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  1. 1. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700694 | P a g eImplementation And Analysis Of Different Types OfTransmultiplexer StructuresKulkarni Pranav R *,Ajinkya Deshmukh**, Desai Suhas R*** (School of Electronics Engineering, VIT University, Vellore)** (School of Electronics Engineering, VIT University, Vellore)** (Department of Electronics, DKT Ichalkaranji, Shivaji University, Kolhapur)ABSTRACTMultirate filter banks have becomeexcellent solution for future wirelesscommunication system. Filter bank basedmulticarrier system provides high spectralefficiency through removal of redundantinformation resulting in efficient use of availablespectrum. In multicarrier communicationsystem, filter bank based transmultiplexer(TMUX) having same analysis and synthesisfilter bank is employed. The TMUXconfiguration which is core of any FBMC is ofour interest here. This paper concentrates onimplementation of filter bank basedmulticarrier/offset quadrature amplitudemodulation (FBMC/OQAM). Different TMUXstructures like maximally decimated, non-maximally decimated and partial TMUX havebeen implemented. In partial transmultiplexer,upsampling and downsampling factor is lessthan number of sub channels. Frequencysampling technique is used for design ofprototype filter and other filters are complexmodulated versions of prototype filter. For allthe TMUX structures perfect reconstruction isobserved with alias cancellation. Further,computation of Intersymbol interference (ISI),Interchannel interference (ICI) will supportfilter designs for two-band and four-bandTMUX. The Optimization criterion is applied tofrequency sampling technique and results arecompared based on ISI, ICI performance ofTMUX.KEYWORDS- Transmultiplexer (TMUX),FBMC/OQAM, maximally decimated filter banks,non-maximally decimated filter banks, modifiedDFT filter banks, complex modulated filter banks,partial TMUX.I. INTRODUCTIONMulticarrier modulation is default choicefor high data rate wireless communication. Inmulticarrier modulation system available channelbandwidth is efficiently subdivided into several sub-channels; each has its associated subcarrier. Inpresent scenario, most commonly used multicarriermodulation technique is orthogonal frequencydivision multiplexing (OFDM). Even though OFDMhas numerous advantages it has certainshortcomings. It uses cyclic prefix (CP) whichconsumes certain amount of available bandwidth(critical in cognitive radio networks) and it usesrectangular prototype filter and IFFT/FFT blockswhich results in less frequency selective sub-channel.Filter bank based multicarrier system(FBMC) is widely used in present communicationtechnology (e.g. cognitive radio) because of itsinherent frequency selectivity and spectralefficiency [11, 12]. FBMC system provides certainadvantages over conventional OFDM like improvedfrequency selectivity through use of longer andspectrally well shaped prototype filter and efficientuse of available spectral bandwidth (spectralefficiency) by removal of CP [10]. Basic FBMCsystem consists of TMUX structure. A generalTMUX consist of synthesis filter bank (SFB) attransmitter, analysis filter bank (AFB) at receiver.Corresponding filters in AFB and SFB are tuned soas to get desired response.In this paper, we have implemented differentTMUX Configurations namely maximallydecimated TMUX and non-maximally decimatedTMUX and partial TMUX. Frequency samplingtechnique is used to design prototype filter. BothAFB and SFB designed such that other filters inrespective banks are complex modulated versions ofprototype filter [3, 4].II. GENERAL TMUX STRUCTURE
