ideally with no gaps or overlaps, each cell being 1
2 INTRODUCTIONserved by its own base station and a set of channel frequencies. Thepower transmitted by each station is controlled in such a way that thelocal mobile stations in the cell are served while co-channel interfer-ence, in the cells using the same set of radio channel frequencies, iskept acceptably minimal. An added characteristic feature of a cellularsystem is its ability to adjust to the increasing traffic demands throughcell splitting. By further dividing a single cell into smaller cells, a set ofchannel frequencies is re-used more often, leading to a higher spectralefficiency. Examples of analogue cellular land mobile radio systemsare AMPS (Advanced Mobile Phone System) in the USA, TACS (TotalAccess Cellular System) in the UK and NAMTS (Nippon AdvancedMobile Telephone System) in Japan ± the latter was the first to becomecommercially available in the Tokyo area in 1979. Cellular systems can offer several hundred thousand users a betterservice than that available for hundreds by conventional systems. It isfair to conclude, therefore, that the adoption of a cellular system isinevitable for any land mobile radio service to survive ever increasingpublic demands, particularly considering the severe spectrum con-gestion which is already occurring within many of the allocatedfrequency bands. It is not surprising then, that almost the only com-mon feature amongst the various proposals for second-generationcellular systems for the USA, Europe and Japan, is the use of thecellular concept. It is generally agreed that a cellular system wouldgreatly improve the spectral efficiency of the mobile radio service.(b) Moving to Higher Frequency BandsThe demand for mobile radio service has been such that serverespectrum congestion is occurring within many of the allocated fre-quency bands. First generation analogue cellular mobile radio occurbelow 1 GHz. Second generation digital celllular mobile radio alsooccur below 1 GHz. Personal Communication Networks (PCN) arerapidly moving into the next GHz band (1.7±1.9 GHz) and a UniversalMobile Telecommunications System (UMTS) ± envisaged for the endof the 1990s, will be using part of the 1.7±2.3 GHz band [1.5]. It isobvious that there are plenty of spectra above 1 GHz which makes it anatural move to go for higher frequency bands than those currently inuse. Frequencies up to the millimetric band (about 60 GHz) are beinginvestigated. In these regions, large amounts of spectrum are availableto accommodate wideband modulation systems and the radio waveattenuation is significantly greater than the free-space loss whichhelps to define a very high capacity cellular system [1.6, 1.7]. Never-theless, it is necessary to conduct detailed propagation measurements
INTRODUCTION 3in these frequency bands as well as to define system parametersadequately. Indeed, it is necessary to solve all the problems whichcan arise at these frequencies before implementation is economicallyviable and technologically possible.(c) Maximizing the Degree to which the Present Mobile Bands are UtilizedDespite the proven success of first-generation cellular systems, whichare predominantly FM/FDMA based, it is strongly believed that morespectrally efficient modulation and multiple access techniques areneeded to meet the increased demand for the service. This hasprompted considerable research into more spectrally efficient techni-ques and modes of information transmission. As a consequence, awide variety of modulation and multiple access techniques are offeredas a solution. Amongst the modulation techniques suggested arewideband and narrowband digital techniques (TDMA and FDMAbased), spread spectrum and ACSSB, alongwith conventional FManalogue systems. Voice channel spacings vary from 5 kHz forACSSB systems up to 300 kHz or more for spread spectrum systems.Furthermore, each multiple access technique ± FDMA, TDMA, CDMAand a hybrid technique ± is claimed, by various proponents, to havethe highest spectral efficiency when applied to cellular systems.From (a), (b) and (c) above, it can be clearly seen that both employingthe cellular concept and maximizing the spectrum usage of the pre-sent frequency bands are necessary to help alleviate spectral conges-tion in the land mobile radio environment and to fulfil the increaseddemands for service. In fact, higher spectral efficiency leads to moresubscribers, cheaper equipment due to mass production, low callcharges and, overall, lower cost per subscriber. It is also obvious that a rigorous and comprehensive approach tothe definition and evaluation of spectral efficiency of cellular mobileradio systems is necessary in order to settle the conflicting claims ofexisting and proposed cellular systems, especially if the British gov-ernment is to go ahead with its plan to involve the private sector in themanagement of the radio spectrum [1.8]. To date many methods have been employed in an attempt toevaluate and compare different modulation and multiple access tech-niques in terms of their spectral efficiency. These methods includepure speculation, mathematical derivations, statistical estimations aswell as methods based upon laboratory measurements. Unfortun-ately, none of the above methods can be said to be rigorous or
4 INTRODUCTIONconclusive. Mathematical methods, for instance, have been used topredict the co-channel protection ratio, yet this is a highly subjectivesystem parameter. Other approaches, such as the statistical methods,are difficult for the practising engineer to apply in general. Resultsbased on computer simulations must be treated with a degree ofsuspicion when the basis of such simulations is not revealed. Notonly have improper ways of comparison appeared in the literature,such as comparing the spectral efficiency of SSB and FM to that ofTDMA, but there is also a lack of a universal measure for spectralefficiency within cellular systems. In fact, a comparison betweenspectral efficiency values is only meaningful if it refers to:. the same service;. the same minimum quality;. the same traffic conditions;. the same assumptions on radio propagation conditions;. the same agreed universal spectral measure.Thus, it is essential to establish a rigorous and comprehensive set ofcriteria with which to evaluate and compare different combinations ofmodulation and multiple access techniques in terms of their spectralefficiency in the cellular land mobile radio environment. This bookdiscusses such a method which must necessarily embrace the follow-ing features.(a) A measure of spectral efficiency which accounts for all pertinent system variables within a cellular land mobile radio network. For such a measure to be successful it must reflect the quality of service offered by different cellular systems.(b) Modulation systems, as well as multiple access techniques, must be assessed for spectral efficiency computation including both analogue and digital formats.(c) It is necessary to model the cellular mobile radio system to account for propagation effects on the radio signal. On the other hand, it is also necessary to model the relative geographical locations of the transmitters and receivers in the system so as to be able to predict the effect of all significant co-channel interfer- ing signals on the desired one.
REFERENCES 5(d) To include the quality of the cellular systems in terms of the grade of service, two traffic models are considered. The first one is a `pure loss or blocking system model, in which the grade of service is simply given by the probability that the call is accepted. The other is a queuing model system in which the grade of service is expressed in terms of the probability of delay being greater than t seconds.(e) The method combines a global approach which accounts for all system parameters influencing the spectral efficiency in cellular land mobile radio systems and the ease of a practical applicabil- ity to all existing and proposed, digital and analogue, cellular land mobile radio systems. Hence such systems can be set in a ranked order of spectral efficiency.This study also demonstrates the crucial importance of the protectionratio in the evaluation of the spectral efficiency of modulation sys-tems. It is also argued that since the protection ratio of a givenmodulation system inherently represents the voice quality undervarying conditions, it is imperative that such a parameter is evaluatedsubjectively. Furthermore, the evaluation of the protection ratioshould be performed under various simulated conditions, e.g. fadingand shadowing, in such a way that the effect of these conditions isaccounted for in the overall value of the protection ratio. In addition,any technique which improves voice quality or overcomes hazardouschannel conditions in the system should also be included in the test.Consequently, the effects of amplitude companding, emphasis/de-emphasis, coding, etc. will influence the overall value of the protec-tion ratio. A number of current and proposed cellular mobile radiosystems are evaluated using the comprehensive spectral efficiencypackage developed.REFERENCES REFERENCES[1.1] Jakes, W. C., 1974 `Microwave Mobile Communications John Wiley and Sons, New York[1.2] Young, W. R., 1979 `Advanced Mobile Phone Services: Introduction, Background and Objectives, Bell Syst. Tech. J., 58 (1) January pp. 1±14[1.3] Matthews, P. A., 1984 `Communications on the Move Electron. Power July pp. 513±8
6 INTRODUCTION[1.4] MacDonald, V. H., 1979 `Advanced Mobile Phone Services: The Cellular Concept Bell Syst. Tech. J., 58 (1) January pp. 15±41[1.5] Horrocks, R. J. and Scarr, R. W. A., 1994 Future Trends in Telecommun- ications John Wiley and Sons, Chichester[1.6] McGeehan, J. P. and Yates, K. W., 1986 `High-Capacity 60 GHz Micro- cellular Mobile Radio Systems Telecommunications September pp. 58±64[1.7] Steele, R., 1985 `Towards a High-Capacity Digital Cellular Mobile Radio System IEE Proc., 158 Pt F pp. 405±15[1.8] Purton, P., 1988 `The American Applaud Trail-Blazing British The Times Monday, 12 December 1988, p. 28
2Measures of SpectralEfficiency in Cellular LandMobile Radio Systems Spectral efficiency in Cellular Land Mobile Radio Systems2.1 INTRODUCTION IntroductionIn order to assess the efficiency of spectral usage in cellular landmobile radio networks, it is imperative to agree upon a measure ofspectral efficiency which accounts for all pertinent system variableswithin such networks. An accurate and comprehensive definition ofspectral efficiency is indeed the first step towards the resolution of thecontemporary conflicting claims regarding the relative spectral effi-ciencies of existing and proposed cellular land mobile radio systems.An accurate spectral efficiency measure will also permit the estima-tion of the ultimate capacity of various existing and proposed cellularsystems as well as setting minimum standards for spectral efficiency.In undertaking the task, the problems currently experienced wherebysome cellular systems claim to have a superior spectral efficiency,either do not show their measure of spectral efficiency or use aspectral efficiency measure which is not universally acceptablecould be avoided. The purpose of this chapter is to survey various possible measuresof spectral efficiency for cellular land mobile radio systems, discuss-ing their advantages, disadvantages and limitations. Our criterion isto look for a suitable measure of spectral efficiency which is universalto all cellular land mobile radio systems and can immediately give acomprehensive measure of how efficient the system is, regardless ofthe modulation and multiple access techniques employed. Such ameasure should also be independent of the technology implemented, 7
