High Reliability Direct-Sequence Spread Spectrum for Underwater Acoustic Communications

Transcription

1 High Reliability Direct-Sequence Spread Spectrum for Underwater Acoustic Communications Fengzhong Qu and Liuqing Yang Department of Electrical and Computer Engineering University of Florida, Gainesville, Florida T. C. Yang Naval Research Laboratory, Washington, DC Abstract Many emerging underwater applications involve the wireless transmission of controlling signals and commands to autonomous underwater vehicles (AUVs) and underwater sensors. Such communication links often require high reliability with low complexity receivers and only a few hydrophones. In this paper, we propose a direct-sequence spread spectrum (DSSS) scheme to meet such a need. DSSS systems are recently introduced to underwater communications because of their capability of resolving multipath and enabling the collection of delay diversity and channel energy. Similar to these existing schemes, our proposed approach also has very low receiver complexity requiring only matched filter operation. However, different from them, we simultaneously transmit multiple symbols during each sequence period. Compared with existing underwater DSSS schemes, our proposed approach requires shorter channel coherence time and is thus more robust against moderate channel variation that is inevitable in underwater scenarios. In addition, our high reliability (HR-)DSSS scheme also facilitates higher and more flexible rates. More importantly, the high reliability and high data rate are achieved with negligible self- and co-channel interference. Besides simulations, our scheme is also tested in sea trials using QPSK modulation without any chip level equalization. I. INTRODUCTION The demand for high quality underwater acoustic communications (UAC) arises in many military, scientific and civilian applications. Many of these involve the wireless transmission of controlling signals and commands to autonomous underwater vehicles (AUVs) and underwater sensors. Due to their nature, the controlling signals and commands often require high reliability. On the other hand, AUV and sensor receivers have limited signal processing capability and only a few hydrophones due to the size and power limitations. All these make reliable communications a challenging problem in the naturally doubly-selective UAC channels. Recently, a few low rate UAC schemes have been proposed in [4], [5], [7], [8]. The multicarrier spread spectrum (MCSS) scheme in [8] and the direct-sequence spread spectrum (DSSS) scheme in [7] adapt to the channel variation through recursive channel estimation and equalization, which have high computational complexity. Orthogonal frequency-division multiplexing (OFDM) schemes in [4], [5] adopt the basis expansion model (BEM) to explicitly model the channel variation. These, however, involve matrix inversions in both channel estimation This work is in part supported by National Science Foundation under grants # and # , and by Office of Naval Research under grant #N and equalization, resulting in increased receiver processing complexity. When the signal block length is shorter than the channel coherence time, UAC channels can be approximated as quasistatic. Based on the quasi-static channel model, several DSSS schemes are proposed in [6], [11] using simple matched filer receivers. These schemes transmit a single BPSK symbol per sequence block duration, which limits the data rate to 1 bit per sequence. In addition, the decision-directed (DD) and differential DSSS approaches in [6], [11] require the channel coherence time to be at least two spreading sequence long, and are thus prone to channel variations. In this paper, we propose a coherent high reliability (HR- )DSSS scheme that also requires simple matched filter at the receiver to collect full multipath diversity. Unlike existing schemes, however, our HR-DSSS transmits multiple distinct symbols on multiple superimposed spreading sequences during each block. Among those symbols, one is used as the pilot for channel estimation and others carry data. Via the superimposed pilot, our HR-DSSS requires only one sequencelong channel coherence time, providing robustness against channel variation. In addition, our HR-DSSS also markedly increases the data rate, by transmitting multiple symbols per sequence duration, and by allowing for arbitrary