A Blind Receiver for Digital Communications In Shallow Water Andreas Waldhorst, Rolf Weber and Johann Böhme Signal Theory Group, Ruhr-Universität Bochum, 44780 Bochum, Germany email:
[email protected] Abstract–In spring 1999, a sea trial in the coastal region of the Dutch North Sea has been conducted in the scope of the EU-MAST III project ROBLINKS to obtain underwater acoustic data for digital communication in shallow water environments. In this paper, we propose a blind receiver architecture and present results of its application to some specific communication signals transmitted during the experiment. The receiver structure used in the analysis is based on a self-trained adaptive equaliser, designed to jointly process the signals from the vertical receiver hydrophone array and to perform the tasks of timing and carrier recovery. The experimental results demonstrate that self-recovering equalisation for coherent communication in shallow water is possible over a range of several kilometres with data rates exceeding 3kbit/s.
I. I NTRODUCTION As there is a growing need for fast and reliable underwater acoustic transmission of large amounts of data, e.g. in the fields of coastal-zone monitoring and communication between submersibles, numerous research activities have focused on digital communication techniques in underwater acoustics during the past years [1], [2]. In connection with the limited bandwidth of the underwater communication channel, so-called ‘blind’ transmission techniques, which avoid the requirements of initial, periodically recurring or permanent training signals, have also become an issue of increasing interest. The EU-MAST III project ROBLINKS was initiated to address the problem of communication through shallow water environments with depths below 20 meters and over ranges between 1km and 10km [3]. The aim is to establish a robust communication link over the horizontal shallow water channel, where ‘robust’ has to be understood in the sense that the transmission should have the least possible sensitivity to channel and noise effects. In this context, reliability of the transmission is given the first priority, especially over data rate which is to be sacrificed in favour of increased safety of the data link. The additional requirement of being bandwidth efficient and the aim of a data rate exceeding 1 kbit s makes the application of coherent communication techniques necessary. Here, we address the problem of practical blind, i.e. selfrecovering equalisation, being one topic under study in the ROBLINKS project among other techniques which make use
of reference signals [4]. Among the abundance in literature for blind equalisation approaches (see, e.g. [5]), we focus in this work on an adaptive equaliser structure based on the Bussgang family of algorithms 1 . One reason for this strategy is the fact that algorithms derived from the Bussgang family have been successfully applied in practice already. This is also true for acoustic telemetry which is indicated by, e.g. [6], [7] and [8]. In the two latter references, the Bussgang principle is linked to special variants of the decision-feedback equaliser (DFE) with embedded PLL [9], [10]. Another reason is that an adaptive scheme seems to be the most appropriate solution to compensate for the dispersive and time-varying effects of the medium on the transmitted signal while an adaptive or recursive formulation for most alternative blind equalisation methods still remains to be developed. Another issue is its relative insensitivity to the channel order which is generally difficult to acquire in practice. Furthermore, it appears that adaptive equalisers allow an easier integration of synchronisation structures as opposed to other blind methods which often rely on perfect timing. However, the necessity of synchronisation becomes apparent in view of the fluctuating and possibly large Doppler shifts which are typical for the underwater channel. As a last point, in our application it was also important to keep the computational complexity low to make a possible real-time implementation feasible [3].
A. Signal Design Aspects To design a blind communication system, yet as reliable as possible in a shallow water environment, we made the following choices regarding the signalling schemes under the constraint that the acoustic source allowed the use of a frequency range from 1 kHz to approximately 12 kHz. To keep the influence of signal phase distortions small, we used Offset Quadriphase-Shift Keying (OQPSK) as a simple PSKmodulation format. Beside a reduction of the signal envelope variation, this scheme forces transitions between adjacent symbols which facilitate the operation of a timing recovery unit in the receiver. To avoid determination of the absolute carrier phase, the information has been differentially encoded onto the symbols. Similar as in the case of BPSK, estimates of the synchronisation parameters do not need to be very accurate for OQPSK, while a successful symbol detection 1 The Bussgang family includes the decision-directed algorithm, the Sato
algorithm, and the constant-modulus algorithm (CMA)
is still possible. Insensitivity to symbol timing uncertainty at the expense of spectral efficiency is supported by using 100% excess-bandwidth in the modulation pulses. To further have the opportunity of exploiting spectral diversity, the same information has also been transmitted in several parallel frequency bands in some signals. The increase of the total signal’s peak-to-average ratio resulting from this multi-carrier approach is counteracted by varying the initial phases of each sub-carrier.
