Non-Uniform Doppler Compensation for Zero-Padded OFDM over Fast-Varying Underwater Acoustic Channels

Transcription

1 Non-Uniform Doler Comensation for Zero-Padded OFDM over Fast-Varying Underwater Acoustic Channels Baosheng Li 1, Shengli Zhou 1, Milica Stojanovic 2, Lee Freitag 3, Peter Willett 1 1 Det. of Elec. and Comuter Engr., University of Connecticut, Storrs, CT Massachusetts Institute of Technology, Cambridge, MA Woods Hole Oceanograhic Institution, Woods Hole, MA Abstract Underwater acoustic channels are wideband in nature due to the fact that the signal bandwidth is not negligible with resect to the center frequency. OFDM transmissions over UWA channels encounter frequency-deendent Doler drifts that destroy the orthogonality among OFDM subcarriers. In this aer, we roose a two-ste aroach to mitigating the frequency-deendent Doler drifts in zero-added OFDM transmissions over fast-varying channels: (1) non-uniform Doler comensation via resamling that converts a wideband roblem into a narrowband roblem; and (2) high-resolution uniform comensation on the residual Doler. Based on blockby-block rocessing, our receiver does not rely on channel deendence across OFDM blocks, and is thus desirable for fastvarying UWA channels. We test our receiver with data from a shallow water exeriment at Buzzards Bay, Massachusetts. Our receiver achieves excellent erformance even when the transmitter and the receivers have a relative seed u to 10 knots, where the Doler drifts are several times larger than the OFDM subcarrier sacing. I. INTRODUCTION The success of multicarrier modulation in the form of OFDM in radio channels motivates its use in underwater acoustic communications; see e.g., [1] [3]. However, underwater acoustic (UWA) channels are far more challenging than their radio counterarts, reventing direct alication of OFDM detection methods develoed for radio channels, and requiring a careful receiver design. Recently, there has been an increased interest in underwater OFDM communication, including [4] on a low-comlexity adative OFDM receiver, [5] on a ilot-tone based block-by-block receiver, and [6] on a non-coherent OFDM receiver based on on-off-keying. In this aer, we adot zero-added OFDM [7] for underwater acoustic communications. The erformance of a conventional ZP-OFDM receiver is severely limited by the intercarrier interference (ICI) due to fast channel variations within each OFDM symbol. Furthermore, the UWA channel is wideband in nature due to the fact that the signal bandwidth is not negligible with resect to the center frequency. The resulting frequency-deendent Doler drifts render existing B. Li and S. Zhou are suorted by UCRF internal grant M. Stojanovic is suorted by ONR grant N L. Freitag is suorted by Office of Naval Research. P. Willett is suorted by Office of Naval Research. ICI reduction techniques used in radio channels not effective. We roose a two-ste aroach to mitigating the frequencydeendent Doler drifts in zero-added OFDM transmissions over fast-varying underwater acoustic channels: (1) nonuniform Doler comensation via resamling that converts a wideband roblem into a narrowband roblem; and (2) high-resolution uniform comensation on the residual Doler for best ICI reduction. Our ractical receiver algorithms rely on the reamble and the ostamble of a acket consisting of multile OFDM blocks to estimate the resamling factor, null subcarriers to facilitate high-resolution residual Doler comensation, and ilot subcarriers for channel estimation. Based on block-byblock rocessing, our coherent receiver does not rely on channel deendence across OFDM blocks, and is thus effective for fast-varying underwater acoustic channels. To verify our aroach, we have conducted an exeriment in shallow water at Mudhole, Buzzards Bay, MA, on Dec. 15, The transmitter was moving from 600 meters towards the receiver with a varying seed between 3 knots to 10 knots. Even when the Doler drifts are several times larger than the OFDM subcarrier sacing, the exerimental results show that the roosed receiver achieves excellent erformance. (With a bandwidth of 12kHz, the data rate was from 10.5 kbs to 14.5 kbs for different settings when no channel coding is used.) The results in this aer suggest that OFDM is an aealing otion for high-rate underwater acoustic communications over fast-varying channels. The rest of the aer is organized as follows. In Section II, the erformance of a conventional receiver is discussed. The aroach to mitigating the Doler effects is resented in Section III, and the receiver algorithms are resented in Section IV. In Section V, we secify the exerimental signal design, and in Section VI we reort on the receiver erformance. We conclude in Section VII. II. ZERO-PADDED OFDM TRANSMISSION Let T denote the OFDM duration and T g the guard interval. The total OFDM block duration is T = T +T g. The frequency sacing is f =1/T.Thekth subcarrier is at frequency f k = f c + k f, k = K/2,...,K/2 1, (1)