  2. 2. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700695 | P a g eFig. 1: General TMUX structure.Fig. 2: Partial TMUX structureThe general TMUX structure consists of Msub-channels each having different input𝑥 𝑘 𝑛 , where k is from 0 to M-1 i.e. time divisionmultiplexed (TDM) data. After passing it through Mfold expander as shown in Fig. it will create M-1images of input signal, this operation is calledupsampling. This upsampled data is passed throughSFB having M different synthesis filters 𝐹𝑘 (𝑧).Each filter will pass particular image out of M-1images, which falls in its passband. Here 𝑦(𝑛) isinterleaved version of filtered inputs, thus TDM datais converted into FDM data. This FDM data ispassed through a communication channel. Atreceiver AFB is present which consist of M filtersdesigned in such way that it will select FDM datacorresponding to particular band of frequency ofrelated filter. After passing this data through M folddecimators FDM data gets converted into TDM data𝑥 𝑘 (𝑛) which is either approximate or correctestimate of input data 𝑥 𝑘 𝑛 . The TMUX structureso implemented is called maximally decimatedTMUX [5] i.e. upsampling and downsampling isperformed by same factor M. In this structureperfect reconstruction, alias cancellation conditionscan be achieved based on design of AFB and SFB.In case of non-maximally decimated TMUX,upsampling and downsampling factors are different[5, 6]. This will increase computational efficiency ofoverall structure and decreases computationalcomplexity. Here perfect reconstruction is notguaranteed, as minimum two filters will have samepass band so distortion will be present but aliascancellation is guaranteed. Nearly perfectreconstruction can be achieved in non-maximallydecimated TMUX. If we relax perfect reconstructioncondition by allowing small amplitude and cross-talk (aliasing) distortion then we can use non-rectangular prototype filter which will in turnimprove stop band performance of sub channelfiltersIII. PARTIAL TMUXThe main processing blocks of partialTMUX [1] includes OQAM pre-processing,synthesis and analysis filter banks and OQAM post-processing. The transmission channel is 𝐶(𝑧),which can be modelled according to communicationchannel effects.IV. OQAM Pre-processingThe first operation is a complex-to-real conversion(C2Rk), where the real and imaginary parts of acomplex-valued symbol 𝐶𝑘,𝑛 are separated to formtwo new symbols:𝑑 𝑘,2𝑛 =𝑅𝑒 [𝑐 𝑘,𝑛 ] ; 𝑘 𝑒𝑣𝑒𝑛𝐼𝑚 𝐶𝑘,𝑛 ; 𝑘 𝑜𝑑𝑑(1)and𝑑 𝑘,2𝑛+1 =𝐼𝑚 [𝐶𝑘,𝑛 ] ; 𝑘 𝑒𝑣𝑒𝑛𝑅𝑒 𝐶𝑘,𝑛 ; 𝑘 𝑜𝑑𝑑(2)As mentioned above one complex symbol𝐶𝑘,𝑛 splitts into two real symbols one corresponds toreal part and other corresponds to imaginary part.This means that the complex-to-real conversionincreases the sample rate by a factor of 2.V. Synthesis and Analysis Filter BanksIn the SFB, input signals are upsampled by(𝑀/2) and then these are passed through respective
  3. 3. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700696 | P a g efilters 𝐺 𝑘 (𝑧) in order to obtain sub-signal for eachsub channel. By adding all these sub-signalstransmitted signal is formed. It is passed throughchannel model before given to receiver in orderintroduce channel effects. In the AFB, each filterwill filter the input received signal based on its passband and then these signals are downsampled byfactor of (𝑀/2) to get recovered signal. This iscritically sampled TMUX. AFB and SFB aredesigned based on the complex modified filter banksor modified filter banks where from the prototypefilter 𝑝(𝑙) all other filters i.e. 𝑓𝑘 𝑙 and 𝑕 𝑘 (𝑙) can bedesigned. It can be shown as [4]:𝑔 𝑘 𝑙 = 𝑝 𝑙 𝑒𝑗2𝜋𝑘𝑀𝑙−𝐿 𝑝 −12 3𝑓𝑘 𝑙 = 𝑔 𝑘∗𝐿 𝑝 − 1 − 𝑙 = 𝑝 𝑙 𝑒𝑗2𝜋𝑘𝑀𝑙−𝐿 𝑝 −12= 𝑔 𝑘 (4)Where 𝑘 = 0,1, … . 