Adaptve Beamformng n ut path fadng Channes for Voce Enhancements usnan Abbas Internatona Isamc Unversty Isamabad Waqas Ahmed Internatona Isamc Unversty Isamabad Shehzad Ashraf Internatona Isamc Unversty Isamabad Imran Saeed Internatona Isamc Unversty Isamabad Dr. Khad Rashd Dean FAS Internatona Isamc Unversty Isamabad Abstract: The ncreasng demand for mobe communcaton servces wthout dstorton due to ot of factors ke mut path and fadng channes motvates the need for new technques to provde dstorton ess and enhanced sgna. We sha consder the sow fadng and frequency non-seectve channes. Ths technque w aso sutabe for CDA(Code dvson mutpe access), FDA(Frequency dvson mutpe access) and TDA(Tme dvson mutpe access) wth tte change n the agorthm. A spata fter beamformer w be desgned that operates on the output of an array of sensors n order to enhance the amptude of a coherent wavefront reatve to background nose and drectona nterference. Ths fter w adopt tsef accordng to the change n the characterstcs of the channe. Ths adoptve fter w be desgn on non bnd adaptaton technques. Data w be receved on array of antennas that are on mut path fadng channes. Our adoptve agorthm w produce the desred out put and w then enhance n such a manner that w not change the characterstcs of the orgna data. Keywords: Beamformer, Auto correaton atr, angrage utper, Egon vaues, Sgna to Nose rato (SNR) Introducton Wreess communcaton s the emergng and most demandng area n modern communcaton. The most popuar area n wreess communcaton s voce. As the number of users s ncreasng due to attenuaton, Crosstak, utpaths and fadng are the major probem n voce communcaton n wreess networks. These effects are very fast for ong dstance and where the channe s changng fast. Ths paper s about those channes whch are sow fadng. Its practca mpementaton coud be n teeconference n whch there are number of mcrophones and speaker s at very far from mcrophone. These mcrophones w get the sgna from speaker but wth bg amount of nose from eterna envronment. So SNR (Sgna to Nose rato) w decrease. Another mportant factor s the mutpath whch s produced due to the eterna envronment and due to array of antennas they w aso decrease SNR. So the receved sgna wth the nose w not provde the quaty of sound. To get the better quaty of sound the receved sgna shoud be manpuated. The sgna w have a cumbersome nose avaabe n both tme doman and frequency doman and t s very dffcut to remove nose n these domans because the nose s orgnated from dfferent coordnates due to the above mentoned factors, so we sha estabsh a new doman to get the better quaty of the sgna and then enhance t. To overcome these effects we sha use the concept of beamformng. A beamformer s a spata fter that operates on the output of an array of sensors n order to enhance the amptude of a coherent wavefront reatve to background nose and drectona nterference due to mutpaths. Its name came from the fact that eary spata fters were desgned to form penc beams whch enhance sgnas n a desred drecton whe attenuatng others. Wth the hep of a beamformer, we can easy dentfy where a sound source s ocated n the mdst of noses and we can reduce these nterferences. Ths s a usefu technque snce often tmes there s an addton of nose whe transmttng sgnas. A wdey-used everyday eampe s satete and antenna technoogy []. A beamformer Each mcrophone n the near array s paced a dstance d apart. To estmate the tme deay of a sgna arrvng at dfferent mcrophones, we frst fnd the ange the sgna's pane wave makes wth respect to the array norma. The sound waves are treated as panar rather than rada to smpfy the cacuatons. The dfference n ength between a pane wave from a gven source arrvng at two adjacent mcrophones s d*sn(theta) [][3].
