VOLUME 3, ISSUE 2 Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade Deparmen of Elecronic and Elecrical Engineering Ladoke Akinola Universiy of echnology, Ogbomoso, Nigeria. zkadeyemo@lauech.edu.ng ABSRAC he increasing demand for mulimedia daa ransmission in mobile wireless communicaion poses a challenge o reliable recepion. In order o have good qualiy, a robus digial modulaion scheme is required a he ransmier. However, he convenional M-ary Phase Shif Keying (MPSK) commonly used in muliple-inpu muliple-oupu (MIMO) communicaion sysems wih non-linear radio frequency (RF) power amplifiers causes a relaive increase in inercarrier inerference (ICI). his paper presens a developmen of offse-mpsk (O-MPSK) modulaion scheme in MIMO spaial mulipleing over he Rayleigh fading channel. he O-MPSK modulaion schemes were developed for 4, 8, 16, 32 and 64 consellaion sizes. he developmen of he O-MPSK was done by shifing he phase of he convenional QPSK, 8-PSK, 16- PSK, 32-PSK and 64-PSK by an odd muliple of pi (π) o give 2 -QPSK, 4-8PSK, 8 DOI: 10.14738/nc.32.1144 Publicaion Dae: 28 h April, 2015 URL: hp://d.doi.org/10.14738/nc.32.1144-16psk, 16-32PSK and 32-64PSK, respecively, wih a view o reducing he specral spreading in he power amplifiers a he receiver of a MIMO sysem. he MIMO echniques used was MIMO Spaial Mulipleing (MIMO SM). he sysem models were developed around hese schemes and laer simulaed using MALAB applicaion oolki. he performances of he O-MPSK schemes were evaluaed using bi error rae (BER) a -o-noise raio (SNR) range of 0 o 20 db and compared wih he convenional MPSK schemes. he resuls obained for all he SNRs in MIMO-SM showed ha mean BER of 0.0024, 0.0040, 0.0085, 0.0183 and 0.036 were obained for 2 -QPSK, 4-8PSK, 8-16PSK, 16-32PSK and 32-64PSK respecively as agains mean BER of 0.0025, 0.0044, 0.0088, 0.0178 and 0.0358 obained for convenional QPSK, 8PSK, 16PSK, 32PSK and 64PSK respecively. he mean BER values obained reveal ha he developed O-MPSK ouperforms he convenional MPSK due o he relaively lower BER of O-MPSK schemes compared wih he MPSK schemes. his is as a resul of he reducion in he ampliude variaions and specral spreading a he receiver of he MIMO sysem. Keywords: Offse, digial modulaion, Spaial Mulipleing, MIMO, M-PSK scheme, Inercarrier Inerference 1 Inroducion he goal of an ideal digial wireless communicaion sysem is o produce he eac replica of ransmied daa a he receiver [1]. his has necessiaed he corresponding numerous remendous researches carried ou in digial communicaions indusry which leads o rapid growh recorded in
Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade; Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing, ransacions on Neworks and Communicaions, Volume 3 No 2, April (2015); pp: 117-127 he pas wo decades especially in is various applicaions [2]. his growh, in urn, has spawned an increasing need o seek auomaed mehods of analyzing he performance of digial modulaion ypes using he laes mahemaical sofware or programming language. Digial modulaion schemes pracically in use now are Ampliude Shif Keying (ASK), Frequency Shif Keying (FSK), Phase Shif Keying (PSK) and Quadraure Ampliude Modulaion (QAM) wih each having heir disincive feaures and characerisics. In he case of ASK, he use of ampliude modulaed analogue carriers o ranspor digial informaion always resuls in a relaively low qualiy oupu. Alhough i is a low cos ype of digial modulaion, his is seldom used ecep for a very low speed elemery circuis. FSK has a poorer error performance han PSK or QAM and consequenly is no used regularly for highperformance