BLIND RECEIVERS FOR MSK SIGNALS TRANSMITTED THROUGH SHALLOW WATER Rolf Weber, Andreas Waldhorst, Florian Schulz, and Johann F. B o¨ hme Ruhr-Universit¨at Bochum, Signal Theory Group, 44780 Bochum, Germany E-mail:
[email protected] ABSTRACT
(FSK) [3] were the method of choice as they were seen intrinsically robust to the time and frequency spreading of the channel. Although reliable, the inefficient use of bandwidth together with the limited availability of bandwidth underwater makes incoherent systems ill-suited for high data rate applications. To increase efficiency, phase-coherent systems should be employed, which was thought to be impossible due to the time variability and dispersive multipath of the medium. It was only in the early 1990’s that Stojanovic, Catipovic, and Proakis successfully demonstrated that long range, high-rate coherent data transmission is possible by jointly optimizing an adaptive multichannel equalizer together with a phase-locked loop (PLL) [4]. However, in a time-varying environment the training of the equalizer implies the recurrent transmission of known data sequences, which especially in adverse environments reduces the effective data throughput considerably. Therefore, blind equalization methods suitable for UWA communication purposes represent an important alternative and are the topic of current research [5, 6, 7, 8]. The EU-MAST III project ROBLINKS has been initiated to address the problem of data transmission through shallow water of depth less than 20 meters over distances between 1 and 10 kilometers [9]. The aim has been to establish a robust communication link over the horizontal shallow water channel, where robust denotes the least possible sensitivity of the transmission to channel and noise effects. Reliability has therefore been preferred over e.g. data rate, which has been sacrificed in favor of an increased safety of the communication link. The minimal requirements, however, have been a data rate exceeding 1 kilobit per second at a horizontal range of at least 2 kilometers, and bandwidth efficient signalling, which requires a coherent receiver. Among other transmission strategies [10, 11], special emphasis has been put on practically working blind receivers. The proposed blind receiver structures are fully digital, and - unlike most other work on equalization for UWA communications - special emphasize is put on blind digital timing recovery to enhance the performance of the receiver. Timing recovery is necessary because like the carrier phase, symbol timing is subject to Doppler effects. The compensation could be left to the equalizer [12], which is able to perform this task as long as the corresponding time span of the equalizer is longer than the cumulated time offset during transmission. As we are interested in demodulation of rather long data sequences (60-400 seconds), however, and to restrict the tasks
In this paper, blind receivers for minimum shift keying signals transmitted through shallow water are proposed. After having introduced the modulation scheme and its favorable properties, two different blind receiver structures are studied. The first processing step in both cases is explicit non-dataaided timing recovery, a task that has often been neglected in other work. Then, joint blind adaptive multichannel equalization and phase recovery is performed. The adaptive setting of the equalizer is attained by either the constant modulus algorithm or a decision-directed approach. Both structures have been tested with measured shallow water data gathered during the ROBLINKS 1999 sea trial. The obtained results suggest MSK as a useful modulation scheme for underwater communications and demonstrate that completely blind processing of the received signals is possible. 1. INTRODUCTION For the past decade, there has been a tremendous increase in research and development of underwater acoustic (UWA) communication systems. This growing interest in UWA communications was the response to the increasing demand for wireless underwater communications, which was initiated by a shift in applications from almost exclusively military to commercial ones. Examples for such commercial applications of UWA communications are remote control in off-shore oil industry, coastal-zone monitoring, and communication between submersibles. This development has been accompanied by an ever growing need for higher data rates to cope with the huge amount of data to be transmitted over large distances. Typical data rates range from a few kilobits per second for simple command and control tasks up to hundreds of kilobits per second for video image transmission [1]. These desired high data rates are in contrast to the transmission conditions induced by the underwater acoustic telemetry channel, which is bandlimited and reverberant, thus posing many obstacles to reliable high-speed digital communications. Therefore, combating the time-varying multipath induced by the transmission channel especially the horizontal shallow water acoustic channel - is considered the most challenging task [2]. For a long time, incoherent modulations schemes like frequency-shift keying This work was supported by the MAST directorate of the European Commission under contract MAS3-CT97-0110.
MTS 0-933957-28-9
1
of the equalizer to inter-symbol interference (ISI) reduction, time synchronization should be better performed by a separate unit. This has to be achieved blindly because no reference signals that support timing were transmitted. The paper is organized as follows. Section 2 introduces the used signalling scheme. Section 3 presents two different receiver structures together with the associated algorithms. Section 4 gives a brief description of the experimental setup as well as some important channel characteristics. The last section presents the results obtained with the two receiver structures together with some comparisons.
MCM Alg.
r N−1 (kTs)
Mixer
dk q(t − kT ) ,
[ak pMSK (t − 2kT ) +
cos
πt
, −T ≤ t < T
0
, otherwise
2T
,
(6)
ak
=
−ak−1 d2k−2 d2k−1
bk
=
−bk−1 d2k−1 d2k ,
(7)
for k ≥ 1, initialized by a 0 = 1 and b0 = d0 . Equations (7) can be interpreted as a differential mapping and precoding step. Differential mapping avoids the necessity to reconstruct the absolute signal phase at the receiver, which would be impossible in a blind start-up, while precoding introduces redundancy that can be exploited. It is apparent from (6) and (7) that at even multiples of T only symbols {+1, −1} out of the finite QPSK alphabet A = {+1, + j, −1, − j } are possible, while at odd multiples of T only symbols {+ j, − j } occur.