2 where f c is the carrier frequency and K subcarriers are used so that the bandwidth is B = K f. Let us consider one ZP-OFDM block. Let d[k] denote the information symbol to be transmitted on the kth subcarrier. We introduce null subcarriers in the transmission. The set of active subcarriers S A and the set of null subcarriers S N satisfy S A S N = { K/2,...,K/2 1}. The transmitted signal in assband is { } s(t) =Re d[k]e j2πk ft g(t) ]e j2πfct,t [0,T+T g ], (2) where g(t) describes the zero-adding oeration as { 1, t [0,T] g(t) = (3) 0, t [T,T + T g ]. We consider a multiath underwater channel that has the imulse resonse as c(t, τ) = A (t)δ(τ τ (t)), (4) FFT rocessing leads to the outut of the demodulator in the m-th subchannel as T y m = 1 [y(t)+y(t + T )]e j2πm ft dt. (8) T 0 Substituting (7) into (8) and assuming that T g is larger than the channel delay sread, we obtain ( ) fm y m = C d[k]ρ m,k + n m (9) where we define C(f) = A e j2πfτ, α m,k = (m k)+af k/ f, (10) ρ m,k = 1 ejα m,k sinc(α m,k ). (11) The desired signal in y m is C(f m /(1 + a))ρ m,m d[m], and the rest is the ICI ulse additive noise. The signal to interferencelus-noise ratio is where A (t) is the ath amlitude and τ (t) is the timevarying ath delay. For ease of resentation, we assume that all aths have similar Doler rate τ (t) τ at, (5) and the ath gains A (t) and the Doler rate are constant over the block duration T. The received signal in assband is then { ] ỹ(t) =Re A d[k]e j2πk f(t+at τ) g(t + at τ ) e j2πfc(t+at τ) } +ñ(t), (6) where ñ(t) is the additive noise. Converting ỹ(t) to its baseband version y(t), wehave y(t) = { d[k]e j2πk ft e j2πaf kt A e j2πf kτ g(t + at τ )] } + n(t), where n(t) is the additive noise in baseband. We observe from (7) two effects: (i) the signal from each ath is scaled in duration, from T to T/(1 + a); (ii) each subcarrier exeriences a Doler shift e j2πaf kt, which deends on the frequency of each subcarrier. Since the bandwidth of OFDM is comarable to the center frequency, the Doler shifts on different OFDM subcarriers differ considerably; i.e., the narrowband assumtion does not hold true. We now resent the erformance of a conventional OFDM receiver that does not erform any Doler comensation [7]. Overlaing and adding of the received signal followed by (7) ρ m,m 2 σd 2 γ m = σv/ C(f 2 m /(1 + a)) 2 + k m ρ m,k 2 σd 2, (12) where σv 2 is the noise variance and σd 2 = E[ d[m] 2 ].Note that γ m has a floor which does not deends on the channel frequency resonse when σv 2 goes to zero. III. MITIGATING THE DOPPLER EFFECT We roose a two-ste aroach to mitigating the frequency-deendent Doler drifts due to fast-varying underwater acoustic channels: 1. Non-uniform Doler comensation via resamling. This ste converts a wideband roblem into a narrowband roblem. 2. High-resolution uniform comensation on residual Doler by modeling it as induced by carrier frequency offset (CFO). This ste fine-tunes the CFO term corresonding to a narrowband model for best ICI reduction. For convenience, let us resent these stes using baseband signals. On the first ste, we resamle the received waveform y(t) with a resamling factor b: z(t) =y ( t 1+b ). (13) Resamling has two effects: (1) it rescales the waveform, and (2) it introduces a frequency-deendent Doler comensation. With y(t) in (7), we have z(t) =e j2πfct a 1+b The target is to make { j2πk f d[k]e 1+b t ( A e j2πf kτ )] } g 1+b t τ. 1+b (14) (15)

3 Inut BPF synchronization Doler scale coarse estimation resamling artition downshifting LPF CFO estimation channel estimation symbol detection VA decoding Outut Block by block rocessing Fig. 1. Block diagram of the receiver as close as ossible to one. After resamling, we have z(t) e j2πfct a 1+b d[k]e j2πk ft ] A e j2πf kτ g(t τ ) k (16) The Doler effect becomes almost the same for all subcarriers. Hence, a wideband OFDM system is converted into a narrowband OFDM system with a single equivalent CFO as ɛ = a 1+b f c. (17) Comensating for CFO in z(t), we obtain e j2πɛt z(t) = ] A e j2πf kτ g(t τ ), d[k]e j2πk ft (18) which leads to ICI-free recetion as the channel is