Suresh Babu, International Journal of Advanced Engineering Technology E-ISSN Int J Adv Engg Tech/Vol. VII/Issue I/Jan.-March.

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1 Research Paper OPTIMUM POWR ALLOCATION AND SYMBOL RROR RAT (SR) PRFORMANC OF VARIOUS SPAC TIM BLOCK CODS (STBC) OVR FADING COGNITIV MIMO CHANNLS IN DIFFRNT WIRLSS NVIRONMNT R. Suresh Babu Address for Correspondence Assocate Professor, Department of lectroncs and Communcaton ngneerng, Kamaraj College of ngneerng and Technology, Vrudhunagar, Tamlnadu, Inda ABSTRACT A cogntve rado (CR) s a transcever whch automatcally detects the avalable unused channels n the wreless spectrum. A cogntve rado network (CRN) s formed by ether allowng the secondary users (SUs) to coexst wth the prmary users (PUs). In ths paper, the ergodc capacty maxmzaton problem s studed n the Raylegh fadng, Nakagam fadng and Rcan fadng Multple Input and Multple Output (MIMO) channel and provdes the optmum power allocaton to acheve the ergodc capacty and outage capacty. Ths study ncludes the Symbol rror Rate (SR) performance of varous Space Tme Block Codes (STBC) such as Alamout code, V-Blast code, Slver code, Golden code for dfferent wreless channels such as Raylegh, Nakagam and Rcan wth varous modulaton schemes. Numercal results are presented to evaluate the power allocaton scheme for Lagrangan multpler algorthm and Water fllng (WF) algorthm schemes for comparson. KYWORDS Cogntve Rado (CR), ergodc capacty, Multple Input Multple Output (MIMO), Power allocaton. 1. INTRODUCTION The Cogntve Rado (CR) technque was frst ntroduced by Mtola n hs poneerng work ( Mtola.J and Magure.G.Q. 1999) and has drawn consderable attenton due to ts advantages of spectrum reusng. In CR networks, the secondary user (SU) usually communcates over the bandwdth orgnally allocated to the prmary network. Spectrum handoff procedures occur when the prmary users appear n the lcensed band temporary occuped by the cogntve rado (CR) users and am to help the CR users to vacate the spectrum rapdly and fnd avalable channel to resume the transmsson. Ths process s also known as Dynamc spectrum management. MIMO, or multple nput multple output (Dongmng Wang et al 2013), s a technque where multple antennas are used at both the transmtter and the recever to ncrease the lnk relablty, the spectral effcency, or both. The performance of MIMO channels can be mproved wth the help of Space Tme Trells code (Ilesanm Banjo Oluwafem 2013). Accordng to the channel power, t s complex to compute the channel capacty. In ths paper, Space Tme Block Code (STBC) s analyzed for fadng MIMO channels whch makes smplcty to compute the channel capacty. The dfferent dgtal modulaton schemes such as BPSK, QPSK, QAM & MFSK are used to calculate the Symbol rror Rate (SR). By combnng STBC and Modulaton schemes, the capacty of MIMO channels are calculated. In general a sgnal propagated between a transmtter and a recever s often affected by fadng (Y.-C. Lang et al 2006). One major source of fadng s multpath propagaton, where dfferent copes of the sgnal partally cancel each other out at certan tmes and ponts n space. Ths ncrease n errors decreases the effectve throughput of the sgnal (Musavan and S. Assa 2007), thereby weakenng the RF lnk. Here, we have consdered the three wreless channels such as Raylegh, Nakagan and Rcan for secondary users seamless communcaton (Yngbn Lang and Venugopal V. Veeravall 2004, ZhangQ.T. 2003, Chengshan Xao et al 2006). In ths paper, we focus our work on the power allocaton for fadng pont-to-pont cogntve MIMO channel wth statstcal State Informaton (CSI). Snce the ergodc capacty functon s very complex, the ergodc capacty maxmzaton s rather hard (L. Zhang 2008, Care.G, 1999). The rest of ths paper s organzed as follows: Secton II provdes the system model of CR MIMO networks. Secton III gves the proposed algorthms. The smulaton results and conclusons are gven n Sectons IV and V respectvely. The followng notatons are used n ths paper.. denotes the determnant; (.) T denotes the transpose of the matrx; (.) * denotes the complex conjugate of the matrx; (.) denotes the