3. Spread Spectrum Systems

Transcription

1 3. Spread Spetrum Systems Jan Šimša Institute of Radio Engineering and Eletronis, Aademy of Sienes of CR Spread spetrum signals are signals arrying digital modulation as a rule. What signal has a spread spetrum? The speifi parameter is the ratio of a signal bandwidth to the transmission rate. The bandwidth of a spread spetrum signal is a multiple of the bandwidth of a modulating data signal (i.e. of its data rate). PSK or QAM modulated signal has the spetrum whose bandwidth is roughly equal to the value of the modulation (symbol) rate of the applied digital modulation. In this ase the ratio of its spetrum bandwidth to the data transmission (modulation) rate reahes a value in the viinity of one. In ontrast, a signal has its spetrum spread if this ratio approahes a value substantially (often by some orders of magnitude) higher than one. As a rule, to reah suh a broad spetrum, an additional modulation by a spreading signal is applied. Spreading signal does not arry any information but only one determining the transmitting user. The spreading modulation is a periodi deterministi digital signal, referred frequently to as a signature, generated by means of a ode sequene (binary or nonbinary). The reeiver of a spread spetrum signal first eliminates the spreading modulation. As the elimination of the spreading modulation of a reeived signal is the first step of the signal proessing performed by a reeiver, the legitimate question an be raised. What is the reason of the spetrum spreading if we aim at its elimination again? Motivation Arguments for appliation of the spread spetrum tehniques are onneted to the harater of an explored ommuniation hannel. We would lak arguments if the ommuniation over an AWGN hannel took plae. This is the ase of a single-path timeinvariant interferene-free ommuniation hannel. Any transmitted signal is orrupted by an additive white Gaussian noise only and the general expression for an error rate of the transmission behaves aording to the well-known rule expressing the error rate as a funtion of the SNR and a orrelation of symbols only. The shape of an applied signal in the time domain and, equivalently, the shape of its spetrum do not influene the value of the error rate. There is no reason to employ a spread spetrum tehnique for transmission of signals in suh environment. The opposite onlusion is reahed if the utilized hannel is a highly signal disturbing one. This lass ontains hannels suh as - hannels with interferene - hannels exhibiting time-variant and frequeny-seletive parameters - hannels with multi-path propagation. Spread spetrum signals are advantageous not only in ommuniations. As broadband signals, spread spetrum signals potentially enable preise loalization in the time domain, whih failitates preise measurement of time intervals, and hene even distanes and positions of objets. Spread spetrum signals exhibit a low value of their mean value of the power spetrum density (PSD) and potentially even its peak value. The detetion of suh signals by methods evaluating the ratio of the signal power to the additive noise power in the band-pass of a

2 reeiver is made diffiult in a hidden area, where the noise PSD has higher value ompared to the transmitted spread spetrum signal. The omplementary area in whih a SS signal is not hidden is a irle around the position of the transmitter. Methods of spetrum spreading Any wide-band spread spetrum signal belongs to one of the three ategories: - signals without a arrier - signals with a single arrier - signals with multiple arriers. Signals without a arrier are relatively new sublass of wide-band signals. These signals are reated by a sequene of very narrow pulses of a proper shape and their spetrum bandwidth is by some orders of magnitude wider than the modulation rate. Suh signals are often referred to as Ultra Wide-Band (UWB) signals (and related UWB systems). Their bandwidth an reah values higher than 5 GHz [4]. The UWB priniple is not limited to radio-ommuniation systems only, but it proved advantageous in optial-ommuniation systems, as well. As a rule, the modulation applied here is a pulse-position modulation or a spreading oded modulation. Single harmoni arrier signals reate the basi ategory of SS signals generated by modulating a harmoni arrier. This ategory an be divided into three basi subgroups. Diret sequene (DS) SS signal is generated by PSK spreading ode modulation. If the BPSK is used, this modulation is equivalent to the keying of the polarity of the transmitted arrier. QPSK an equivalently be regarded as a polarity keying of both quadrature omponents. The BPSK modulated signal of the k-th user an be expressed as s (t) = A. (t). b (t). os( ω t + ϕ ), () k k k k 0 0k where A is the amplitude of the signal, ( t) is a spreading ode modulation, k k () t =±. Let the shaping funtion p θ (t) be defined as a retangular one in our ase. Using the unit step funtion (t), this funtion is p θ (t) = (t)-(t- θ ). The spreading modulation k (t) an be expressed as k() t = ki. pt ( t it), (2) i where T is the bit interval of this modulation referred to as the hip interval. The sequene ki, i=..,,0,,... is a periodi one having period L, i.e., a spreading modulation (signature) (t) is periodi as well k k(t) = k(t - i. L.T ), i integer (3) The data modulation bk ( t ) arries a binary data sequene { b ki}, i=0,,2,... b k(t) = b p ki T ( t it ), (4) i where T is the data (symbol) interval. The partiular ase when this interval equals to the spreading ode modulation period T = L. T (5) is alled short ode spreading. The ase of the spreading modulation period muh longer than the data interval is referred to as the long ode spreading. In the former k 2

