PERFORMANCE EVALUATION ON THE BASIS OF BIT ERROR RATE FOR DIFFERENT ORDER OF MODULATION AND DIFFERENT LENGTH OF SUBCHANNELS IN OFDM SYSTEM

Transcription

1 PERFORMANCE EVALUATION ON THE BASIS OF BIT ERROR RATE FOR DIFFERENT ORDER OF MODULATION AND DIFFERENT LENGTH OF SUBCHANNELS IN OFDM SYSTEM ABSTRACT Sutanu Ghoh Department of Electronc and Communcaton Engneerng Dr Sudhr Chandra Sur Degree Engneerng College. Kolkata, Inda. Today, we have requred to accommodate a large number of uer under a ngle bae taton. Th can be poble only f we have ome flexblty over the pectrum. Prevouly we have lot of multplexng method to accommodate large number of gnal n tme and frequency doman. But now we have requred to accommodate a large number of uer n the ame bandwdth, wthout any fadng over the receved gnal. So, orthogonalty can be mantaned over the frequency repone. Th technology now more popular n the moble communcaton doman, called Orthogonal Frequency Dvon Multplexng (OFDM). Actually uer data can be converted nto the parallel form and then they are modulated ung dgtal modulaton technque. Fnally, they have followed by OFDM Modulator and cyclc prefx can be nerted nto the OFDM ymbol. Here, I have worked on the meaurement of Bt error rate for dfferent modulaton technque n OFDM technology. It ha been condered that ubchannel ze not contant. Accordng to that I have concluded the overall dea regardng the performance under OFDM technology. KEYWORDS OFDM ymbol, Cyclc Prefx, bt error rate, modulaton order, ubchannel length. 1. INTRODUCTION From lat two decade communcaton doman ha centered of attenton on modulaton and multplexng technque to provde broadband tranmon over wrele channel. OFDM a mult carrer tranmon technque [1] ued to provde hgh peed data rate over wrele noy channel at low amount of network complexty. Here the dfferent ubcarrer can be modulated eparately [2]. It ha the ablty to reduce the ISI and ICI, even t doen t requre equalzer. ISI can be drectly mnmzed ung Cyclc Prefx (CP), whch mply a guard tme. Th technology mot ueful due to t better pectral effcency and power effcency. But OFDM ha ome dadvantage - hgh peak to average power rato (PAPR) [3] and bt error rate (BER). Bt error rate the mportant parameter to calculate the end to end performance meaurement. There have o many tep to generate th OFDM gnal. The OFDM trancever acton can be made on a block by block ba. Here, nvere Fat Fourer Tranform (IFFT) and Fat Fourer Tranform (FFT) operaton can be performed at the tranmtter and recever end, repectvely. At the mappng area and eral to parallel converter before IFFT of tranmttng end, dfferent modulaton technque can be ued to modulate the ymbol. The revere demodulaton operaton can be performed at the demappng area and parallel to eral converter after FFT of recevng end. The type of modulaton can be decded n accordance wth the type of nformaton. There have preent dfferent order of modulaton. In accordance to the modulaton order the DOI : /jmnct