modulations including QPSK, QAM etc. We will also prove that, in our HR-DSSS, inter-block-interference (IBI) is entirely eliminated, the self-interference due to multipath and the co-channel interference from simultaneously transmitted multiple symbols are controllable and negligible by our judicious design. Notation: Upper (lower) boldface letters are used for matrices (column vectors). ( ) H for Hermitian, ( ) T for transposition, ( ) for conjugation. I N denotes the N N identity matrix. denotes the floor, 2 the squared Frobenius norm of a matrix or vector, the norm of a scalar, E{ } the expected value, and [A] i,j denotes the element in the ith row and the jth column of matrix A. II. HIGH RELIABILITY (HR)-DSSS SCHEME A. Transmitted Signals In traditional DSSS systems, a single symbol is modulated per spreading sequence. In a vector form, the ith modulated signal block is: x(i) s(i)c, (1) MTS

2 where s(i) represents the ith transmitted symbol and c the spreading sequence. In [11], such a DSSS system was introduced to underwater communications, where the spreading code is the maximum length sequence (m-sequence). Here we also employ the m-sequence as the spreading code as in [11]. However, instead of transmitting one symbol per block as in (1), our HR-DSSS scheme simultaneously modulates multiple symbols on circularly shifted versions of an m-sequence during each block. Define the circular shift matrix as: [ ] 01 (M 1) 1 T :, (2) I M 1 0 (M 1) 1 which introduces a circular shift by 1 upon pre-multiplying an (M 1) vector. Accordingly, vector T j c is the circularly shifted m-sequence by j chips. Note that an m-sequence and its circularly shifted version has the following autocorrelation property: { c T T m M, m mod M 0, c (3) 1, otherwise. Hence, in a flat-fading channel, distinct symbols riding on c and T m c will induce negligible interferences among themselves, as long as the circular shift m 1. However, UAC channels are well known to have extensive multipath. Let τ max denote the maximum delay spread and T c as the chip duration. The multipath essentially spreads over (L +1) chips, where L : τ max /T c. (4) In order to separate the delayed multipath components of neighboring symbols, the circular shift between the m- sequences conveying adjacent symbols should be at least (L +1) chips. Hence, the transmitted signal block in our HR- DSSS is given by: x(i) s(i; j)t j(l+1) c, (5) j0 where s(i; j) is the jth transmitted symbol during the ith block, and the J is the number of superimposed sequences, at most M J max. (6) L +1 It is also worth mentioning that J max is the maximum number of symbols that can be simultaneously transmitted when the distribution and strength of the actual (and possibly sparse) channel taps are not available at the transmitter. If these information is also available, then it is possible to increase J max by smartly scheduling the signals. In addition, in a very low rate system, one can also choose to transmit J (2 J J max ) symbols to further reduce the inter-symbol interference. Note that in this design, the only information about the channel needed at the transmitter is the channel delay spread or an upper bound on it. B. UAC Channel Propagation The quasi-static channel model is widely adopted in radio frequency (RF) communications, where the propagation channel is assumed to be time-invariant within the channel coherence time. In UAC, the channel coherence time varies from about hundreds of milliseconds to tens of minutes [10]. For a typical UAC DSSS system with 10k chips per second using a spreading sequence consisting of about 1000 chips, the sequence block duration is about 100ms. Hence, it is reasonable to assume that the channel remains time-invariant within a sequence block and is allowed to change across blocks. For block-wise transmissions over multipath channels, the ith (M 1) received block r(i) contains not only the signals from the ith transmitted block, but also the IBI from the previous block. The I/O relationship in vector form can be written as: r(i) H(i)x(i)+H IBI (i)x(i 1) + z(i), (7) where the second term H IBI (i)x(i 1) is the IBI, the (M M) channel matrices are given by [H(i)] m,n h(i; m n) and [H(i) IBI ] m,n h(i; M + m n), form, n 1,...,M, and z(i) is the additive white Gaussian noise (AWGN). In order to eliminate the IBI in (7), at least two remedies are available (see