e t Interntionl Journl on Emerging Technologies (): 34-39(11) ISSN No. (Print) : 975-8364 ISSN No. (Online) : 49-355 SCM for Brobn Wireless Systems Anubhuti Khre*, Mnish Sxen** n Vijy Nerkr** *Deprtment of Electronics n Communiction, University Institute of Technology, Rjeev Gnhi Technicl University, Bhopl, (MP) **Deprtment of Electronics n Communiction Deprtment, Bnsl Institure of Science n Technology, Bhopl, (MP) (Receive 17 July, 11, Accepte 5 September, 11) ABSTRACT : This pper seeks to present wys to eliminte the inherent quntiztion noise component in igitl communictions, inste of conventionlly mking it miniml. It els with new concept of signling clle the Signl Coe Moultion (SCM) Technique. The primry nlog signl is represente by: smple which is quntize n encoe igitlly, n n nlog component, which is function of the quntiztion component of the igitl smple. The vntges of such system re two sie offering vntges of both nlog n igitl signling. The presence of the nlog resiul llows for the system performnce to improve when excess chnnel is vilble. The igitl component provies increse n mkes it possible for coing to be employe to chieve ner error-free trnsmission. Keywors: SCM, Hybri Moultion, Quntize resiul mplifiction. I. INTRODUCTION Let us consier the trnsmission of n nlog signl over bn-limite chnnel. This coul be possible by two conventionl techniques: nlog trnsmission, n igitl trnsmission, of which the ltter uses smpling n quntiztion principles. Anlog Moultion techniques such s Frequency n Phse Moultions provie significnt noise immunity s known n provie improvement proportionl to the squre root of moultion inex, n re thus ble to tre off bnwith for. However, the improvement provie by these techniques is much lower thn the iel performnce s shown by the Shnnon's cpcity theorem [1]. On the other hn, Digitl techniques of trnsmission cn utilize error correction coes tht provie performnce close to theoreticl preiction. However, the mjor isvntge of igitl trnsmission techniques is the inherent quntiztion error introuce, which is imminent ll the while the signl is relye. This error cuses istortion in the originl signl being relye n cnnot be lter recovere by ny mens possible. If we quntize the smple signl using QAM or ny other metho, using fixe number of bits, fixe igitl istortion is introuce in the evelopmentl stge itself. This istortion is present regrless of the trnsmission qulity of the chnnel being use. Thus the originl signl cn be consiere to be permnently impire. Communictions systems re normlly constructe for much higher thn the minimum tht is require, so s to leve mrgin for fing n other effects which might Occsionlly reuce the []. So, it is essentil to esign communictions system where the output increses s the chnnel increses. While, s lrey stte, this technique is not fesible through igitl moultion, it is n inherent property in nlog moultion. Here, we introuce the concept of Signl Coe Moultion (SCM) which utilizes both the nlog, s well s, igitl moultion techniques. The primry nlog input signl is smple t the pproprite rte n quntize. The igitl smples re enote by symbols D. The resulting D symbols re then trnsmitte using igitl trnsmission techniques (like QAM) optimize for tht chnnel. Those D symbols represent N bits per nlog input smple.the quntiztion resiul, which is not left behin, is trnsmitte over the noisy chnnel s n nlog symbol A, corresponing to the igitl symbol D, s shown in the Fig. 1. To proucethe quntiztion error A, the quntize t is converte bck into nlog form n subtrcte from the originl nlog input signl. This symbol A, for noise immunity, is mplifie by gin of N (or ny proportionl fctor tht will optimize the voltge swing of the signl with tht of the chnnel). The SCM receiver performs the opposite opertion by combining the D symbol n its corresponing resiul. This woul not bring bout significnt improvement if trnsmitte over noisy chnnel s noise coul vry the symbol A n cuse bit errors in the D symbols. However, the N mplitue gin of the nlog components provies noise immunity of N to boost the n provie ner iel scheme
