Bandwidth-Efficient MIMO Underwater Acoustic Communications with Frequency-Domain Equalization

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1 Bandwidth-Efficient MIMO Underwater Acoutic Communication with Frequency-Domain Equalization Jian Zhang and Yahong Roa Zheng Dept of Electrical & Computer Eng, Miouri Univerity of Science & Technology, Rolla, MO 6549, USA Abtract Thi paper propoe a bandwidth-efficient frequency-domain equalization (FDE) for ingle carrier (SC) underwater acoutic (UWA) communication with multiple tranducer and hydrophone The propoed algorithm implement an overlapped-window FDE by partitioning a large block into mall ubblock A deciion-directed channel etimation cheme i alo propoed to track the channel variation by the detect ymbol The propoed algorithm i teted by underea data collected during the Recheduled Acoutic Communication Experiment (RACE) in March 8 The experimental reult demontrate the propoed receive algorithm effectively track the time variation of the channel impule repone and ignificantly improve the performance of uncoded bit error rate (BER) Compared with traditional SC-FDE ytem, the propoed overlapped-window FDE achieve 744% and 846% average BER reduction for the 4 m and m range ytem, repectively at the ame data efficiency and ha only 84% tranmiion overhead, which i much maller than over % of other exiting UWA OFDM and SC-FDE ytem at the ame BER level I INTRODUCTION High data-rate hallow underwater acoutic (UWA) communication have alway been challenging due to the advere effect impoed by hotile underwater propagation environment []-[3] The exceively long multi-path delay pread and frequency-dependent propagation attenuation lead to evere inter-ymbol interference (ISI) Beide, relative motion between tranceiver and dynamic motion of water urface reult in not only time-varying Doppler pread but alo fat time-varying channel In order to mitigate ISI and Doppler effect, time-domain deciion feedback equalization (TD-DFE) with a phae-locked loop (PLL) ha been uccefully applied in ingle-input ingle-output (SISO) [4] and multiple-input multiple output (MIMO) [5] UWA communication However, due to the fat time-varying fading channel with long channel length, the TD-DFE with PLL i often untable and le robut to channel variation And the computational complexity of time-domain equalizer i prohibitive for long delay pread Therefore, frequency-domain equalization (FDE) which provide lower complexity and better robutne ha recently been applied to UWA communication with both multicarrier [6], [7] and ingle carrier tranmiion [8], [9], which all exhibit excellent performance in real-world underea experiment However, the challenge of the current frequency-domain (FD) method (OFDM and SC-FDE) i the conflicting goal of improving bandwidth efficiency and tracking channel variation Generally, the FD method require block tranmiion and zero padding (ZP) or cyclic prefix (CP) [], which i part of the overhead, ha to be inerted between block to avoid interblock interference (IBI) For high date-rate UWA communication, the channel memory length i often on the order of a hundred tap, while the channel coherent time only pan about a couple of hundred ymbol The data block length ha to be maller than the coherent time to effectively tracking the channel variation, while the length of the overhead need to be larger than the channel memory length Therefore, mall block length can track channel variation and enure good BER performance but uffering from low data efficiency Increaing data block length may improve bandwidth efficiency but uffering from reduced performance due to poor channel etimation and tracking In order to olve the dilemma between the data efficiency and channel tracking, we propoe a bandwidth-efficient SC- FDE with a deciion-directed channel etimation cheme in thi paper The propoed method employ an overlappedwindow for FDE [], [] with large block length to imultaneouly maintain high bandwidth efficiency and improve capability of channel tracking In the propoed cheme, the data block with a large length i divided into mall ubblock, and a data window coniting of the current ubblock and part of previou and ubequent ubblock i employed to ave the input data for the FDE The ymbol of previou and ubequent ubblock are ued for precuror and potcuror interference