statstcal expectaton; Tr(.) denotes the trace of the matrx. The dentty matrx s denoted by I. II. SYSTM MODL Ths paper consders the CR networks wth one secondary transmtter-recever par shares the spectrum wth the prmary rado networks, whch conssts of N number of Prmary Transmtters (PT) and K number of Prmary Recevers (PR). Fg. 1 shows the block dagram of the proposed method. Ths block dagram explans the flow of STBC and modulaton schemes for MIMO channels. We assume that there are N p number of receve antennas at each PR, and M p number of transmt antennas at each PT, N s receve antennas at each Secondary Recever (SR), and M s transmt antennas at each Secondary Transmtter (ST). Snce the prmary users and the secondary users smultaneously transmt n the same bandwdth, the receved sgnal at SR can be expressed as TXp, + N o (1) Y s = HX s + Where H denotes the channel matrx from ST to SR, T denotes the channel matrx from the th PT to SR, X s s the transmtted sgnal vector at ST, X p, s the transmtted sgnal vector at the th PT, and N o s the normalzed addtve whte complex Gaussan nose vector wth zero mean and varance of σ 2 H. The capacty of the SU lnk s gven as C s = log 2 I + R -1 HQH * (2) Where Q s the transmt covarance matrx of ST, R s the nose plus nterference covarance matrx at SR. Then the SU capacty maxmzaton problem s gven by maxmze log 2 I+R -1 HQH *

2 subject to Tr(Q) < P T Where P T s the maxmum total transmt power of ST. III. POWR ALLOCATION ALGORITHMS Snce Q s a postve sem defnte matrx, we can express Q nto ts gen value Decomposton (D) as Q=FΛF *, where Λ=dag(P 1, P 2,..,P Ms ) where P 1, P 2, P Ms are the ndvdual transmtted antenna power. In MIMO sgnal processng (Junlng Mao et al 2012), we also call F as the precodng matrx. Substtutng the D of Q nto the objectve functon we have (log 2 I+R -1 HQH * ) = (log 2 I+R -1 (HF)Λ(HF) * ) (3) Fg. 1. Block dagram of MIMO system wth STBC and modulaton schemes. Then t can be transformed nto equvalent problem as maxmze (log 2 I+R -1 HQH * ) Ms P Subject to < P T 1 P > 0 for all Where P s the ntal transmtted power. Secondary users capacty maxmzaton s convex for P but nonconvex for F, so t s hard to drectly solve. In ths secton, we ntend to maxmze some bounds of the objectve functon. Although solvng bound maxmzaton problems (Junlng Mao et al 2012) cannot get optmal power soluton, t can get some nearly optmal power solutons that are close to the optmal power soluton. A. Lagrangan Multpler Algorthm One upper bound of the ergodc capacty can be gven by (log 2 I+R -1 HQH * ) (log 2 I+(R -1 ) HΛH * ) (4) Where (R -1 ) s a dagonal matrx. One lower bound of the ergodc capacty can be gven by (log 2 I+R -1 HQH * ) (log 2 I+(R) -1 HΛH * ) (5) Where (R) -1 s a dagonal matrx and ts dagonal elements have the same value. The elements of H are dstrbuted as statstcally ndependent dentcally dstrbuted (..d.) and F s a untary matrx, so the elements of HF are also dstrbuted as..d. Accordng to the aforementoned analyss, we gve the followng teraton procedure for Lagrangan Multpler algorthm to solve the power problem. The loop s used to solve the Lagangan dual problem. t 1 and t 2 are the step length of the loop. Lagrangan Multpler Algorthm also converges to the optmal pont wthn a small range. If the gradent of the ergodc capacty functon s known (or obtaned by Monte Carlo smulaton) the framework of Lagrangan Multpler Algorthm can be used to solve the optmal power allocaton. Table 1 gves the comparson of closed formula and Monte Carlo constants for varous antenna confguratons. Table 1. Closed formula versus Monte Carlo: M s =4 and N s =5 Λ(P ) Ψ (α,λ) (Monte Carlo) Ψ (α,λ) (Closed formula) Algorthm: Intalzaton: U > 0, V k > 0, P > 0 Where U and V k are Lagrangan Multplers. Repeat 1. Update F 2. Repeat P = (P + t 1 *(Ψ (α,λ) U - Untl all P converge 3. Update V k G k f )) U = (U+t 2 *(P T - )) 1 V k = (V k +t 2 *( G k f 2 P )) Untl U, V k converge Wth the value of (Ψ (α,λ)) and F, the gradent of the maxmzaton objectve functon can be solved, and optmal P can also be calculated B. Water Fllng Algorthm Ms P Fg. 2 Flow dagram of Water fllng algorthm.