8 SPECTRAL EFFICIENCY IN CELLULAR LAND MOBILE RADIO SYSTEMSwith an allowance for the introduction of any technique which mayimprove the spectral efficiency and/or system quality. Furthermore,no changes or adaptations in the spectral efficiency measure should benecessary to accommodate any cellular system which may be pro-posed in the future. With the above considerations, the most suitablespectral efficiency measure will be adopted to establish a rigorous andcomprehensive set of criteria with which to evaluate and comparecellular systems which employ different combinations of modulationand multiple access techniques in terms of their spectral efficiency.This will be the subject of the following chapters.2.2 IMPORTANCE OF SPECTRAL EFFICIENCY MEASURESMeasures of spectral efficiency are necessary in order to resolve thecontemporary conflicting claims of spectral efficiency in cellular landmobile radio systems. In such systems, an objective spectral efficiencymeasure is needed for the following reasons.(a) It allows a bench mark comparison of all existing and proposedcellular land mobile radio systems in term of their spectral efficiency. ÂFor the GSM (Groupe Special Mobile) Pan-European cellular system,for example, there are conflicting claims regarding the relative spec-tral efficiencies of proposed digital systems [2.1]. On the other hand,there are at least seven different analogue cellular land mobile radiosystems in operation throughout the world, including five in Europe[2.2], which also have conflicting spectral efficiency claims. The res-olution of such claims is complicated even further by the present lackof a precise definition of spectral efficiency within cellular systemswhich all parties can agree upon.(b) An objective measure of spectral efficiency will help toestimate the ultimate capacity of different cellular land mobileradio systems. Hence, recommendations towards more spectrallyefficient modulation and multiple access techniques can be put for-ward. Recommendations of this nature will certainly influenceresearch and development to move in parallel with more spectrallyefficient techniques and technologies and perhaps reaching higherspectral efficiency by approaching their limits. Estimates of the ulti-mate capacity of various cellular systems would also help to forecastthe point of spectral saturation, when coupled with demand growthprojections.
POSSIBLE MEASURES OF SPECTRAL EFFICIENCY 9(c) An accurate measure of spectral efficiency is also useful insetting minimum spectral efficiency standards, especially in urbanareas and city centres where frequency congestion is most likely tooccur. Such standards will prevent manufacturers lowering systemcosts or offering higher quality services at the expense of squanderingthe spectrum. This is particularly necessary with services that areprovided by competitive companies, which is very much the casenowadays. Setting thse standards will also lead to either moreresearch and development into systems which do not comply withthe minimum spectral efficiency standards or, perhaps more sensibly,to concentration of more research on systems which initially complywith the efficiency standards so as to achieve an even higher spectralefficiency. The task of setting minimum efficiency standards would becarried out by independent consultative committees such as the Inter-national Radio Consultative Committee (CCIR) and the InternationalTelegraph and Telephone Consultative Committee (CCITT), andenforced by regulatory authorities, such as the Radio RegulatoryDivision (RRD) of the Department of Trade and Industry (DTI) inthe UK and the Federal Communications Commission (FCC) inthe USA.2.3 POSSIBLE MEASURES OF SPECTRAL EFFICIENCY Possible Measures of Spectral EfficiencyThe planned spatial re-use of frequency, characteristic to cellularsystems, requires a spectral efficiency measure at the system level.In this context, spectral efficiency for a cellular system is the way thesystem uses its total resources to offer a particular public service to itshighest capacity. Hatfield [2.3] surveyed various proposed measures of spectral effi-ciency for land mobile radio systems, reviewing the advantages, dis-advantages and limitations of each. In this section possible measuresof spectral efficiency will be examined, paying particular attention totheir relevance and adequacy to cellular systems, both present andfuture.2.3.1 Mobiles/ChannelIn the measure `Mobiles/Channel, the number of mobile units pervoice channel is used to indicate the spectral efficiency. The measure`Users/Channel has also been used with the same meaning. This is
10 SPECTRAL EFFICIENCY IN CELLULAR LAND MOBILE RADIO SYSTEMSprobably the simplest way of measuring the spectral efficiency of amobile radio system. Nevertheless, this measure has certain short-comings.(a) In this spectral efficiency measure, traffic considerations arenot taken into account. Take, for example, the case of two systemsbeing compared, where the mobiles in the two systems do notgenerate the same amount of traffic. If the users in one systemgenerate twice as much busy hour traffic as the other system, forinstance, and both systems could carry the same total traffic,then that system can appear to be twice as efficient in terms ofmobiles per channel. It is obvious that using the above spectralefficiency measure, one system can purposely try to inflate itsefficiency by adding more mobiles that generate little or no traffic tothe system.(b) Channel spacing is not taken into consideration. A wide varietyof cellular land mobile radio systems can be offered as a solutionto spectral congestion. Channel spacings used could vary from5 kHz for cellular systems employing SSB modulation techniques,up to 300 kHz or more for spread spectrum systems. Unfortun-ately, the spectral efficiency measure in terms of Mobiles/Channeldoes not account for channel spacing, and hence any advantages ordisadvantages of using one channel spacing over another are simplynot shown in the measure. This problem can be solved by usingmobiles per unit bandwidth as a measure of spectral efficiency. Infact, both Mobiles/MHz and Users/MHz have been used by someauthors [2.4, 2.5].(c) The above measure of spectral efficiency does not take intoaccount the geographic area covered by the system. To exemplifythis, consider two land mobile radio systems, whereby one of themuses a base station with a very high antenna which covers a large areaof a 50 km radius and the other system uses a base station with a lowantenna covering only a small area of a 10 km radius. The two systemsmay be serving the same number of mobiles (or users), however, inthe latter case, more base stations can be spaced at closer distances soas to re-use the same radio frequencies, and hence serve more mobileswithin the same frequency band allocated for the service. In cellularland mobile radio systems, the geographic area covered by the systemis a particularly important parameter which needs to be part of thespectral efficiency measure.
POSSIBLE MEASURES OF SPECTRAL EFFICIENCY 112.3.2 Users/CellThe measure of spectral efficiency as the number of users (or mobiles)in a cell was introduced to account for cellular coverage, characteristicto cellular land mobile radio systems. Although used by some authors[2.5], the users/Cell measure also has certain deficiencies:(a) The problem of unequal traffic still exists. This problem can besolved by considering the amount of traffic which a particular systemcan provide per cell.(b) The problem of unequal channel spacings used by differentsystems remains unsolved. Even by using the Channels/Cell meas-ure, the number of channels the system can provide per cell raises theobjection of systems operating in different sizes of frequency bands.Indeed, this can be adjusted by assuming all systems that are beingcompared use the same amount of spectrum. Nevertheless, the meas-ure as Channels/Cell does not instantly reflect that.(c) Adopting Users/Cell seems to overcome the problem ofunequal coverage ± one of the objections of using Users/Channel asa spectral efficiency measure. Unfortunately, it can still be arguedthat different systems may use different cell sizes and different num-bers of cells to offer the same service within one region. This isbecause cellular systems employing different modulation techniques,with possibly different channel spacings, may have different immun-ities against co-channel interference. Consequently, some systems canemploy smaller cells than others to offer the same quality of service. Itis obvious then, that a more accurate measure of the geographic areacovered by the system needs to be used. The most sensible measure ofthe service area is to use square kilometres or square miles to replacethe concept of `cell in the above spectral efficiency measure.2.3.3 Channels/MHzThe measure of spectral efficiency as the number of channels which amobile radio system can provide per MHz appears in the literature[2.6]. It gets around some of the deficiencies in the previous measures.It particularly solves the problem of unequal channel spacingsemployed by different systems by specifying the number of channelswhich a system can provide per given MHz of the frequency band
12 SPECTRAL EFFICIENCY IN CELLULAR LAND MOBILE RADIO SYSTEMSallocated for the service. The problem of unequal traffic is a minor onehere since the amount of traffic on the channel can be used instead.Nonetheless, the problem of unequal coverage remains unsolved.Although the spectral efficiency measure Channel/MHz is suitablefor point-to-point radio communications or one cell mobile radiosystems, it is not adequate for cellular land mobile radio systems.2.3.4 Erlangs/MHzIn this measure of spectral efficiency, the Erlang* is used as a measureof traffic intensity. The Erlang (E) measures the quantity of traffic on avoice channel or a group of channels per unit time and, as a ratio oftime, it is dimensionless. One Erlang of traffic would occupy onechannel full time and 0.05 E would occupy it 5% of the time. Thus,the number of Erlangs carried cannot exceed the number of channels[2.7]. Using the above measure of spectral efficiency obviates some ofthe shortcomings in the previous measures. It certainly solves theproblem of unequal traffic by using the Erlang as a definite measureof traffic on a given number of voice channels provided by the system.It implicitly accounts for the different channel spacings provided bydifferent systems by measuring the amount of traffic in Erlangs perMHz of the frequency band allocated for the service. In other words,the spectral efficiency in Erlangs/MHz is directly related to the meas-ure in Channels/MHz, provided that blocking probabilities or wait-ing times are equal when systems are being compared. The measurein Erlangs/MHz seems to be a good one, however, its principaldisadvantage is that the geographic area is still not included. In the following section, the `spacial efficiency factor will be addedto the above measure, in an attempt to arrive at the best measure (ormeasures) of spectral efficiency in cellular systems.2.4 BEST MEASURES OF SPECTRAL EFFICIENCY IN CELLULAR SYSTEMS Best Measures of Spectral Efficiency in Cellular SystemsSome proposed measures of spectral efficiency for cellular landmobile radio systems were discussed in the previous section.Although none of the suggested measures can be said to be totally* The unit of telephone traffic is the Erlang, named after the Danish telephone engineerA. K. Erlang, whose paper on traffic theory, published in 1909, is now considered a standardtext.