cancellation The deired equalized ubblock data i obtained by dicarding the precuror and potcuror part of the equalized data window The phae rotation of equalized ymbol i corrected by a group-wie phae correction algorithm The UWA MIMO channel are initially etimated by pilot ymbol and re-etimated by the detected ubblock ymbol in a deciion-directed method The novelty of the propoed FDE cheme lie in that tranmiion with large block length i allowed in the UWA FDE ytem, and the channel impule repone are etimated and tracked adaptively by the detected ymbol Hence, the propoed cheme greatly improve the bandwidth efficiency and channel tracking capacity at the cot of lightly increaed complexity The performance of the propoed algorithm ha been teted

2 by the underea data collected in the Rechedule Acoutic Communication Experiment (RACE) in Narraganett Bay, Rhode Iland from March t to March 7th, 8 Thi experiment wa deigned for 4 m and m range, with tranducer and hydrophone The QPSK-modulated ignal with a bandwidth of 3965 khz were tranmitted over the UWA channel at the carrier frequency 5 khz Experimental reult how that the propoed cheme effectively track the time-varying UWA channel, and the average uncoded BER achieve more than 7% reduction of bit error rate over the traditional SC-FDE at the ame data efficiency The tranmiion overhead of the propoed FDE cheme i only 84%, which i ignificantly reduced compared with more than % overhead of other UWA OFDM [6] and SC-FDE ytem [8], [4] at the ame level of BER Throughout the paper, we ue boldface letter to denote vector and matrice, and the upercript [ ] T, [ ] H, [ ], and [ ] to denote the matrix tranpoe, Hermitian tranpoe, invere, and peudo-invere, repectively II SYSTEM MODEL AND PRELIMINARIES A MIMO UWA communication ytem with N t tranducer and N r hydrophone i conidered here At the tranmit end, N t uncoded bit tream are independently mapped to phae hift keying (PSK) modulated data ymbol grouped into data block For the ake of aving tranmit power, a gap with zero, rather than CP, i appended to each block The zeropadded N t data tream are tranmitted imultaneouly and independently over the UWA channel at the ame carrier frequency The receiver tructure with N r hydrophone i hown in Fig, where the received ignal are firt preproceed by a front-end component to remove out-of-band noie, ynchronize, compenate average Doppler hift, and covert the paband ignal to baeband Next the overlappedwindow MIMO FDE i performed to mitigate the ISI and cochannel interference (CCI) The phae rotation caued by Doppler pread i compenated by a group-wie phae rotation algorithm The UWA channel are initially etimated by known pilot ymbol and then tracked by the detected ymbol in a deciion-directed way Front End y y p Fig y Nr y p Nr Overlapped x window FDE H Pilot aited chnn et H The diagram of receiver tructure Phae Correct Deciion directed chnn et The equivalent baeband received ignal are decribed in ˆx dicrete time domain a y m (k)= n=l= L h m,n (l,k)x n (k l+)e j(πf m,n,kkt +θ m,n) +v m (k), () where T i the ymbol period, y m (k) i the received ymbol at the m-th hydrophone, v m (k) i the Gauian noie with an average power of σ, x n (k) i the tranmitted ymbol from the nth tranducer, h m,n (l, k) i the compoite impule repone of the (m, n)-th ubchannel, L i the channel length, f m,n,k i the time-varying intantaneou Doppler drift, and θ m,n i the phae error after ymbol ynchronization At the receiver, overlap-adding i performed on each data block before applying FD method Then the ytem model i repreented in a matrix format a y m = D m,n T m,n x n + v m () n= where y m, v m and x n are the received ignal vector, noie vector and tranmitted ignal vector, repectively, with length N The diagonal matrix D m,n contain phae rotation on it diagonal entrie a D m,n =diag { e j(πfm,n,t+θm,n) e j(πfm,n,n NT+θm,n)} (3) and T m,n i the impule repone matrix of ize N N correponding to the (m, n)-th ubchannel If the block duration T b =(N + N zp )T i le than the channel coherence time τ c, then the time variation of channel impule repone (CIR) i negligible, and T m,n approximate a circulant matrix Multiplying normalized DFT matrix F N on both ide of (), we obtain the FD repreentation a Y m = Φ m,n H m,n X n + V m (4) n= where Y m = F N y m, X n = F N x n,v m = F N v m, H m,n = F N T m,n F H