ELECTRICAL ENGINEERING Vol. I - Modulation and Detection - Sven Erik Nordholm, Hans-Jürgen Zepernick

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1 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik MODULATION AND DETECTION Sven Erik Nordholm Western Australian Teleommuniations Researh Institute, Nedlands, Australia Hans-Jürgen Zepernik Blekinge Institute of Tehnology, Ronneby, Sweden Keywords: Continuous wave modulation, Amplitude modulation, Frequeny modulation, Phase modulation, Pulse amplitude modulation, Pulse modulation, Pulse amplitude modulation, Pulse duration modulation, Pulse position modulation, Pulse ode modulation, Digital modulation, Phase shift keying, Frequeny shift keying, Amplitude shift keying, Quadrature amplitude modulation, In-phase omponent, Quadrature omponent, Continuous-phase modulation, Multiplexing, Additive white Gaussian noise, Signal spae, Signal vetor, Orthonormal basis funtions, Coherent detetor, Mathed filter, Maximum likelihood detetor, Non-oherent detetor Contents 1. Introdution 2. Priniples of Modulation 2.1. Continuous Wave Modulation Linear Modulation Frequeny and Phase Modulation 2.2. Pulse Modulation Pulse Amplitude Modulation Pulse Position Modulation Pulse Code Modulation 2.3. Digital Modulation Geometri Representations of Digital Modulation Signals Phase Shift Keying Frequeny Shift Keying Amplitude Shift Keying Amplitude Phase Keying Continuous Phase Modulation 3. Detetion and Reeiver Strutures 3.1. Coherent Detetion 3.2. Non-oherent Detetion 4. Future Development, Eonomi and Environmental Impliations Aknowledgements Glossary Bibliography Biographial Skethes Summary This hapter presents priniples of modulation tehniques for modern ommuniation systems along with the orresponding signal detetion shemes and prominent reeiver Enylopedia of Life Support Systems (EOLSS)

2 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik strutures. Modulation is an integral part of every modern ommuniation systems and provides a means of mathing an information-arrying signal to the transmission medium or transmission hannel. Modulation tehniques are ommonly lassified into ontinuous wave (CW) modulation and pulse (PU) modulation. While modulation takes plae at the transmitting end of a ommuniation system, an inverse operation alled detetion needs to be performed at the reeiving end. In general, detetion aims at reovering the information-bearing signal from the reeived signal as lose as possible in terms of a speified optimization riterion. Digital ommuniations, whih usually stands for the digitized representation of originally analogue signals by disrete amplitude and disrete time, is ommon pratie with today s ommuniation systems. In digital ommuniation systems, disrete information is onveyed between the ommuniating entities using signal formats from a finite set of waveforms. This allows for the design of very robust transmission systems with the deployed waveforms onstruted in suh a manner as to failitate easy information reovery. 1. Introdution Communiation between people plays a vital role in today s soiety serving the fundamental human needs of exhanging information and ideas. Sine the invention of telegraph and telephone, more sophistiated forms of teleommuniation devies and servies have been developed over the years suh as wireless ommuniation systems and the Internet. In addition, the tremendous advanes in integrated iruit tehnology enabled the prodution of small and low ost ommuniation devies, whih nowadays onsume only little energy and are affordable by almost anyone. The demand to ommuniate from anywhere in the world and at any time has lead to the development of mobile radio systems. Espeially, with the deployment of the digital mobile radio systems in the early 1990 s, global penetration of mobile phones has reahed a penetration of lose to perent of the population in some regions. A similar rapid inrease of users has been observed with the able-based ommuniation systems. All these ommuniation systems depend heavily on the engineering efforts that have been put into the design of the underlying transmission system and the assoiated physial layer funtions. Apart from operations suh as soure enoding, hannel enoding, equalization, and the respetive deoding funtions, modulation and detetion are ruial omponents in the physial layer of modern ommuniation systems. Modulation not only transforms information-bearing signals into a format that is suitable for transmission over a given hannel but also takes are that the available transmission resoures are effiiently used. Furthermore, modulation failitates the multiplexing of large numbers of users onto a ommon transmission hannel, whih in view of the global user penetration is a hallenging task. At the reeiver, powerful detetors are required that an reover information-bearing signals out of severely orrupted reeived signal. 2. Priniples of Modulation The purpose of a ommuniation system is to deliver a ommuniation servie from an information soure to an information sink. Typially, soure and sink are spatially separated and a transmission hannel is needed to serve as link between the Enylopedia of Life Support Systems (EOLSS)