BEST MEASURES OF SPECTRAL EFFICIENCY IN CELLULAR SYSTEMS 13appropriate for cellular systems, it can be deduced that a successfulspectral efficiency measure must have the following features:(a) It must measure the traffic intensity on the radio channels avail-able for the cellular service. The Erlang as a suitable and definitemeasure of traffic intensity will be used for this purpose.(b) The amount of traffic intensity should be measured per unitbandwidth of the frequency band allocated for the service (in MHz).This will inherently account for different channel spacings employedby various systems.(c) The spacial efficiency factor or the geographic re-use of fre-quency must also be included in the measure in terms of unit areaof the geographic zone covered by the service (in km2 or miles2 ).The measure of spectral efficiency as Erlangs/MHz seems to satisfyboth (a) and (b) above. To include the spatial frequency re-use factor,it is necessary to know the amount of traffic per unit bandwidth perunit area covered by the service. This leads to the spectral efficiencymeasure of Erlangs/MHz/km2 .By Using the above measure of spectral efficiency to compare differ-ent cellular systems, the system which can carry more traffic in termsof Erlangs per MHz of bandwidth in a given unit area of service canbe said to be spectrally more efficient.2.4.1 Practical Considerations of the Measure Erlangs/MHz/km2The measure of spectral efficiency in terms of Erlangs/MHz/km2proves to be adequate, comprehensive and appropriate for cellularland mobile radio systems. In the following, the choice of units for thismeasure is justified and the practical considerations and assumptionsare pointed out.(a) In the above measure of spectral efficiency, MHz is used as thebandwidth unit, not kHz or Hz. This is because the measure dealsmainly with voice transmission (telephony), with possible channelspacings of 5 kHz for SSB cellular systems and up to 300 kHz ormore for spread spectrum. In this case, a MHz can give rise to severalvoice channels, and since the number of Erlangs cannot exceed the
14 SPECTRAL EFFICIENCY IN CELLULAR LAND MOBILE RADIO SYSTEMSnumber of channels, a reasonable number of Erlangs per MHz can beobtained. However, if kHz or Hz is used in the measure instead ofMHz, a very small fraction of an Erlang per kHz or per Hz is obtained,which is not favourable for practical systems comparisons.(b) It is also practicable to use km2 (or miles2 ) as a measure of unitarea since it can accommodate a reasonable number of mobiles (orusers), which will in turn give rise to a reasonable spectral efficiencyfigure for practical systems.(c) In the above measure of spectral efficiency, there is an inherentassumption that the traffic is uniformly distributed across the entireservice area, which is usually not the case in realistic systems. How-ever, his does not seem to be a serious defect in the measure for tworeasons. Firstly, the relative spectral efficiency of cellular systemsunder identical conditions is of prime interest, and hence any assump-tions made will be equally applicable to all systems under compar-ison. Secondly, average traffic figures can be adequately used,assuming uniform traffic within individual cells and not the entireservice area. Conversely, relative and absolute spectral efficiencies aremostly needed in areas where the greatest demands in terms ofcapacity exist. In these areas, such as city centres and metropolitanareas, the smallest possible cell sizes must be used to give rise to amaximum capacity, and hence the traffic can be considered to beuniformly distributed within each individual cell.(d) The above spectral efficiency measure can be used in such a waythat the efficiency of the multiple access technique employed by thecellular system is accounted for. This is achieved by considering thetraffic on the voice channels during communication only, henceexcluding guard bands, supervision and set-up channels, etc. Thiscan be represented by the use of `paid Erlangs in the above measure,which reflects the amount of traffic intensity in the channels dedicatedto voice transmission during communication.2.4.2 Alternative Spectral Efficiency MeasuresAn alternative and conceptually simpler measure of spectral effi-ciency in cellular land mobile radio systems is presented in terms of: Voice Channels/MHz/km2 .
BEST MEASURES OF SPECTRAL EFFICIENCY IN CELLULAR SYSTEMS 15In this measure, the more voice channels per MHz a cellular systemcan provide in a unit area, the more spectrally efficient it is consideredto be. `Voice Channels is used in the measure to exclude guard bands,supervision and set up channels, etc. Hence, the measure accounts forthe efficiency of the multiple access technique employed by the cel-lular system. This measure is particularly useful for cellular systemswhich employ analogue modulation techniques, for which the chan-nel spacing is directly known. Nevertheless, the spectral efficiencymeasure in Channels/MHz/km2 is also applicable to digital systemsif the number of voice channels in the frequency band allocated for theservice is known. This is usually specified in terms of the number ofchannels per carrier, where the carrier spacing is given. This is equallyapplicable to digital systems which use time division multiple access(TDMA) techniques. The spectral efficiency measure in Channels/MHz/km2 is directlyrelated to the previous measure in Erlangs/MHz/km2 . The conver-sion from Channels/MHz/km2 to E/MHz/km2 is readily obtainedgiven an equivalent blocking probability or waiting time on the voicechannels, when the service is required (Figure 2.1), depending on thetraffic model used.Another alternative measure of spectral efficiency for cellular systemsis: Users/MHz/km2 . Figure 2.1 Best Measures of Spectral Efficiency in Cellular Systems
MEASURES OF SPECTRAL EFFICIENCY AND QUALITY CELLULAR SYSTEMS 17terms of E/MHz/km2 is superior to that in terms of kbps/MHz/km2because the former is equally applicable to both analogue and digitalcellular systems. Furthermore, the amount of traffic (in Erlangs)which can be carried by a group of analogue voice channels is nodifferent from the traffic which can be carried by the same number ofdigitized voice channels.(b) The measure in terms of kbps/MHz/km2 does not account forthe channel spacing or the digitized channel bit rate. This is due to thefact that the measure kbps/MHz/km2 was constructed using thespectral efficiency of a digital system in bps/Hz without consideringthe bit rate of the digitized channel in kbps. In this case, the spectralefficiencies of the same digital system employing two different digit-ized voice channels bit rates will falsely appear to be identical. To givean example, if a cellular system employs a digital modulation techni-que with a spectral efficiency of say 2 bps/Hz and uses a channel bitrate of 16 kbps and another cellular system employs the same digitalmodulation technique but uses a different channel bit rate of say 32kbps, then the spectral efficiencies of the two cellular systems in termsof kbps/MHz/km2 will be identical. Nevertheless, considering thechannel bit rate in kbps, it is obvious that the former digital cellularsystem can be twice as spectrally efficient as the latter. In fact, thespectral efficiency of a digital cellular system in terms of kbps/MHz/km2 can be presented in terms of Channels/MHz/km2 if coupledwith the bit rate of the digitized voice channel in kbps. For the above reasons, measures in terms of Channels/MHz/km2 ,E/MHz/km2 and Users/MHz/km2 are superior and more compre-hensive than the measure in kbps/MHz/km2 . Indeed, the measurekbps/MHz/km2 is useful to use with data-based cellular servicessuch as telex and facsimile.2.6 MEASURES OF SPECTRAL EFFICIENCY AND THE QUALITY OF CELLULAR SYSTEMS Measures of Spectral Efficiency and Quality Cellular SystemsFrom the previous analysis, the best measures of spectral efficiencyfor cellular land mobile radio systems are:. Channels/MHz/km2. Erlangs/MHz/km2. Users/MHz/km2
18 SPECTRAL EFFICIENCY IN CELLULAR LAND MOBILE RADIO SYSTEMSThe above spectral efficiency measures prove to be adequate, com-prehensive and appropriate for cellular systems. For these spectralefficiency measures to be completely successful, the quality of serviceoffered by different cellular systems has to be included. However,when we talk about quality in terms of cellular land mobile radiosystems, typically, the following three kinds of quality requirementsare considered [2.11]:(a) The degree of coverage in terms of traffic or area. That is to say,the percentage of the total area in which the service is available.(b) The grade of service in terms of blocking probability or waitingtime, when the service is required.(c) The interference levels within the cellular system. This is judgedby the protection ratio of a given modulation technique employed bythe cellular system, which gives rise to a particular voice quality.Of the above three quality requirements, only (b) and (c) are relevantto our spectral efficiency measures. Quality in terms of the grade ofservice directly applies to the spectral efficiency measures in Erlangs/MHz/km2 and Users/MHz/km2 since these include traffic considera-tions which are functions of the blocking probability or waiting time,when the service is required. On the other hand, the voice qualityrequirement is applicable to the measure in Channels/MHz/km2 ,since the number of channels obtainable per MHz is limited by thevoice quality offered to the users of the system (i.e. the number ofchannels per MHz should not be increased at the expense of voicequality). However, since the above spectral efficiency measures areinterrelated (Figure 2.1), it can be deduced that the quality in terms ofboth the grade of service and voice quality apply to all of our candid-ate spectral efficiency measures. In general, the grade of service andvoice quality can be fixed to a given standard which all mobile radiosystems in comparison have to comply with, and hence, a uniformquality is maintained throughout the comparison.REFERENCES REFERENCES[2.1] Maloberti, A., 1987 `Definition of the Radio Subsystem for the GSM Pan-European Digital Mobile Communications System, Proc. International Conference on Digital Land Mobile Radio Communications Venice, 30 June ± 3 July 1987 pp. 37±47