II. R ECEIVER A RCHITECTURE A. Overview O&M Alg. ε^
-j ωckTs
e r1 (kTs)
hRF (kTs)
B. Receiver Design Aspects In connection with the receiver architecture, we address the problem of fully digital timing recovery explicitly for the following reasons: (i) also symbol timing, beside carrier phase, is subject to Doppler effects, (ii) relatively long continuous signals (60 s – 400 s) have to be demodulated, (iii) due to the blind nature of the receiver, no reference signal frames can be used to resolve timing, and (iv) the acoustic data were obtained by fixed-rate sampling of the sensor outputs. We prefer the use of a separate unit to perform clock recovery rather than leaving this additional task to the equaliser as is commonly done. Instead of using a fractionally-spaced equaliser for these two purposes [11], we propose a combination of feedforward clock recovery and baud-spaced equalisation. On one hand, this allows to keep the equaliser simple and on the other hand, especially in connection with the large signal durations, it minimises the risk that the respective portions of the signal, each corresponding to the currently detected symbol, gradually run out of the equaliser taps. In addition, a higher efficiency is to be expected from a system which consists of a separate synchroniser and equaliser unit since each of them can be specifically designed to perform their special tasks. Moreover, blind equalisation is often desirable in situations of burst-mode operation where rapid acquisition plays a key role. As will be shown, the proposed system is well suited to operate under such conditions in connection with shallow water communication. In view of a possible real-time implementation, we headed for a (sub-optimal) baud-rate multichannel equaliser to keep the computational complexity low. However, the presented structure can readily be extended to a fractionally spaced form. As no training signal is available, the receiver can only exploit the basic characteristics of the modulation format. It is therefore important to build the equaliser as closely as possible upon the OQPSK pattern selected here. The paper is organised as follows. In section II, we present the receiver architecture and the associated algorithms. Section III gives a brief description of the experiment and some important channel characteristics. The performance of the receiver with experimental data is finally examined in section IV.
Multichannel Equalizer and Phase-Offset Compensator
-j ωckTs
e r N-1 (kTs)
hRF (kTs)
-j ωckTs
e r N (kTs)
hRF (kTs)
Mixer
Receive Filter
Timing Est. / Resampler
Figure 1: Multichannel receiver architecture
An overview of the proposed blind space-time-processing algorithm is shown in Fig. 1. It uses fixed-rate oversampled data r1 (kTs ), ..., r N (kTs ) coming from a vertical array of N hydrophones. The passband communication signals are first frequency translated to baseband using the nominal carrier frequency ω c , differing from the actual one because of Doppler. Additional input channels can be obtained by processing a multi-carrier signal. The succeeding receive filters with impulse responses h R F (kTs ) consist of a cascadation of a low-pass and a pulse-matched filter which in our case is root-raised cosine pulse with roll-off factor α = 1. Timing information is extracted from one sensor signal yielding the estimate ˆ of the fractional symbol delay , representing the misalignment between the receiver and transmitter sampling grids, is restricted to || ≤ 12 . It is used to dynamically adjust the sampling rate on all input channels simultaneously. This results in baud-rate samples of the signals impinging on the different hydrophones which are fed into the joint decision-directed multichannel equalisation and carrier recovery unit. To obtain these symbol decisions, we introduce a ’toggling decision rule’ which exploits the OQPSK modulation format and allows for a blind system startup. The equaliser coefficients are adjusted under the minimum mean-squared error criterion using a simple gradient-type complex LMS algorithm. The residual time-varying carrierphase offset is compensated for using a second order decisiondirected digital phase-locked loop (PLL) which is updated in conjunction with the filter coefficients.
