Pilot Symbol Aited Modulation uing 16-Level QAM for a Wirele Sytem Pilot Symbol Aited Modulation uing 16-Level QAM for a Wirele Sytem Angela DARIE, Ion BOGDAN Rezumat. Modulaţia cu imbol pilot(psam) ete o metodă eficientă pentru a reduce efectul fadingului într-un item de comunicaţii mobile. În itemele PSAM emiţătorul înerează periodic în fluxul de date imboluri pilot cunocute, din care receptorul extrage amplitudinea şi faza emnalului recepţionat. În proceul de imulare am foloit o ecvenţă de date generată aleator uniform ditribuite şi o anumită ecvenţă pilot (ecvenţă Barker), care apoi au fot mapate într-un et de date 16-QAM. S-au imulat efectele zgomotului şi influenţa fadingului în componentele emnalului. Cuvinte cheie: Modulaţie cu imbol pilot (PSAM), contelaţia ortogonală 16-QAM, ecvenţe Barker. Abtract. A fundamental iue of a communication ytem i the reliability and integrity of the received data a they are often been corrupted. Tranmiion error may be attributed to everal factor. One epecially typical and important factor i the fading. PSAM (Pilot Symbol Aited Modulation) i a technique to compenate the effect of fading in wirele mobile communication. With PSAM, at the tranmitter a known et of pilot ymbol are periodically inerted into the generated data ymbol tream. The receiver i able to derive the amplitude and phae reference for data ymbol detection by uing thee ymbol. Keyword: Pilot Symbol Aited Modulation (PSAM), 16-QAM contellation, Barker equence. Introduction In mot of the wirele communication channel there can be more than one path between the tranmitter and the receiver antenna, making the reception very difficult. The channel fading not only degrade the bit error rate (BER), but alo inhibit the ue of multilevel modulation cheme, uch a QAM, a modulation format that ha greater pectral efficiency. Pilot Symbol Aited Modulation (PSAM) can compenate the fading effect in land mobile communication and can make the ue of multilevel modulation format poible. To overcome the impact of fading and to facilitate the ue of QAM cheme, a good way i to etimate the channel fading ignal and ue thi information to revere the effect of fading. The etimation of fading ignal can be achieved with the aid of a reference ignal (or a pilot ignal) [1-4]. In Fig.1 i illutrated the idea of a PSAM technique, where the tranmitter periodically inert known ymbol into the information-bearig ymbol tream, denoted a pilot ymbol, and thee one can be ued by the receiver to etimate the fading ditorion. The paper i organized a follow. The data model and PSAM ytem are decribed in Section 2. Section 3 ue a uitable modulation cheme to accomplih the tranmiion between ditant ender and receiver. A compreive theoretical decription of Nyquit filtering i provided in Section 4. Since the tranmiion channel i often the limiting factor that influence the performance of any communication TELECOMUNICAŢII Anul LII, nr. 1/2009 25
Angela DARIE, Ion BOGDAN ytem, both AWGN and Rayleigh fading channel are conidered in Section 5. Simulation reult are included in Section 6 and concludind remark follow in Section 7. PSAM Sytem Decription The block diagram of a general PSAM cheme i depicted in Fig. 1, the tranmitter periodically inert known pilot ymbol into data tream, from which the receiver derive it amplitude and phae reference. The combined pilot and data frame illutrated in Fig. 2 contain a pecific equence of N pilot ymbol inerted at ymbol interval of length L. The compoite ymbol equence (k) i modulated by a quare root Nyquit pule, p(t), and then tranmitted over a channel characterized by flat low fading and additive white Gauian noie channel. Pilot ymbol have the ame pule hape a the data ymbol. The tranmitted ignal ha a complex envelope given by: t () = A npt ( ) ( nt ) (1) n= where (k) i the input pule ignal, T i the ymbol time, A i an amplitude factor and p(t) i a unit energy pule, which can be decribed in following equation: 2 pt () dt= 1 (2) * p( τ ) = () ( τ)d R p t p t t (3) Rp( k) = Rp( kt) =δ ( k) (4) where R ( τ ) i the autocorrelation function of the p pule waveform p(t) and δ( k) i the Kronecker delta function [1]. Fig. 1. PSAM tranmitter and receiver tructure. For channel with multi-path