digial radio sysems [3];[4];[5];[6];[7]. QAM is a modulaion scheme in which wo schemes (ASK and PSK) are combined o improve he performance of he convenional counerpar modulaion making his echnique a lile comple [8];[9]. I is mainly used for few specific applicaions [10]. he PSK schemes have consan envelope bu disconinuous phase ransiions from symbol o symbol and i is he mos commonly used digial modulaion echnique. Some muli-level modulaion echniques ha permi high daa raes wihin fied bandwidh known as M-ary PSK schemes are employed in quasi-opical wireless array applicaions, compressed image communicaion in mobile fading channel, space applicaions, racking and Daa Relay Saellies Sysem (DRSS) [1]. he demands for high daa rae wireless communicaion in recen years have coninued o increase rapidly for wireless mulimedia services. Muliple-inpu, muliple-oupu (MIMO) sysems are now he popular approaches o mee hese demands [11];[12]. he use of muliple anennas a boh ransmier and receiver in wireless communicaion links provides a means of maimizing he sysem performance of wireless sysems. MIMO echnology provides diversiy by making he receiver o receive muliple replicas of he same informaion-bearing ; and his provides a more reliable recepion [13];[14];[15];[16];[17]. he convenional M-ary phase shif keying such as QPSK does no have consan ampliude for ransiion wih a phase shif equal o π (±180 o ). he phase ransiions make QPSK s suffer from large envelope variaions when passed hrough a nonlinear power amplifier operaing a sauraion. he resuling effecs are nonlinear ampliude and phase disorions which cause specral spreading of he ransmied, inercarrier inerference (ICI) and degradaion of he performance of he communicaion sysem. However, Offse Quadraure Phase Shif Keying, OQPSK, suffers from lower envelope variaions as a resul of he smaller phase ransiions as each ransiion is limied o ±90 o. his resuls in relaively more consan envelope afer pulse shaping [18];[19]. Many researchers have worked using differen modulaion schemes like [20] carried ou performance analysis of a 22 spaial mulipleing MIMO echnique wih high order M-PSK and a combinaion of ZF and minimum mean square error (MMSE) equalizers wihou channel sae informaion (CSI) a he ransmier. he sysem was simulaed over he Rician fading channel. Simulaion resuls showed significan improvemen in BER performance a SNR value of 40 db and above for 32-PSK, 64-PSK, 128- PSK, 256-PSK, 512-PSK and 1024-PSK. he implicaion of he resuls is ha more power is needed o achieving a arge BER; and his would no provide he desired power efficiency of he sysem especially for mobile applicaions. Mangla and Singh in [22] compared he BER performances of higher order M-QAM and M-PSK modulaion schemes in a MIMO-OFDM sysem. he sysem was simulaed for M = 16, 64, 256, 512 and 1024. he resuls showed ha URL: hp://d.doi.org/10.14738/nc.32.1144 118
r a n s a c i o n s o n N e w o r k s a n d C o m m u n i c a i o n s ; V o l u m e 3, I s s u e 2, A p r i l 2 0 1 5 specral efficiency increases wih increasing modulaion order M. Also, M-QAM gives beer BER performance han M-PSK. he BER of he higher order modulaions can be reduced bu a he cos of increasing he SNR. Increasing he SNR is however no advisable because ecessive power consumpion would adversely affec sysem lifespan. Hence, his paper presens O-MPSK in MIMO spaial mulipleing (MIMO-SM) communicaion sysems in order o reduce he ICI owards improving he sysems performances. 