2 amount of error n the bt nformaton can be changed. So, I have worked on that ue to fnd the bt error rate for dfferent modulaton order and the dfferent number of ubchannel. Th reearch ue baed on the mulaton work on the ba of bt error rate of dfferent modulaton technque. Before th work, there wa lttle reearch on performance evaluaton of OFDM. Ref. [4] performed on the ba of ymbol error rate. In th reearch, new technque wa propoed to mnmze SER of OFDM ytem by adjutng the dtrbuton of tranmon power among the ubcarrer. The performance analy n Ref. [5] performed on the ba of error correcton codng and nterleavng. Here, the reearch reult wa capable to provde an average bt and frame error rate and outage probablte. The work under Ref. [6] wa capable to provde the ytem bt-error rate on the ba of an expreon, whch take nto an account of both AWGN and nonlnear noe effect. Thee work are not uffcent for the analy of ytem performance on the ue of bt error rate for dfferent modulaton technque wth dfferent ze of ubchannel n OFDM ytem. To the bet of my knowledge, th knd of work ha not been done for OFDM ytem. So, I have worked on th ue to execute a performance analy on the ba of a comparatve graphcal reult. The remanng part of th paper are organzed a follow: In Secton II and III, I gve an overvew of the bac prncple of OFDM technology and Mathematcal repreentaton of OFDM gnal, repectvely. Secton IV preent an OFDM ytem wth the proper mathematcal vew and the way of nerton of cyclc prefx. The reource allocaton method n OFDM technology can be decrbed n Secton V. Secton VI gve the dea about method of modulaton n OFDM technque. The performance evaluaton of my work are preented n Secton VII. Fnally, I conclude th paper n Secton VIII. 2. BASIC PRINCIPLE OF OFDM TECHNOLOGY In a tradtonal eral data tranmon, the ymbol can be tranmtted equentally, wth the frequency pectrum of each data ymbol allowed to occupy the whole avalable bandwdth [7]. A parallel data tranmon ytem provde the poblte to olve many of the problem encountered wth eral data tranmon ytem. In cae of parallel ytem, the everal equental tream of data are tranmtted multaneouly, o that at any ntant of tme many data element are beng tranmtted. In uch knd of ytem, the avalable pectrum of an ndvdual data element normally occupe only a mall part of the whole bandwdth a decrbed n fgure 1. Fgure 1: Spectrum of (a) OFDM ubchannel and (b) OFDM gnal overlappng ubcarrer [7] 34

3 I. Mathematcal repreentaton of an OFDM gnal From the very begnnng of a lot t = t, the contnuou tme OFDM ymbol can be decrbed a - N 1 T g( t) = Re{ brect ( t t ) exp[ j2π ( f + )( t t )]}..(1) 2 T = In the above equaton t ha requred to meet t t +T. g(t) = for t <t or, t>t +T.. (1.a) where, N denote the number of ubchannel and T denote the tme duraton of an OFDM ymbol; b ( =,1,2,..,N-1) data ymbol allocated to each ubchannel, f the carrer frequency of frt ubcarrer; and the functon (t) = 1, for t T /2. The real part called a n-phae component of the OFDM ymbol; and the magnary part a called quadrature component. Now, the output of an OFDM gnal ung a complex decrpton of equvalent baeband gnal can be expreed a: N 1 T g( t) = b rect( t t )exp[ j2π ( )( t t )] (1.b) 2 T = II. OFDM Sytem wth the nerton of Cyclc Prefx Fgure 3 depct the overall modulaton-demodulaton technque n OFDM ytem. One end of the tranmtter, block of nformaton-carryng ymbol are converted onto an N number of ubtream ung eral to parallel converter. Thoe tream can be modulated ung an N number of orthogonal waveform wth frequency f k, where, k=,,n-1. Th orthogonal waveform modulaton performed ung an IFFT and a parallel to eral converter. The OFDM modulated gnal can be computed a the IFFT of the bac mallet elementary unt aocated wth dfferent ubcarrer. The output of the IFFT condered a the um of complex exponental functon known a ba functon, complex nuod, harmonc, or the tone of a multtone gnal [8]. Now, let u conder one of thee tone or harmonc, whch the complex exponental functon aocated wth a partcular ubcarrer. That can be decrbed through the dcrete repreentaton: = k f = N k = 1 k j 2 π k n N x ( n ) ω a e.(2) where, f k = k/t = k f [ f amount of ubcarrer pacng and T ymbol duraton]; here, ω equvalent wth f k. If the channel repone H (there are total L+1 number of channel) can be operated on the nput tranmtted gnal then fnal output can be defned a y( n) L = = H x( n d ).(3) where, d the amount of multpath delay for the partcular agned channel. Now, due to lnearty ue concerned, when the OFDM gnal condered for a multpath fadng channel then each of t complex exponental component alo ubjected to the dentcal channel model. Therefore, t can be computed that the receved veron of each ubcarrer 35