N, and Φ m,n = F N D m,n F H N The frequencydomain channel repone matrix H m,n i diagonal due to the circulant property of T m,n,andthei-th diagonal component i the frequency repone at the i-th frequency tone for the (m, n)-th channel Although Φ m,n i generally a nondiagonal matrix, the diagonal element of Φ m,n are ignificant comparing to the non-diagonal element if the block duration T b i le than one third of the quantity /max(f m,n,k ),which i alway atified becaue T b <τ c and τ c /max(f m,n,k ) for fixed-to-fixed UWA channel Hence Φ m,n i a diagonaldominant matrix which can be approximated a a diagonal matrix with identical diagonal element being Φ m,n (i, i) = N N e j(πf m,n,kkt +θ m,n), k= i =,,,N (5)

3 III THE PROPOSED FDE WITH PHASE CORRECTION AND CHANNEL ESTIMATION ALGORITHM A Overlapped-Window FDE with Phae Correction The overlap-window FDE i implemented baed on the overlap-ave method, which i hown in Fig The data block with a large block ize N i divided into mall ubblock, and each ubblock ha a length N Thu, there are totally M = N/N ubblock for one data block If N/N i not an integer, then zero are padded to the lat ubblock to make it ize to be N A overlapped data window i ued to form the input data to the equalization It contain the lat K point of the previou ubblock, the N point of the current ubblock, and the firt K point of the ubequent ubblock The K point of the previou ubblock and the K point of the ubequent ubblock are aved in the overlapped window to mitigate the precuror and potcuror interference TheizeofFFTiN f = N +K +K The deired equalized ubblock data x n,n=,,n t,=,,m, are obtained by dicarding the firt K and the lat K ymbol of the overlapped window zero N Received ignal ubblock Equalized ignal K K K ubblock Fig K K ubblock N ubblock N N K ubblock3 ubblock3 Data tructure for the overlapped-window FDE zero We define the etimated channel matrix of the -th ubblock in the frequency domain a λ,ĥ, λ,n t Ĥ,N t H =, (6) λ N r,ĥ N r, λ N r,n t Ĥ N r,n t where λ m,n = Nf N f k= ej(πf m,n,k kt+θm,n), which i the effect of Doppler and phae error on the -th ubblock of the (m, n)-th ubchannel, and Ĥ m,n i the diagonal frequency repone matrix of the (m, n)-th ubchannel for the -th ubblock Baed on the minimum mean quare error (MMSE) criterion, the frequency-domain equalized ubblock data i obtained a ˇX = H H (H H H + σ I Nf N r ) ˇX N t Y Y N r, (7) where Y m i the frequency-domain repreentation of the th ubblock received at the m-th hydrophone, and ˇX n i the etimation of the frequency-domain repreentation of the correponding ubblock at the n-th tranducer It ha been demontrated [3] that the equalized data ˇX n can be repreented in frequency domain a ( ˇX N r n ) X n + ˆV n, (8) m= Δ m,n Φ m,n where Δ m,n i approximately a diagonal matrix related to the channel repone and equalizer coefficient, and Φ m,n i a diagonal-dominant matrix Then applying the N f -point IFFT to ˇX n yield the time-domain data vector ˇx n a ˇx n = N r m= F H N f Δ m,nφ m,nf Nf x n + ˆv n (9) where x n and ˆv n are the T -paced tranmitted ignal vector and error vector, repectively By dicarding the firt K ymbol and the lat K ymbol of the equalized overlapped window, the deired equalized ymbol of the -th ubblock for the n-th tranducer can be obtained by x n = ˇx n (K +:N f K ) () Since Δ m,n Φ m,n i a diagonal-dominant matrix and the ubblock length i much maller than the channel coherence time, all the non-diagonal element of FN H f Δ m,n Φ m,n F N f are inignificant comparing to it diagonal element Therefore, the k-th equalized data ymbol in the -th ubblock of the n-th tranducer i expreed by [ Nr ] x n(k) = βm,n(k) e j β m,n (k) x n(k)+ˆv n(k) m= = α n(k) e j α n (k) x n(k)+ˆv n(k), k =,,N, () where α n (k) = N r m= β m,n (k) with β m,n (k) being the k-th diagonal element of the matrix (F H N f Δ m,n Φ m,n F N f ) From (), we conclude that the equalized data ymbol x n(k) i approximately an amplitude-caled and phae-rotated verion of the tranmitted data ymbol x n(k) Whenx n(k) i a PSK-modulated ymbol, the time-varying rotating phae α n(k) mut be compenated before detection Since the intantaneou Doppler hift f m,n,k varie gradually over a hort period of time, the rotating phae α n(k) alo change lowly and moothly over time Therefore, we ued an effective and robut group-wie phae correction algorithm [8], [3] to compenate the phae rotation α n(k) In the phae correction algorithm, each equalized ubblock i partitioned into N g group, and each group ha N b = N /N g ymbol