3 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik ommuniating entities. Depending on the partiular transmission medium, the original messages as released by the soure are mapped onto a different format or signal representation before the atual transmission suh that it suits the hannel harateristis. This operation is performed at the transmitting end of a ommuniation system and is referred to as modulation. At the reeiver, a reverse operation takes plae, whih is alled detetion or demodulation aiming at reovering the original message. In the sequel of this hapter, we will mainly onentrate on priniples of prominent modulation tehniques. The different types of modulation tehniques an be lassified into Continuous Wave (CW) modulation and Pulse (PU) modulation. In the ase of CW modulation, a sinusoidal wave is used as arrier of the messages. If the amplitude of the arrier wave is varied aording to the amplitude of the message signal, amplitude modulation (AM) is obtained. Similarly, angle modulation refers to those CW shemes in whih the angle of the arrier is hanged aording to the message signal. It is noted that angle modulation an be further differentiated into frequeny modulation (FM) and phase modulation (PM) shemes indiating that either instantaneous frequeny of the arrier or arrier phase is modified by the message signal. In pulse modulation, on the other hand, a pulse train is used as the arrier wave and a suitable pulse parameter is modified in aordane with the message signal rather than modifying a sinusoidal arrier wave. Espeially, amplitudes, durations, or positions of the pulses in a pulse train are suitable for representing the message signal. The orresponding pulse modulation tehniques are referred to as Pulse Amplitude Modulation (PAM), Pulse Duration Modulation (PDM) also known as Pulse Width Modulation (PWM), and Pulse Position Modulation (PPM). These three PM tehniques are lassified as analog pulse modulation, whih aounts for the fat that the respetive pulse harateristis are modified with the sample value of the message signal. A seond lass of PM tehniques is known as digital pulse modulation in whih not only time but also amplitude of the message is represented and proessed in disrete form. For example, Pulse Code Modulation (PCM) is a prominent digital pulse modulation tehnique. In a first proessing step, PCM applies an analog-to-digital onversion to the analog message signal resulting in a PAM signal. Then, the obtained pulse amplitudes are quantized, thus, giving a finite set of possible amplitude values. In a final proessing step, eah quantized amplitude value is represented by a binary ode word. This type of disrete time and enoded disrete amplitude modulation shemes are used in many digital ommuniation systems. Apart from mathing messages to the harateristis of a given transmission medium, the onept of modulation also provides a framework for multiplexing messages of different users onto a ommon but shared hannel. The three major types of multiplexing are as follows: 1. Frequeny-Division Multiplexing (FDM). This tehnique is based on CW modulation and translates the message signals of the different users into different frequeny bands where eah band is identified by a distint arrier frequeny. 2. Time-Division Multiplexing (TDM). This tehnique exploits PM tehniques and as suh positions the message signals of the different users into non-overlapping time slots. Enylopedia of Life Support Systems (EOLSS)

4 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik 3. Code-Division Multiplexing (CDM). This tehnique uses different spreading sequenes or signatures to separate the messages of the various users. In that way, all users an use the total available frequeny band simultaneously while the individual user an still be identified by its unique spreading sequene Continuous Wave Modulation The ontinuous wave modulation shemes an be desribed mathematially by way of a modulated sinusoidal signal s(t) = a(t)os t + (t) ω ϕ (1) where a(t) denotes instantaneous signal amplitude, ω t+ϕ (t) represents instantaneous phase, ω =2π f is referred to as angular veloity with f being the arrier frequeny, and ϕ (t) denotes a time-varying phase. In CW modulation the message signal m(t) is used to modify either amplitude or the phase of a high frequeny arrier signal Linear Modulation Linear modulation tehniques vary the amplitude of a high frequeny arrier signal ( t ) = a os( ω t ) (2) linearly with the instantaneous amplitude of the baseband message signal m(t). Aordingly, the modulated signal is given by s(t) = a(t)(t) (3) In partiular, amplitude modulation shemes impose the following modifiation to the arrier amplitude: a( t ) = 1 + μm( t ) (4) where μ is referred to as modulation index. This type of modulation auses the envelope of the arrier waveform to hange proportionally with the instantaneous amplitude of the baseband message signal. In order to avoid an over-modulation of the arrier signal, whih would result in undesirable arrier phase reversals, it is neessary to keep a(t) always positive by requiring μ m( t ) < 1 (5) If this ondition is fulfilled, then an envelope detetor may be deployed for demodulation purposes, whih would simply trak the slowly hanging envelope of the high frequeny arrier signal. A frequeny domain representation of an AM signal an be obtained by Fourier transform and is given by Enylopedia of Life Support Systems (EOLSS)