3 ase the bandwidth of SS signal is inreased L-times ompared to the data only modulated signal as the signal bandwidth of the signal before spreading is T and that after spreading is = L. T T The value L is often referred to as the system (or spreading) gain. Frequeny hopping (FH) is spetrum spreading by step-wise hanges of the arrier frequeny. The arrier is data modulated by any digital modulation as FSK, PSK or QAM. The slow FH is the ase when the data symbol interval is a fration of the (hip) interval between two adjaent frequeny steps. The ase of multiple frequeny steps within one data symbol interval is referred to as the fast FH. The sequene of frequeny values whih are hopped over is usually reated as an equidistant set of frequenies, the frequeny step being higher than the bandwidth of the spetrum of the data modulated signal before spreading. It avoids the ase when two adjaent frequeny positions are interfered by a single narrow-band (line) interferene beause their spetra overlap. This method is effetive in the ase of a small number of narrowband interferenes. The system an be designed as adaptive, whih means that it is able to exlude instantly interfered frequenies from the set of frequenies the system is hopped on. The sequene of these frequenies is ontrolled by a ode sequene with proper harateristis. Time hopping (TH). The ontrolling ode sequene defines a position of eah short interval within whih the aumulated data are transmitted as a paket. The rate of this modulation within a paket is a multiple of the mean value of data transmission. As a rule this multipliity is one or more orders of magnitude. The randomness of the paket position avoids the dangerous regularity of interferene in the worst ase. Among multi-arrier signal formats, it were the promising parameters of orthogonal frequeny division multiplexing (OFDM) that attrated the ommuniation system designers. This ase is haraterized by transmitting a high number of arriers with equidistant frequenies. This distane is hosen with respet to the orthogonality of arriers on a data or hip interval, respetively. The input binary data sequene is serial-to-parallel onverted and transmitted through low-rate, frequeny overlapping but orthogonal sub-hannels. The narrow-band nature of signals generated by modulation of arriers provides high immunity against multipath dispersion and narrow band interferene. Any appliation of OFDM onsisting of a higher number of arriers would not be possible without appliation of DSP to signal generation and detetion. Majority of appliation uses Fast Fourier Transform (FFT) transformers realized in a form of integrated iruits (IC). OFDM in itself does not ause signal spetrum spreading. This spreading is reahed by additional frequeny hopping or more frequently by diret sequene spreading. The latter method is usually referred to as multiarrier CDMA. The appliation of CDMA spreading an be done by multipliation of i-th modulated arrier of k-th user (frequeny f i = f + (i ) ), by a value ki of a hosen spreading ode. The spreading ode length equals the number of arriers. The data stream is not subjeted to any serial-to-parallel onversion; the same data bit modulates all the arriers. This method is often referred to as Frequeny domain spreading. The alternative method uses data sequene serialto-parallel onversion and all modulated arriers are spread by the same spreading modulation. The frequeny distane is hosen suh that the arriers are orthogonal on the hip interval T, i.e., the orthogonality ondition T. = n, n positive integer, holds. 3

