Smulnk-baed Smulaton of Quadrature Ampltude Modulaton (QAM) Sytem Xaolong L Indana State Unverty xl3@ugw.ndtate.edu Paper 205, ENG 105 Abtract Adaptve modulaton ytem one of the key technque n buldng a broadband moble communcaton network becaue of ncreang hortage of wrele communcaton channel. Quadrature ampltude modulaton (QAM) ha been wdely ued n adaptve modulaton becaue of t effcency n power and bandwdth. To better undertand the QAM ytem, a Smulnk-baed mulaton ytem degned. In the paper, the theory of M-ary QAM and the detal of the mulaton model are provded. In the mulaton model, the parameter ettng for random generator, QAM modulaton and demodulaton, AWGN wrele channel are provded. Error rate of QAM ytem veru the gnal-to-noe rato (SNR) are ued to evaluate the QAM ytem for adaptve modulaton. The model can be ued not only for the crtera for adaptve modulaton but alo for a platform to degn other modulaton ytem. Introducton Wth the fat development of modern communcaton technque, the demand for relable hgh date rate tranmon ncreaed gnfcantly, whch tmulate much nteret n modulaton technque. Dfferent modulaton technque allow you to end dfferent bt per ymbol and thu acheve dfferent throughput or effcence. QAM one of wdely ued modulaton technque becaue of t effcency n power and bandwdth. In QAM ytem, two ampltude-modulated (AM) gnal are combned nto a ngle channel, thereby doublng the effectve bandwdth. However, t mut alo be noted that when ung a modulaton technque uch a 64-QAM, better gnal-to-noe rato (SNR) are needed to overcome any nterference and mantan a certan bt error rato (BER). The ue of adaptve modulaton can ncreae the tranmon rate conderable by matchng modulaton cheme to tme varyng channel condton, whch jutfe t popularty for future hgh-rate wrele applcaton. Crucal to adaptve modulaton the requrement of channel tate nformaton at the tranmtter. In fgure 1, a general etmate of the channel tate nformaton for dfferent modulaton technque provded. A you ncreae your range, you tep down to lower modulaton (n other word, QPSK), but a you are cloer you can utlze hgher order modulaton lke QAM for ncreaed throughput. In addton, adaptve modulaton allow the ytem to overcome fadng and other nterference. Both QAM and QPSK are modulaton technque ued n IEEE 802.11 (W-F), IEEE 802.16
(WMAX), and 3G (WCDMA/HSDPA) wrele technologe. The modulated gnal are then demodulated at the recever where the orgnal dgtal meage can be recovered. The ue of adaptve modulaton allow wrele technologe to optmze throughput, yeldng hgher throughput whle alo coverng long dtance. Fgure 1: Adaptve Modulaton and Codng [1] To better undertand the QAM ytem, a MATLAB/Smulnk-baed mulaton ytem degned n th paper. In the mulaton model, the parameter ettng for random generator, QAM modulaton and demodulaton, AWGN wrele channel are provded. Error rate of QAM ytem veru the SNR are ued to evaluate the QAM ytem for adaptve modulaton. The model can be ued not only for the crtera of adaptve modulaton but alo for a platform to mulate other modulaton technque. M-ary QAM Modern modulaton technque explot the fact that dgtal baeband data may be ent by varyng both envelope and phae/frequency of a carrer wave. Becaue the envelope and phae offer two degree of freedom, uch modulaton technque map baeband data nto four or more poble carrer gnal. Such modulaton technque are called M-ary modulaton, nce they can repreent more gnal than f jut the ampltude or phae were vared alone. In an M-ary gnalng cheme, two or more bt are grouped together to form ymbol and one of M poble gnal tranmtted durng each ymbol perod. Uually, the number of poble gnal M =2 n, where n an nteger. Dependng on whether the ampltude, phae, or frequency vared, the modulaton technque called M-ary ASK, M-ary PSK, or M-ary FSK. Modulaton whch alter both ampltude and phae M-ary QAM. A wth many dgtal modulaton technque, the contellaton dagram a ueful repreentaton. It provde a graphcal repreentaton of the complex envelop of each poble ymbol tate. The contellaton dagram of 16-QAM hown n Fgure 2. The contellaton
cont of a quare lattce of gnal pont. The general form of an M-ary gnal can be defned a [2] S 2E mn T 2E mn π 0 0 =, (2) T () t = a co( 2 f t) + b n( 2πf t) 0 t T 1,2,..., M Where E mn the energy of the gnal wth the lowet ampltude, a and b are a par of ndependent nteger choen accordng to the locaton of the partcular gnal pont; f 0 the carrer frequency; T the ymbol perod. Fgure 2: 16-QAM Contellaton Dagram If rectangular pule hape are aumed, the gnal S ( t) may be expanded n term of a par of ba functon defne a 2 φ 1() t = co( 2πf 0t) 0 t T. (3) T 2 φ. (4) () t = n( 2 f 0t) 0 t T 2 π T The coordnate of the th meage pont are element of the L by L matrx gven by a Emn and Emn b where ( ) a, an b [( a, b )] = ( L + 1, L 1) ( L + 3, L 1) L ( L 1, L 1) ( L + 1, L 3) ( L + 3, L 3) L ( L 1, L 3) M M ( L + 1, L + 1) ( L + 3, L + 1) L ( L 1, L 3) M, (5) Where L = M