REFERENCES 19[2.2] Callender, M., 1987 `Future Public Land Mobile Telecommunication Systems ± A North American Perspective Proc International Conference on Digital Land Mobile Radio Communications, Venice, 30 June ± 3 July 1987 pp. 73±83[2.3] Hatfield, D. N., 1977 `Measures of Spectral Efficiency in Land Mobile Radio IEEE Trans. Electromag. Compat. EMC±19 August pp. 266±8[2.4] Lane, R. N., 1973 `Spectral and Economic Efficiencies of Land Mobile Radio Systems IEEE Trans. Veh. Technol. VT±22, (4) November pp. 93±103[2.5] Cooper, G. R., 1983 `Cellular Mobile Technology: The Great Multi- plier, IEEE Spectrum, June pp. 30±7[2.6] Matthews, P. A. and Rashidzadeh, B., 1986 `A Comparative Study of Wideband TDMA and TD/FDMA Systems for Digital Cellular Mobile Radio, Second Nordic Seminar on Digital Land Mobile Radio Communications, 14±16 October 1986 pp. 291±5[2.7] Bear, D., 1980 `Principles of Telecommunications ± Traffic Engineering IEE Telecommunications Series 2[2.8] Eckert, K. D., 1987 `Conception and Performance of the Cellular Digital Mobile Radio Communication System CD 900 37th IEEE Vehicular Techno- logy Conference, Tampa, Florida, 1±3 June 1987 pp. 369±77[2.9] Tarallo, J. A. and Zysman, G. I., 1987 `A Digital Narrow-Band Cellular System 37th IEEE Vehicular Technology Conference Tampa, Floridag 1±3 June 1987 pp. 279±80[2.10] Akaiwa, Y. and Nagata, Y., 1987 `Highly Efficient Digital Mobile Communications with a Linear Modulation Method IEEE J. Sel. Areas Commun. SAC±5, (5) June pp. 890±5[2.11] Gamst, A., 1987 `Remarks on Radio Network Planning 37th IEEE Vehicular Technology Conference, Tampa, Florida, 1±3 June 1987 pp. 160±5
3Spectral Efficiency ofAnalogue ModulationTechniques SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES3.1 INTRODUCTION IntroductionIn the previous chapter, various measures of spectral efficiency incellular land mobile radio systems were discussed and possiblemeasures of spectral efficiency measures were presented. The mostappropriate measures of spectral efficiency for cellular systems are:. Channels/MHz/km2. Erlangs/MHz/km2. Users/MHz/km2 These spectral efficiency measures prove to be adequate, compre-hensive and appropriate for cellular systems. Also, they include thequality of service offered by different cellular systems in terms of bothvoice quality and grade of service. Nevertheless, these spectral effi-ciency measures need to be mathematically interpreted to be able tocalculate the spectral efficiency of various cellular systems. In cellularland mobile radio systems, there are two major parameters whichgovern the spectral efficiency: the modulation technique employedand the multiple access technique used to trunk the signals in thesystem. For the sake of convenience as well as flexibility, we proposeto calculate the efficiency of the modulation technique and the effici-ency of multiple access of a given cellular system in isolation. Theoverall spectral efficiency of a particular land mobile radio system is 21
22 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESthen obtained by combining the two types of efficiency due to themodulation technique employed and the multiple access techniqueused in conjunction. The main purpose of this chapter is to devise a criterion bywhich the spectral efficiency of various analogue modulation tech-niques can be evaluated, when employed in cellular systems. Toaid this objective, it is necessary to have an overview of the basicanalogue modulation techniques, with particular emphasis on theprime parameters which determine the efficiency of a modulationtechnique. The spectral efficiency measure in terms of Channels/MHz/km2 is then mathematically interpreted and the efficiency ofa cellular system employing a particular modulation technique ispresented as a function of channel spacing, number of cells per clusterand cell area. The concept of cellular geometry is also introduced in order torelate the number of cells per cluster to the co-channel re-use ratio,and hence the spectral efficiency due to a modulation technique isgiven in terms of the channel spacing, co-channel re-use ratio and thecell area. It is of great importance, however, to relate the spectralefficiency of modulation techniques to speech quality experiencedby the users in the cellular system. The speech quality, in turn, isinfluenced by the signal to co-channel protection ratio determined bythe modulation technique used. To establish a relationship betweenthe protection ratio and the co-channel re-use ratio, it is necessary tomodel the cellular land mobile radio environment in such a way thatpropagation effects on the radio signal are accounted for. It is alsonecessary to model the relative geographical locations of the transmit-ters and the receivers in the system so as to be able to predict all thesignificant co-channel interference affecting the desired signal. Forthis purpose, a thorough comparative study of six different modelsis conducted and the best model of all is used. The modulationefficiency is given in terms of channel spacing, protection ratio, pro-pagation constant and cell area.3.2 BASIC ANALOGUE MODULATION TECHNIQUES Basic Analogue Modulation TechniquesAll information-bearing signals must ultimately be transmitted oversome intervening medium (channel) separating the transmitter andthe receiver. In the case of land mobile radio communications, thismedium is free space. Modulation is the process whereby signalswhich naturally occur in a given frequency band, known as the
BASIC ANALOGUE MODULATION TECHNIQUES 23baseband, are translated into another frequency band so that they canbe matched to the characteristics of the transmission medium [3.1].Thus, for example, electrical signals created by a human voice need tobe translated into the radio frequency (RF) spectrum before they canbe translated for radio communication purposes. They then have to betransmitted back into the baseband, by a complementary processknown as demodulation before they can be used to reproduce thesignals which are audible to the recipient. Also, modulation is theprocess of transferring information to a carrier, and the reverse opera-tion of extracting the information-bearing signal from the modulatedcarrier is called demodulation [3.2]. The information to be transmitted is contained in the basebandsignal; however, it is not feasible to transmit it in this form andmodulation is required for the following reasons(a) To match the signal to the frequency characteristics of the trans-mission medium, as mentioned before.(b) For the ease of radiation. If the communication channel consistsof free space, such as in land mobile radio, then antennas are neces-sary to radiate and receive the signal. For efficient electromagneticradiation, antennas need to have physical dimensions of the sameorder of magnitude as the wavelength of the radiated signal. Voicesignals, for example, have frequency components down to 300 Hz.Hence, antennas some 100 km long would be necessary if the signal isradiated directly. If modulation is used to impress the voice signal ona high-frequency carrier, say 900 MHz, then antennas need be nolonger than ten centimetres or so.(c) To overcome equipment complexity. Modulation can be used fortranslating the signal to a location in the frequency domain wheredesign requirements of signal processing devices (e.g. filters andamplifiers) are easily met.(d) To reduce noise and interference. It is possible to minimize theeffect of noise in communication systems by using certain types ofmodulation techniques. These techniques generally trade bandwidthfor noise reduction and thus require a transmission bandwidth muchlarger than the bandwidth of the baseband signal.(e) For multiplexing. Land mobile radio systems are mainly usedfor voice transmission (telephony). A band-limited voice signalhas components between 300 Hz and 3 kHz, thus, modulation
24 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESis used to translate different baseband signals to different spectrallocations to enable different receivers to select the desired voicechannel.(f) For frequency assignment. In land mobile radio systems, the useof modulation allows several hundreds of users to transmit andreceive simultaneously at different carrier frequencies, using thesame radio frequency band. This kind of need for modulation andthe previous case (e) are grouped under the multiple access tech-niques, and hence their efficiencies will not be considered in thischapter.In analogue modulation, a parameter of a continuous high-frequencycarrier is varied in proportion to a low-frequency baseband messagesignal. The carrier to be modulated is usually sinusoidal and has thefollowing general mathematical form: xc t v t cos wc t t wc 2 fc 3:1where v t is the instantaneous amplitude of the carrier, fc is thecarrier frequency and t is the instantaneous phase deviation ofthe carrier. The carrier can be modulated by varying one of the above para-meters in accordance with the amplitude of the baseband messagesignal. In principle, all analogue modulation techniques fall into two majorcategories: linear or amplitude modulation techniques and non-linearor angle modulation techniques. If v t is linearly related to the mes-sage signal m t, then we have linear or amplitude modulation. If tor its time derivative is linearly related to m t, then we have anglemodulation, which is a non-linear modulation. The following is anoverview of basic analogue modulation techniques, paying particularattention to three important parameters. These parameters are: thetransmission bandwidth, the transmitted power and the average sig-nal to noise power ratio performance of each modulation technique.Whenever possible, the message signal m(t) will be taken as a band-limited voice signal, normalized such that À1 m t 1 and havingfrequency components between 300 Hz and 3 kHz. The noise at theinput to the receiver is considered to be additive white Gaussian noise(AWGN). Furthermore, for the signal to noise ratio comparisons, allmodulation systems will be assumed to operate with the same aver-age transmitted power.