athematca Formuaton: Frst we sha desgn the mathematca mode of our probem so that we use t n deveopng the agorthm. We sha consder case of teeconference where we have array of antennas and source a generatng a sgna whch arrve at dfferent antennas on dfferent paths and nose s aso wth t as shown n foowng fg. We have the m sgnas and n antenna. [ () ] j π f c ( t) Re s t t e () (t) ere s a hgh pass sgna and ts ow equvaent sgna s s () t represented by and f c s the centra frequency. When the sgna w be transmtted and receved on mth antenna at kth tme t w be represented as [5] m ( s ( e jπ ( dm / λc) snθ n ( m () processes are assumed to be mutuay statstcay ndependent, wth dentca autocorreaton functons. Thus the ow pass equvaent of mth transmtted sgna on L channe can be epressed as [6]. ^ jθ ( ρ e s ( n ( (3) m ^ ( s receved ow pass sgna for L channes. j ρe θ s the attenuaton factor and phase shft for the L channes. s m ( s the transmtted sgna. n ( Addtve whte Gaussan nose for th channe ere the sgna energy for a m sgnas are assumed to be same. The optmum demoduator for the receved sgna on kth channe consst of two matched fter havng mpuse response * bk ( t) sk ( T t) (4) And * bk ( t) sk ( T t) (5) For bnary PSK moduaton method to transmt the sgna we have s t) s ( ) k( k t The above scenaro s shown n foowng fg. k dm dstance of the mth antenna eement measured from the reference source eement s ( Transmtted ow pass sgna from the th sgna source as receved at the reference antenna θ Incdent ange of s ( λ c Waveength at the carrer frequency of the sgnas n m ( Addtve whte nose Each antenna eement s assumed as omn drectona. In ths paper, the matr w be represented by upper case wth an upper bar and vector quanttes are denoted ower case and wth an upper bar. Now we have L channes and our assumpton s that the channes are sow fadng and frequency non-seectve wth Raegh dstrbuted enveope statstcs. The fadng process among the L channes s assumed to be mutuay statstcay ndependent. The sgna n each channe s corrupted by an addtve zero-mean whte Gaussan nose process. The nose ς represents the fadng co-effcent assocated wth tme deay of dfferent antennas. It foows the Raegh dstrbuton []. So t can be found by Raegh PDF. each n ( s statstcay ndependent. We sha use Rake demoduator [7] for demoduaton where the no of deay are K than above equaton becomes ( Φ,n K ς s ( n j n j σ ζ jϕ, ns ( k ), ne where denotes the phase deay at the nth path of the th sgna source reatvey to the correspondng desred sgna source. For a near array of haf-waveength spacng, the receved sgna of the mth antenna eement appears at the jth output becomes (6)
jπ ( m ) snθ j, n ς nsj ( e K j m m( [ π ( ) snθ, n ϕ, n n ) σ j ns k e, ζ, ( ) j n m ( (7) where nm( s the addtve nose at the mth antenna eement and Θ,n for,,, and n,, K s the ncdent ange determned by the nth propagaton path of the th subscrber. The auto correaton matr of the receved sgna s computed as: R ( k ) fr ( k ) ( k ) ( k ) (8) where the forgettng factor f es n 0 f<, and ( s the receved sgna vector at the kth tme nterva,.e., [ ( (... ( )] ( n k As shown n [5], when the desred sgna s suffcenty arger than each of the nterferers, the mamum egen vector e of the auto correaton matr R ( can be appromated as e a (θ ) (9) where (θ ) s the arrva ange of the desred sgna, whch changes at every snapshot as the sgna source moves. That means, the mamum egen vector e of the auto correaton matr R ( forms better weght vector, once the desred sgna transmtted from the target subscrber s suffcenty arger than each nterferer at the recevng array. Snce the weght vector s obtaned form the mamum egen vector, n order for the computed egen vector to be appromatey equa the steerng vector of\f the target subscrber, the desred sgna transmtted from the target subscrber must be suffcenty arger than each of nterferers. The more domnant s the desred sgna, the coser the egen vector s to the steerng vector. Therefore, the accuracy of the computed weght vector by the proposed technque s affected by the spreadng rato L. The Adaptve Agorthm: The adaptve procedure n ths secton s based on the mamzaton of the foowng functona [8]: J ( w, γ ) w R w γ ( w w ) (0) R [ N N] Autocorreaton matr of the receved sgnas γ Lagrange mutper [9] w [N ] coumn weght vector The mamum egen vector can be found by searchng for a vector w that mamzes the functona n equaton (0) wth a constrant w w.