non-elective fading, the time-delay pread of the channel i much le than the ymbol duration. When a ignal pule i tranmitted, the mobile receive the uperpoition of many pule approximately at the ame time. Therefore, the frequency non-elective and low Rayleigh fading channel can be aproximated into a multiplicative factor of the tranmitted ignal. The received ignal can be expreed a : rt () = tct ()() + nt () (5) where r(t) i the baeband received ignal, c(t) denote the multiplicative fading ditorion with a Rayleigh ditribution envelope, (t) i the tranmitted baeband ignal, and n(t) i the additive white 26 TELECOMUNICAŢII Anul LII, nr. 1/2009
Pilot Symbol Aited Modulation uing 16-Level QAM for a Wirele Sytem Gauian noie with zero mean and power pectral denity N 0. The received ignal i fed to an ideal low-pa filter (LPF), which avoid interymbol interference (ISI). The receiver detect the pule uing a matched filter with impule repone p * ( t)/ N0 and ampled at the ymbol time t = nt : * ( ) = ( ) ( τ) ( τ ) ( τ )d τ+ ( ) n = r kt A n c p nt p kt n kt where ( ) (6) rkt i the repone of the matched filter and ymbol ampler. After matched filter detection, the receiver plit the ymbol ample into two tream. The reference branch decimate the ample to extract only thoe due to the pilot ymbol, and interpolate thee ymbol to form an etimate of the channel tate. In the QAM ytem illutrated in Fig.3 it i aumed that the input information i a tream of random binary bit. Thi bit tream i firt mapped into Ι and Q QAM ymbol. In a 16-QAM ytem, the binary bit tream i mapped into 4-bit ymbol and the quare contellation uing Gray coding i illutrated in Fig.4. For a 16-QAM contellation, each point repreent a 4-bit ymbol, compoed by two in-phae bit on I axi and two quadrature bit on Q axi. The bit 01, 00, 10, 11 are mapped to the level 3d, d, -d, -3d. Such algorithm it i called Gray code. In Fig. 4 the ditance between adjacent code point i alway 1 and larger than 1 for the other cae. Thi i a fundamental feature of Gray coding proce o that when a received ymbol i corrupted by noie an it i miinterpreted a an adjacent contellation point, it enure that the demodulator will make a ingle bit error. Nyquit filtering (quare root raied coine filter) Fig. 2. Tranmitted frame tructure. 16 State Quadrature Amplitude Modulation (16-QAM) The major difficulty of uing bandwidth-efficient multi-level QAM cheme i that over fading channel the tranmitted ignal magnitude i modified and the phae i rotated, wich caue error tranmiion of QAM difficult to compenate, unle pecial procedure are introduced at both the tranmitter and the receiver end. By uing a PSAM ytem, the impact of fading can be reduced and the ue of AM become poible. A an illutration in thi paper we chooe 16-QAM a the modulation format. The input data for the 16-QAM modulator are rectangular pule. If not pule haped appropriately, thi pule hape may caue evere interymbol interference (ISI) with adjacent pule for mot communication channel that are bandwidth-contrained. An ideal linear low-pa filter (LPF) ha a cut-off frequency of f = f / 2, where f = 1/ T i the N ymbol rate, T i the ymbol interval duration and f N = 1/ (2 T ) i the o-called Nyquit frequency. Thi filter ha a (in ) / x x haped impule repone with equiditant zero-croing at the ampling intant nt. When ampled at the correct intant, thi lowpa filter avoid ISI. TELECOMUNICAŢII Anul LII, nr. 1/2009 27
Angela DARIE, Ion BOGDAN a) Tranmitter b) Receiver Fig. 3. A QAM cheme. Fig. 4. 16-QAM quare contellation uing Gray encoding. 28 TELECOMUNICAŢII Anul LII, nr. 1/2009
Pilot Symbol Aited Modulation uing 16-Level QAM for a Wirele Sytem A particular pule hape that atifie the characteritic mentioned above for an ideal low-pa filter and ha been widely ued in practice i the Nyquit raied coine pule [6]: 1 β T 0 f 2T T πt 1 β 1 β 1+β F{ f() t } = 1+ co f f 2 β 2T 2T 2T 1+β 0 f 2T (7) where T i the ymbol duration and β i the roll-off factor which take value in the range [0, 1]. The correponding time domain impule repone of a raied coine filter above i given a by [6]: πt πβt inc co T T ft () = 2 βt 1 4 T (8) The raied coine pule pectral characteritic and correponding pule for β= 0,0.5 and 1 are illutrated in Fig. 