BASIC ANALOGUE MODULATION TECHNIQUES 253.2.1 Analogue Baseband Signal TransmissionBaseband systems are communication systems in which signal trans-mission takes place without modulation. They are useful as a basis forthe comparison of various analogue modulation techniques. Figure3.1(a) shows a typical block diagram of a baseband communicationsystem, where signal power amplification and necessary filtering areperformed by the transmitter and the receiver. No modulation ordemodulation is performed and the message signal is modified atthe output by the non-ideal characteristics of the channel and theaddition of noise in the system. If the baseband system is to bedistortionless, then the message signal at the output should satisfythe following equation: mo t kmi t À td 3:2where mi t is the input message signal, mo t is the output messagesignal, k is constant representing the attenuation caused by the chan-nel and td is a constant representing the time delay caused by thechannel. From Equation (3.2), it is clear that for distortionless transmission,the message is simply attenuated and delayed in time, and hence thecontent of the message is unaltered. Nevertheless, some distortionwill always occur in signal transmission, and three common types ofdistortion can be identified as follows:(a) Amplitude distortion which occurs when the amplituderesponse of the channel over the range of frequencies for the inputFigure 3.1 Baseband Communication System. Tx, Transmitter; Rx, Receiver. (a)Distortionless System. (b) Baseband System and White Noise
26 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESsignal is not flat. In this case, different spectral components of theinput message are attenuated differently. The attenuation shown inEquation (3.2) will not be constant but will be a function of frequencyk f. The most common forms of amplitude distortion are excessattenuation of high or low frequencies in the signal spectrum and itis worse for wideband signals.(b) Phase or delay distortion which occurs when different frequencycomponents of the input message signal suffer different amounts oftime delay. In this case, the time delay in Equation (3.2) is not constantbut a function of frequency td f. For voice transmission, delay dis-tortion is not a problem since the human ear is insensitive to this typeof distortion.(c) Non-linear distortion due to the presence of non-linear elementsin the channel such as amplifiers. Non-linear elements have transfercharacteristics which act linearly when the input signal is small, butdistort the signal when the input amplitude is large. Mathematically,the non-linear device can be modelled by: mo t k1 mi t k2 m2 t k3 m3 t F F F i i 3:3where k1 , k2 , k3 ; F F F, are constants. To demonstrate the effect of non-linear distortion, consider the input to be the sum of two cosinesignals with frequencies f1 and f2 . In this case, the output will containharmonic distortion terms at frequencies 2 f1 , 2 f2 and intermodulationdistortion terms at frequencies f1 Æ f2 , 2f1 Æ f2 , 2 f2 Æ f1 , etc. This prob-lem is of great concern in systems where a number of differentmessage signals are multiplexed together and transmitted over thesame channel.The types of distortion mentioned in (a) and (b) above are called lineardistortion and can be cured by the use of equalizers which are essen-tially designed to compensate for the different attenuation and delaylevels of the signal at different frequency components. The non-lineardistortion mentioned in (c) can be reduced using companders whichcompress the signal prior to transmission for its amplitude to fallwithin the linear range of the channel. Then, the signal at the receiveris expanded to restore its appropriate level. Companding is widelyused in telephone systems to reduce non-linear distortion and also tocompensate for signal levels which differ between soft and loudtalkers.
BASIC ANALOGUE MODULATION TECHNIQUES 27Signal to noise performance of baseband systemsThe signal quality at the output of an analogue modulation system isusually measured in terms of the average signal power to noisepower, defined as: Efm2 tg o S9=No 3:4 Efn2 tg owhere mo t is the output signal message, no t is the noise at theoutput of the system and Efxg denotes the average of x. The message signal will be taken as a voice signal, band-limited tofm and hence satisfies the condition: Mo f 0 for f ! fm and f Àfm 3:5where Mo f is the Fourier transform of mo t. Since our objective is the comparison of various analoguemodulation techniques in terms of their signal to noise ratio (SNR)performance, it suffices to consider the special case of an ideal channelwith additive white noise with a power spectral density (psd) of =2W/Hz (see Figure 3.1(b) ). Also, assuming ideal filters, in the case of abaseband system, a lowpass filter with cut-off frequency fm is neededat the receiver. Now, if Efm2 tg is the recovered average signal opower PR at the output, then: PR S=No say 3:6 fmHence: received signal power S=No : 3:7 in-band noise powerIf the channel is not ideal but distortionless, then using Equation (3.2),the signal to noise power ratio can be presented in terms of trans-mitted signal power PT at the input to the system: PT S=No k2 : 3:8 fmIn general, the signal to noise power ratio given in Equation (3.8) isconsidered to be an upper limit for practical analogue basebandperformance. The signal to noise ratios shown in Equations (3.6) and
28 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES(3.8) will be taken as a basis to compare the performance of variousmodulation techniques.3.2.2 Double-Sideband (DSB) ModulationThis is probably the simplest form of linear or amplitude modulation.It is achieved by multiplying the message signal m t by a high-frequency carrier xc t as shown in Figure 3.2(a), where: xc t cos wc t: 3:9For simplicity, the phase of the carrier is dropped and the amplitudeis made equal to unity, since this will not affect the generality of theanalysis. The modulated message signal is hence given by: x t m t cos wc t 3:10 45 Ay X f 1 M f fc M f À fc 3:11 2 BFigure 3.2 (a) DSB Modulator. (b) DSB Modulation in the Frequency Domain
BASIC ANALOGUE MODULATION TECHNIQUES 29where X f and M f are the Fourier transforms of x t and m trespectively. The result is graphically represented in Figure 3.2(b) in the fre-quency domain. Using this type of modulation simply translates thespectrum of the baseband message signal to the carrier frequency.This is called double-sideband suppressed carrier (DSB-SC) modula-tion, since there is no carrier term in the modulated signal.Demodulation of DSB signalsTo demodulate a DSB signal, it is multiplied by a carrier replica andthen the resultant is passed through a lowpass filter as shown inFigure 3.3(a). The spectrum of the demodulated signal before andafter filtering is shown in Figure 3.3(b). Assuming an ideal channel,Y f is given by:Figure 3.3 (a) DSB Demodulator. (b) DSB Demodulation in the FrequencyDomain
30 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES Y f 1 M f 1 M f 2 fc M f À 2 fc : 3:12 2 4After lowpass filtering: Z f 1 M f 3:13 2 ; z t 1 m t: 3:14 2The message signal m t is hence fully recovered provided that: fc fm :The demodulation scheme used above is called synchronous or coher-ent demodulation. It requires a local oscillator at the receiver which isprecisely synchronous with the carrier signal used to demodulate themessage signal. This is a very stringent condition which cannot besatisfied easily in practice. There are other demodulation techniquesthat are used to generate a coherent carrier and these are described in[3.2] and [3.3].Transmitted signal power and bandwidth of DSB signalsFrom Figure 3.2(b), it can be seen that the bandwidth BT required totransmit a message signal of bandwidth fm using DSB-SC is: BT 2 fm : 3:15It is obvious that this is a waste of spectrum since both sidebands of thesignal are transmitted, yet they carry identical information. The average transmitted power PT of the DSB modulated signal x tis given by: PT Efx2 tg Assuming 1 load 3:16 2 2 PT Efm t cos wc tg 3:17 ; PT 1 Pm 3:18 2where Pm is the average message signal power.