B. Timing Recovery
estimates using
Timing recovery is accomplished in two steps, (i) timing estimation and (ii) timing adjustment. The feed-forward timing estimator we applied is based on the principle introduced in [12], which we have slightly modified. It exploits the (wide-sense) cyclo-stationarity property of the baseband communication signal. The basic idea is to derive the squared signal’s spectral component c 1,n at the baud-rate T1 from its complex Fourier coefficient whose phase leads to an unbiased estimate of the fractional symbol delay . It is free of hangup, independent of the transmitted data and carrier phase, has a rapid acquisition and allows efficient implementation. Though originally derived for AWGN channels, the application of this technique to our problem showed a relatively low channel distortion sensitivity. The timing estimator chain is depicted in Fig. 2. Let z(kTs ) be the received, fixed-rate sampled and filtered baseband communication signal from one input channel. As linear pulse amplitude modulation is considered, we may write z(kTs ) =
an h(kTs − nT − T ) e j θ + m(kTs ).
(1)
n=−∞
The transmitted symbols are represented by {a n } and assumed to be mutually uncorrelated. h(t) includes the transmit and receive filter of the communication system as well as the channel impulse response. As before, T denotes the symbol duration and the fractional symbol delay (it is assumed that the beginning of the transmission has been previously detected). A residual carrier phase offset is represented by θ and m(t) is an additive (filtered) noise process. The scale of temporal variation of the synchronisation parameters and θ is assumed to be large with respect to the symbol duration. Note that in (1), we have dropped their explicit temporal dependence to simplify the notation. It will, however, appear in the sequel, when estimates of these quantities are considered. After computing the squared magnitude of this signal, the phasor cˆ1,n is determined from M successive samples x k for each symbol n, according to M−1
xl+nM e− j
2π Ml
,
n = 0, 1, ...,
(2)
l=0
with x k = |z(kTs )|2 . M is the nominal oversampling factor with respect to the symbol rate. Because of Doppler and sampling clock deviations, only the approximate relation M ≈ T Ts holds and M cannot even be assumed to be a rational number. In a further step, cˆ 1,n is averaged over successive z(kTs)
2 xk M−1 l=0
− j 2π Ml
xl+n M e
c^1,n
Smooth αsm
Figure 2: Feed-forward timing estimator
c~1,n
arg(·) − 2π
ε^ n
Unwrap
εn ~
(3)
where αsm is a small number controlling the degree of the smoothing process but also affecting the transient behaviour of the estimator. This step is important as it reduces the variance of the timing estimates and thus decreases jitter caused by channel and noise. In contrast to the original formulation, we apply this smoothing step directly, without first computing the average over non-overlapping blocks containing a fixed number of symbols. The estimate ˆ n , being computed for each set of M signal samples is obtained from ˆn = −
1 arg(c˜1,n ). 2π
(4)
Finally, the estimates ˆn need to be unwrapped, as their values are restricted to the basic interval [− 12 , 12 ] but parameter drifts exceeding this range must be tracked as well. Therefore, ˜n = ˜n−1 + saw (ˆn − ˜n−1 )
∞
cˆ1,n =
c˜1,n = c˜1,n−1 + αsm (cˆ1,n − c˜1,n−1 )
(5)
is computed, where saw(x) denotes the ’sawtooth’ function with saw(x) = x, for − 12 ≤ x < 12 being periodically continued outside this interval. In order to obtain the desired baud-spaced samples z(nT + T ) from z(kTs ), timing adjustment is performed by digital interpolation and decimator control, [13], [14]. The unknown symbol instances are first expressed in terms of the receiver time scale defined by the times kTs . Introducing the timing parameters m n (basepoint) and µ n (fractional delay), one obtains T T Ts nT + T = n + (6) Ts Ts = (m n + µn ) Ts (7) with m n being defined by T T , mn = n + Ts Ts
(8)
where x denotes the greatest integer less than or equal to x. It follows that 0 ≤ µn < 1 and using the estimate ˆ n for and M as the nominal value for TTs , the timing parameters can be determined. Their recursive computation from the estimated symbol delay variation ˆ n = ˆn − ˆn−1 is obtained via (9) m n+1 = m n + µn + M (1 + ˆn )
µn+1 = µn + M (1 + ˆn ) mod 1 . (10) For starting values, the trivial initialisations µ 0 = 0 and m 0 = 0 may be used. Approximation of the samples z(nT +T ) = z[(m n +µn )Ts ] is carried out in two steps. First, interpolation using an FIRfilter with time-varying coefficients is performed to obtain
π z[(k − l)Ts ] si (lTs +µn Ts ) (11) Ts
l=−∞
≈
L2
z[(k − l)Ts ] h I (lTs , µn ) =: y(k)(12)
l=L 1
where si (x) is defined by si (x) = sinx x and h I (lTs , µn ) is an FIR interpolator impulse response depending on the fractional delay µn . It is well justified [15], to use a simple polynomial, or even linear interpolator for this task, so that for the latter case h I (kTs , µn ) becomes l=0 µn h I (lTs , µn ) = 1 − µn l = 1 (13) 0 otherwise with L 1 = 0, L 2 = 1 in (12). From (12), only the subset of samples {y(m n ) ≈ z[(m n + µn )Ts ]} needs to be computed out of {y(k)}. Therefore, a second, time-variant decimation step is used to select the samples indicated in the sequence of basepoints {m n }.2 Although the entire process of timing extraction and resampling would be required for each individual input channel, we follow the simpler procedure of estimating timing from a single channel. All hydrophone outputs are then resampled based on the same parameter sets {(m n , µn )} resulting from these estimates. This method still leads to very satisfactory results. However, it leaves the part of timing adjustment associated with inter-sensor timing fluctuations to the equaliser.