4 The initial phae rotation for the ubblock i ame a the phae rotation of the lat group of the previou ubblock The phae correction in each group i conducted in a deciion-directed way The detailed algorithm i omitted here for brevity B Channel Etimation and Tracking A deciion-directed time-domain leat quare (TD-LS) method i propoed in thi paper to etimate and track the channel impule repone (CIR) of fat-varying UWA channel The initial channel etimation i obtained by the fixed-length pilot ymbol, and the detected ubblock ymbol are ued to re-etimate the channel which are employed to equalize the next ubblock In thi method, for the large data block, channel variation are probed by the detected ymbol ubblock by ubblock, rather than inerting more known pilot ymbol Therefore, the overhead of data tranmiion for channel etimation i greatly reduced, and the variation of channel i effectively tracked in thi channel etimation cheme In our underea experiment, the data block contain N = 48 ymbol, and N zp =4zero are padded to each block The length of pilot ymbol N p = 5 Hence, the tranmiion overhead i 84% which i much maller than many conventional FDE algorithm with % pilot overhead [8], [4] and the OFDM tranmiion with 5% pilot overhead [6], [7] under imilar performance Let ˆx n denote the detected -th ubblock of the n-th tranducer Then the etimated time-domain CIR for the m-th hydrophone ĥ m = [(ĥ m, )T,, (ĥ m,n t ) T ] T can be repreented a ĥ m =(x ) ym, () where x =[P P N t ] with ˆx n (L) ˆx n (L ) ˆx n () P ˆx n(l +) ˆx n(l) ˆx n() n= (3) ˆx n(n p ) ˆx n(n p ) ˆx n(n p L+) where n =,,N t, ĥ m,n = [ĥ m,n(),, ĥ m,n(l)] T, and y m =[y m (L),,y m (N p)] T which i the correponding MIMO channel output vector The initial channel etimation i alo obtained by () except that known pilot ymbol are adopted in (3) IV FIELD TEST RESULTS FROM THE RACE8 EXPERIMENT In thi ection, the propoed bandwidth-efficient receive algorithm i teted by the real-word experimental data The experimental data wa collected during the Recheduled Acoutic Communication Experiment (RACE) in Narraganett Bay, Rhode Iland, conducted by Wood Hole Oceanographic Intitution (WHOI), in March 8 Two receiver were located at 4 meter and meter away from the tranmitter The receiver were equipped with hydrophone, located meter above the bottom of ea, and the tranmitter wa mounted with tranducer, located 4 meter above the bottom of ea The water depth varied between 9 to 4 meter The carrier frequency f c = 5 khz, the ampling rate f = 3965 khz, and the bandwidth B = f / = 3965 khz Binary information bit without error correction coding were mapped into QPSK ymbol which were grouped into block with ize of N = 48 A m-equence with length of 5 wa adopted at the beginning of each frame to ynchronize the data frame The received data were downampled at ample/ymbol, thu the N f -point FFT wa employed in the equalizer to improve the BER performance [4] The length of ubblock wa et to N =, thu one data block wa eparated into ubblock The channel pan 5 ymbol period, and we choe K = K = 4 The typical time-varying channel impule repone (CIR) of one repreentative data block are hown in Fig 3 and Fig 4 for the 4 m and m ytem, repectively Thee two figure depict the channel etimated by the pilot ymbol, the 5-th ubblock and the -th ubblock, repectively Due to le attenuation caued by the horter range communication, the amplitude of CIR of the 4 m ytem are larger than that of the m ytem It i een clearly that even in one data block duration, the amplitude of CIR are till varying fat The fat variation of the channel will caue the degradation of performance of the equalizer Our deciion-directed channel etimation method effectively track the variation of the channel for both ytem and provide more accurate channel etimation for the equalization Amplitude of CIR Tx Rx Chnn et by pilot Chnn et by 5 th ubblock Chnn et by th ubblock Channel tap (T ) Fig 3 The CIR in one block duration for the 4 m ytem The uncoded bit error rate (BER) and error reduction rate of the propoed receive algorithm are hown in Table I for the 4 m ytem and Table II for the meter ytem For each ytem, repreentative data packet were proceed, and each packet had totally information bit tranmitted For comparion, the performance of the traditional FDE method which perform FDE on the whole data block uing the channel etimated by pilot ymbol were alo included We can ee that the propoed algorithm outperform the traditional