4 Transient methods between these two different methods ombining features of both of them are reported in [8]. The last sublass of MC-CDMA utilizes S/P onversion, the idential spreading modulation in all hannels and the frequeny distane is hosen to satisfy orthogonality on the data symbol interval. Orthogonality in time and frequeny domains Time-domain orthogonality Two signals x (t) and x (t) are orthogonal on the interval t 2 (a,b), a<b, a,b real, if and only if b x() t x2() t dt = 0 (6) a In the ase of digital ommuniations, x (t) and x 2 (t) are usually real and time-limited signals having interval of nonzero values (0,T), i.e., a=0, b=t. Frequeny domain orthogonality The question about the relation of orthogonality in the time and frequeny domains is answered by the Parseval theorem, the ommon shape of whih is expressed as x ( t ) x 2( t ) dt = ( ) 2( ) 2 X ω X ω d ω π (7) Here, X (ω ) and X 2 ( ω ) are Fourier transforms of (finite energy) signals x (t) and x 2 (t), respetively. If both signals have fully or mostly disjoint (nonoverlapping) spetra, the signals are orthogonal or weekly orrelated, respetively This an be seen as a mehanism of orthogonality or weak orrelation between a broadband (i.e., inluding SS) and a narrowband signal. Any weekly orrelated pair of signals an be disriminated by a orrelator. That mehanism is utilized in any kind of multiplexing of signals inluding ode division multiplex / ode division multiple aess - CDMA. The number of mutually orthogonal signals is limited by the dimensionality of the utilized signal spae. The double of produt of the utilized frequeny bandwidth B and the length T of orthogonality interval, i.e. the symbol interval in our ase, give dimensionality. This dimensionality does not suppose any limitation on a lass of funtions reating an orthogonal basis. If we onfine ourself on e.g. orthogonal binary signals, their number will usually not reah the signal spae dimensionality. Advantages and potential of SS ommuniation Interferene suppression Signal spreading was originally reognized as a powerful tool for suppression of narrow band interferenes. Generally, orrelator/mathed filter reeiver an suppress any weakly orrelated interferene. The lower the orrelation, the higher the interferene suppression. The degradation by a narrow-band interferene an be eliminated by means of the synergy of an OFDM multiarrier signal and a forward error ontrol oding. A signal hiding in additive noise is a onsequene of an inrease of the spetrum width given by a spreading fator equal to one, two or more orders of magnitude, respetively, keeping the total power of this signal unhanged. Therefore, the values of the power spetral density are lowered inversely proportionally to the spreading fator. To keep the power 4

5 spetral density low in the whole bandwidth of spreading, the applied spreading modulation has to have orresponding property. Multipath propagation, whih an ause severe signal distortion, is mitigated by strutures based on the Rake reeiver [], [2], [3]. If mutually delayed signal omponents an by resolved by orrelator/mathed filter, the reeiver proesses the delayed signal replias separately. This resolution an be done, if the differenes of signal omponents delays are higher than the width of the signal autoorrelation funtion main lobe. This has to be taken into aount when designing the spreading ode modulation. Intersymbol interferene (ISI) aused by multipath propagation an be redued by inreasing the length of the data symbol interval. One of possible ways to do it is the appliation of the OFDM priniple, where the data symbol interval is lengthened proportionally to the number of arriers. Mitigation of seletive fading in frequeny seletive hannels an be done by two different methods. The first is based on the idea that this fading will not ause a severe deterioration in OFDM if the number of faded sub hannels is limited and the signal drop-outs an be eliminated by the FEC (Forward Error Corretion) oding. Interleaving an inrease the robustness of this method. The seond method relies on frequeny diversity, whih is a mehanism leading to lower degradation of a signal whose bandwidth is substantially broader than the bandwidth of the fading noth. This is an area of implementation of spread spetrum onto OFDM. Applying the OFDM-CDMA methods an mitigate ombination of seletive fading and multipath propagation. Resistane to seletive fading Behavior of a hannel in the frequeny domain an be desribed in terms of the hannel oherene bandwidth defined as the maximum value of the bandwidth in whih the values of the hannel transfer funtion (as a funtion of frequeny) are strongly orrelated. A hannel whose bandwidth of oherene is lower than the spetrum width of a transmitted signal is referred to as a frequeny seletive hannel. If the opposite is true, the hannel is said to be frequeny nonseletive. The same hannel an at as frequeny seletive, when a wide band signal is transmitted, as well as a frequeny nonseletive, when a narrow band signal is transmitted. The bandwidth of a transmitted signal determines signal distortion. In general, a total outage of the signal at the output of a frequeny nonseletive hannel has more severe onsequenes than the signal distortion aused by a frequeny seletive hannel. To hange the signal aneling frequeny nonseletive fades to the less atastrophi frequeny seletive ones, one has to broaden the bandwidth of a transmitted signal. This alls for appliation of a spread spetrum tehnique. To visualize a signal distortion by a frequeny seletive hannel, a simple - though unpublished - worst ase approximation is given below. The DS-SS signal s(t) () passes through a frequeny seletive hannel whose transfer funtion H(jω) exhibits one deep retangular fade of bandwidth ω = 2πB loated around ω 0.The retangular shape is less favourable than any real frequeny seletive fade). This band-stop transfer funtion H(jω) an by expressed as H(j ω) = for ω ( ω0 - πb, ω0 + πb) (8) 0 ω ( ω - πb, ω + πb) 0 0 or H(j ω) = - H (j ω ) (9) where 5