4 component of the OFDM gnal (y(n) ω=k f ) a the convoluton between tranmtted gnal and channel mpule repone. That can be llutrated by eq. 4 L ω= k f = = y( n) H x( n).(4) ω= k f After the converter, lat L number of pont can be appended to the begnnng of the equence a the CP. Th CP a pecal knd of pectral tme guard n the ymbol tranton. Fnally the reultng ample are then haped and tranmtted. Thee tranmtted block are then referred to a a proceed OFDM ymbol. After the addton of CP we can ubttute the expreon of x(n) ω=k f = a k e j2πkn/n, f and only f the multpath propagaton delay le than or equal to the length of CP. Otherwe, wth even a ngle delay value outde the range of the length of CP, we cro the OFDM ymbol boundary and the orthogonalty between the ubcarrer component can be lot. Now, t can be aumed that the delay pread lyng wthn the range of the length of CP. So, receved ubcarrer component can be defned a a functon of tranmtted ubcarrer y ( n) ω = k f = L H =..(5) a k e ( n d ) j 2πk N Cyclc prefx nerton an eental functon durng the generaton of OFDM gnal. A cyclc prefx neceary to avod the nterference from prevouly tranmtted OFDM ymbol. Cyclc prefx nerton may be oberved a a uele operaton nce t mply repeat a copy of the extng data n the OFDM ymbol and doe not add any new nformaton. But t neceary for multple reaon. It help to mantan orthogonalty between the ubcarrer n the recever, whch one of the bae of an orthogonal frequency dvon tranmon. Th CP ued to provde a perodc extenon to the OFDM gnal through whch a lnear convoluton operaton can be performed on the tranmtted gnal by the channel, can be approxmated by a crcular convoluton operaton [9]. Fgure 2: OFDM ymbol wth CP Fgure 2 depct the OFDM ymbol wth the CP. There are two knd of applcable CP n the preent day cenaro normal and extended. T ym the ymbol duraton. The mathematcal defnton of th ymbol duraton T ym = M/W + T g, where, M the number of ample can be choen to be the power of 2 and W the total bandwdth, and T g the duraton of cyclc prefx. Now, the recever can be able to do the revere operaton of tranmtter, ung a FFT operaton. At th end the ampled gnal are proceed to fnd ther orgn pont of a block and the proper demodulaton wndow. In the next tep, t ha requred to remove the CP (whch contan the ISI) and an N (N = N) pont equence to be converted from eral to parallel form and fed t to the 36

5 FFT. The output of the FFT are ymbol modulated on N ubcarrer, each multpled by a complex channel gan. Dependng upon the avalablty of the channel nformaton, dfferent type of demodulaton or decodng can be ued to recover the nformaton bt. The output of the multpler are then ntegrated over the perod of to T to get back the etmated gnal A k, A k,n -1, whch are then converted from parallel to eral data; after the decodng, bnary form of tranmtted gnal obtaned. Fgure 3: Block dagram of OFDM trancever ytem 3. RESOURCE ALLOCATION The tradtonal fxed reource allocaton not optmal, nce the cheme predetermned regardle of current channel condton. On the other hand, dynamc reource allocaton agn a dmenon adaptvely to the uer baed on ther channel gan. Due to the caue of tme-varyng nature of the wrele channel, dynamc reource allocaton make full utlzaton of multuer dverty to acheve hgher performance [1]. So, multcarrer applcaton OFDM mot ueful to acheve good performance over the other tradton fxed channel applcaton. In cae of OFDM acce mechanm, a ubet of ubcarrer agned to each uer and thu, the number of ubcarrer to be agned to each uer mut be pre-cheduled by the ytem. A bac unt of th reource allocaton n OFDM acce mechanm ubchannel. Th ubchannel a group of ubcarrer. On the ba of the allocaton of ubchannel, reource allocaton mechanm of OFDM can be categorzed n three dfferent clae Block, Comb and Random type allocaton method. Block type ued under the aumpton of low fadng channel. Comb Type ued to atfy the need for equalzaton, when the channel varyng too fat. Random ued under the conderaton of fat fadng channel. Block type confguraton ued to map the plot ubcarrer on all the ubcarrer. Comb type ued to map on the certan number of ubcarrer. In cae of Random type, plot ubcarrer ndexe can be changed perodcally [11-12]. There dfferent length of thee ubchannel. I have worked wth only three dfferent length - 256, 512 and 496 number of ubchannel. 4. MODULATION TECHNIQUES In fgure 3 the nput data tream can be modulated by a QAM modulator and the complex ymbol tream can be produced a S, S 1, S N-1. Th ymbol tream paed through a eral-toparallel converter. The output of th converter a et of N parallel QAM ymbol lke S, S 1, S N-1 correpondng to the tranmtted ymbol over each ubcarrer [13-14]. At the recever end the output of the FFT can be paed through the parallel to eral converter and ultmately the 37