e.g., [9]). One inserts a CP with length L to each block at the transmitter, and removes the CP at the receiver. The equivalent channel after CP insertion and removal becomes a circulant matrix. The other simply pads L trailing zeros to each block at the transmitter, giving rise to an Toeplitz channel matrix. Since we are going to separate the delayed multipath components of symbols by taking advantage of the circular autocorrelation property of m-sequences in (3), as will be detailed later, the circulant channel matrix is preferable. Therefore, we adopt the CP approach. After the CP insertion and removal on a block-by-block basis, the equivalent I/O is given by y(i) H(i)x(i)+z(i), (8) where the equivalent circulant channel matrix with the first column [h(i;0),...,h(i; L), 0 1 (M L 1) ] T. Using the circular shift matrix in (2), it can be re-expressed as H(i) h(i; l)t l. (9) With this block-wise equivalent I/O, the block index i will be dropped in the rest of the paper for notational brevity. C. Receiver Processing Substituting (5) and (9) into (8), we obtain the received block as: y h(l)t l s(j)t j(l+1) c + z j0 j0 s(j) h(l)t j(l+1)+l c + z. (10)

3 In (10), for each symbol s(j), the I/O relationship is transformed from one where a single sequence experiences a circulant multipath channel to one where (L+1) superimposed circularly shifted sequences, each being multiplied by a single channel tap. For all J symbols, we obtain J(L +1) superimposed different circularly shifted sequences, which are ready to be separated by the nice circular autocorrelation property of m-sequence in (3). Multiplying y by [T j(l+1)+l c] T, which is a circularly shifted sequence serving as a matched filter, we obtain v(j; l) [T j(l+1)+l c] T y Mh(l)s(j) v I (j; l)+η(j; l) where η(j; l) [T j(l+1)+l c] T z is the noise and v I (j; l) j 0 l 0 (11) h(l )s(j ), l l or j j (12) is the interference introduced by the sidelobe of the circular autocorrelation of m-sequences. Note that this term contains both the self-interference due to multipath, and the co-channel interference from multiple symbols transmitted simultaneously. We will show later that this interference is bounded, and practically negligible. In (11), we observe that all the delayed multipath components of all symbols are separated. We use one symbol (say, s(0)) as the pilot to form a channel estimate as v(0; l) ĥ(l), l 0, 1,...,L. (13) Ms(0) This channel estimate can be then used to demodulate the (J 1) data symbols as follows: ĥ (l)v(j; l) ŝ(j) M. (14) ĥ(l) 2 In the derivations above, the pilot and data symbols ride on the sequences in the same block; that is, the pilot and the data symbols experience exactly the same channel, even in the presence of channel variation. This ensures the reliability against moderate channel variation, as long as it is not severe enough to ruin the matched filter output in (11). It is also worth mentioning that our HR-DSSS does coherent detection without any phase ambiguity, which enables arbitrary modulations (we adopt QPSK in the sea experiments), not limited to BPSK. Fig. 1 shows the baseband transceiver diagram. At the transmitter, multiple symbols are modulated on different circularly shifted versions of an m-sequence, and the receiver only consists of the channel estimation and demodulation modules, which are illustrated in Fig. 2 and 3, where only simple matched filter is required. D. Performance Analysis In this subsection, we will analyze the interference term in (11) quantitatively. Consider phase modulation with s(j) 1 and independent channel taps with zero mean. Data c Data Pilot S/P. Add CP D/A Shift L +1 P/S ŝ(j) Fig. 1. y c ĥ Demod 1. Demod J 1 1 Ms(0) Shift L +1 Channel estimator Remove CP The baseband transceiver diagram. Shift 1 Shift 1 ĥ(0). ĥ(l) A/D Tx Channel Fig. 2. The channel estimation block in Fig. 1. Let us assume phase modulation with s(j) 1 and independent taps of the channel with zero mean. The following result holds: Proposition 1 Given the received signal after a simple matched filter, the signal-to-interference ratio (SIR) in (11) for any symbol is lower bounded by the m-sequence length M. When J equals J max in (6), this lower bound is very tight. Proof: In (11), the first term, the lth delayed multipath component of the jth symbol, is the signal and the second term v I (j; l) is the interference. Accumulating the signal and the interference energy from all (L +1) taps as the numerator and the denominator as in [3], we get the SIR for the jth symbol as y ĥ (0). ĥ (L) T j(l+1) c Shift 1 Shift 1 Decision Fig. 3. The jth demodulation block in Fig. 1. ŝ(j) Rx