6 H (j ω) = for ω ( ω - πb, ω + B) 0 0 for ω ( ω - πb, ω + πb) π The impulse response of this hannel is an inverse Fourier transform, whih is a δ t of ideal linear non band-limited hannel and of the superposition of the impulse response ( ) impulse response of a band-stop retangle h t () h(t) = jωt H( jω). e dω δ( t) h ( t) 2π = where h(t) = ( ). =2Bos sinπ Bt t. πbt ωo+ πb ωo+ πb jωt jωt jωt H jω e dω = e dω + e dω ω0 2π 2π 2π ωo πb ωo πb The relevant omponent of the hannel response is sinπbτ y() t = s() t h() t = 2 B. os ω 0τ..( t τ).sin ω0( t τ) + ϕ 0 dτ πbτ () The substitution (2) leads to sinπbτ y() t = B.sin( ω 0t+ ϕ0). i. pt ( t τ it ) dτ = i πbτ π Bt ( it ) (2) sinϑ =.sin( ω0t+ ϕ0). i dϑ π ϑ i π Bt ( i+ ) T (0) This response is a superposition of responses to individual hips. The response to the positive hip is π Bt ( it ) sinϑ y i() t =.sin( ω 0t+ ϕ0). d π ϑ (3) ϑ π Bt ( it) i π Bt ( i+ ) T sinϑ A graph of the funtion. d ϑ π is given in Fig.. ϑ π Bt ( i+ ) T As this response has the interval of nonzero values some tens of symbol intervals long, the noth omponent will ause intersymbol interferene (ISI), not neessarily severe. The omplete fading of a signal in a nonseletive faded hannel is onverted to a relatively long but weak ISI omponent indued by this fade. The narrower the bandwidth of a fade the longer and weaker this omponent is. The positive influene of the frequeny diversity is obvious. Fig.. Response of the noth to single retangular hip 6