timeinvariant. De-scaling and de-rotation of the received signal restore the orthogonality of the subcarriers of ZP-OFDM. In ractice, the scale factor b and the CFO ɛ need to be determined from the received data. They can be estimated either searately or jointly. In the next section, we will develo ractical algorithms for Doler scale and CFO estimation. IV. RECEIVER ALGORITHMS The received signal is directly samled and all rocessing is erformed on discrete-time signal. Fig. 1 deicts the receiver rocessing. Many stes in the receiver diagram are selfexlanatory. We next resent several key modules. A. Doler scale estimation Doler scale coarse estimation is based on the reamble and ostamble of a data acket 1. The acket structure is shown in Fig. 2. This idea has been used in [8] for single carrier transmissions. Via synchronization with the reamble and ostamble, the receiver estimates the time duration of a acket as T rx. The time duration of this acket at the transmitter side is T tr. By comaring T rx with T tx, the receiver infers how the received signal has been comressed or dilated by the channel: T rx =()T tx â = T rx T tx 1. (19) 1 This re- and ost-amble aroach requires a nearly constant moving seed during the transmission of a acket. Seed changes within a acket might considerably deteriorate the receiver erformance of such an aroach. The Doler scale factor is related to the relative seed v between the transmitter and the receiver by a = v/c, where c is the seed of sound. Hence, the seed estimate is ˆv = c â. (20) The receiver then resamles the acket using a resamling factor b =â. The resamling oeration introduces frequencydeendent Doler offsets: at the kth subcarrier, the Doler offset is f Doler =âf k. (21) B. CFO estimation We use null subcarriers to facilitate the finding of the CFO. We collect K + L samles after the resamling oeration for each OFDM block into a vector z = [z(0),...,z(k + L 1)] T, where L is the channel length in discrete-time. Let ( ) T and ( ) H denote transose and Hermitian transose, resectively. Define a (K + L) 1 vector as f m = [1,e j2πm/k,...,e j2πm(k+l 1)/K ] T. Define a (K + L) (K + L) diagonal matrix as Γ(ɛ) = diag(1,e j2πtcɛ,,e j2πtc(k+l 1)ɛ ), where T c = T/K is the time interval for each samle. The energy on the null subcarriers is used as the cost function J(ɛ) = fm H Γ H (ɛ)z 2. (22) m S N If the receiver comensates the data samles with the correct CFO before FFT oeration, the null subcarriers will not see the ICI silled over from neighboring data subcarriers. Hence, an estimate of ɛ can be found through ˆɛ = arg min ɛ J(ɛ), (23) which can be solved via one-dimensional search on ɛ. This high-resolution algorithm corresonds to the MUSIC-like algorithm roosed in [9] for OFDM with cyclic refix. C. Pilot-tone based channel estimation After resamling and CFO comensation, the ICI is greatly reduced. We use equi-saced ilot tones for channel estimation, as in [5].

4 TABLE I INPUT DATA STRUCTURE AND ACHIEVED BIT RATES inut bits # of active # of null # of blocks raw bit rates bit rates excluding K/4 K or symbols subcarriers subcarriers in a acket over B =12kHz ilot tones (uncoded) (N d ) (K a) (K n) (N b ) 2K a/(t + T g) 2(K a K/4)/(T + T g) kbs kbs kbs kbs kbs kbs SWP 100ms Syn 110ms T=1/df=K/B Tg T Tg T Tg SWP 100ms Syn 110ms Nb blocks er acket Fig. 2. Each acket consists of reamble, N b OFDM blocks, and ostamble. Sto T_acket Sto T_acket Sto 3 ackets er data burst T_acket K=512 K=1024 K=2048 Fig. 3. Each data burst consists of three ackets, with K = 512, K = 1024, and K = 2048, resectively. V. SIGNAL DESIGN FOR UNDERWATER EXPERIMENTS Our transmitted signal is designed as follows. The bandwidth of our OFDM signal is B =12kHz, and the carrier frequency is f c = 27 khz. The transmitted OFDM signal occuies the frequency band of 21 to 33 khz. We use zeroadded OFDM with a guard interval of T g =25ms er OFDM symbol. We test three different settings for the number of subcarriers: K = 512, K = 1024, and K = Weuserate 2/3 convolutional coding (obtained by uncturing a rate 1/2 code with olynomial (23,35)) and QPSK modulation. We let each acket have N d = information bits. Hence, each acket will contain N b = N d /K a OFDM blocks, where K a is the number of active carriers. For K = 512, 1024, 2048, each acket contains N b =64, 32, 16 OFDM blocks, resectively. These arameters are summarized in Table I. Fig. 3 deicts one data burst that consists of three ackets with K = 512, K = 1024, and K = 2048, resectively. During the exeriments, the same data burst was transmitted multile times while the transmitter was moving. 