2 Developmen of he Offse M-PSK Schemes A modulaed consiss of a combinaion of he carrier and he message (or informaion). he M-ary PSK modulaion is achieved by shifing he carrier in phase according o he message daa. A modulaed s() in ime () domain can be epressed as: s() = Re{g()ep (jω c )} (1) where Re{.} denoes he real componen of he comple funcion indicaed by j, ω c = 2πf c, f c = he carrier frequency, g() = he comple baseband envelope of s(). his comple baseband envelope g() is a funcion of he message m () and can be epressed as: g() = Am()ep [jθ()] (2) where A is a consan ampliude θ() = he phase of he Subsiuing equaion (2) ino (1) gives: s() = Am()cos [ω c + θ()] (3) Applying rigonomeric ideniy o Equaion (3), he equaion can be epressed in cosine and sine forms as: s() = Am()[cosω c cosθ() sinω c sinθ()] (4) he consan ampliude A is a funcion of he power; and i is given as: A = 2P (5) where P is he power. Also, P is a funcion of he energy conained in symbol duraion; and is given as: P = E s (6) where s is he symbol period; E is he energy conained in he symbol period. Subsiuing Equaion (6) ino (5) gives: Wih A ino equaion 4 gives: A = s (7) By shifing he carrier in phase, Equaion 8 becomes: s() = m() s [cosω c cosθ sinω c sinθ] (8) wih s() = m() s [cosω c cos(θ i θ 0 ) sinω c sin(θ i θ 0 )] (9) C o p y r i g h S o c i e y f o r S c i e n c e a n d E d u c a i o n U n i e d K i n g d o m 119
Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade; Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing, ransacions on Neworks and Communicaions, Volume 3 No 2, April (2015); pp: 117-127 and θ o is he iniial phase given as: θ i = 2π i, for i = 1,2,3, M (10) M θ 0 = 2π M where M is he consellaion size of he M-ary PSK; he phase akes on one of M possible values. (11) Equaion (9) represens an M-ary PSK modulaed. he phases of an MPSK consellaion can be represened wih a polar diagram in Inphase/Quadraure (I/Q) forma. he cosine componen of he modulaed s () akes he inphase ais while he sine componen akes he quadraure ais. he offse MPSK (OMPSK) modulaion can be implemened by delaying he inpu bi sream of he quadraure par by one bi period b. he bi period is given as: b s s (12) k log 2 M where k is he number of bis ha represens a symbol. herefore, he convenional MPSK modulaion Equaion 9 can be modified for he OMPSK as: s( ) m( ) cos c cos( i 0) sinc sin[( i 0)( b )] (13) 2.1 Offse QPSK Scheme s he leas comple form of he offse M-ary PSK is he offse 4-ary PSK (OQPSK). For he OQPSK he number of bis per symbol k is 2; hence, he bi periodb s 2. Also, Equaion 11 shows ha he phase is shifed by 2 when M = 4. Figure 1(a) shows he designed scheme for implemening OQPSK modulaion. he modulaion is achieved by ransmiing he odd-numbered inpu bis via he inphase, I() branch while he even-numbered bis are ransmied via he quadraure, Q() branch wih he use of a serial-o-parallel (S/P) converer. he daa on he Q() par is delayed by s 2 wih respec o ha on he I() par o creae an offse. his is followed by unipolar-o-bipolar () converers which conver he daa o polar non reurn-o-zero (NRZ). he bipolar (±1) s are hen passed hrough recangular pulse-shaping filers, and hen modulaed by cosine and sine carriers. A he receiver, he is demodulaed as shown in Figure 1(b). he arriving OQPSK is passed hrough a carrier recovery circui which demodulaes he by he inphase and quadraure carriers. he resuling I() and Q() s are hen passed hrough he Inegrae and Dump filers followed by he deecion of he daa by he hreshold deecor. he inphase, I() sream is hen delayed wih respec o ha on he Q() sream by s 2 o remove he offse inroduced a he modulaor. he I() and Q() sreams are hen combined by a parallel-o-serial (P/S) converer o produce he received bi sream. his sraegy helps o reduce specral spreading when he passes hrough a nonlinear high power amplifier because he offse makes he o have lower envelope variaion when compared wih he convenional QPSK. URL: hp://d.doi.org/10.14738/nc.32.1144 120