6 output of th converter can be demodulated by the QAM demodulator to recover the orgnal data. Here, I have ued dfferent order of modulaton wth dfferent number of ubchannel to oberve the bt error rate for OFDM gnal. Modulaton order ha been taken a 4 (QPSK), 8 (8- QAM) and 16 (16-QAM). 5. SIMULATION AND EXPERIMENTAL RESULTS In th reearch work, 3 dfferent ubchannel can be taken to perform a comparatve analy. Here I have done my expermental work through MATLAB mulaton oftware. 1 number of teraton taken for each of the expermental reult. I have taken the followng parameter and et ther value a gven n Table I. Parameter Table I. Set up Value of Expermental parameter Value Number of Subchannel 256, 512 and 496 Total number of plot 32 for 256 number of ubchannel; 64 for 512 number of ubchannel; 512 for 496 number of ubchabnnel SNR Varaton (For th - 27 db ue) Total number teraton taken for each evaluaton 1 Cae tudy :1 Number of ubchannel taken 256 Fgure 4: Bt error rate for dfferent level of SNR (n db) for (a) modulaton order 4, (b) modulaton order 8, and (c) modulaton order 16 wth256 number of ubchannel If we oberve the above fgure then we wll get an dea about the amount of bt error rate and bet performer (modulaton order of 4) wthn the dfferent order of modulaton at db level of SNR, wherea the ame knd of reult alo can be oberved at hgher level of SNR. The bet performer (4 th order modulaton) ha the bt error rate of around.144 (whch the lowet wth repect to 38

7 the other 2 dfferent order of modulaton). Fnally, I got rght opton for the hgher level of SNR and that 4 th order modulaton mean QPSK. Cae tudy :2 Number of ubchannel taken 512 Fgure 5 :Bt error rate for dfferent level of SNR (n db) for (a) modulaton order 4, (b) modulaton order 8, and (c) modulaton order 16 wth 512 number of ubchannel If we compare above two fgure (fgure 4 and 5), t can be oberved that the amount of bt error can be mnmzed for the two hgher order modulaton (modulaton order 8 and 16) n fgure 5 wth repect to fgure 4, wherea the bt error rate almot ame for lower order modulaton (modulaton order 4). So, t can be ad a, the bt error rate can be nfluenced by the length of the ubchannel. Cae tudy :3 Number of ubchannel taken

8 Fgure 6 :Bt error rate for dfferent level of SNR (n db) for (a) modulaton order 4, (b) modulaton order 8, and (c) modulaton order 16 wth 496 number of ubchannel In th cae, I have taken an extra large number of ubchannel to oberve the contnuaton of the above reult under the cae tudy 2. Dcuon of the above reult Fnally, I got the expected reult, whch mlar wth the analytcal work. If we ncreae the level of SNR, then the amount of bt error rate for modulaton order 16 can be aturated after a certan level of the threhold value. 6. CONCLUSION In th paper, I explore an dea about the comparatve performance evaluaton on the ba of bt error rate of a dfferent order of modulaton wth repect to dfferent ze of ubchannel. I tuded that bt error rate can be ncreaed wth the ncreang ze of channel length and bt error rate can be decreaed wth the ncreang ze of ubchannel. We know that the hgher amount of data accommodaton can be poble through the hgher order modulaton. So, t can be concluded that the better performance wth hgher data accommodaton capacty n OFDM ytem can be avalable through the large length of ubchannel wth hgher order of modulaton. REFERENCES [1] Wong, C. Y., Cheng, R. S., Lataef, K. B., and Murch, R. D., Multuer OFDM wth adaptve ubcarrer, bt, and power allocaton, IEEE Journal on Selected Area n Communcaton, vol. 17, no. 1, pp , Oct [2] Wang, F., and He, X., The Performance Analy of AFH_OFDM Sytem Baed on Smulnk, IEEE 7th Internatonal Conference on Wrele Communcaton, Networkng and Moble Computng (WCOM 211), pp. 1-4, Wuhan, DOI: 1.119/wcom , Sept [3] Lafta, Y. A., and Johnon, P., Hgh performance OFDM ytem for dgtal vdeo broadcatngterretral (DVB-T), Internatonal Journal of Dgtal Informaton and Wrele Communcaton (IJDIWC), vol. 2, no. 1, pp ,

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