5 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik a S(f) = (f f ) (f f ) 2 δ + δ + aμ + M( f f ) + M( f + f ) 2 (6) where δ(f) denotes the Dira delta funtion. It an be onluded from Eq. (6) that the spetrum S(f) of the modulated signal s(t) onsists of two disrete spetral lines whih are loated at the positive and virtual negative arrier frequeny. In addition, the baseband spetrum M(f) of the modulating message signal m(t) appears now shifted in frequeny and is entered around the disrete spetral lines of the arrier signal. This onstitutes a lower and an upper sideband of the spetrum M(f±f ) with respet to the arrier frequeny ±f giving rise to all suh an approah a Double Sideband (DSB) tehnique. DSB tehniques with Suppressed Carrier (DSB-SC) aim at onserving transmission power by not transmitting the arrier waveform a(t)=a m(t) but only the informationbearing signal omponents within the sidebands. The benefit of DSB-SC being more power effiient than the onventional AM shemes omes at the expense of the required more involved oherent detetor at the reeiver (see Setion 3). Single Sideband (SSB) tehniques address the seond shortoming of DSB tehniques, whih is their ineffiieny in the use of bandwidth. Sine the information assoiated with the message signal m(t) is ompletely ontained within a single sideband of the modulated signal, either upper sideband or lower sideband may be suppressed before transmission. In partiular, an SSB signal ontaining only the lower sideband (+) or the upper sideband ( ) is given in the time domain by a a ω ˆ s(t) = m(t)os( t) ± m(t)sin( ω t) (7) 2 2 where the Hilbert transform ˆm( t ) of the band-limited message signal m(t) is defined as 1 m( τ ) ˆm( t ) = dτ π (8) t τ The orresponding frequeny domain representation of the Hilbert transform is given by ˆM( f) = jsgn(f)m(f) (9) where sgn(f) denotes the signum funtion and is defined as 1, f > 0 sgn( f ) = 0, f = 0 1 (10) 1 f < 0 Enylopedia of Life Support Systems (EOLSS)

6 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik Frequeny and Phase Modulation Instead of using the message signal to modify the amplitude of a sinusoidal arrier wave, the message signal may be utilized to vary the angle of the arrier while keeping its amplitude onstant. Either varying the frequeny or the phase of the arrier signal in aordane with the message signal may be applied. The numerous advantages of frequeny and phase modulation tehniques over the above desribed linear modulation shemes inlude: 1. Better disrimination of noise and interferene. 2. Less stringent requirements on the linearity of the front-end power amplifiation enable the use of more effiient lass C power amplifiers. 3. Trade-off possibilities between bandwidth and noise suppression. Given the general formulation of the ontinuous wave modulation shemes as defined in Eq. (1), an angle-modulated signal an be desribed as s( t ) = a os[ ω t + ϕ ( t )] (11) Then, the instantaneous angle θ (t) of the angle-modulated signal s(t) is given by θ (t) = ω t + ϕ(t) (12) with the instantaneous frequeny f (t) being the derivative of the instantaneous angle θ (t), i.e. 1 d θ(t) f(t) = (13) 2π dt Among the many means of varying the instantaneous angle of the arrier wave in aordane with the message signal, we will onsider in the sequel the two ommonly used methods of phase modulation and frequeny modulation. In the ase of a PM sheme, the message signal m(t) linearly varies the instantaneous angle θ (t) of the arrier signal. In view of Eq. (12), we have p θ (t) = ω t+ k m(t) (14) where k p denotes the phase sensitivity of the modulator. Similarly and in view of Eq. (13), an FM sheme varies the instantaneous frequeny f (t) of the arrier signal aording to f (t) = ft+ kfm(t) (15) where k f denotes the frequeny sensitivity of the modulator. The instantaneous angle θ (t) is then obtained by simply integrating the instantaneous frequeny f (t), that is Enylopedia of Life Support Systems (EOLSS)