r a n s a c i o n s o n N e w o r k s a n d C o m m u n i c a i o n s ; V o l u m e 3, I s s u e 2, A p r i l 2 0 1 5 2.2 Offse 8-PSK Scheme he offse 8-PSK (O8-PSK) modulaor and demodulaor are shown in Figures 2(a) and (b) respecively. he modulaion and demodulaion processes of O8-PSK are similar o hose of OQPSK ecep ha he phase is shifed by 4 and he number of bis per symbol k is 3. 2.3 Offse 16-PSK Scheme he offse 16-PSK (O16-PSK) modulaor and demodulaor are shown in Figures 3(a) and (b) respecively. he modulaion and demodulaion processes of O16-PSK are similar o hose of OQPSK ecep ha he phase is shifed by 8 and he number of bis per symbol k is 4. Inpu daa b s 2 b I() S/P 1 Local Oscillaor 2 cos c + OQPSK Q() s 2 b 1 Delay = s/2 Q ( s 2) sin c (a) OQPSK Carrier Recovery Circui 2 cos c Inegrae hreshold Deecor Delay = s/2 P/S daa sin c Inegrae hreshold Deecor (b) Figure 1: Offse QPSK Scheme (a) Modulaor (b) Demodulaor Inpu daa b s 3 b I() S/P 1 Local Oscillaor 4 cos c + O8-PSK Q() s 3 b 1 Delay = s/3 Q ( s 3) sin c (a) C o p y r i g h S o c i e y f o r S c i e n c e a n d E d u c a i o n U n i e d K i n g d o m 121
Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade; Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing, ransacions on Neworks and Communicaions, Volume 3 No 2, April (2015); pp: 117-127 O8-PSK Carrier Recovery Circui 4 cos c sin c Inegrae Inegrae (b) hreshold Deecor hreshold Deecor Delay = s/3 P/S Figure 2: Offse 8-PSK Scheme (a) Modulaor (b) Demodulaor daa Inpu daa b 4 I() s b S/P 1 Local Oscillaor 8 cos c + O16-PSK Q() s 4 b 1 Delay = s/4 Q ( s 4) sin c (a) O16-PSK Carrier Recovery Circui 8 cos c Inegrae hreshold Deecor Delay = s/4 P/S daa sin c Inegrae (b) hreshold Deecor 2.4 Offse 32-PSK Scheme Figure 3: Offse 16-PSK Scheme (a) Modulaor (b) Demodulaor he offse 32-PSK (O32-PSK) modulaor and demodulaor are similar o hose of OQPSK ecep ha he phase is shifed by 16 and he number of bis per symbol k is 5. 2.5 Offse 64-PSK Scheme he modulaion and demodulaion processes of O64-PSK scheme are similar o hose of OQPSK ecep ha he phase is shifed by 32 and he number of bis per symbol k is 6. URL: hp://d.doi.org/10.14738/nc.32.1144 122
r a n s a c i o n s o n N e w o r k s a n d C o m m u n i c a i o n s ; V o l u m e 3, I s s u e 2, A p r i l 2 0 1 5 3 Sysem Simulaion Model and ool he invesigaion was carried ou by developing he MIMO-SM sysem simulaion models using he OMPSK modulaion schemes. he developed sysem models were implemened by simulaion of he developed models. 3.1 Sysem Simulaion Models A simulaion model for 22 MIMO-SM wih OMPSK modulaion scheme is shown in Figure 4. he ransmied message is a randomly generaed bi sream. A he ransmier, he bi sream is passed hrough he OMPSK modulaor. he oupu from he modulaor is spli ino even and odd symbols; and he even symbols are ransmied hrough he anenna 1 while he odd symbols are ransmied hrough anenna 2. he wo s pass hrough a Rayleigh fading channel wih he addiive whie Gaussian noise (AWGN). A he receiver, channel esimaion is performed on he received s o nullify he effec of fading. he s are hen mulipleed and he resuling OMPSK is demodulaed o obain he received daa. Inpu daa OMPSK modulaor Demulipleer Rician Fading Channel AWGN Channel Esimaor wih Mulipleer Oupu daa OMPSK Demodulaor Figure 4: Sysem simulaion model for 22 