[] Ths can be done by usng some teratve procedure. The term ``teratve method'' refers to a wde range of technques that use successve appromatons to obtan more accurate soutons to a near system at each step. There are two types of teratve methods. Statonary methods Non-statonary methods Statonary methods: Iteratve method that performs n each teraton the same operatons on the current teraton vectors. These are oder, smper to understand and mpement, but usuay not as effectve. Non-statonary methods: Iteratve method that has teratondependent coeffcents. These are a reatvey recent deveopment; ther anayss s usuay harder to understand, but they can be hghy effectve. The conjugate gradent method s one of the non-statonary teraton methods whch proceeds by generatng vector sequences of terates (.e., successve appromatons to the souton), resduas correspondng to the terates, and search drectons used n updatng the terates and resduas. In order to fnd the target Egen vector n an teratve way, startng from the nta guess w (0), the weght vector s computed as foows: [8] w ( k ) w ( k ) 0. 5 µ ( k ) () k snapshot nde Gradent vector of the functona J ( w, γ ) wth respect to w µ adaptve gan of a postve rea constant whch s determned for the convergence of the adaptve procedure. The gradent can be computed as [5] ( R w γw ) () Whch states that the souton for the etreme vaues of the functona J ( w, γ ) s an Egen vaue for γ and correspondng Egen vector for w. Ths can be easy found by observng 0 when γ λ and w e where λ and e denote the th egen vaue and correspondng egen vector for γ and w, respectvey, woud provde a oca etreme vaue of the objectve functona. The update equaton n () can be rewrtten n a form of geometrc seres as foows: µγ ( k )]Ι µ R ( } w w {[- ( (3)
where I s the [N N] dentty matr. The adaptve gan µ must be chosen such that [8] 0 < µ < ( /( λ λ )) (4) When the desred sgna s much stronger than each of nterferng sgnas, t s very advantageous to take the nta guess for the weght vector w (0) from the nta sgna vector, (0)[ ( 0) (0)... n (0)]T, where (0) for,, N denotes the sgna receved at the th antenna eement at the nta snapshot. Startng from the nta guess obtaned from the sgna vector,.e., w (0) ( (0)/ (0) ), the weght vector s updated as shown n () for a gven matr R and preset vaue for µ that guarantees the convergence as shown n (4). To update the weght vector, however, γ ( shoud be cacuated at each teraton step. Notng that the constrant shoud aso be satsfed at each teraton step,.e. w w,, the vaue for γ ( can be found to be the souton of the foowng quadratc equaton: [8] µγ ( ) [ µw ( R( ] γ ( k µ w ( R ( w ( R( 0 (5) From (4), the vaue of γ ( satsfyng the constrant s b ± ( b * b) ac γ ( a a µ b µ w c µ w ( R ( R ( ( w ( R( (6) But for the teratons to converge, we need to take the smaer vaue of γ (,.e., the negatve sgn n (7) shoud be taken at each teraton. b γ ( ( b * b) ac a (7) as foows: [9] Step ) Set the nta guess as w (0) (0)/ (0) ),where the nta auto covarance matr s determned wth the receved sgna vector by R ( 0 ) ( 0 ) ( 0 ) Step ) Update the auto covarance matr wth the new sgna vector R ( k ) fr ( k ) ( k ) ( k ) where f denotes the forgettng factor that s pre-determned n the nterva 0 f< Step3) Update the weght vector by () wth the up-dated vaue for as shown n (5). Step4) Go back to <step> f the procedure s to be contnued. The fowchart descrbng the above agorthm s shown n Fgure.. The array output y( can be computed by w ( (. As shown n the fgure the tota amount of computaton at each snap shot s about 0(N), ncudng the matr update as we as the vector tsef, where N denotes the