𝑀 − 1 𝑎𝑛𝑑 𝑙 = 0,1, … 𝐿 𝑝 − 1and 𝐿 𝑝 is length of prototype filter.If 𝑝(𝑙) will have linear phase then due tomodulation function,𝑓𝑘 𝑙 and 𝑔 𝑘 𝑙 will also havelinear phase.VI. OQAM Post-processingThe second operation is real-to complex conversion(R2Ck), in which two successive real valuedsymbols (with one multiplied by j) form a complexvalued symbol 𝑐 𝑘,𝑛 , i.e,𝑐 𝑘,𝑛 =𝑑 𝑘,2𝑛 + 𝑗𝑑 𝑘,2𝑛+1 ; 𝑘 𝑒𝑣𝑒𝑛𝑑 𝑘,2𝑛+1 + 𝑗𝑑 𝑘,2𝑛 ; 𝑘 𝑜𝑑𝑑(5)In this sense, the real-to-complex conversiondecreases the sample rate by a factor 2.VII. PROTOTYPE FILTER DESIGNThe prototype filter can be designed insuch a manner that the TMUX configurationguarantees perfect reconstruction (PR) or nearlyperfect reconstruction (NPR) of the transmitted dataat the receiving end. There are different methods ofdesigning prototype filter like directly optimizingimpulse response coefficients, windowing basedmethod or frequency sampling technique.In this paper, we are using frequency samplingtechnique to design prototype filter of odd lengthi.e.𝐿 𝑝 = 𝐾𝑀 − 1, which can be given as [2]𝑝 𝑙 =1𝐾𝑀𝐴 0 + 2 (−1) 𝑘𝐴[𝑘]cos⁡2 𝑘𝑀(𝑙 +𝑈𝑘=11) (6)Where 𝑘 = 0,1, … . 𝐾𝑀 − 2, 𝑈 =𝐾𝑀−22, 𝐾 isoverlapping factor and 𝐴 𝑘 is frequency responsevalues.Frequency sampling technique can be summarizedas:Impulse response coefficients can be obtained fromthe desired frequency response by sampling 𝐾𝑀uniformly spaced points2 𝑘𝐾𝑀is inverse Fouriertransformed.Generally prototype filter is low pass filter (LPF)only. LPF having requirements like Magnitude =1 at=0; Magnitude =0.707 at =  𝑀 ; and highstopband attenuation (>13dB), which can beachieved by: 𝐴 0 = 1; 𝐴 𝑙 2+ 𝐴 𝐾 − 𝑙 2= 1 ; 𝑓𝑜𝑟 𝑙 =1,2, . . , [𝐾/2] 𝐴 𝑙 = 0 ; 𝑓𝑜𝑟𝑙 = 𝐾, 𝐾 + 1, … 𝑈As mentioned above, very few adjustableparameters, like ′𝑥’ are needed for this frequencysampling method of designing prototype filter. 𝐾 = 3: 𝐴 0 = 1, 𝐴 1 = 𝑥, 𝐴 2 = 1 − 𝑥2 𝐾 = 4: 𝐴 0 = 1, 𝐴 1 = 𝑥, 𝐴 2 =0.707, 𝐴 3 = 1 − 𝑥2Least square criterion [7, 8, 9] is applied tominimize stopband attenuation so that entire energyis concentrated only in passband. This will giveoptimized filter response.VIII. SIMULATION RESULTS1. Maximally Decimated TMUX Structure:Four Channel TMUXFig. 3 shows results for four channels TMUX. It hasfour different inputs as shown. Perfectreconstruction is observed in Fig. 4 at output of fourchannels TMUX with amplitude reduction by afactor of 4 is because of following downsamplingrelation (M = 4). Similar structure can beimplemented for two channel TMUX (M = 2).𝑌 𝑍 =1𝑀𝑋 𝑍1𝑀 𝑊𝑀𝑘𝑀−1𝑘=0 (7)Fig. 3: Reconstructed output for four channelTMUX-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.51ip0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1012ip1-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1012ip2-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.51ip3
  4. 4. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700697 | P a g e2. Prototype filters for differentTransmultiplexersFor M-band TMUX, prototype filter should havefollowing design requirements Low pass frequency response. Cut-off frequency should be 𝑀 Good transition band response Stop-band attenuation as minimum as possibleFig. 4: Reconstructed output for four channelTMUXAs per results from Fig. 5 (a), we haveachieved some of the above requirements byselecting frequency sampling technique for this typeof filter design. For two-band case, cut-offfrequency we got is 𝑐  0.5, but still perfectstopband characteristics is not achieved (as seenfrom Fig. 15 (a), stopband attenuation is consideredas practically very less).So we minimized stopband energy using leastsquare criterion [7]. This will give good prototypedesign for complex modulated filter banks, whichcan be clearly observed in Fig. 5 (b).3. Non-Maximally Decimated TMUX:The AFB and SFB for Non-maximally decimatedTMUX are as shown in Fig. 6 and 7. Prototype filteris designed using frequency sampling techniquehaving length 𝐿 𝑝 = 𝐾𝑀 − 1. Here K is overlappingfactor and M is number of sub channels and 𝐿 𝑝 islength of prototype filter.