MIMO-SM wih OMPSK modulaion scheme 4 Resuls and Discussion MIMO Spaial Mulipleing (MIMO-SM) and MIMO Beamforming (MIMO-BF) schemes were simulaed using he O-MPSK modulaion echnique as well as he convenional MPSK modulaion echnique over a Rayleigh fading channel; and comparisons are made in erms of BER beween he wo schemes. he BER is evaluaed for SNR values of 0 o 20 db as presened in able 1. he BER performances of QPSK and 2 -QPSK in MIMO-SM over Rayleigh fading channel are shown in Figure 5. aking SNR of 10 db, QPSK gives a BER value of 0.0012 while 2 -QPSK gives 0.0010; also, he mean BER values for all he SNRs are 0.0025 and 0.0024 for QPSK and 2 -QPSK respecively. he subsequen lower BER values given by 2 QPSK. -QPSK reveals he efficiency of 2 -QPSK over he Figure 6 presens he BER performances of 8PSK and 4-8PSK in MIMO-SM over Rayleigh fading channel. aking SNR of 10 db, he BER values for 8PSK and 4-8PSK are 0.0018 and 0.0016 respecively, and he mean BER values are 0.0044 and 0.0040 for 8PSK and 4-8PSK respecively. he 4-8PSK has relaively lower BER compared o 8PSK. he BER performances of 16PSK and 8-16PSK in MIMO-SM over Rayleigh fading channel are shown in Figure 7; he 16PSK modulaion gives a BER value of 0.0044 while he 8-16PSK modulaion gives a closer 0.0045 a SNR of 10 db. he C o p y r i g h S o c i e y f o r S c i e n c e a n d E d u c a i o n U n i e d K i n g d o m 123
Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade; Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing, ransacions on Neworks and Communicaions, Volume 3 No 2, April (2015); pp: 117-127 mean BER values for 16PSK and 8-16PSK are 0.0088 and 0.0085 respecively. his resul reveals ha he 8-16PSK has relaively beer BER performance compared o 16PSK. able 1: BER values for 22 MIMO spaial mulipleing over Rayleigh fading channel SNR[dB] QPSK ( π )- 8PSK ( π )- 16PSK ( π )- 32PSK ( π )- 64PSK ( π )- 2 4 8 16 32 QPSK 8PSK 16PSK 32PSK 64PSK 0 0.0075 0.0083 0.0153 0.0136 0.0310 0.0279 0.0585 0.0583 0.1040 0.1043 2 0.0064 0.0062 0.0117 0.0110 0.0215 0.0208 0.0430 0.0444 0.0796 0.0807 4 0.0045 0.0044 0.0084 0.0078 0.0158 0.0156 0.0323 0.0336 0.0634 0.0642 6 0.0032 0.0029 0.0056 0.0053 0.0104 0.0109 0.0221 0.0235 0.0470 0.0476 8 0.0022 0.0017 0.0032 0.0031 0.0071 0.0074 0.0153 0.0157 0.0344 0.0349 10 0.0012 0.0010 0.0018 0.0016 0.0044 0.0045 0.0100 0.0105 0.0244 0.0245 12 0.0009 0.0007 0.0011 0.0009 0.0026 0.0026 0.0065 0.0069 0.0170 0.0172 14 0.0006 0.0005 0.0005 0.0005 0.0017 0.0017 0.0040 0.0041 0.0110 0.0108 16 0.0004 0.0003 0.0003 0.0004 0.0010 0.0008 0.0026 0.0027 0.0070 0.0068 18 0.0002 0.0002 0.0002 0.0002 0.0005 0.0005 0.0011 0.0012 0.0042 0.0038 20 0.0002 0.0001 0 0 0.0004 0.0004 0.0007 0.0006 0.0014 0.0013 10 0 22 MIMO-SM over Rician channel (K=5) QPSK (/2)-QPSK 10-1 BER 10-2 10-3 10-4 0 2 4 6 8 10 12 14 16 18 20 SNR [db] Figure 5: BER performances of QPSK and 2 -QPSK in22 MIMO-SM over Rayleigh Fading Channel 10 0 22 MIMO-SM over Rician channel (K=5) 8PSK (/4)-8PSK 10-1 BER 10-2 10-3 10-4 0 2 4 6 8 10 12 14 16 18 20 SNR [db] Figure 6: BER performances of 8PSK and 4-8PSK in22 MIMO-SM over Rayleigh Fading Channel URL: hp://d.doi.org/10.14738/nc.32.1144 124