3 Although Lagrangan Multpler Algorthm can fnd a nearly optmal soluton t s very complex. In ths secton we ntend to propose a low complexty algorthm to solve another bound maxmzaton problem wth ( Gastpar.M 2007). Fg. 2 shows the flow dagram of water fllng algorthm whch s based on channel power or energy. Unlke the upper bound gven by (4), ths upper bound s derved from both the statstcal expectaton of H and R -1. It can make the optmzaton problem easer. We get a bound maxmzaton problem as maxmze G k f P < P T P > 0 for all Water fllng Algorthm Steps: We do not need to reorder the MIMO-OFDM sub channel gan realzaton n a descendng order. Take the nverse of the channel gans. Water fllng has non unform step structure due to the nverse of the channel gan. Intally take the sum of the Total Power Pt and the Inverse of the channel gan. It gves the complete area n the water fllng and nverse power gan. Decde the ntal water level by the formula gven below by takng the average power allocated (average water Level) The power values of each sub channel are calculated by subtractng the nverse channel gan of each channel. In case the Power allocated value becomes negatve stop the teraton process. Algorthm: Intalzaton Number of s; m=n t =N r =2 and N 1 =1, N 2= 7; Total transmtted power; P t =10 db, 20dB, 30dB.. qual power dstrbuton P = P t / m; = 1, 2 Capacty C=B * log 2 (1+P ) bts/sec. Waterfllng capacty m C wf = ½* log 2 (1+ P / N ) bts/sec. 1 Snce the Lagrangan dual problem holds the strong dualty, Water fllng Algorthm can converge to the optmal pont wthn a small range. IV. SIMULATION RSULTS In ths secton, we consder the cogntve rado network where a secondary transmtter-recever par coexsts wth two prmary transmtter recever pars. The antenna confguraton of the secondary system s set as M s = N s = 2. We change P t /N 0 at the secondary transmtter from 0 to 30 db. Numercal results are gven to compare the average capacty of Shannon s capacty, MIMO wth NT=NR=2, Lagrangan multpler algorthm and Waterfllng algorthm. Here four dfferent STBC codes are taken for wreless channel for smulaton. Symbol rror Rate (SR) for fadng channels are calculated based on Space Tme Block Codes and Modulaton schemes such as QAM, BPSK, QPSK and MFSK and the smulated results are compared wth the theoretcal values. The average symbol energy avg for QAM modulaton s gven by, avg 1 M M 2 2 a b 1 (6) Wth the defnton of energy n mnd, symbol error s approxmated by, P e 1 1 erfc M 2 2 avg 2 (7) M 1 No Where avg s calculated by equaton (8). The Symbol error rate for QPSK s gven by, Pe erfc( ) (8) 2N o Ths brngs up the dstncton between symbol error and bt error. The Symbol error rate for BPSK modulaton s gven by, = (9) Where n s Gaussan wth mean 0 and varance N o /2. The error expresson for MFSK modulaton wth the usual notaton s gven by, Pe 1 M 1 erfc (10) 2 2 N o MFSK s dfferent from MPSK n that each sgnal sts on an orthogonal axs (bass). Fg. 3 Symbol rror Rate for Raylegh Fadng usng QAM for dfferent STBC Technques Fg. 3 shows the Symbol rror Rate (SR) for Raylegh fadng channel usng QAM for dfferent STBC technques. From the analyss of the result, Golden code has mnmum SR at SNR=20dB. Fg. 4 Symbol rror Rate for Nakagam Fadng usng QAM for dfferent STBC Technques Fg. 4 shows the Symbol rror Rate (SR) for Nakagam fadng channel usng QAM for dfferent STBC technques. From the analyss of the result, V- Blast code has mnmum SR at SNR=20dB. Fg. 5 shows the Symbol rror Rate (SR) for Rcan fadng channel usng QAM for dfferent STBC technques. From the analyss of the result, Slver code has mnmum SR at SNR=20dB.