2.5 m Fig. 4. Source 6137 VI. EXPERIMENTAL RESULTS Mytilus 600 m~-110 m Receiver HTI-96 Array Sto The exeriment setu for the Dec. 15, 2006 exeriment Tioga 6 m 0.5 m The WHOI acoustic communication grou conducted the exeriment on Dec. 15, The exeriment location was at Mudhole, Buzzards Bay, MA. The transmitter was submerged at a deth of about 2.5 meters. The receiver was a four-element array (of length 0.5 m) submerged at a deth of about 6 meters. The transmitter was mounted on the arm of the vessel Mytilus, and the receiver array was mounted on the arm of the vessel Tioga. OFDM signals were transmitted while Mytilus was moving towards Tioga, starting at 600 m, assing by Toiga, and ending at about -100 m in distance. The configuration is shown in Fig. 4. The data burst in Fig. 3 was transmitted multile times when Mytilus was moving towards Tioga. The received signal was directly A/D converted. The receiver array has four elements, roviding four arallel received data streams. The received signal observed on one element is shown in Fig. 5, which contains 7 data bursts (21 ackets). We directly observe that: 1) The received ower is increasing before acket 19 and decreasing after acket 19. This is because Mytilus assed Tioga around that time. Hence, the transmitter was moving towards the receiver before acket 19 while moving away from the receiver after acket 19. 2) An increase in the noise level is observed around acket 19. This noise is from the Mytilus when it is very close to Toiga. Simle data rocessing reveals the following: 3) The signal rior to acket 19 is comressed, which means that the transmitter was moving towards the receiver. The signals after that is dilated, which means that transmitter was moving away from the receiver. This agrees with the observation based on the received ower. We next resent numerical results based on the receiver rocessing outlined in Section IV. A. Doler scale estimation As shown in Fig. 5, we have 21 ackets transmitted. We use the algorithm of Section IV-A to estimate the Doler scale on the acket level. Hence, we have 21 estimated Doler scales. Based on each Doler scale, we estimate

5 6 CFO estimations Hz knots 8.26 knots OFDM block Fig. 5. The received signal the relative seed between the transmitter and the receiver using (20) and a nominal sound seed of c = 1500 m/s. Note that the waveform comression/dilation introduces frequencydeendent Doler shifts. We evaluate the Doler shifts at the carrier frequency f c (which is the same as the frequency f 0 of the 0th subcarrier). Table II summarizes the results for element 1. We see from Table II that the Doler shifts are much larger than the OFDM subcarrier sacing. For examle, if ˆv = 8.30 knots, which means Mytilus was moving towards Tioga at such a seed, the Doler shift is Hz at f c =27kHz, while the subcarrier sacing is only f = 23.44, 11.72, 5.86 Hz when K = 512, 1024, Re-scaling the waveform (even coarsely) is a necessary ste to reduce the Doler effect considerably, in a non-uniform fashion. Table II also reveals how Mytilus was moving. At first, Mytilus was accelerating towards Tioga. When it was aroaching Tioga, it slowed down but continued to move until it assed Tioga. During the time of transmitting ackets 18 and 19, Mytilus was assing by Tioga, as the seed changed from a negative value to a ositive value. B. High-resolution residual Doler estimation The high-resolution CFO estimation is done on a block-byblock basis, as detailed in Section IV-B. Fig. 6 shows the CFO estimates for ackets 5 and 17, resectively, where K = 1024 and each acket has 32 OFDM blocks. We observe that the CFO changes from block to block roughly continuously but cannot be regarded as constant. The CFO estimate is on the order of half of the subcarrier sacing. Without the CFO fine tuning, the receiver does not work. C. Uncoded erformance, single channel recetion Due to the large amount of blocks received on each of the four elements, we choose to demonstrate one set of results. In articular, we show the results for the K = 512 case, which corresonds to the ackets 1, 4, 7, 10, 13, 16, 19. FortheK = 512 case, each acket consists of 64 OFDM blocks. Fig. 6. The estimated residual Doler is shown for two examles. One is for acket 5 with a relative seed of 4.25 knots, the other is for acket 17 with a the relative seed of 8.26 knots. It can be seen that the CFO fluctuates raidly from block to block. We have the following observations on data demodulation. 