C. Blind Adaptive Equalisation and Carrier Recovery A simplified signal flow-graph of the equaliser and phase synchroniser is shown in Fig. 3. It is similar to a multichannel version of the scheme introduced in [16]. The baud-spaced samples y 1,n , ..., y N,n of the N-element sensor array obtained from the previous timing recovery step enter a bank of N length L adaptive FIR filters. Their coefficients at (symbol) time index n are represented by the L-element vectors c 1,n , ..., c N,n . The filter outputs are all added to produce an equalised symbol q n which is further processed in the subsequent decision-directed phase-locked loop (DDPLL). We first describe the equaliser adaptation procedure. The last baud-rate array observations are stacked into the multichannel delay line d n according to T (14) d n = y1,n , .., y1,n−L+1 , ..., y N,n , .., y N,n−L+1 , 2 Equivalently, interpolation may only be performed at times (m + µ )T . n n s
The filter bank output is therefore given by qn = w nH d n ,
(17)
denoting the complex conjugate transpose by (·) H . Given the rotated symbol estimate qˆ n provided by the PLL, the instant error en is en = qˆn − qn .
(18)
A simple complex gradient-type update algorithm for the filter coefficients yields wn+1 = w n + β d n en∗ ,
(19)
where β is the small, real-valued step size parameter and e n∗ is the complex conjugate of the instant error. The computational steps of the DD-PLL are the following. The equaliser output q n is first ’de-spun’ by the phase-offset estimate θˆn computed from the last iteration: ˆ
yn = q n e− j θ n .
(20)
Based on yn , a tentative decision aˆ n on the transmitted symbol is made in the toggling OQPSK slicer, represented by the complex non-linear function g(x, n), so that aˆ n = g(yn , n).
(21)
The slicer g(x, n) is defined by: switching OQPSK slicer
DD-PLL
y 1,n
c- 1,n
qn
+
yn
e
y (N-1),n
-c (N-1),n
a^ n
+
z[(k + µn )Ts ] =
∞
where the superscript T denotes vector and matrix transpose. A vector of filter bank tap weights is defined accordingly: T T , ..., c TN,n (15) wn = c1,n T (16) = w1,n , ..., w L N ,n .
-j( )
phase comput. & loop filt.
+ θ^ n
yN,n
c-N,n
en
e
+
j( )
q^ n
+
samples corresponding to z[(k + µ n )Ts ]:
Figure 3: Multichannel equaliser with DPLL
+j −j g(x, n) = +1 −1
Im {x} ≥ 0 ∧ n = 2l + 1 Im {x} < 0 ∧ n = 2l + 1 Re {x} ≥ 0 ∧ n = 2l Re {x} < 0 ∧ n = 2l
(22)
and l ∈ . As is clear from (22), the slicer distinguishes between even- and odd-indexed symbols, toggling its decision regions between two perpendicular BPSK constellations (see Fig. 4). This exactly takes into account the permitted symbol transitions associated with OQPSK. An extension of this concept can readily be made so that fractional samples can be processed in an equivalent manner. After slicing, the rotated symbol estimate qˆ n is obtained from qˆn = aˆ n e
j θˆn
.