4 Amplitude SIR(j) Delay (ms) Fig. 4. One snapshot of the channel in GOMEX { L } E h(l)s(j) 2 { L } E v I(j; l) 2 j 0 l 0 L E { h(l) 2} E { s(j) 2} E{ h(l ) 2 }E{ s(j ) 2 } E{ h(l) 2 }E{ s(j) 2 } L [J(L +1) 1] E { h(l) 2} E { h(l) 2} J(L +1) 1 J max(l +1) 1. (15) From (6), we know J max (L +1) M and thereby obtain the tight lower bound of SIR as M. The interference stated here includes the self-channel interference from the jth symbol itself (j j), and the co-channel interference from other symbols riding on other sequences (j j). In UAC, the channels have long delay spread, typically from 5 to tens of milliseconds. Fig. 4 shows one snapshot of the channels in the Gulf of Mexico Experiment (GOMEX), where the the channel delay spread is more than 20ms. With T c 0.2ms, we obtain the number of the delay taps as L 100 from (4). The block should be much longer than L for the CP to be sufficiently bandwidth efficient [9], such as M 511, 1023 or even larger. Therefore, the SIR in (15) is sufficiently high and the interference in (11) becomes negligible. In addition, the SIR can be further improved by reducing J, as shown in (15). III. DISCUSSIONS AND COMPARISONS A. HR-DSSS with Other Sequences In the preceding section, we described our HR-DSSS scheme transmitting J distinct symbols riding on J sequences simultaneously. For the J sequences, we adopted the circularly shifted versions of an m-sequence. Recall that it was its nice circular autocorrelation property with small sidelobe shown in (3) that ensures a high SIR. The natural question is whether it is possible to do better by employing any sequence with perfectly zero sidelobe to completely eliminate the interference? Binary zero correlation zone (ZCZ) sequences proposed in [1] have perfectly zero sidelobe within a certain shift zone that is a half of the sequence length M. Since the circular autocorrelation has a period M, without loss of generality, considering m [ M/2,M/2), wehave { c T T m M, m 0 c (16) 0, m [ M/4,M/4] for a ZCZ sequence c. From (16), we know that ZCZ sequence can be used instead of m-sequence in our proposed HR-DSSS. However, for the ZCZ sequences, because the shift region is reduced from M to M/2 and accordingly Jmax ZCZ M 2(L+1), the data rate is reduced by at least 50%. Thus, there is a tradeoff between the SIR and the data rate by choosing ZCZ sequences or m-sequences. As analyzed in the preceding section, the interference of using m-sequences is small enough to be negligible. From this point of view, the m-sequence seems to provide a better rate and error performance tradeoff than the ZCZ sequence, as we will show by simulations. B. OFDM The CP insertion and removal in Section II-B are also used in OFDM systems, which are extensively employed for multipath quasi-static channels. It can also be adopted to lowrate high-reliability systems by transmitting J(< M) symbols over M subcarriers in OFDM. Each symbol is repeated over (L +1) subcarriers so that full multipath diversity can be collected. This simple scheme provides the same data rate as our proposed HR-DSSS, but is interference-free. However, OFDM is much more sensitive to Doppler, which is inevitable in UAC, as we will verify in the next section. IV. SIMULATIONS In our simulations, the bandwidth is 10kHz and the carrier frequency is 14kHz. We choose the maximum delay spread as 20.3ms and accordingly L 203. The multipath power profile is e 0.1l. In { fading channels, the average channel gain L } is normalized as E h(i; l) 2 1. In all figures, the signal-to-noise ratio (SNR) is defined on a per symbol basis. In addition to our HR-DSSS (m-sequence) and HR-DSSS (ZCZ), we also simulate a low-rate OFDM scheme as described in Section III-B, and a decision-directed (DD-)DSSS scheme in [11, Section II-C] which uses the ith decoded symbol as the pilot for the (i+1)st symbol. For a fair comparison, we choose similar lengths of all sequences: M 1023 for the