number of antenna eements. It means that, when the number of antenna eements s 0, about 50 mutpcatons and addtons are enough to update the beef vector at each snapshot.snce the above procedure requres 50 operatons, when N0, knowng that a norma dgta sgna processor (DSP) takes no more than 00 ns per numerca operaton, the tme nterva between the adjacent snapshots woud be about 60 mcro seconds. Wth the snap shot perod of 60 mcroseconds, f the veocty of each subscrber s about 00 km/hr, the ncdent ange of the target subscrber can change by at most 0.0 degrees per snapshot f the user s n a regon that s 0 km away from the base staton. An ange change of ess than 0.0 degree aways produces a meanngfu weght vector. ence ths agorthm s fast enough to adapt to the mobty of subscrbers. Therefore t s reasonabe to concude that In ths technque, the weght vector s updated n a snge teraton as a new sgna vector s receved at each snap shot. Snce the auto covarance matr s updated at each snapshot, t shoud be assumed that the mamum egen vector must not change too much at every snapshot. The computatona oad of the adaptve procedure can be reduced further by appromatng the covarance matr wth the nstantaneous sgna vector at each snap shot as foows: R ( k ) f R ( k ) ( k ) ( k ) (8) The adaptve procedure descrbed above can be summarzed
Concuson and Resuts : In ths paper we dscussed the technque of adoptve beamformng n mutpath faded channes for voce enhancement. The weght vector was computed teratvey and was found to converge after eght teratons. We used the angrage mutper concepts for constrant satsfactons. We mpemented ths agorthm practcay by usng foowng. The mcrophones were paced 6.4 cm apart so that at a sampng rate of.050 kz, deays corresponded to a whoe number of sampes at certan anges. The sources were postoned at these anges to ensure accuracy. The mcrophone array was paced on an uphostered char to dampen nterferng sounds propagatng through the tabe. The mcrophones were samped at.050 kz nto two separate computers. Because the mcrophones had mted cord ength, and the computers were secured to the desks, we were mted to usng two mcrophones. The two sgnas were synchronzed by havng a strong mpuse sgna desgned to arrve at both mcrophones at the same tme (.e. perpendcuar to the mcrophone array), ndcatng the begnnng of the sgna. Resuts of mpementaton s ATLab s shown beow References: [] R. G. Prdham and R. A. ucc, "Dgta Interpoaton Beamformng for Low-Pass and Bandpass Sgnas." Proceedngs of the IEEE, vo. 67, no. 6, pp. 904-99, June 979. [] R. A. ucc, "A Comparson of Effcent Beamformng Agorthms." IEEE Transactons on Acoustcs, Speech, and Sgna Processng, vo. ASSP-3, no. 3, 548-558, June 984. [3] R. G. Prdham and R. A. ucc, "A Nove Approach to Dgta Beamformng." Journa of the Acoustca Socety of Amerca, vo. 63, no., pp. 45-434, Feb. 978. [4] S. Cho and D.yun, Desgn of adaptve antenna array for trackng the source of mamum power and ts appcaton to CDA mobe communcatons, IEEE Trans. on Antenna propogaton. Vo. 45, pp 393-404 Sep997 [5] Course project Report, A study of a varous beamformng technques and mpementaton of the Constraned Least ean Squares (LS) agorthm for beamformng,enee 64, Fa 00S.Cho, D.Yun and [6] Proaks J.G, Dgta communcaton, 4 th eddton, c Graw,00. [7] Shannon C.E. A ethematca Theory of Communcaton Be System Tech. J., vo. 7,pp63-656, October 948 [8] S. Cho, D. Shm "A Nove Adaptve Beamformng Agorthm for a Smart Antenna System n a CDA obe Communcaton Envronment" IEEE Trans. on Vehcuar Technoogy. Vo. 49, No.5, pp 793-806 Sep. 000 [9] S. Cho, S. Ahn and T. K. Sarkar "An Adaptve Beamformng Agorthm wth a Lnear compety for a utpath Fadng CDA Channe" IEICE Trans. on Communcaton. Vo. E84-B, No.8, pp 37-370 Aug. 00 [0].Lee, Bnd adaptve beamformng agorthms based on etreme egen vaue probems, n proc IEEE, vo4, Juy 997 [] W..Press, S.A. Teukosky, W.T. Vetterng, and B>P> Fannery, Numerca Recpes n C, nd ed, Cambrdge U.K. Cambrdge Unv Press,99 Convergence of weght vector wth number of teratons