5 Amplitude of CIR 9 x Tx Rx Chnn et by pilot Chnn et by 5 th ubblock Chnn et by th ubblock Channel tap (T ) Fig 4 The CIR in one block duration for the m ytem FDE method with more than 7% reduction of average bit error for thee two range ytem TABLE I UNCODED BER OF QPSK-48 BLOCKS FOR 4 M SYSTEM Identifier Traditional Propoed Error of packet FDE method FDE method Reduction 79756F6 C S % 79756F6 C S % 7956F6 C S % 856F6 C S % 8556F6 C S % 8556F6 C S % 8356F6 C S % 8956F6 C S % 8356F6 C S % 8756F6 C S % Avg % TABLE II UNCODED BERSOFQPSK-48 BLOCKS FOR M SYSTEM Identifier Traditional Propoed Error of packet FDE method FDE method Reduction 79355F6 C S % 858F6 C S % 8355F6 C S % 79755F6 C S % 8955F6 C S % 855F6 C S % 84955F6 C S % 855F6 C S % 8955F6 C S % 84755F6 C S % Avg % V CONCLUSION In thi paper, a bandwidth efficient FDE with the deciiondirected channel etimation wa propoed for SC MIMO UWA communication The propoed receiving algorithm greatly increaed the data efficiency of tranmiion and ignificantly improved the ytem performance The algorithm ha been applied to proce underea data collected during the RACE8 ocean experiment The time-varying multipath underwater acoutic MIMO channel were tracked well by the deciiondirected channel etimation method, and the average uncoded BER of QPSK modulation achieved 4% for the 4 m range ytem and 6% for the m range ytem with only approximate one third of tranmiion overhead of traditional FDE Compared with traditional FDE at the ame bandwidth efficiency, the propoed algorithm ha error reduction rate varying from 63% to 93% at the ubblock ize N = ACKNOWLEDGMENTS Thi work wa upported in part by the National Science Foundation under Grant ECCS and the Office of Naval Reearch under Grant N The author are grateful to Dr J Preiig for hi leaderhip of conducting the RACE8 experiment REFERENCES [] M Stojanovic and J Preiig, Underwater acoutic communication channel: propagation model and tatitical characterization, IEEE Commun Mag, pp 84-89, Jan 9 [] A C Singer, J K Nelon, S S Kozat, Signal proceing for underwater acoutic communication, IEEE Commun Mag, pp 9-96, Jan 9 [3] D B Kilfoyle and A B Baggeroer, The tate of the art in underwater acoutic telemetry, IEEE J Ocean Eng, vol 5, pp 4-7, Jan [4] M Stojanovic, J Catipovic, and J Proaki, Phae-coherent digital communicaiton for underwater acoutic channel, IEEE J Ocean Eng, vol 9, pp -, Jan 994 [5] S Roy, T M Duman, V McDonald, and J Proaki, High rate communication for underwater acoutic channel uing multiple tranmitter and pace-time coding: receiver tructure and experimental reult, IEEE J Ocean Eng, vol 3, pp , July 7 [6] B Li, S Zhou, M Stojanovic, and L Freitag, Pilot-tone baed ZP- OFDM demodulation for an underwater acoutic channel, in Proc IEEE OCEANS6, Boton, USA, Sept 6 [7] B Li, S Zhou, M Stojanovic, L Freitag, and P Willet, Multicarrier communication over underwater acoutic channel with nonuniform Doppler hift, IEEE J Ocean Eng, vol 33, pp 98-9, Apr 8 [8] J Zhang, Y R Zheng, and C Xiao, Frequency-domain equalization for ingle carrier MIMO underwater acoutic communication, in Proc IEEE OCEANS8, Quebec city, Canada, 8 [9] Y R Zheng, Channel etimationg and phae-correction for robut underwater acoutic communiction, in Proc IEEE MilCom7, Orlando, USA, 7 [] N Benvenuto, R Dini, D Falconer, and S Tomain, Single carrier modulation with nonlinear frequency domain equalization: an idea whoe time ha come-again, Proceeding of the IEEE, vol 98, pp 69-96, Jan [] J G Proaki, C M Rader, F Ling, C L Nikia, M Moonen, and I K Proudler, Algorithm for tatitical ignal proceing, Prentice Hall, [] A V Oppenheim and R W Schafer, Digital ignal proceing, New Jerey: Prentice-Hall, 975 [3] J Zhang, Y R Zheng, C Xiao, and K B Lataief, Channel Equalization and Symbol detection for ingle carrier MIMO ytem in the preence of multiple carrier frequency offet, IEEE Tran Veh Technol, to be publihed [4] M V Clark, Adaptive frequency-domain equalization and diverity combining for broadband wirele communication, IEEE J Select Area Commun, vol6, pp , Oct 998