BASIC ANALOGUE MODULATION TECHNIQUES 31Signal to noise performance of DSB-SC systemsTo find the signal to noise performance of a DSB-SC modulationsystem, consider the model depicted in Figure 3.4, with ideal channeland ideal subsystems. The signal is assumed to be corrupted withadditive white Gaussian noise (AWGN) n t, with the following quad-rature representation [3.4]: n t nc t cos wc t À ns t sin wc t 3:19where n t is the Narrowband or bandpass AWGN, nc t is the in-phase, lowpass AWGN component and ns t is the quadrature, low-pass AWGN component. The psds of n t, nc t and ns t are shown in Figure 3.5. Figure 3.4 Model of DSB Modulation System Corrupted with AWGNFigure 3.5 (a) Bandpass AWGN Representation. (b) Lowpass AWGN Represent-ation
32 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES The bandpass filter shown in Figure 3.4 (also referred to as the pre-detection filter) is used to remove the out of band noise and anyharmonic signal terms. At point (1) in figure 3.4, the DSB signal plusnoise is given by: m t cos wc t nc t cos wc t À ns t sin wc t: 3:20At point (2), the DSB signal plus noise is multiplied by a synchronousreplica of the carrier signal. The resultant is given by:m t cos 2 wc t nc t cos 2 wc t À ns t sin wc t cos wc t 3:21 1 m tf1 cos 2w tg 1 n tf1 cos 2w tg À 1 n t sin 2w t: 3:22 c 2 2 c c 2 s cAt point (3), the double-frequency terms are removed by the lowpassfilter (also referred to as the post-detection filter), and the output willbe: 1 m t 1 n t m t n t: 3:23 2 2 c o oUsing the definition of the average signal to noise power ratio inEquation (3.4): Ef1 m2 tg 4 S=No 3:24 Ef1 n2 tg 4 c Efm2 tg S=No 3:25 Efn2 tg c Efn2 tg BT c 2 fm 3:26 P ; S=No m : 3:27 2 fmBut: 1 P Efm2 t cos 2 w tg P 3:28 2 m c R P ; S=No R : 3:39 fmFor a distortionless channel, the signal to noise ratio is given in termsof the transmitted power, hence:
BASIC ANALOGUE MODULATION TECHNIQUES 33 k2 PT ; S=No : 3:30 fmTherefore, the signal to noise power ratio for DSB-SC systems isidentical to that for analogue baseband transmission.3.2.3 Amplitude Modulation (AM)This is another type of linear modulation which can be generated byadding a large carrier component to a DSB signal. The amplitudemodulated signal has the following form: x t 1 m t cos wc t 3:31 x t cos wc t m t cos wc t 3:32 ; AM carrier DSB-SC: 3:33It can be seen that the envelope of the AM signal resembles themessage signal provided that the following conditions are met: fc ) fm and 1 m t 0:An important parameter of an amplitude modulated signal is themodulation index mx defined as: peak DSB-SC amplitude mx : 3:34 peak carrier amplitudeHence, a more general form of an amplitude modulated signal is: x t 1 mx m t cos wc t: 3:35The message signal can be completely recovered from the AM signalby simply using an envelope detector provided that mx does notexceed one. If mx does exceed one, then the carrier is said to beovermodulated, which results in envelope distortion and hence envel-ope detection is not possible in this case.Transmitted signal power and bandwidth of AM signalsThe transmission bandwidth of an AM signal is the same as that for aDSB-SC:
34 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES BT 2 fm :Using Equation (3.32), the average transmitted power PT of an AMsignal is: PT Pc 1 Pm : 3:36 2where Pc is the average carrier signal power. For a sinusoidal carrier with unity amplitude, Pc equals a half andthe average transmitted power is hence given by: PT 1 1 Pm : 3:37 2 2The power efficiency of an AM signal is given by the ratio of thepower which is used to convey information (i.e. the message signal) tothe total transmitted power, hence: 1 2 Pm power efficiency 1 1 3:38 2 2 Pm Pm : 3:39 1 PmA more general expression for the power efficiency includes themodulation index mx : m2 Pm x Power Efficiency : 3:40 1 m2 Pm xIt can be shown that the maximum power efficiency is achieved whenthe modulation index mx is one. For an arbitrary message signal (e.g. avoice signal), the maximum power efficiency is 50% and for a sinewave message signal the maximum power efficiency is 33.3%. We canconclude that AM is power inefficient due to the power Pc expendedin the carrier. Nevertheless, this carrier power is vital for simpleamplitude demodulation.Signal to noise performance of AM systemsThe signal to noise performance of AM systems can be derived ina similar fashion as for DSB systems. Only the result is given for
BASIC ANALOGUE MODULATION TECHNIQUES 35envelope detection (non-coherent modulation) of an AM signal, withthe assumption that the signal power at the receiver input is muchhigher than the inband noise power. The average signal to noise ratioat the output of the receiver is then given by [3.2]: PR S=No 3:41 fm ; S=No 3:42where is the power efficiency of the AM signal as given by Equation(3.40) and is the equivalent average signal to noise power ratio foranalogue baseband transmission. For 100% modulation (i.e. mx 1)and an arbitrary message signal, the maximum value for is a half.Hence, the average signal to noise ratio for an AM system is: S=No 1 3:43 2which is at least 3 dB poorer than for baseband transmission and forDSB-SC modulation.3.2.4 Single-Sideband (SSB) ModulationIn cellular land mobile radio systems, it is essential that the modula-tion techniques employed are spectrally efficient. It can be seen fromthe previous sections that DSB-SC and AM techniques are both waste-ful in terms of spectrum since the transmission bandwidth is twicethat of the message signal. Furthermore, AM techniques are alsowasteful in terms of transmitted power and have a poor signal tonoise performance compared with DSB-SC techniques. In SSB mod-ulation, only one of the two sidebands which result in multiplying themessage signal m t with the carrier is transmitted. Conceptually, thesimplest way of generating a SSB signal is to first generate a DSBsignal and then suppress one of the sidebands using a bandpass filter.Coherent demodulation of a SSB signal is possible using a synchron-ous carrier, in the same way as for a DSB signal. Modulation and demodulation of SSB signals as described aboveseem to be simple and straightforward, however, practical implemen-tation of the SSB technique is not trivial for two reasons. First, themodulator needs an ideal bandpass sideband filter with sharp cut-offcharacteristics which cannot be exactly achieved in practice. Second,
36 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUEScoherent demodulation requires a carrier reference at the receiverwhich is precisely synchronous with the carrier signal used to generatethe modulated message signal. Voice message signals do not containsignificant low-frequency components. Consequently, there will be nosignificant frequency components in the vicinity of the carrier fre-quency fc after modulation and hence the use of `brickwall sidebandfiltering is not really necessary. Alternatively, SSB signals can be gen-erated by a proper phase shifting of the message signal, which does notrequire a sideband filter. Envelope detection of SSB signals can beemployed instead of synchronous demodulation by adding a carrierfrequency component to the SSB signal at the transmitter, in the sameway described for AM. Nevertheless, this will lead to a waste oftransmitted power and to an inferior signal to noise performance.Transmitted signal power and bandwidth of SSB signalsThe bandwidth BT required to transmit a message signal of band-width fm using SSB modulation is: BT f m : 3:44The average transmitted power PT of a SSB modulated signal can beeasily verified to be half that of a SSB-SC signal, provided that theaverage message signal power is identical in both cases. That is, for aSSB: PT 1 Pm : 3:45 4Signal to noise performance of SSB systemsFor coherent demodulation of SSB signals, the average signal to noiseperformance can be derived in the same way as for DSB-SC signals.The average signal to noise ratio at the output of the receiver is givenby [3.2]: PR S=No : 3:46 fmEquation (3.46) indicates that S=No for SSB systems is identical tothat for baseband and DSB-SC systems, in the presence of white noise.