for error-free trnsmission. II. THE SCM TECHNIQUE : AN ANALYTICAL APPROACH Suppose we re given bnlimite signl of bnwith B Hz, which nees to be trnsmitte over chnnel of bnwith BC with Gussin noise of spectrl ensity N wtts per Hz. Let the trnsmitter hve n verge power of P wtts. We consier tht the signl is smple t the Nyquist rte of B smples per secon, to prouce smple signl x(n). Next, let the signl be quntize to prouce iscrete mplitue signl of M = blevels. Where b is the no. of bits per smple of the igitl symbol D, which is to be encoe. More explicitly, let the vlues of the b levels be, q 1 q q 3 q 4.. q M which re istribute over the rnge [ 1, +1],where is the proportionlity fctor etermine reltive to the signl. Given smple x(n) we fin the nerest level q i (n). Here, q i (n) is the igitl symbol n x(n) = x(n) q i (n) is the nlog representtion. The exct representtion of the nlog signl is given by x(n) = q i (n) + x (n). We cn ccomplish the trnsmission of this informtion over the noisy chnnel by iviing it into two chnnels: one for nlog informtion n nother for igitl informtion. The nlog chnnel bnwith is B = B n the igitl chnnel bnwith being B = B, where B + B = B c, the chnnel bnwith. Let = B c /B, be the bnwith expnsion fctor, i.e. the rtio of the bnwith of the chnnel to the bnwith of the signl. Similrly, the vribles n re the rtios of B /B n B /B. Here we will ssume tht = 1 so tht = 1. The totl power is lso ivie mongst the two chnnels with frction p for the nlog chnnel n frction p for the igitl one, so tht p + p = 1. The of the chnnels is first conveniently efine where no bnwith expnsion is use P... (1) BN The of the nlog chnnel is given by: p P P B N An the of the igitl chnnel is given by: p P p B N Khre, Sxen n Nerkr 35... ()... (3) Of specil interest is the cse where the signl power is ivie in proportion to bnwith. This is the cse where the nlog n igitl chnnels hve the sme spectrl ensity of the trnsmitte signl. Inferring tht in this cse:... (4) The objective of the communiction system is to trnsmit the signl x(n) s ccurtely s possible. In other wors, we wnt to esign the system so s to mximize, the output of the emoulte signl xˆ( n), where the output is: E{( xˆ ( n) x( n) }... (5) E{ x ( n)} In the following, we clculte the output s the function of the chnnel n the bnwith expnsion fctor n plot the corresponing grph. III. MAXIMUM OUTPUT Let us consier the best possible tht cn be obtine by bnwith expnsion, when we wish to trnsmit signl of bnwith B through Gussin chnnel of bnwith B. It cn be erive using Shnnon's cpcity theorem tht the formul for cpcity of Gussin Chnnel is given by: C P log 1 While t the emoultor en, we hve,... (6) C B log (1 )... (7) The two cpcities must be equl since both contin the sme informtion. Equting the two yiels: 11... (8) The Fig. epicts the Output versus for ifferent bnwith expnsion fctors. Fig.. Output versus (chnnel ) for ifferent bnwith expnsion fctors. IV. PERFORMANCE COMPARISON SCM offers ner iel communictions performnce. To show this is true, let us consier the role of communictions link esigner who hs noisy trnsmission
36 Khre, Sxen n Nerkr chnnel of bnwith B n limite. Let us choose igitl link s first n best choice. Here, the nlog smples re converte to igitl with resolution of b bits per smple. Accoring to Shnnon's principle of the cpcity of noisy trnsmission chnnel, by using n iel error correction coing technique the informtion cn be psse error free t bit rte equl to chnnel cpcity, given by eqution (7). If the nlog signl is smple t rte of R smples per secon. Then, the number of bits per symbol cnnot excee b = C/R. Thus M = b is fixe n quntiztion error is unvoible. The esigner my consier nlog moultion, such s FM, which is known to increse the output. FM ccomplishes this vntge t the expense of bnwith increse. FM is inferior to PCM t the minimum chnnel. This is becuse FM suffers from threshol phenomenon where the performnce ecreses rsticlly with chnnel [3]. A. The Iel SCM Now let us consier the SCM technique with the mixe nlog/igitl link: Assume for the moment tht the igitl symbols re trnsmitte error free. Note: the nlog symbol x(n) prouce by the SCM process escribe bove, hs smller vrince thn the originl symbol x(n). Consier the cse when x(n) is uniformly istribute rnom vrible. Assuming tht x(n) [, + ]. As there re B symbols/sec n C bits/sec, we hve b = C/B bits per symbol. Now the nlog smple in the rnge [, + ] is not trnsmitte in full, inste it is ivie into M = b equl segments n only one segment consists of the nlog informtion. This segment is mgnifie to the rnge [, + ] n trnsmitte with PAM. The b bits ssocite with it re trnsmitte through the igitl chnnel n recovere. The receiver in turn will tke the nlog signl, shrink it by b times n trnslte