4 Fg. 8 shows the performance of Symbol rror Rate (SR) for Slver code under dfferent modulatons for Nakagam fadng channel. From the analyss of the result, BPSK modulaton has mnmum SR upto SNR=16dB. Fg. 5 Symbol rror Rate for Rcan Fadng usng QAM for dfferent STBC Technques Fg. 6 Performance of Symbol rror Rate for Golden code under dfferent modulatons for Raylegh Fadng Fg. 6 shows shows the performamce of Symbol rror Rate (SR) for Golden code under dfferent modulatons for Raylegh fadng channel. From the analyss of the result, QAM modulaton has mnmum SR upto SNR=30dB. Fg. 9 Comparson of the average capacty of dfferent algorthms for Raylegh channel wth M p = N p = 2. Fg 9 shows comparsons between Shannon s algorthm for Raylegh fadng channel. Lagrangan multplers are ntalzed wth U=0.6 and V k =0.8. Water fllng algorthm s performed for MIMO wth two transmtters and two recevers. By comparng these algorthms water fllng algorthm reaches maxmum capacty. Fg. 7 Performance of Symbol rror Rate for V-Blast under dfferent modulatons for Nakagam Fadng channel Fg. 7 shows the performamce of Symbol rror Rate (SR) for V-Blast under dfferent modulatons for Nakagam fadng channel. From the analyss of the result, QPSK modulaton has mnmum SR upto SNR=30dB. Fg. 10 Comparson of the average capacty of dfferent algorthms for Nakagam channel wth M p = N p = 2. Fg 10 shows comparsons between Shannon s algorthm for Nakagam fadng channel. Lagrangan multplers are ntalzed wth U=0.6 and V k =0.8. Water fllng algorthm s performed for MIMO wth two transmtters and two recevers. By comparng these algorthms water fllng algorthm reaches maxmum capacty Fg. 8 Performance of Symbol rror Rate for Slver code under dfferent modulatons for Rcan Fadng channel Fg. 11 Comparson of the average capacty of dfferent algorthms for Rcan channel wth M p = N p = 2. Fg 11 shows comparsons between Shannon s algorthm for Rcan fadng channel respectvely. Lagrangan multplers are ntalzed wth U=0.6 and V k =0.8. Water fllng algorthm s performed for MIMO wth two transmtters and two recevers. By

5 comparng these algorthms water fllng algorthm reaches maxmum capacty. Table 2 compares the channel capacty of the system wthout usng STBC and wth usng STBC codes. From that we clearly understand STBC wth dfferent modulaton schemes gves very good performance n channel capacty for all the three wreless channels. Table 2 Compares the Capacty of prevous and proposed algorthms. Type Capacty wthout STBC and Modulaton Schemes (bts/s/hz) Capacty wth STBC and Modulaton Schemes (bts/s/hz) Raylegh Fadng Nakagam 5 9 Fadng Rcan Fadng V. CONCLUSION Space tme block code (STBC) s a technque used n wreless communcaton to transmt multple copes of data stream across a number of antennas. In ths paper, wth the assumpton of prmary communcaton and secondary communcaton are gong n a smultaneous manner. Based on the STBC code, the symbol error rate (SR) s calculated for varous modulaton schemes. Accordng to the SR, Lagrangan multpler algorthm and water fllng algorthm are proposed to maxmze the ergodc capacty. From the performance analyss, we fnd that water fllng algorthm can approach maxmum capacty. Further t s recommended for practcal systems because t can acheve the better tradeoff between complexty of algorthm and throughput performance. RFRNCS 1. Care.G, Tarcco.G,, and Bgler.,,1999, Optmum power control over fadng channels, I Trans. Inform. Theory, Vol. 45, no. 5, pp Chengshan Xao, Yahong Rosa Zheng and Norman C. Beauleu, 2006, Novel Sum of Snusods Smulaton Models for Raylegh and Rcan fadng Model, I Transacton on Wreless Communcaton, Vol..5, No Dongmng Wang, Jangzhou Wang, Xaohu You, Yan Wang,Mng Chen, and Xaoyun Hou, 2013, Spectral ffcency of Dstrbuted MIMO Systems, Journal on Selected areas n Communcatons, Vol.. 31, No Gastpar.M, 2007, On capacty under receve and spatal spectrum-sharng constrants, I Trans. Inform. Theory, Vol. 53,No. 2, pp Ilesanm Banjo Oluwafem, 2013, Improved superorthogonal space tme trells coded MIMO OFDM system, IT Journal of Research (Impact Factor: 0.2).Vol.59, No.6, pp Junlng Mao, Jnchun Gao, Yuanan Lu, Gang Xe, and Xuwen L, 2012, Power Allocaton Over Fadng Cogntve MIMO s: An rgodc Capacty Perspectve, I Transactons on Vehcular Technology, Vol. 61, No Lang.Y.C., Zhang.R,, and Coff.J, 2006, Subchannel groupng and statstcal waterfllng for vector block-fadng channels, I Trans. Commun., Vol. 54, No. 6, pp Mtola.J and Magure.G.Q., 1999, Cogntve rado: Makeng software rados more personal, I Pers. Commun., Vol. 6,No. 6, pp Musavan.L, and Assa,.S, 2007, rgodc and outage capactes of spectrum-sharng systems n fadng channels, n Proc. I Global Telecommuncatons Conference (GLOBCOM07), Washngton. DC, USA, pp Yngbn Lang and Venugopal V. Veeravall, 2004, Capacty of Non coherent Tme Selectve Raylegh Fadng, I Transacton on Informaton Theory, Vol.50, No Zhang,.L, Lang,,Y.C. and Xn,.Y, 2008, Jont beam formng and power allocaton for multple access channels n cogntve rado networks, I J. Select. Areas Communcaton., Vol. 26, No. 1, pp , Zhang Q.T., 2003, A Generc Correlated Nakagam Fadng Model for Wreless Communcaton, I Transacton on Communcaton, Vol.51, No.11.