5 QAM 10 1 BER BPSK HR DSSS (m sequence) HR DSSS (ZCZ) OFDM DD DSSS QPSK HR DSSS (m sequence) HR DSSS (ZCZ) OFDM DD DSSS SNR (db) Fig. 5. BER vs. SNR performance for the nonfading channels. m-sequence, M 1024 for the ZCZ sequence, and M 1025 subcarriers for OFDM. As a result, the data rate in all 4 schemes are (symbols/sequence duration): 4 for HR-DSSS (msequence), 1 for HR-DSSS (ZCZ), 4 for low-rate OFDM, and 1 for DD-DSSS. Next, we will present the simulation results in non-fading and fading channels separately. A. Time-Invariant Non-Fading Channels First, we consider HR-DSSS (m-sequence and ZCZ) and low-rate OFDM. With QPSK modulation, the HR-DSSS (msequence) and OFDM schemes have the same data rate, which is 4 times that of the HR-DSSS (ZCZ). As shown in Fig. 5, they provide identical performance. Recall that both the OFDM and HR-DSSS (ZCZ) schemes are strictly interference free. This comparison confirms that the self- and co-channel interference is indeed negligible in our HR-DSSS (m-sequence) scheme as indicated by Proposition 1. Then, we compare HR-DSSS (m-sequence and ZCZ) with DD-DSSS, both using BPSK modulation. Typical decisiondirected (DD) operations can lead to error propagation. In our simulations, we assume that the ith symbol is perfectly known when being used as the pilot for the (i +1)st symbol; that is, the error propagation effect is neglected in our simulations. With BPSK modulation, this is essentially a differential DSSS scheme as detailed in [11, Section II-D]. Fig. 5 shows that all three give similar performance, with HR-DSSS (ZCZ) being slightly better. This is because HR-DSSS (ZCZ) is strictly interference free, while HR-DSSS (m-sequence) suffers from self- and co-channel interference and DD-DSSS suffers from self- and inter-symbol interference. Clearly, both interferences are negligible. In the previous comparison, all three schemes use the same modulation but have very different data rates. With BPSK modulation, the HR-DSSS (m-sequence) gives 4 bits/sequence duration, whereas the other two only give 1 bit/sequence duration. To equate their rates, we simulate HR-DSSS (ZCZ) and DD-DSSS again with 16QAM, leading to 4 bits/sequence. The BER curves are also plotted in Fig. 5. We observe that Fig. 6. BER vs. SNR performance for the time-varying fading channels with f max 4.7Hz both significantly underperform the HR-DSSS (m-sequence) at the same rate (BPSK) or double rate (QPSK). B. Time-Varying Fading Channels To simulate time-varying fading channels, each channel tap is generated according to independent Rayleigh distributions, and using Jakes model [2] with a maximum Doppler of f max 4.7Hz. Here we use QPSK for all four schemes. Hence, HR-DSSS (m-sequence) and OFDM provide 4 times the data rate of HR-DSSS (ZCZ) and DD-DSSS. The BER performance is shown in Fig. 6. We observe that: i) the OFDM scheme exhibits significant performance degradation due to the Doppler-induced inter-carrier interference; ii) the DD-DSSS scheme has nearly 50% error rate because the channel changes from one symbol to another, rendering the decision-directed or differential operations ineffective; and iii) our HR-DSSS with both m-sequence and ZCZ provides the best performance, and remains robust against channel variation. V. EXPERIMENT RESULTS A. GLINT08 Sea Experiment With the help of Woods Hole Oceanographic Institution (WHOI), GLINT08 sea experiment was held in the area around Pianosa, south of Elba, off Italy in July The water depth was up to 100m. The sample rate at the transmitter and the receiver is 250kHz, the carrier frequency is 14kHz and the chip rate is f s / k/s. Assuming the maximum delay spread is no more than 19.6ms, we choose the CP length and the phase shift step of m-sequences as 204. The m-sequence length is chosen as M 1023 so that each sequence duration contains J 5symbols. One is used as pilot and the other 4 as data. With QPSK modulation, the data rate is 68bps. During 5 days of the experiment, we collected a total of 51 packets, with various settings including different ranges and station moving speeds. Each packet contains 480 data bits collected by the 4 vertically placed hydrophones in the experiment. Thus, each packet provides bits