it to its originl level. Anlyticlly, the resiul x (n) b [, + ]. Tht is to sy, the mplitue of x (n) is exctly g = b times smller thn tht of the originl signl. This mens tht we cn mplify the nlog resiul by g to give it the sme size n power of the originl signl.here, we cn efine g s, g E{ x ( n)}... (9) E{ x ( n)} The mplifie nlog signl g x (n) will be trnsmitte through the nlog chnnel which hs signl to noise rtio. At the receiver, the originl signl will be reconstructe by, xˆ ( n) qˆ ( n) xˆ ( n)... (1) i where, xˆ( n ) is the estimte nlog symbol, n qˆ i ( n) is the estimte igitl symbol, both of which re ssume to be equl to the trnsmitte symbol. Becuse the trnsmitte nlog symbol ws g x (n), the receive nlog symbol will nee to be ivie by g to prouce xˆ ( n). This will reuce chnnel noise by g n consequently improve the experience by the nlog symbol by the fctor of g. We coul conclue tht in generl, An therefore = g... (11) g P... (1) The nlog gin of n uniformly istribute input is g = b n therefore P b... (13) Here we cn note tht, ifferent istributions of the nlog signl le to ifferent nlog gin fctors. The gin is lrgest for uniformly istribute input n becomes smller s the istribution pproches Gussin istribution. The bove result ssumes tht the igitl symbol is trnsmitte error-free. However, this is not totlly true. This rises questions, how mny bits in the chnnel cn be trnsmitte error free? Which les us to the Shnnon erive cpcity of igitl chnnel, which is C P B log 1... (14) If we ssume tht the signl x(t) ws smple t the Nyquist rte of B smples per secon, then the number of bits per smple will be C P log 1 b B... (15) Note: The b is continuous function of the of the chnnel,. If we wnt the number of bits to be integer, then P b log 1 where [x] enotes the integer prt of x. Finlly, P log 1 P... (16)... (17) If we ssume, tht the trnsit power is llocte in proportion to the bnwith, we hve P log 1... (18)
Fig. 3. Number of bits in igitl symbol s function of chnnel, for n integer no. of bits (soli) n frctionl number of bits (she). = 4 If we llow for frctionl bits, the bove eqution becomes, 1 Khre, Sxen n Nerkr 37... (19) Figs. 3 n 4 illustrte the performnce of the iel SCM s given by eqution (18). Figure 3 shows how the bits vry with chnnel, n figure 4 shows how the output vries with the chnnel. Here we cn note tht the iel SCM provies performnce, which is quite close to the boun. The close mtch between the SCM performnce n the boun cn be prove nlyticlly. For lrge, the boun is 1. Iel SCM with Power Optimiztion The performnce of the SCM technique cn be further improve by justing the power lloction between the nlog n igitl chnnels so s to mximize the output. Figs. 5 n 6 epict the performnce of the iel SCM for lloction of optiml power, compute by justing p in eqution (17) so s to mximize. We see from Fig. 5 tht the iel SCM chrcteristics pproch tht of the Shnnon boun for both high n low input vlues. Fig. 6 shows the number of bits use, n the power lloction to the igitl chnnel. These results cn be verifie nlyticlly by computing the optimum vlue of p for the cse of frctionl bits, n evluting the corresponing. Reclling eqution (17) n moifying it by removing the "[ ]", we get P 1 (1 P )... () Differentiting with respect to, setting the erivtive to zero to fin the mximum p, we get for > 1. 1 P... (3) 1 While for < 1, we hve p =. Inserting this into eqution () we get, fter some strightforwr mnipultions, n using the reltion = + 1, tht for > 1. 11... () Similrly, for lrge, the of iel SCM (19) becomes 1... (1) Eqution () n (1) re the sme since, + 1 = For smll, the boun gives, while for iel SCM we hve /. 1 1... (4) It is strightforwr to check tht for >>1 n for << 1 the output of the iel SCM pproches the Shnnon boun. Fig. 4. The output s function of chnnel, for the boun (sh), the iel SCM with integer bits (soli) n the iel SCM with frctionl number of bits (sh-ot). = 4. Fig. 5. The output s function of chnnel, for the iel cse (soli), n the iel SCM with the integer bits, with power optimiztion. ( = 4). Iel SCM with fixe no. of bits When the number of bits trnsmitte through the chnnel re fixe, sy b = b. In this cse, the nlog gin g will be fixe, n the output will be, = b