5. Fig. 5. Nyquit pule and raied coine pectrum. Tranmiion channel After the baeband ignal I and Q have been filtered, they are paed through an I-Q modulator with two quadrature carrier a illutrated in Fig.3. Thee two ignal are tranmitted and received over a ingle channel within the ame bandwidth. Two common channel model are ued: the additive white Gauian noie channel and the multipath Rayleigh fading channel [5]. Additive White Gauian Noie Channel The additive white Gauian noie (AWGN) i aumed to have a contant power pectral denity over the whole channel bandwidth and it amplitude probability denity function (PDF) obey the tatitic of a Gauian ditribution. Multi-path Rayleigh Fading Channel The baic model of Rayleigh fading aume a received multipath ignal to conit of a (theoretically infinitely) large number of reflected wave with identically ditributed inphae and quadrature amplitude. Fading Channel Effect The delay aociated with different ignal path in a multipath fading channel change in an unpredictable manner and can only be characterized tatitically. The effect of the channel on a tranmitted ignal in general i repreented a : j2 f t [ ] () t = Re () t e π c (9) p where Re[ ] i the real part of a complex ignal, p( t) i the bandpa tranmitted ignal, (t) i the baeband input ignal band-limited by the tranmitter filter and f c i the carrier frequency. Further, if there are multiple propagation path, aociated with each path there are a propagation time delay τ () t and an amplitude attenuation factor a(t) both time-variant. The received bandpa ignal after multi-path propagation may be expreed a: x() t = an() t p[ t τn()] t (10) n TELECOMUNICAŢII Anul LII, nr. 1/2009 29
Angela DARIE, Ion BOGDAN where a ( t ) i the amplitude attenuation factor of n the received ignal in the n th path and n () t τ i the propagation time delay for n th path. The equivalent lowpa baeband received ignal i : 2 ( ) rt () a() c n n te j π f π = t t [ τn() t] (11) n The fading channel repone can be modeled a a random proce: jθ ( ) (,) () n t h τ t = an t e δ[ t τn() t ] (12) n where θ () t = 2 πf τ () t. The received ignal i n c n compoed of different time-variant vector that have different amplitude factor and phae ( an ( t ), θ n( t) ). Thi mean that the time-variant fading repone h(,) τ t i a random proce of variable t, too. The random proce of multi-path channel fading can be modeled by a Rayleigh ditribution or a Rice ditribution. Parameter of a fading channel In a typical wirele communication environment, multiple propagation path often exit from a tranmitter to a receiver due to cattering by different object. Signal copie following different path can undergo different attenuation, ditorion, delay and phae hift. When radio wave with different Doppler hift combine detructively to cancel at one time and combine contructively at another time, they produce a time-variant channel fading. Thi type of channel i claified a fat and low fading baed on the normalized fading rate f d fm fcvcoα fd = = (13) B Bc where f m i the maximum Doppler hift, B i the bandwidth of the baeband ignal, v i the velocity of the mobile uer, f c i the carrier frequency, α i the arrival angle of the path that ha maximum Doppler hift, and c i the light peed. If the fading rate i maller than one, it mean that the Doppler frequency hift i much maller than the bandwidth of the ignal. If the bandwidth of the tranmitted ignal i mall compared to the coherence bandwidth of the channel ( Δ f coh. ), then the channel i claified a frequency non-elective (flat) fading. The coherence bandwidth of the channel can be expreed a [6]: 1 Δ fcoh. = (14) T where T m i the maximum difference of any two path delay in a fading multi-path channel. Therefore, the frequency non-elective and low Rayleigh fading channel can be achieved approximating a multiplicative factor of the tranmitted ignal. The general expreion of the received ignal i : rt () = ctt ()() + nt () (15) where rt ( ) i the baeband received ignal, ct ( ) give the multiplicative fading ditorion and it envelope ha a Rayleigh ditribution, t () i the tranmitted baeband ignal and nt ( ) i the additive white Gauian noie with zero mean and power pectral denity N 0. The channel model i illutrated a in Fig. 6. Fig. 6. Tranmiion channel model. Simulation Reult In the imulation proce, data ymbol and pilot ymbol are both elected from a 16-QAM data et. m 30 TELECOMUNICAŢII Anul LII, nr. 1/2009