BASIC ANALOGUE MODULATION TECHNIQUES 373.2.5 Angle (Non-linear) ModulationIn contrast to the linear modulation techniques discussed in the pre-ceding sections, angle modulation is a non-linear process where thespectral components of the modulated message signal are not relatedin any simple fashion to the baseband message signal. Consideringthe sinusoidal carrier given by Equation (3.1), and assuming a con-stant amplitude such that v t Vc X xc t Vc cos wc t t: 3:47Angle modulation is achieved by relating t or its derivative to themessage signal m t, while keeping the amplitude of the carrier Vcconstant (for convenience, let Vc 1). Hence, an angle modulatedsignal will have the following general form: x t cos wc t f m t: 3:48The relation between t and m t can take any mathematicalform which can lead to many types of angle modulation techniques.However, only two types of angle modulation techniques haveproved to be practical: phase modulation (PM) and frequency mod-ulation (FM). In PM, t is linearly related to the message signal m tand in FM the time derivative of t is linearly related to m t.Mathematically: t kp m t for PM 3:49 d=dt kf m t for FM 3:50where t is the instantaneous phase deviation of x t, d=dt is theinstantaneous frequency deviation of x t, kp is the phase deviationconstant, expressed in rad/V and, kf is the frequency deviation con-stant, expressed in rad/s/V. Hence, an angle modulated signal can be expressed in the followingforms: x t cos wc t kp m t for PM 3:51 t x t cos wc t kf m udu for FM: 3:52 0
38 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESTransmitted signal power and bandwidth of FM signalsThe spectrum of an angle modulated signal for an arbitrary messagesignal is difficult to describe because of the non-linearity of the anglemodulation process. Instead, the spectra for a frequency modulatedsinusoidal message signal is usually examined and the result is thengeneralized for arbitrary message signals. Giving the result only, thebandwidth BT required to transmit a message signal of bandwidth fmusing FM modulation is [3.2]: BT 2
1 fm : 3:53The above expression is referred to as Carsons rule and
is definedas follows: peak frequency deviation fÁ
: 3:54 message signalbandwith fmThe peak frequency deviation is given by Equation (3.50), when theabsolute value of m t is maximum. Based on the value of
, FMsignals fall into two categories as follows. a For
( 1; BT 2 fm : 3:55 This is called narrowband FM (NBFM), and the transmission band-width in this case is the same as for DSB and AM. NBFM modulationhas no inherent advantages over linear modulation techniques. b For
fm 2 fÁ : 3:56 In this case, the FM signal is called a wideband FM (WBFM) signal.It is obvious that the transmission bandwidth of a WBFM signal ismuch larger than fm and is dependent upon the value of
(or fÁ ). From equation (3.52), the average normalized transmitted power ofthe FM modulated signal m t is: PT Efx2 tg 3:57 PT 1 : 2Hence, the average transmitted power of a frequency modulatedsignal is a function of the amplitude of the carrier signal and is
BASIC ANALOGUE MODULATION TECHNIQUES 39independent of the message signal m t. This is an expected resultsince the message signal causes only the `angle of the carrier tochange without altering its amplitude.Signal to noise performance of FM systemsThe signal to noise ratio of a FM system is taken as the ratio of themean signal power without noise to the mean noise power in thepresence of an unmodulated carrier. Hence, assuming that the outputnoise power can be calculated independently of the modulating signalpower yields the following result [3.2]: S=No 3
2 Pm : 3:58The above expression is valid provided that the signal power at thereceiver (detector) is much higher than the noise power. This isreferred to as the threshold effect of FM systems, below which thesignal to noise performance of the FM system deteriorates markedly.From Equation (3.58), it is obvious that S=No can be increased byincreasing
(or fÁ ), without having to increase the transmitted power.Increasing
will increase the transmission bandwidth BT as shown inEquation (3.56). Thus, in WBFM systems, it is possible to trade offbandwidth for improved signal to noise performance without havingto increase the transmitted signal power, provided that the system isoperating above threshold.3.2.6 General Comparison of Various Analogue Modulation TechniquesIn the previous section, an overview of the basic analogue modulationtechniques was presented. A general comparison of the variousanalogue modulation techniques in terms of transmission bandwidthand the average signal to noise performance is given in Table 3.1. It isassumed that a normalized voice message signal is used, such that: À1 m t 1 and Efm2 tg Pm 1 : 2 The transmission bandwidth is vital for spectral efficiency consid-erations and the signal to noise performance reflects the signal qualityat the receiver. Equipment complexity is not considered since spectral
40 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESTable 3.1 General Comparison of Various Analogue Modulation TechniquesModulation BT S=N0 Suitability to Cellular SystemsBaseband fm ÐÐDSB-SC 2 fm Wasteful of bandwidthAM 2 fm =3 Wasteful of power and bandwidth and poor S=N0 performanceSSB fm Spectrally efficient and good S=N0 performanceWBFM 2
2 Superior S=N0 performance but excessive use of bandwidthNBFM 2 fm ( Same bandwidth as DSB and AM but S=N0 performance is far inferiorefficiency is of prime importance in cellular land mobile radio sys-tems. From Table 3.1, amongst linear modulation techniques, SSB isboth spectrally efficient and has a good signal to noise performance.On the other hand, FM has a superior signal to noise performanceover all other modulation techniques. However, the excessive use ofbandwidth in FM systems is yet to be justified for cellular systems.Furthermore, the FM system has a superior signal to noise perfor-mance above threshold but for small signal to noise conditions the FMsystem may actually be inferior to other linear modulation techniques. The above comparison is incomplete and can only show the poten-tial spectral efficiency of various modulation techniques because ofthe idealized conditions assumed for their operation. A more realisticapproach is first to establish a rigorous and comprehensive set ofcriteria with which the spectral efficiency of various modulation tech-niques can be evaluated in terms of their important parameters. Sec-ond, the spectral efficiency of different modulation techniques shouldbe considered within the cellular environment. In the following, thespectral efficiency measure in terms of Channels/MHz/km2 is used todevise a method to evaluate the spectral efficiency of various modula-tion techniques when implemented by cellular systems.3.3 MATHEMATICAL INTERPRETATION OF CHANNELS/ MHZ/KM2 Mathematical Interpretation of ChannelsConsider a cellular land mobile radio system with a service areadivided into a number of clusters of equal area, every cluster is
MATHEMATICAL INTERPRETATION OF CHANNELS 41 Figure 3.6 Service Area Divided into Cells and Clusterssub-divided into Nc cells of equal area, each is A km2 (see Figure 3.6).A total bandwidth of Bt MHz is assumed to be available to the systemand this total bandwidth is divided into voice channels, each is BcMHz in bandwidth. In this case, the number of channels available tothe system is given by Bt =Bc , and Bc will be mainly governed by themodulation technique employed. Adopting the measure of spectralefficiency in cellular systems as Channels/MHz/km2 , the spectralefficiency of a modulation technique can be mathematically inter-preted by the following equations: total number of channels available to the system M 3:59 total available bandwith Â cluster area Bt =Bc M 3:60 Bt Nc A M 1 3:61 Bc N c Awhere M is called the modulation efficiency of the cellular system,expressed in terms of Channels/MHz/km2 .
42 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES From the above equations, we note the following:(a) For point-to-point and non-cellular radio systems, the spectralefficiency can be simply presented in terms of the number of channelsavailable to the system and is given by Bt =Bc (channels). In suchsystems the spectral efficiency is a function of the channel spacingBc only.(b) In cellular systems, the modulation efficiency measured in Chan-nels/MHz/km2 is inversely proportional to the channel spacing Bc .The modulation efficiency is independent of the total bandwidth Btallocated to the cellular system, excluding multiple access efficiencyconsiderations.(c) The spectral efficiency of a cellular system is inversely pro-portional to the cluster area given by Nc A. This is because thecluster is the repetition unit in cellular systems and not the cell.Consequently, the more clusters a cellular system can accommodatein a given service area, the more spectrally efficient it is consideredto be.(d) The modulation efficiency M can be maximized by minimisingBc , Nc or A. The channel spacing Bc is dependant on the modulationtechnique employed by the cellular system. The theoretical minimumof Nc is one and in this case one cell per cluster will give rise tomaximum efficiency, as far as Nc is concerned. Furthermore, min-imizing the cell area will depend upon several factors such as thetransmitted power, hand-off rate and the availability and tolerance ofcell sites.3.4 CALCULATION OF THE NUMBER OF CELLS PER CLUSTER Nc Calculation of the Number of Cells per ClusterFrom the previous section, the spectral efficiency of a modulationtechnique within cellular systems is shown to be a function of threeparameters ± channel spacing Bc , number of cells per cluster Nc andcell area A. It will be shown that Nc is a very important parameterwhich relates to some parameters of the modulation techniqueemployed. On the other hand, Nc depends on the cell shape as wellas the model used to calculate the co-channel interference in thesystem.