1) Without coding, our receiver is able to rovide good erformance. 2) The ercentage of erroneously detected bits was zero when the moving seed is low (e.g., acket 1) or when the moving seed is very stable (e.g., acket 16). 3) Our receiver is able to handle a moving seed u to 9.04 knots. 4) There are several consecutive bad blocks in ackets 19 and 20, which led to a high number of bit errors. The reason is that the TX was moving from 600m to the RX. At the time of transmitting ackets 19 and 20, the TX was just assing by the RX. The Doler frequencies may have some unexected jitting when they were changing from negative to ositive values. Also, the noise level was suddenly high during the assing. When the TX had assed by the RX and went away from it, which was the case in acket 21, everything worked again and the number of bit errors went to almost zero. D. Coded erformance, single channel recetion All the information bits have been coded by a rate 2/3 convolutional code obtained by uncturing a rate 1/2 code. To test the coded erformance, we aly the Viterbi algorithm after the OFDM demodulation. Most of the observed errors on the block level disaear. Corresonding to all cases listed in Table III, only blocks 23 to 33 of acket 19 have decoding errors, and the rest do not. The errors occur in a few consecutive blocks in acket 19, where the signal exerienced a change from a negative Doler to a ositive Doler and a suddenly increased noise. Once the Doler becomes stable, our receiver has an accetable erformance. Thanks to the block-by-block rocessing, decoding errors in revious blocks have no imact on future blocks. This is desirable for fast-varying channels.

6 TABLE II COARSE ESTIMATION OF RELATIVE SPEED AND DOPPLER SHIFTS FOR ELEMENT 1. Packet Doler shift due to Relative seed (knots) Packet Doler shift due to Relative seed (knots) to scaling at f c (Hz) to scaling at f c (Hz) TABLE III UNCODED BIT ERROR RATE FOR K = 512, ELEMENT 4. (I) Packet Block (-1.86 knots) (-4.35 knots) (-4.52 knots) (-4.26 knots) (-4.58 knots) (-9.04 knots) (5.82 knots) Average BER of 64 blocks VII. CONCLUSIONS In this aer we investigated the alication of zeroadded OFDM in fast-varying underwater acoustic channels. We roosed a two-ste aroach to mitigating the frequencydeendent Doler drifts, namely non-uniform Doler comensation via resamling, followed by high-resolution uniform comensation on the residual Doler. We used null subcarriers to facilitate the Doler comensation, and ilot subcarriers for channel estimation. Our receiver is based on block-by-block rocessing, byassing the need of channel deendence across OFDM blocks, and is thus suitable for fastvarying underwater acoustic channels. We tested our methods in a shallow water exeriment. Excellent erformance was achieved even when the transmitter and the receivers had a relative seed u to 10 knots, where the Doler drifts were several times larger than the OFDM subcarrier sacing. REFERENCES [1] S. Coatelan and A. Glavieux, Design and test of a coded OFDM system on the shallow water acoustic channel, in Proc. of OCEANS, Set [2] B. Kim and I. Lu, Sea trial results of a robust and sectral-efficient OFDM underwater communication system (Abstract), The Journal of the Acoustical Society of America, vol. 109, no. 5,. 2477, May 1, [3] R. Bradbeer, E. Law, and L. F. Yeung, Using multi-frequency modulation in a modem for the transmission of near-realtime video in an underwater environment, in Proc. of IEEE International Conference on Consumer Electronics, June [4] M. Stojanovic, Low comlexity OFDM detector for underwater channels, in Proc. of MTS/IEEE OCEANS conference, Boston, MA, Set , [5] B. Li, S. Zhou, M. Stojanovic, and L. Freitag, Pilot-tone based ZP- OFDM demodulation for an underwater acoustic channel, in Proc. of MTS/IEEE OCEANS conference, Boston, MA, Set , [6] P. J. Gendron, Orthogonal frequency division multilexing with on-offkeying: Noncoherent erformance bounds, receiver design and exerimental results, Prerint from the author, [7] B. Muquet, Z. Wang, G. B. Giannakis, M. de Courville, and P. Duhamel, Cyclic refix or zero-adding for multi-carrier transmissions? IEEE Transactions on Communications, vol. 50, , Dec [8] B. S. Sharif, J. Neasham, O. R. Hinton, and A. E. Adams, A comutationally efficient Doler comensation system for underwater acoustic communications, IEEE Journal of Oceanic Engineering, vol. 25, no. 1, , Jan [9] U. Tureli and H. Liu, A high-efficiency carrier estimator for OFDM communications, IEEE Communications Letters, vol. 2, no. 4, , Ar