Pilot Symbol Aited Modulation uing 16-Level QAM for a Wirele Sytem The inertion rate of pilot ymbol i L p = 10, which mean pilot ymbol i inerted every 10 ymbol and the firt ymbol each ubframe i a pilot ymbol. It i generally deirable to chooe a pilot ymbol pattern with good autocorrelation propertie. In thi paper 7, 11, 13 Barker equence, Neuman-Hofman 13, and PN 15(ee Table 1) are ued. the roll-off factor i et to 0.5. The output of SRRC filter i then tranmitted over the communication channel. Table 1. Lit of pilot equence Sequence Bipolar Binary Sequence BK7 [-1,-1,-1,1,1,-1,1] BK11 [-1,-1,-1,1,1,1,-1,1,1,-1,1] BK13 [-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1] NH13 [1,1,1,1,1,1,1,-1,-1,1,1,-1,1,-1] PN15 [-1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1] For each cae, one full frame obervation i thu 70, 110, 130, and 150 ymbol, repectively. A compoite equence of un-haped ymbol from the ignal generator i illutrated in Fig. 7. A tated above, pilot ymbol occur at interval of 10 ymbol. Fig. 7. A compoite equence of un-haped ymbol from he ignal generator. The compoite ignal i next filtered by a bandlimiting Nyquit filter uing a root raied coine filter (SRRC). The input ignal of the tranmitter filter i linearly modulated and upampled by a factor of 16, Fig. 8. Input and output ignal of tranmitter filter. To imulate the fading channel effect we ue the additive white Gauian noie, which we chooed to run in a ignal to noie ratio mode. For the multipath Rayleigh fading channel cae, we will conider both fading and additive white Gauian noie. The channel i modeled a in equation decribed above: rt () = ctt ()() + nt (). According to the channel model, additive Gauian noie i added to the baeband ignal after it firt pae through the multi-path Rayleigh fading channel. The ideal 16-QAM contellation i imulated a hown in Fig.9 (a) and the received 16-QAM ignal corrupted by a time-varying Rayleigh fading channel i hown in Fig.9(b). A indicated in Fig.9 (b), fading cale and rotate the ignal contellation and therefore the magnitude i changed. In Fig.9 (b) it i clear that the tranmitted ignal i everely degraded by fading effect. Fig.10 how the received ignal over an AWGN channel till with very clear boundarie beetwen ymbol. A the noie level increae, the ymbol are blurred more. In Fig.11 after the Gauian noie i added the tranmitted ignal i corrupted more everely. TELECOMUNICAŢII Anul LII, nr. 1/2009 31
Angela DARIE, Ion BOGDAN Concluion (a) Pilot ymbol aited modulation i relatively imple to implement. The tranmitter jut inert known ymbol periodically, o there i no change in pule hape or peak to average power ratio. PSAM wa teted with AWGN and Rayleigh fading land mobile channel. Acknowledgement. Financial upport from the BRAIN project i gratefully acknowledged. Reference ( b) Fig. 9. 16-QAM ignal corrupted by multi-path Rayleigh fading. Fig. 10. 16-QAM ignal corrupted by AWGN channel. [1] J.K.Caver, An analyi of pilot ymbol aited modulation for Rayleigh fading channel, IEEE Tranaction on Vehicular Technology, vol.40, pp.686-693, November 1991. [2] J.M.Torrance, L. Hanzo, Comparative Study Of Pilot Symbol Aited Modem Radio Receiver and Aociated Sytem, Conference Publication No 415, 26-28 September 1995. [3] A. Ganman,M.P.Fitz and J.V.Krogmeierm, Optimum and Suboptimum Frame Synchronization for Pilot-Symbol-Aited Modulation, IEEE Tranaction on Communication,vol.45, No.10,pp.1327-1337, October 1997. [4] Tai-Ann Chen, Michael P. Fitz, Shengchao, Michael D. Zoltowki, Two-Dimenional Spece-Time Pilot- Symbol-Aited-Demodulation For Frequency-Nonelective Rayleigh Fading Channel IEEE Tranaction on Communication,vol. 52, No.6,June2006. [5] Hamid GHaravi, Pilot Aited 16- Level QAM for Wirele Level, IEEE Tranaction on circuit and ytem for video technology, Vol. 12, No. 2, February 2002. [6] John G. Proaki, Communication ytem engineering, Pretince Hall, 1994. Fig. 11. 16-QAM ignal degraded by multi-path Rayleigh fading and AWGN. 32 TELECOMUNICAŢII Anul LII, nr. 1/2009