7 Spreading oded modulation signatures Requirements The spread spetrum signal should have the envelope onstant to keep the sensitivity to nonlinearities low Appliations of binary and quaternary PSK modulations are prevailing, i.e., attention is onentrated on binary and quaternary sequenes Smooth spreading as uniform power density in the spreading bandwidth as possible without disrete lines in the spetrum Narrow main lobe and very low side lobes of the autoorrelation funtion (for simple and unique ode synhronization and delay measurements) Low ross-orrelations within the set of CDMA signatures The harater of a speifi appliation determines the proper definition of the orrelation funtions. The well-known [], [2], [3] optimized sequenes determining spreading modulation-signature are pseudorandom m-sequenes are e.g. Gold sequenes, Kasami sequenes, bent sequenes, Walsh-Hadamard sequenes and many others; in the meantime even some non binary ones have been proposed. Their orrelation properties have been thoroughly studied. Reeiver struture Taking into aount omplexity of a spread spetrum signal reeiver, the lass of reeivers is usually limited to the linear one. The optimum reeiver of a signal having a priori known shape in AWGN hannel is a orrelator or its equivalent - mathed filter (MF) [], [2], [3]. This reeiver is an optimum solution even in the ase of disrimination of orthogonal signals in AWGN hannel [5]. This solution enables a resolution of a number of mutually orthogonal signals in suh a way, that the response of MF/orrelator is a funtion of amplitude (energy) of a signal the MF is mathed to (target signal), and it is ompletely independent of amplitudes of signals at the MF input whih are orthogonal to this target signal. The signal disrimination is ideal in this ase. If the deteted target signal is orrupted by the superposition of non-orthogonal signals, the MF response has an interfering omponent proportional to the orrelations with the target signal and amplitudes of the interferers. The optimality of MF is not valid in this environment any more; the optimum linear reeiver is a reeiver maximizing the value of signal to interferene plus noise ratio. The sensitivity of detetor response to amplitudes of interferenes is referred to as near-far problem [5]. Code Division Multiplex / Code division Multiple Aess (CDMA) When a hannel is shared by a number of users, it an be taken as a speial ase of interfering signals in this hannel. The methods of multiplexing of signals are an effiient tool of multiuser ommuniation, if the signals of individual users an be seleted by a detetor from their superposition at the hannel output without any severe interferene. The higher the signal-to-interferene ratio, the loser the multiplex is to the ideal one. The approah to single-arrier (per user) CDMA historially evolved from Frequeny Division Multiplex (FDM), through Time Division Multiplex (TDM) to the multiplex based on the general orthogonality of user-speifi signatures odes. This most ontemporary multiplex is referred to as Code Division Multiplex (CDM) or Code Division Multiple Aess (CDMA). The problem of suh systems is preservation of orthogonality of multiplexed signals at the 7

8 reeiver input. In ase of orthogonal signatures of users, a bank of mathed filters is the optimum linear reeiver. But due to the harater of a ommuniation hannel this orthogonality is usually impaired. Consequently, mutual interferene of users annot be ompletely aneled by the optimum linear reeiver, either. This interferene is referred to as multi-user interferene (MUI) or multiple-aess interferene (MAI) [5]. In this ase a deorrelating reeiver and a bank of mathed filters are asymptotially optimum solutions for high SNR and low SNR ase, respetively. Minimum Mean Square Error (MMSE) reeiver is an optimum solution in a transient ases in whih neither influene of additive noise nor influene of interferenes is stritly dominant [5], [9] Multiarrier ode division multiplex Utilization of OFDM priniple is not onneted to the spread spetrum priniple, as OFDM an be applied without any spetrum broadening. In suh ase the MC signal is a means for lowering the sensitivity of transmission to ISI aused by multipath propagation. Let us explain the approah using a few simple equations; this approah has been proved more spae effetive. Inlusion of figures into this ontribution would inrease its length substantially. The starting point of MC system design are the parameters of the ommuniation hannel, its power delay profile and the delay-spread intervalt DEL. Further main parameters of the hannel are its bandwidth B and its bandwidth of oherene B COH. To suppress the influene of a delay spread, the symbol interval T of MC modulation is hosen T T (4) 0 DEL Appliation of PSK/QAM modulation generates modulated arriers having BS = T bandwidths. The seond set of parameters is reated by the signal and system parameters. Among them the ratio N SP N SP T = (5) T where Tb = R b are the required bit interval and the transmission bit rate, respetively. MC transmission without spetrum spreading oupies the hannel bandwidth B0 = NSP = NSP BS (6) Tb T Multiplexing of signals of multiple users alls for a muh broader bandwidth, beause only the inrease of the signal spae dimensionality makes the loation of a higher number of orthogonal or weekly orrelated signals possible. Let the total bandwidth of a hannel be B spread Bspread b = M B (7) Now, there are N P parallel hannels NP = M NSP (8) whih an be utilized for multiuser exploitation. There are three basi multiplexing methods [6], [7]: Eah user-speifi signature has the number of hips equal to the number of arriers N P. The transmitted data hips are not S/P onverted, eah bit is transmitted in all hannels simultaneously, i.e., the symbol intervals of the hannels have their initial values. Eah symbol in the MC hannel is multiplied by one hip of the signature. This multipliation fator is onstant during the transmission by a speifi user. The 0 8