7 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik f 0 t θ (t) = 2π f t+ 2πk m( τ )dτ (16) Therefore, phase-modulated and frequeny-modulated signal s(t), respetively, an be desribed in the time domain as s( t ) a os 2π ft + kpm(t) for PM a os 2π ft + 2πk f m( τ )dτ for FM 0 = t (17) Clearly, Eq. (17) indiates that PM and FM signals are very losely related. For example, an FM signal may be onsidered as a PM signal in whih the message signal was replaed by the integral over the message signal: t m( t ) m( τ )dτ (18) 0 As a onsequene, the harateristis and properties of PM signals an be dedued from FM signals. On the other hand, it is noted that the properties of FM signals, suh as their spetrum and required transmission bandwidth, are more ompliated to derive analytially ompared to the ase of linear modulation. This is due to the fat that an FM signal is a nonlinear funtion of the message signal. An estimation of the bandwidth that is oupied by an FM signal when the message signal is sinusoidal is given by the so-alled Carson s rule (see Communiation Systems): BT 2k f a + 2 fm (19) where f m denotes the frequeny of the sinusoidal message signal m(t) Pulse Modulation A fundamental operation assoiated with all pulse modulation tehniques is the sampling proess. To be more speifi, sampling onverts an analog signal into a orresponding sequene of samples, whih in view of appliations in pratial systems are spaed uniformly in time. Given an arbitrary signal m(t) of finite energy, then the instantaneously sampled version of the signal an be formulated mathematially as S δ S (20) n= s( t ) = m( nt ) ( t nt ) where T S is the sampling period, m(nt S ) is the sample value of m(t), and δ(t) denotes the Dira delta funtion. This operation is alled ideal sampling. Let the analog signal m(t) be stritly band-limited to a bandwidth B. Then, the instantaneously sampled version s(t) uniquely defines m(t) if the sampling rate f S =1/T S is hosen as fs 2B (21) Enylopedia of Life Support Systems (EOLSS)

8 ELECTRICAL ENGINEERING Vol. I - Modulation and Detetion - Sven Erik Nordholm, Hans-Jürgen Zepernik where 2B is alled the Nyquist rate and 1/2B is alled the Nyquist interval. As long as the sampling rate is equal or greater than the Nyquist rate, the original signal m(t) an be ompletely reonstruted from its instantaneously sampled version s(t) (Shannon- Nyquist sampling Theorem) Bibliography TO ACCESS ALL THE 25 PAGES OF THIS CHAPTER, Visit: Anderson J. B., Aulin T., and Sundberg C.-E. (1986) Digital Phase Modulation, New York: Plenum Press. [This book offers a omprehensive overage of digital phase modulation tehniques on an advaned level] Haykin S. (2001). Communiation Systems, New York: John Wiley & Sons. [This book presents an overview of ommuniation systems on an aessible level] Papoulis A. (1991). Probability, Random Variables, and Stohasti Proesses, New York: MGraw-Hill. [This book presents a bakground on stohasti proesses] Proakis J. G. (2001). Digital Communiations, New York: MGraw-Hill. [This book gives a detailed overage of the theoretial aspets of digital ommuniations on an advaned level] Sklar B.(1988) Digital Communiations: Fundamentals and Appliations, Englewood Cliffs: Prentie Hall. [This book presents an overview of digital ommuniation systems on an aessible level] Biographial Skethes Sven Erik Nordholm reeived his MS. EE, Li. Eng. and PhD degree from the University of Lund, Sweden, in 1983, 1989 and From 1983 to 1986, he was a Researh and Development Engineer with Gambro AB a biotehnial ompany. From he hold various positions at Blekinge Institute of Tehnology starting from leturer to full Professor. Currently, Dr. Nordholm holds the positions of a Professor in Teleommuniations at Curtin University of Tehnology, Diretor of the Signal Proessing Laboratory of the Western Australian Teleommuniations Researh Institute (WATRI), and Researh Exeutive of the Australian Teleommuniations Cooperative Researh Centre (ATr), Perth, Australia. His researh interests inlude speeh enhanement, array signal proessing, multi-rate proessing and signal proessing for ommuniation systems. Hans-Jürgen Zepernik reeived his MS degree from the University of Siegen, Germany, in 1987, and his Ph.D. degree from the University of Hagen, Germany, in 1994, both in eletrial engineering. Currently, he holds the position of Professor in Radio Communiations at the Department of Signal Proessing of the Blekinge Institute of Tehnology, Ronneby, Sweden. His researh interests inlude radio hannel haraterization and modeling, oding and modulation, equalization, spread-spetrum systems, wireless multimedia ommuniations, and future generation wireless systems. Enylopedia of Life Support Systems (EOLSS)