38 Khre, Sxen n Nerkr /, provie tht the igitl trnsmission is error free. This will occur only when the is lrger thn some threshol vlue. Using eqution (15) we get b 1... (5) For vlues below the threshol there will be high probbility of error n we ssume for simplicity tht the output will rop to zero. Though this is n extreme consiertion, in relity, the egrtion in will be more grul. Fig. 6. The number of bits n the optiml power p s function of for the cse shown in Fig. 5. = 4 Fig. 7 epicts the output s function of chnnel with fixe number of bits. As expecte, the output increses linerly with n there is constnt gin equl to the nlog gin g. Fig. 7. The output s function of chnnel for the boun (soli), n the iel SCM with fixe number bits n = 4. From bottom to top b =, 6, 8, 1. V. PROSPECTIVE APPLICATIONS 1. Brobn Wireless Trnsmission An SCM-bse communictions link is bsiclly trnsprent, bn-limite nlog pipe with ner-iel performnce in noisy chnnels. Every nlog signl coul potentilly use SCM becuse it cn outperform other existing moultion schemes. However, SCM hs compelling vntge for igitl communictions pplictions s well. For exmple, SCM cn pss igitl informtion by cting s repeter of igitl chnnel. This ppliction provies wireless extension of cble moem igitl informtion. As illustrte in Figure 8, cble moem termintion system (CMTS) trnsmits 4 Mb/s 56-QAM signl in 6 MHz cble chnnel shre mong the cble moems locte t the subscribers' premises. The return upstrem pth from the cble moems is 1 Mb/s 16-SQAM signl in 3. MHz cble chnnel. The signls re crrie by combintion of fiber n cox referre to s hybri fiber/cox (HFC) network. The fiber elivers lrge mount of bnwith over long istnces with strong noise immunity. Cox cbles istribute the signl between the fiber n ech subscriber. To rech sttion locte beyon the rech of the existing HFC network, the cble opertor instlls n SCM-bse point-to multipoint wireless ccess system t ny point on the HFC network tht hs line-of-sight to the unrechble sttion. All customers locte t prticulr site shre the SCM rio locte t tht site. The subscribers simply use low-cost cble moems tht connect to the SCM rio vi shre cox cble. The wireless subscribers cn even shre the sme cble chnnels with purely wire subscribers becuse the wireless link is trnsprent to the cble equipment. The significnce of SCM in this ppliction is its bility to tke 56-QAM signl n trnsport it over wireless link suitble only for lower moultion scheme, such s 16-QAM. SCM provies significnt itionl noise immunity, s is epicte in Figure becuse it uses bnwith expnsion to improve the estintion. There is non-scm lterntive: the 56-QAM signl coul first be emoulte bck to the originl t bits, then moulte s 16-QAM, trnsmitte over the wireless link, emoulte t the estintion, n finlly remoulte using 56-QAM. This lterntive woul be much more costly, given the mount of processing require. It woul lso significnt ltency to the informtion trnsporte becuse n efficient chnnel must perform the error correction of the originl signl before trnsmitting it over the wireless link. Furthermore, becuse SCM provies trnsprent link tht is not sensitive to protocol evolution or vritions, it is more future-proof n verstile thn specific igitl stnrs.. Superior Digitl Auio Recoring n Plybck A new-genertion uio CD coul inclue igitl trck ienticl to n comptible with the existing CD trcks, n in ition, hve n nlog trck to provie the
enhnce quntiztion error. Such n nlog trck woul provie uio performnce tht epens on the qulity of the recoring n of the isc plyer. The most iscriminting uio enthusists coul use the more sophisticte plyer for true nlog reprouction, while the less iscriminting users woul enjoy the low-cost CD technology in its current formt. Khre, Sxen n Nerkr 39 VI. ACKNOWLEDGEMENT Mrs. Anubhuti Khre one of the uthors is inebte to Director UIT RGPV Bhopl for giving permission for sening the pper to the journl. Mnish Sxen is lso thnkful to the Chirmen, Bnsl Institute of Science & Technology Bhopl for giving permission to sen the pper for publiction. Lst but not lest, I woul lso like to thnks our HOD n collegues for supporting us. Fig. 8. Communiction using the SCM technique coul increse efficiency n relibility while reucing interfce n processing costs. REFERENCES [1] B.P. Lthi, Moern Digitl n Anlog Communiction Systems, Oxfor Press, (1998) : p.711. [] Simon Hykin, Communiction Systems, 4th Eition, John Wiley & Sons, () : p.54. [3] Simon Hykin, Communiction Systems, 4th Eition, John Wiley & Sons, () : p.151 n p.164, Fig..55. [4] B. Frielner n E. Psternk's publishe work t the Asilomr Conference on Signls, Systems n Computers, November (1).