(23)
Then, the angular phase difference between y n and the estimated symbol aˆ n is computed by θˆn = Im yn aˆ n∗ . (24) This quantity is processed in a loop filter and integrated to get an update of the phase estimate for the next iteration: θˆn+1 vn+1
= =
θˆn + α1 θˆn + vn vn + α2 θˆn
(25) (26)
This corresponds to a second order type II loop with filter coefficients α1 , α2 and its state variable vn . Equations (25) and (26) complete one iteration of the algorithm. To obtain its starting values, the common central tap initialisation strategy can be applied for w n . The initial carrier phase estimate is normally θˆ0 = 0. An a-priori known frequency offset may be used to set the initial state-value v 0 in order to speed-up acquisition. Otherwise, use v 0 = 0. As differential encoding is applied, the initial symbol parity for the slicer can arbitrarily be set to even, resulting in the slicer regions defined by the last two lines of (22). To obtain a good dynamic behaviour of the coupled system, the phase synchroniser should be able to react more rapidly than the ISI equaliser to provide the latter with reasonably phase compensated symbol decisions. We therefore usually selected α1 about a factor of 10 larger than the value for β.
TABLE 1 R ECEIVER PARAMETERS USED FOR DATA ANALYSIS
Parameter M L β α1 α2 αS M
α1 10 10−3
IV. E XPERIMENTAL R ESULTS This section presents a selection of results obtained from the application of the proposed receiver to the acoustic data gathered during the ROBLINKS trial. Three signals recorded on three different days are examined in this work: A. fixedpoint to fixed-point transmission over 2 km at 3.77 kbit/s data rate, B. fixed-point to fixed-point transmission over 5km at
a2l+1
1 Re{an } -j
Figure 4: Constellation switching for OQPSK-symbol detection
0.01
Fig. 5 shows a sketch of the experimental setup for the sea trial which was carried out in spring 1999, a few kilometres off the coast of the Netherlands. Additional details can be found in [17]. A quasi-omnidirectional source was lowered to a depth of approximately 9 m below the sea-surface from the stern of the research vessel Tydeman and served as the transmitter. The signals were received by either of two vertical arrays, the one consisting of 20, the other of 6 hydrophones. These arrays were fixed to the oceanographic platform ’Meetpost Noordwijk’. The water depth in this area varies between 18 and 22 m. The 20-element array (array 1) sampled the sound field from a depth of 4.4 m to 15.8 m with equally spaced sensors. The smaller array (array 2) consisted of 6 hydrophones placed in pairs, separated horizontally by 15 cm and at depths of approximately 7, 11 and 15 m. The Tydeman anchored at various positions with distances of 1, 2, 5 and 10 kilometres from the platform to carry out fixed-point to fixed-point transmissions. In addition, the ship was sailing at moderate speed on the last two days to obtain measurements from a moving platform.
a2l
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III. T RIAL
Im{an } +j
Value 3 20
Figure 5: Experimental Setup
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1.56 kbit/s, and C. moving point to fixed-point communication over approximately 4.7 km at 1.56 kbit/s. No signal specific receiver parameter fine-tuning has been made. The quantities listed in Table 1 are used for all detections described here. Differences regard the array type, the number of sensors used, the channel from which timing is extracted and signal carrier frequencies (see below). Results are summarised in Figures 6, 7 and 8 containing the following information. Sub-figure a) shows the channel responses measured by matched filtering of a 200 ms linear FM pulse from 1 kHz to 5 kHz, transmitted a few seconds before the communication signal; b) gives a scatterplot of the received symbols, i.e. after resampling, obtained from the sensor used for timing estimation; c) shows the evolution of the carrier phase as compensated by the PLL during signal reception. To get an idea of the amount of Doppler effects, a spectral analysis of the phase fluctuation is also shown immediately below this graph. Next to the phase plots, we find the drift and spectrum of the timing offset. A constant Doppler shift, i.e. a linear trend in the carrier and timing phase, has been previously removed in these graphs. The bottom left of the figure presents the output scatter of the receiver (symbols {y n }) and on the right, the estimated a-priori mean-squared error is shown versus time. It is obtained from smoothed samples of {|e n |2 }. Bit error rates (BER) have also been computed. The values given below all refer to uncoded transmission.