9 signatures of individual users are mutually orthogonal. This method is alled frequeny domain spreading or MC CDMA. Eah S/P onverted symbol having its interval T = NSP Tb is spread by its speifi spreading modulation over the bandwidth M BS. Beause there are N SP suh parallel hannels, the total bandwidth of suh signal is B (6), (7). This method is referred to as MC DS CDMA. After S/P data onversion the MC OFDM signal is reated. Its symbol interval is T and its bandwidth is B 0. The single user spreads the whole OFDM superposition speifi spreading DS modulation. As individual modulated arriers have the frequeny distane of adjaent sub hannels = T = B S, these signals have after spreading strongly overlapped spetra as eah spread arrier has the bandwidth approx. M BS, i.e., M-times broader than the frequeny distane. This signal pattern is usually referred to as the multitone CDMA (MT-CDMA). Synhronization The advantageous features of spread spetrum signals appliations in ommuniation and measurements are reahed at the expense of higher omplexity of system realization. One of the most demanding proessing is ode synhronization, whih is a method of determination of the a priori unknown time position of the spreading modulation (signatures) at the reeiver input. Without this synhronization any despreading and demodulation of a reeived signal, i.e., any data transmission would not be possible. The ode synhronization onsists of two steps aquisition a oarse time position estimation having error less than one hip interval traking minimizing of estimation error to a small fration of a hip interval and traking of time variations of the position As the ode synhronization has to be ahieved in a very short time interval, sophistiated methods of ode aquisition have been elaborated. This proess has a speifi mathematial model that differs from the lassial formulation of parameter estimation. Instead of minimization of the error of an estimate based on a fixed extent of observation, the ode position estimation does not minimize the error, but it minimizes the time of the estimation proess whih results in a limited error and the extent of observation is a free parameter or a sequene of parameters whih has to be optimized. The error of the final estimate has to be lower than its presribed maximum value. For ode traking a delay traking loop or tau dither traking loop is utilized. Conlusions This ontribution attempts to very briefly summarize an evolution of the area of spread spetrum ommuniation systems inluding CDMA. Some topis, with whih perhaps the targeted group of readers is not quite familiar, are dealt with in more detail. In ontrast to the general pratie the equations are used in this ontribution for more preise desription of some proesses. This approah seems to be more onise than explanation using figures. These will be used in the oral presentation. spread 9

10 Aknowledgment Author of this ontribution would like to express his gratitude to all his olleagues that have been ative and ooperative in the area of spread spetrum ommuniation. Among them V. Cizek, S. Durovi, T. Novosad, I. Triska and V. Zalud influened the author more than the others. The partial support by the Grant No. 02/05/0852 of the Grant Ageny of CR is aknowledged. Referenes: [] Holmes, J.K.: Coherent Spread Spetrum Systems, John Wiley, New York 982 [2] Simon, M.K. et al.: Spread Spetrum Communiations Handbook, M Graw-Hill, New York 994 [3] Peterson, R. L., Ziemer, R. E., Borth, D. E.: Introdution to Spread Spetrum Communiations, Prentie Hall, Upper Saddle River 995 [4] Yang, L., Giannakis, G.B.: Ultra-Wideband Communiations, IEEE Signal Proessing Magazine 2, Nov. 2004, [5] Verdu, S.: Multiuser Detetion, Cambridge Univ. Press, 998 [6] Hara, S., Prasad, R.: Overview of Multiarrier CDMA, IEEE Commun. Magazine, De.997, 26-33wledg(e) [7] Yee, N., Linnartz, J.P., Fettweis, G.: Multi-Carrier CDMA in Indoor Wireless Radio Networks, Pro.PIMRC Conf., Yokohama, Japan 993, D.3. D.3.5 [8] Yang, L.L., Hanzo, L.: Multiarrier DS-CDMA: A Multiple Aess Sheme for Ubiquitous Broadband Wireless Communiations, IEEE Signal Proessing Magazine 20, Nov. 2004, [9] Honig, M., Tsatsanis, M.K.: Multiuser CDMA Reeivers, IEEE Signal Proessing Mag. vol.7, No.3, May 2000,