6 TABLE I UNCODED BER FOR COHERENT DSSS WITH A SINGLE HYDROPHONE IN GLINT08 Date Range Moving speed Demodulated packets All bits Error bits Failed packets July m Anchored July m 0 0.9knots July m knots July m Anchored July m Anchored experiment is shown in Fig. 7, where we observe significant Doppler. We do not adopt any complicated Doppler estimation and compensation techniques, but simple carrier frequency offset (CFO) estimation by an OFDM preamble. There are only 2 erroneous bits out of all It confirms that our proposed HR-DSSS scheme is reliable. Delay (ms) 5 0 Fig Doppler (Hz) The scattering function in the GOMEX experiment. for performance evaluation. Table I shows the uncoded BERs with only 1 hydrophone, by a simple matched filer without resorting to any Doppler estimation or compensation. From the table, we observe that in 49 out of all 51 packets, our HR-DSSS scheme achieves nearly 0 uncoded BER. There are 2 packets that cannot be demodulated due to the very low SNR. Combining all the available 4 hydrophones, we get 0 error for all 49 packets. The outstanding performance in the experiment confirms that our proposed HR-DSSS scheme with m-sequence is reliable, whenever the station is fixed or moving. B. GOMEX sea experiment With the help of Naval Research Laboratory (NRL), GOMEX sea experiment was held in the area south of Mobile, Alabama in The water depth was 92 97m, the transducer and the hydrophones were placed 46 56m and 37 47m below surface, and the range was approximately one nautical mile, 1852m. In the GOMEX sea experiment, the sample rate is 80kHz, the carrier frequency is 20kHz and the chip rate is 5k/s. The m-sequence length is M 511, thecp length and the phase shift step of the m-sequences are chosen as 127, and thereby each sequence duration contains J 4 symbols. With QPSK modulation, the data rate is 47bps. We collected a total of 15 packets, each of which contains 540 data bits. From 8 hydrophones in the experiment, a total of uncoded bits are available for analysis with a single hydrophone. The delay-doppler scattering function of one packet in the VI. CONCLUSIONS In this paper, we developed a HR-DSSS scheme that provides high reliability UAC communications with a simple matched filter receiver. Different from existing DSSS approaches, we transmit multiple symbols modulated on the shifted versions of an m-sequence during each sequence duration. We showed that our judicious design can enhance reliable channel estimation and symbol demodulation in the presence of channel variation, as well as enable higher data rate with negligible (self- and co-channel) interference. Simulations and experiment results confirmed that our HR-DSSS scheme provides high-quality performance even with a single hydrophone. We have also shown that it is operational with QPSK modulation without any chip-level equalization. REFERENCES [1] P. Z. Fan, N. Suehiro, N. Kuroyanagi, and X. M. Deng, Class of binary sequences with zero correlation zone, IEEE Electronics Letters, vol. 35, no. 10, pp , May [2] W. C. Jakes, Microwave mobile communication. New York: Wiley, [3] F. C. M. Lau, Achievable-SIR-based predictive closed-loop power control in a CDMA mobile system, IEEE Trans. on Vehicular Tech., vol. 51, no. 4, pp , July [4] G. Leus and P. van Walree, Multiband OFDM for covert acoustic communications, IEEE Journal on Selected Areas in Communications, vol. 26, no. 9, pp , December [5] G. Leus, P. Walree, J. Boschma, C. Fanciullacci, H. Gerritsen, and P. Tusoni, Covert underwater communications with multiband OFDM, in Proc. of MTS/IEEE Oceans Conf., Quebec, Canada, September 15-18, [6] S. Mason, S. Zhou, P. Gendron, and W. B. Yang, A comparative study of differential and noncoherent direct sequence spread spectrum over underwater acoustic channels with multiuser interference, in Proc. of MTS/IEEE Oceans Conf., Quebec, Canada, September 15-18, [7] M. Stojanovic and L. Freitag, Multichannel detection for wideband underwater acoustic CDMA communications, IEEE Journal of Oceanic Engineering, vol. 31, no. 3, pp , July [8] P. van Walree, E. Sangfelt, and G. Leus, Multicarrier spread spectrum for covert acoustic communications, in Proc. of MTS/IEEE Oceans Conf., Quebec, Canada, September 15-18, [9] Z. Wang and G. B. Giannakis, Wireless multicarrier communications, IEEE Signal Processing Magazine, vol. 17, no. 3, pp , May [10] T. C. Yang, Measurements of temporal coherence of sound transmissions through shallow water, Journal of the Acoustical Society of America, vol. 12, no. 5, pp , November [11] T. C. Yang and W. Yang, Performance analysis of direct-sequence spread-spectrum underwater acoustic communications with low signalto-noise-ratio input signals, Journal of the Acoustical Society of America, vol. 123, no. 2, pp , February 2008.