0
-8 -0.5
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A. 2km-Distance
-1
This signal was analysed using sensors 1, 3 and 5 of array 2 with the first channel being used for timing extraction. Its nominal carrier frequency was 4618 Hz and the transmission lasted for 27.28 s. As can be seen from Fig. 6a) showing the results for all 6 array elements, significant channel impulse response lengths are approximately between 10 ms and 15 ms corresponding to 38 to 57 symbols at the given baud-rate of 3772 s−1 . The close vicinity of sensors (1,2), (3,4) and (5,6) is reflected by the associated channel responses, showing a certain degree of correlation in these pairs. Doppler variations do not significantly exceed 0.25 Hz. The input-SNR was about 27 dB for this signal. The receiver achieved a bit error rate of 9.98·10 −5 with an estimated output-SNR of ≈ 9.31 dB. It is defined by SNRout = 10 log10
1 Ns
|an |2 , Ns 2 n=1 |aˆ n − yn |
(27)
where Ns is the number of received symbols (in all three cases, Ns = 100224).
B. 5km-Distance The second signal under analysis has the bit-rate 1561 s −1 and the carrier frequency is now 3079 Hz. Mainly due to the larger distance from the source, the input-SNR has decreased to approximately 25 dB. Since the same amount
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Figure 6: Distance: 2 km; Data rate: 3.77 kbit/s; Sensors 1,3 and 5 of array 2; SNR≈27 dB
of data symbols as in A. have been transmitted, the signal duration is now 65.28 s. Again, three sensors have been used for demodulation; but this time, the first array with the larger aperture was applied. We picked sensors 1, 7 and 13 for processing, resulting in a sensor spacing of 3.6 m. Timing was again estimated from the first sensor. As evident from Fig. 7a) which shows the channel responses obtained at 7 equi-spaced hydrophones, the range of propagation delays to the array elements is larger than in the former case. The Doppler frequency range is somewhat lower than in A. For both experiments, the Doppler effect has probably mainly to be attributed to oscillating movements of the source, caused by sea-surface motion. The transmission resulted in a BER of 4.29·10 −4 at an output-SNR of 12.46 dB.
C. Moving Source The greatest challenge was put on the receiver algorithm by processing the third signal. It was recorded while the Tydeman headed for the platform at a constant speed of approximately 4 knots. The transmission distance at the beginning of the signal was about 4.7 km. Beside the movement of the
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1.5
Figure 7: Distance: 5 km; Data rate: 1.56 kbit/s; Sensors 1,7 and 13 of array 1; SNR≈25 dB
Figure 8: Distance: 4.7 km; Data rate: 1.56 kbit/s; Sensors 1-6 of array 2; SNR≈15 dB
transmitter itself, causing an increased temporal variability of the communication channel, the receiver has to cope with additional masking, attenuation and interference effects induced by the ships hull and the propeller revolutions affecting the sound radiation from the source. The signalling parameters are identical to case B. Now, all 6 sensor outputs of the second array are integrated in the equalisation process. Timing is estimated from the 3rd hydrophone. The input-SNR is determined as approximately 15 dB in the communication band. It becomes clear from Fig. 8c) and especially d), that the stronger interferences and higher temporal fluctuations of the medium result in a considerable amount of timing (and phase) jitter, increasing the MSE. However, the receiver still manages to demodulate the signal, achieving a BER of 1.59·10 −3 with 8.49 dB output-SNR. The mean Doppler shift compensated by the algorithm is approximately 3Hz for this transmission.
is driven by the outputs of a toggling slicer for detection of OQPSK signals. The satisfactory performance of the system in its application to experimental data for shallow water communications under various operational and environmental conditions makes it a good candidate for solving the problem of blind equalisation in the given context.
ACKNOWLEDGEMENT We greatly acknowledge the teams of TNO and Thomson Marconi Sonar as well as the crews on board the HNLMS Tydeman and on the Meetpost Noordwijk for their valuable work and collaboration that lead to the successful execution of the ROBLINKS sea trial. This work is funded by the European Commission — DG XII under Contract No. MAS3-CT97-0110.
C ONCLUSION
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