r a n s a c i o n s o n N e w o r k s a n d C o m m u n i c a i o n s ; V o l u m e 3, I s s u e 2, A p r i l 2 0 1 5 10 0 16PSK (/8)-16PSK 10-1 BER 10-2 10-3 10-4 0 2 4 6 8 10 12 14 16 18 20 SNR [db] Figure 7: BER performances of 16PSK and 8-16PSK in22 MIMO-SM over Rayleigh Fading Channel he BER performances of he off-se M-PSK in MIMO-SM for comparison over Rayleigh fading channel are presened in Figure 8. A SNR of 10 db, he BER values for 32PSK and 16-32PSK are 0.0100 and 0.0105 respecively, and he mean BER values are 0.0178 and 0.0183 for 32PSK and 16-32PSK respecively. his resul revealed ha 32PSK has beer BER performance compared o 16-32PSK. he BER performances of 64PSK and 32-64PSK gave BER values of 0.0244 and 0.0245 respecively a SNR of 10 db. he mean BER values for 64PSK and 32-64PSK are 0.0358 and 0.036 respecively. his resul revealed ha he 64PSK gave relaively beer BER performance compared o 32-64PSK. 10 0 10-1 22 MIMO-SM wih Offse-MPSK over Rician channel (K=5) (/2)-QPSK (/4)-8PSK (/8)-16PSK (/16)-32PSK (/32)-64PSK BER 10-2 10-3 10-4 0 2 4 6 8 10 12 14 16 18 20 SNR [db] Figure 8: Comparison of he O-MPSK in 22MIMO-SM over Rayleigh Fading Channel 5 Conclusion In his paper, O-QPSK, O-8PSK, O-16PSK, O-32PSK and O-64PSK modulaion schemes have been developed, he sysem simulaion models incorporaing a 22 MIMO Spaial Mulipleing (MIMO SM) using he O-MPSK modulaion schemes was developed over Rayleigh fading channel, simulaed using MALAB applicaion package. he models were evaluaed o deermine he performance using C o p y r i g h S o c i e y f o r S c i e n c e a n d E d u c a i o n U n i e d K i n g d o m 125
Adeyemo, Z. Kayode, Rabiu, E. Oluwaosin and Rober, O. Abolade; Offse Phase Shif Keying Modulaion in Muliple-Inpu Muliple-Oupu Spaial Mulipleing, ransacions on Neworks and Communicaions, Volume 3 No 2, April (2015); pp: 117-127 bi error rae (BER) and compare wih he convenional (non-offse) MPSK. he O-MPSK schemes were compared wih MPSK scheme in erms of BER for SNR values of 0 o 20 db. he O-MPSK invesigaed include 2 -QPSK, 4-8PSK, 8-16PSK, 16-32PSK and 32-64PSK. he resuls revealed ha he O-MPSK schemes ouperform he MPSK schemes in MIMO-SM as he O-MPSK schemes gave relaively lower mean BER compared o he MPSK schemes. Also, he resuls revealed ha he bes performance was obained wih he 2 -QPSK scheme. REFERENCES [1]. Harjo K., Bindiya J. and Ami V., Comparaive Performance Analysis of M-ary PSK Modulaion Schemes using Simulink Inernaional Journal of elecronic & Communicaion echnology, 2. 3, (2011): 204 209. [2]. Gesse, M. K. and Oladele O. P., Performance Evaluaion of LE Downlink wih MIMO echniques, M.ech hesis, Blekinge Insiue of echnology, Karlskrona, Sweden, (2010). [3]. Proakis, J. G. and Salehi, M., Communicaion Sysems Engineering, 2nd Ed., Prenice-Hall Inc., USA, (2002). [4]. Proakis, J. G., Digial Communicaions, McGraw Hill Companies, inc, Inernaional Ediion, New York Ciy, USA, (2001). [5]. Rappapor,. S., Wireless Communicaions Principles and Pracice, 2nd Ed., Prenice-Hall Inc., USA, (2002). [6]. Bernard, S., Digial Communicaions: Fundamenals and Applicaions, 2nd ediion, Prenice Hall, USA, (2001). [7]. Amin, A. (2011), Compuaion of Bi-Error Rae of Coheren and Non-Coheren Deecion M-ary PSK wih Gray Code in BFWA Sysems, Inernaional Journal of Advancemens in Compuing echnology, 3.1 (2011):27-38. [8]. Ani V. R. and Aro L., Radio Engineering for Wireless Communicaion and Sensor Applicaions, Arech House, Boson, London, (2003) [9]. Poongodi, C., Ramya, P. and Shanmugam A., BER Analysis of MIMO OFDM Sysem using M-QAM over Rayleigh Fading Channel, Inernaional Conference on Communicaion and Compuaional Inelligence, Kongu Engineering College, Perundurai, erode,. N., India, (2010): 284-288. [10]. Ippolio, L. J. Saellie communicaion sysem engineering: Amospheric Effec, Saellie link Design, and Sysem Performance, firs ediion John Wiley & Sons, Singapore, (2008). URL: hp://d.doi.org/10.14738/nc.32.1144 126
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