It can be hown that the average probablty of error n an AWGN channel for M-ary QAM, ung coherent detecton, can be approxmated by [3] 1 3E av Pe 4 1 Q M, (6) 0 ( M 1) N Where E av / N 0 the average gnal to noe rato. M-ary QAM Smulaton Model Smulnk, developed by The MathWork, an envronment for multdoman mulaton and Model-Baed Degn for dynamc and embedded ytem. It provde an nteractve graphcal envronment and a cutomzable et of block lbrare that let you degn, mulate, mplement, and tet a varety of tme-varyng ytem, ncludng communcaton, control, gnal proceng, vdeo proceng, and mage proceng. Wth Smulnk, you buld model by draggng and droppng block from the lbrary brower onto the graphcal edtor and connectng them wth lne that etablh mathematcal relatonhp between block. You can et up mulaton parameter by double clckng the block. The modulaton lbrary n Communcaton Blocket of Smulnk contan four ublbrare: dgtal baeband modulaton, analog baeband modulaton, dgtal paband modulaton, and analog paband modulaton. For a gven modulaton technque, two way to mulate modulaton technque are called baeband and paband. Paband mulaton requre hgher ample rate nce t contan the carrer wave. Baeband mulaton, alo known a the lowpa equvalent method, requre le computaton. Becaue baeband mulaton more prevalent, th paper focue on baeband mulaton. The baeband mulaton model of M-ary QAM gven n Fgure 3. The parameter ettng for each block are gven n table 1 to 4. Table 1: Parameter Settng for General QAM Modulator/Demodulator Parameter Value Sgnal contellaton Coordnate of gnal pont n contellaton dagram (row by row) Sample per ymbol 1
Fgure 3: QAM Smulaton Model Table 2: Parameter Settng for Random Integer Parameter M-ary number Intal eed Sample tme Frame-baed output Interpret Vector parameter a 1- D Value n M = 2, n an nteger Any potve nteger 1/ymbol rate Unchecked Unchecked Table 3: Parameter Settng for AWGN Channel Parameter Value Intal ee Any potve nteger Mode SNR E (db) Contant or varable / N 0 Input gnal power (watt) Symbol perod 1 1/ymbol rate Table 4: Parameter Settng for Error Rate Calculaton Parameter Value Receve delay 0 Computaton delay 0 Computaton mode Entre frame Output data Workpace Varable name Name of a varable
Gven dfferent gnal contellaton n table 1, th mulaton model can be ued to mulate dffer order of M-ary QAM ytem. In order to compare the performance of dfferent modulaton technque, SNR (db) n table 3 et a a varable. Wrte a.m fle to get the error probablty veru SNR for each order of QAM technque. Smulaton Reult 4-QAM, 16-QAM, and 64-QAM technque are mulated n th paper. The ymbol rate 10 baud/econd. Accordng to Equaton 5, the contellaton dagram gven by [-3+3* - 1+3* 1+3* 3+3* -3+1* -1+1* 1+1* 3+1* -3-1* -1-1* 1-1* 3-1* -3-3* -1-3* 1-3* 3-3* ]. Connect the block a n the Fgure 3. Before you run the mulaton, you need to chooe the Smulaton parameter: et Stop tme to 2000. In order to get the performance of QAM technque under dfferent channel condton, a.m fle needed. The mulaton reult are hown n Fgure 4. M = 16; X= 0:0.5:10; Err_vec = []; for =1:length(X); SNR = X(); Sm( QAM_16 ); err_vec() = Error_QAM16(1); end Fgure 4: QAM Error Rate veru SNR (db)
From the mulaton reult n Fgure 4, we can fnd that the error rate are ncreaed wth the order of QAM technque. Th becaue the ymbol pont get cloer a the order of QAM ncreae f the tranmon power contant. However, hgher order of QAM technque can ncreae the tranmon rate. Th the tradeoff between relablty and effcency n the communcaton ytem. The mulaton model can not only be ued for QAM ytem, t can alo be ued for other dgtal modulaton technque, uch a M-PSK, DQPSK, etc. The MPSK mulaton model hown n the Fgure 5. Fgure 5: MPSK Smulaton Model Concluon MATLAB/Smulnk a very powerful tool that can be ued for mulaton n communcaton, control, DSP, etc. Th paper buld a mple mulaton model to llutrate the QAM technque and how the Communcaton Blocket of the Smulnk allow you to mplement t. The mulaton model verfed the theory of QAM and can be ued not only for the crtera for adaptve modulaton but alo for a platform to degn other modulaton ytem. Reference [1] Ho, W. S., "Adaptve modulaton (QPSK, QAM), " www.ntel.com/netcomm/technologe/wmax/303788.pdf, acceed on December 30, 2007.. [2] Rappaport, T. S.,.Wrele Communcaton: Prncple & Practce, 2 nd edton, Prentce Hall, 2003. [3] Zemer, R. E. and Peteron, R. L., Introducton to Dgtal Communcaton, Macmllan Publhng Company, 1992.. Bography
XIAOLONG LI, Ph.D., Atant Profeor of the Electronc, Computer and Mechancal Engneerng Technology Department at Indana State Unverty. H reearch nteret are n wrele networkng, wrele ad hoc network, modelng and performance analy, and mcrocontroller-baed applcaton.