(a)(b)Fig. 5: (a) Prototype filter frequency samplingtechnique for M=2 (b) Prototype filter usingoptimization technique for M=2Fig. 6: Analysis Filter bank for Non-MaximallyDecimated TMUX-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.20.4yf0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.20.4yf1-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.20.4yf2-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 100.20.4yf30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-9-8-7-6-5-4-3-2-10Prototype Filter For M=2:Frequency Sampling Technique0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-30-25-20-15-10-505Optimized Prototype Filter For M=20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.51Analysis Filter Banks0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.510 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.510 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.51
  5. 5. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700698 | P a g eFig. 7: Synthesis filter bank Non-MaximallyDecimated TMUXHere, upsampling and downsampling is performedby a factor of L which is less than number of subchannels M. (L=3 and M=4). From [5] and [6]implementation of this non-maximally decimatedTMUX results in alias cancellation but perfectreconstruction is not gurranted which is observed inFig. 8 .Fig. 8: Original and reconstructed signal for Non-maximally decimated TMUX4. Partial TMUXImplementation of partial TMUX where upsamplingand downsampling is performed by factor of M/2.Frequency responses corresponding to four differentusers complex data shows nearly perfectreconstruction (some distortions are allowed).Thisimplementation is shown in below Fig. 9 and 10.(a)(b)Fig. 9: (a) spectrum of original signal 𝑐 𝑜,𝑛 andreconstructed signal 𝑐0,𝑛 (b) spectrum of originalsignal 𝑐1,𝑛 and reconstructed signal 𝑐1,𝑛(c)(d)Fig. 10: (c) spectrum of original signal 𝑐2,𝑛 andreconstructed signal 𝑐2,𝑛 (d) spectrum of originalsignal 𝑐3,𝑛 and reconstructed signal 𝑐3,𝑛0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.51Synthesis Filter Banks0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.510 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.510 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.510 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 and Reconstructed SignalReconstructed SignalOriginal Signal0 200 400 600 800 1000 120012340 200 400 600 800 1000 12000. 200 400 600 800 1000 120002460 200 400 600 800 1000 120000.511.50 200 400 600 800 1000 120012340 200 400 600 800 1000 120000.511.50 200 400 600 800 1000 12000123450 200 400 600 800 1000 12000.
  6. 6. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700699 | P a g e5. ICI and ISI calculationThere are two quality measures which decideperformance of TMUX system.1. Inter-channel Interference (ICI):-It is nothing but 𝑘th input signal have effects on 𝑙thoutput signal for 𝑘 ≠ 𝑙 .The ICI in the 𝑙th output isthe sum of effects of rest input signals 𝑘 ≠ 𝑙 onthis output. For 𝑙th output ICI can be calculatedfrom below relation [8]:𝐸𝐼𝐶𝐼 𝑙 =1𝜋|𝑇𝑙𝑘 (𝑒 𝑗𝑤)|2𝑀−1𝑘=0,𝑘≠𝑙 𝑑𝑤𝜋0(8)Where, 𝑇𝑙𝑘 (𝑧) is transfer function of TMUX between𝑙th output and 𝑘th output channel.2. Inter-symbol Interference (ISI):-Effect of (𝑁 − 1)th symbol or any of total 𝑁symbols on 𝑁th symbol will result in ISI. ISI can bemeasured using following relation [8]:𝐸𝐼𝑆𝐼 𝑙 = 𝑡𝑙𝑙 𝑛 − 𝛿[𝑛 − [𝑁/𝑀]] 2𝑛(9)Where, 𝑡𝑙𝑙 𝑛 is impulse response between 𝑙th outputand 𝑘th input 𝑘 = 𝑙 and 𝛿(𝑛) is unit impulseresponse. Above equation in frequency domain is[9]:𝐸𝐼𝑆𝐼 𝑙 =1𝜋𝑇𝑙𝑘 𝑒 𝑗𝑤 2𝑀−1𝑘=0,𝑘≠𝑙 𝑑𝑤𝜋0(10)𝑤𝑕𝑒𝑟𝑒 𝑙, 𝑘 = 0 𝑡𝑜 𝑀 − 1TMUXConfigurationFilter designtechniqueICI(dB)ISI(dB)Four band-partial TMUXFrequencysampling-34.82 -29.52Two band-maximallydecimatedTMUXFrequencysamplingwithoptimization-72.68 -5.69Four band-maximallydecimatedTMUXFrequencysampling-26.69-11.63Four band-maximallydecimatedTMUXFrequencysampling-26.69-11.63Table 1: ICI and ISI values for different TMUXstructuresIX. CONCLUSIONSIn this