CALCULATION OF THE NUMBER OF CELLS PER CLUSTER 433.4.1 Cellular GeometryThe main reason for defining cells in a cellular land mobile radiosystem is to outline areas in which specific channels and specific cellsites are used. However, designers realize that visualizing all cells ashaving the same geometrical shape helps to ease the design of cellularsystems, not only in locating transmitter sites relative to one anotherand making economical use of equipment, but it also makes theadaptation to traffic much easier. From our viewpoint, cellular geo-metry helps to ease the assessment of spectral efficiency of variouscellular systems, in particular to calculate the significant co-channelinterference in the system.3.4.2 Cell ShapesThere are only certain patterns of cells or tessellations which can berepeated over a plane: the regular hexagon, the square and the trian-gle. The regular hexagon is favoured by system designers for thefollowing reasons:(a) It provides the best approximation to the circular omnidirec- tional radio patterns achieved in practice.(b) It is more economical to use, since a hexagonal layout requires fewer cells and hence fewer base stations.(c) It combines ease of geometry to the practical realization of over- lapping circles.3.4.3 Principles of Hexagonal GeometryThe are several objectives for describing the fundamentals ofhexagonal geometry. First, to outline clusters of cells and calculatethe number of cells per cluster Nc in terms of other parameters ofthe cellular system. Second, to locate co-channel cells and calculate theco-channel cell separation D in terms of Nc . To be able to do this, theco-channel re-use ratio is defined as: minimum co-channel cell separation co-channel re-use ratio 3:62 cell radius Q D: 3:63 R
44 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESIt can be seen that the co-channel interference can be reduced if Qis made large enough. For this reason, Q is also referred to as theco-channel interference reduction factor [3.5]. This is an importantand useful factor in cellular land mobile radio systems. For a fixedcell size, co-channel interference is independent of the transmittedpower of the base station in each cell. In fact, co-channel interferenceis a function of Q only, as will be shown later. Figure 3.7 shows a cellular pattern using regular hexagons and aconvenient set of axes intersecting at 608 [3.6]. Cearly: R cos 30 1 1 giving R p : 3:64 2 3To find the distance r of a point P u; v from the origin and using x±yto u±v co-ordinates transformations: r2 x2 y2 x u cos 30and y v u sin 30 : Figure 3.7 Hexagonal Cell Geometry with a Convenient Set of Axes
CALCULATION OF THE NUMBER OF CELLS PER CLUSTER 45Hence: 1=2 r v2 uv u2 : 3:65Using Equation (3.65) to locate co-channel cells, we start from areference cell and move i hexagons along the u-axis then j hexagonsalong the v-axis. Hence, the distance D between co-channel cells inadjacent clusters is given by: 1=2 D i2 ij j2 : 3:66The number of cells Nc in a cluster is proportional to D2 , i.e. Nc !D2and it is shown in [3.6] that: Nc D2 precisely 3:67 2 2 ; Nc i ij j 3:68Since i and j can only take integer values, Equation (3.68) suggeststhat Nc can only take particular values, e.g. Nc 1, 3, 4, 7, 9, 12, 13,etc., are possible values of Nc . In Figure 3.7, the heavy border outlinesa cluster of seven cells and the shaded cells are co-channel cells (i.e.using the same set of voice channels with the same radio frequencies).In fact, there are precisely six proximate co-channel cells for all valuesof Nc .Relationship between the co-channel re-use ratio D/R and the number ofcells per cluster NcFrom Equations (3.64) and (3.66): 1=2 D=R f3 i2 ij j2 g and using Equation (3.68): p D=R 3Nc : 3:69Hence, the modulation efficiency is given in terms of D=R as follows: M 3 : 3:70 Bc D=R2 A
46 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUES In practice, co-channel interference considerations influence thechoice of the number of cells per cluster. Making D=R smaller leadsto a spectrally more efficient cellular system, a result confirmed byEquation (3.70). However, for a better transmission quality in terms ofsignal to co-channel interference, D=R needs to be large. A trade offbetween the two objectives ± spectral efficiency and transmissionquality ± must be achieved when comparing different modulationsystems in terms of spectral efficiency. Hence, we conclude that tocompare different modulation systems in terms of spectral efficiency,a certain voice quality standard has to be set and user satisfaction hasto be achieved.3.5 RELATIONSHIP BETWEEN CO-CHANNEL RE-USE RATIO AND PROTECTION RATIO IN A CELLULAR SYSTEM Relationship Between Co-channel Re-use RatioThe spectral efficiency of a cellular land mobile radio system employ-ing a particular modulation technique is a function of three mainsystem parameters: channel spacing, cell area and the co-channel re-use ratio. It is of great importance, however, to relate the spectralefficiency of modulation techniques to the speech quality experiencedby the users in the cellular system. The speech quality is influenced bythe signal to co-channel interference protection ratio determined bythe modulation technique used. To help establish the relationshipbetween the co-channel re-use ratio D=R and the protection ratio ina cellular system, the protection ratio needs to be defined.3.5.1 Definition of Protection RatioIn general terms, the co-channel protection ratio of a cellular landmobile radio system can be defined as `its capability to reject co-channel interference. In [3.7], co-channel protection ratio was definedas ``the minimum ratio of wanted to unwanted signal level for satis-factory reception. In other words, it is the ability of a given modula-tion system to `discriminate the desired signal from the undesiredinterferences such that satisfactory signal reception is achieved. Theprotection ratio is either a ratio of voltages or signal powers, and inthe latter case it is presented in decibels. Another definition of theprotection ratio is ``The level at which 75% of the users state that thevoice quality is either good or excellent in 90% of the service area
CO-CHANNEL INTERFERENCE MODELS 47[3.6]. The World Administrative Radio Conference, Geneva, 1979,defined the protection ratio as ``the minimum value of the wanted-to-unwanted signal ratio, usually expressed in decibels, at the receiverinput determined under specified conditions such that a specifiedquality of the wanted signal is achieved at the receiver output [3.8].This ratio may have different values according to the type of modula-tion system used. The latter definition of protection ratio appears to bea comprehensive one. Nevertheless, it is necessary to have a standardset of conditions under which the protection ratio is assessed as wellas a standard for voice quality. This will ensure that consistent valuesof protection ratios are obtained. More details of the evaluation of theco-channel protection ratio can be found in Chapter 7. It is worth mentioning that in cellular land mobile radio systems theco-channel interference is actually the limiting factor in their effi-ciency and performance and not the total noise in the system. This isbecause the unwanted signal power is very much higher than the totalnoise power in the system (i.e. thermal, man-made and indigenousnoise), hence the latter can be ignored. Mathematically: protection ratio; a S 3:71 I Ns ; protection ratio; a % S for I ) Ns 3:72 Iwhere S is the wanted signal power, I is the unwanted co-channelinterfering signal power and Ns is the total inband noise power in thesystem. A more precise mathematical representation of the protection ratiocan also be found in Chapter 7. The co-channel protection ratio is a valuable measure of theperformance of a modulation technique in cellular systems and itcan indeed influence its spectral efficiency. We now need to look atthe co-channel interference models.3.6 CO-CHANNEL INTERFERENCE MODELS Co-channel Interference ModelsTo establish a relationship between the protection ratio of a modula-tion system and the co-channel re-use distance, it is necessary tomodel the cellular land mobile radio system in order to include thepropagation effects on the radio signal. It is also necessary to modelthe relative geographical locations of the transmitters and receivers in
48 SPECTRAL EFFICIENCY OF ANALOGUE MODULATION TECHNIQUESthe system so as to be able to predict all the significant co-channelinterference affecting the desired signal. In general, two main categories of co-channel interference modelscan be visualized. The first category is a geographical one, where themodels are constructed by considering the relative geographical loca-tions of the transmitters and receivers, considering different possiblenumbers of interferers in the cellular system. The second category is astatistically based group of models, in which the propagation effects,mainly fading and shadowing, are included in a statistical fashion. Bothcategories of models are based on the following general assumptions:(a) A cellular land mobile radio system with regular hexagonal cellshapes is adopted for the reasons mentioned earlier (Section 3.4.2).(b) Base stations are located at cell centres and employ omnidirec-tional antennas.(c) Considering signal path loss: the long-term median value of thesignal power decreases with radial distance from the base station andis inversely proportional to some power of the distance. Analyticalresults over a `flat earth by Bullington [3.9] show that the powerreceived by the mobile station antenna is inversely proportional tothe fourth power of its distance from the base station. This oftenreferred to as `the inverse fourth-power dependence of mean receivedpower on range. However, field measurements at approximately900 MHz by independent workers in three different cities ± Kantothe heart of Tokyo [3.10], New York [3.11] and Philadelphia [3.12] ±showed that is always less than four and greater than two. A fulland more recent survey on various propagation models for mobileradio systems in the 800/900 MHz range can be found in [3.13]. Ingeneral, is dependent upon the nature of the terrain and degree ofurbanization and usually has values between three and four [3.14].(d) In both categories of models, only co-channel interference is con-sidered. An acceptable adjacent channel interference would bebetween 60 dB [3.5] and 70 dB [3.15]. The adjacent channel interferenceeffect can be substantially reduced by the use of an intermediate fre-quency (IF) filter at the receiver with sharp cut-off characteristics. Theadjacent channel interference can be reduced even further with the useof a good frequency allocation plan [3.16], which ensures frequencyseparation between adjacent channels within each cell in the system.(e) No intermodulation products will be produced from a base sta-tion antenna with a large number of frequency channels. The channel