paper, different TMUX structuresi.e. maximally, non-maximally decimated andpartial structures have been implemented. Inmaximally decimated structure for two-channelTMUX and four-channel TMUX, perfectreconstruction of input signal is observed. Resultsobtained for non-maximally decimate TMUX for(L<M) shows that alias cancellation is achieved butperfect reconstruction is not guaranteed.In case of partial TMUX, even after upsamplingand downsampling factor is reduced to M/2, almostperfect reconstruction of complex input symbols isobserved. The compensation of upsampling anddownsampling factor by 2 is due to OQAM pre-processing and OQAM post-processing. In OQAMpre-processing, each complex QAM symbol isconverted into two real symbols thereby increasingdata rate by 2. Similarly, in OQAM post-processing,two real symbols are combined to form one complexQAM symbol, thereby decreasing sampling rate by2. Frequency sampling technique is used to designprototype filter. Length of prototype filter can becontrolled by overlapping factor (K). Proper designof prototype filter gives good TMUX performance,which is observed by comparing ICI, ISI values andreconstructed signals. for partial TMUXconfiguration will give good ICI and ISI results (i.e.low values) as compared to maximally decimatedTMUX when for both the cases, frequency samplingtechnique is used. If we incorporate optimizationcriterion [7], then we get better ICI i.e. -72dB here.It is also observed that for ideal channel, ISI and ICIvalues are same which is very much expected.REFERENCES[1] T. Ihalainen, A. Viholaien, T. Hidalgo Stitzand M.Renfors,“Generation of filter bankbased multicarrier waveform using partialsynthesis and time domain interpolation”,IEEE Trans. On signal and systems,pp.1767-1778, July 2010.[2] A. Viholainen, T. Ihalainen, T. HidalgoStitz, M. Renfors, and M. Bellanger,“Prototype filter design for filter bankbased multicarrier transmission”, in Proc.Eur. Signal Process. Conf., Glasgow,Scotland, pp. 1359–1363, Aug.2009.[3] S. Mirabbasi and K. Martin, “Overlappedcomplex-modulated transmultiplexer filterswith simplified design and superiorstopbands”, IEEE Trans. Circuits Syst. II,Exp. Briefs, vol. 50, no.8, pp. 456–469,Aug. 2003.[4] T. Karp and N. J. Fliege, “Modified DFTfilter banks with perfect reconstruction,”IEEE Trans. Circuits Syst. II, Exp. Briefs,vol. 46, no. 11, pp. 1404–1414, Nov. 1999.[5] P. P. Vaidyanathan, Multirate Systems andFilter Banks.,Prentice-Hall, 1993.[6] N. J. Flinge, Multirate DigitalSignalProcessing, John Wiley and Sons,1994.[7] Jie Yan, Wu-Sheng Lu, “Towards globaldesign of orthogonal filter banks andwavelets”, CAN. J. ELECT. COMPUT.ENG., Vol. 34, No. 4, pp.145-151, 2009.[8] Pilar Martin, Fernando Cruz-Roldán andTapio Saramäki, “A New Window for theDesign of Cosine-Modulated MultirateSystems”, IEEE conference on circuits and
  7. 7. Kulkarni Pranav R , Ajinkya Deshmukh, Desai Suhas R/ International Journal of EngineeringResearch and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.694-700700 | P a g esystems, ISCAS’04 volume 03, pp. 529-532, 2004.[9] Ram Kumar Soni, Alok Jain, Rajiv Saxena,“An improved and simplified design ofpseudo- transmultiplexer using Blackmanwindow”, Science Direct Digital SignalProcessing 20, pp. 743–749, 2010.[10] L. G. Baltar, D. S. Waldhauser, and J. A.Nossek, “Out-of-band radiation inmulticarrier systems: A comparison,” inProc. Multi-Carrier Spread SpectrumLecture Notes Elect. Eng., vol. 1, pp.107–116, Jun. 2007.[11] B. Farhang-Boroujeny, “Filter bankspectrum sensing for cognitiveradios,”IEEE Trans. Signal Process., vol.56, no. 5, pp. 1801–1811, May2008.[12] T. Ihalainen, A. Viholainen, and M.Renfors, “On spectrally efficientmultiplexing in cognitive radio systems,” inProc. IEEE Int. Symp.Wirel. PervasiveComput., Santorini, Greece pp. 675–679,May 2008