(2)
.
Timing Est. / Resampler
and
(3)
3. RECEIVER ARCHITECTURE ,
(4)
An overview of the proposed blind space-time processing receiver architecture is given in Fig. 1. The signals received at an array of N hydrophones are sampled at a fixed rate 1/T s and subsequently shifted to baseband using the nominal carrier frequency ω c . This leads to an error as the actual carrier frequency deviates from the nominal one due to Doppler, which has to be compensated by further processing steps. To reject additive noise outside the frequency band occupied by the transmitted signal, the baseband signals are low-pass filtered utilizing h RF (k). Subsequently, the mean signal power of each sensor output is normalized to one using an adaptive gain control (AGC). Then, non-data-aided timing recovery is performed from the output of one sensor only yielding
where φ(kT ) is the phase at the beginning of the current symbol interval. An input symbol d k = +1 results in a phase change of + π2 during T , while an input symbol d k = −1 leads to a phase change of − π2 . It is apparent from (4) that there is an inherent phase memory making MSK a special form of full-response binary continuous-phase modulation (CPM). The baseband signal (4) can also be re-written as an offset quadriphase-shift keying (OQPSK) signal ∞
Gain Control
pMSK (t) =
Consider the time interval of length T associated with each symbol: t ∈ [kT, (k + 1)T ]. The continuous-phase baseband communication signal in this interval is then given by
=
Receive Filter
k=0
sMSK (t)
AGC
with pulse form
with the initial phase φ(0) = 0 and
=e
hRF (kTs)
Fig. 1. Multichannel Receiver Architecture
(1)
j φ(kT )+ π2 dk t−kT T
AGC
−j ωc kTs
sMSK (t) = eφ(t) ,
k (t) sMSK
hRF (kTs)
e
Minimum shift keying (MSK) [3] offers attractive properties for data transmission that made its derivative Gaussian minimum shift keying (GMSK) the modulation scheme of choice in the European mobile phone standard GSM. Among those characteristics are that 99.5% of the signal energy being contained within a bandwidth of 1.5 times the symbol rate, and a constant envelope of the transmitted signal. At the receiver it is especially the last property, which can be exploited successfully for blind data recovery. Let dk ∈ {−1, +1}, k ∈ N 0 , be an independent and identically distributed (i.i.d.) sequence of binary symbols to be modulated. The continuous-time baseband MSK communication signal can be written as
where T is the symbol duration and 0 ,t < 0 t ,0 ≤ t ≤ T q(t) = 2T 1 ,t > T 2
Multichannel Equalizer and Phase−Offset Compensator
−j ωc kTs
r N (kTs)
∞
AGC
hRF (kTs)
e
2. SIGNALLING SCHEME
φ(t) = j π
ε^
−j ωc kTs
e r1 (kTs)
Timing Synchronizer
(5)
k=0
+ j bk pMSK (t − (2k + 1)T )] ,
2
an estimate ˆ of the residual timing error , representing the misalignment between the transmitter and receiver time grids, where −0.5 ≤ ≤ 0.5 is assumed. This estimate is used to dynamically resample the signals in all channels simultaneously, leaving the task of timing adjustment associated with inter-sensor timing fluctuations to the equalizer. The input to the multichannel equalizer and phase-offset compensator are N signals sampled at a fraction p of the symbol interval T . The multichannel equalizer adaptively reduces ISI induced by the transmission channel. The residual time-varying carrierphase offset is compensated using a first order digital PLL, which is jointly optimized with the equalizer.
so that =−
2 x k := x(kTs ) = r (kTs )r ∗ ([k − M]Ts )
cˆ1,n =
c˜1,n = c˜1,n−1 + α pp (cˆ1,n − c˜1,n−1 ) ,
ˆn = −
E {x(t)}
2π ξ2 1 + cos (t − T ) e j 2ωT . (10) = − 2 T
M−1 − j 2π Ml |xl+n M | e l=0
c^1,n
h pp(n)
c~1,n
−
arg(·) 2π
1 arg c˜1,n . 2π
= (m i + µˆ i )Ts with m i being defined by T T mi = i + ˆ , pTs Ts
From (10) it is apparent that the magnitude |x(t)| ¯ depends on alone. Therefore, calculating the Fourier coefficient of |x(t)| ¯ associated with frequency 1/T leads to 2π 1 T ξ 4 − j 2π e |x(t)| ¯ e− j T t dt = , (11) c1 := T 0 4 xk
(15)
(16)
This estimated timing error is now used to control a postprocessing unit that performs timing adjustment. In order to obtain from r (kT s ) the desired fractionally-spaced samples r (i Tp + ˆ T ) of the inputs to the equalizer, where p represents the factor of oversampling with respect to T , timing adjustment is performed by digital interpolation and decimator control [15, 16]. The unknown symbol instances are first expressed in terms of the receiver time scale defined by the times kTs . Introducing the timing parameters m i (basepoint) and µˆ i (fractional delay), one obtains T T T i + ˆ T = i + ˆ Ts p pTs Ts
contains a spectral component at frequency 1/T from which an estimate of may be obtained. This can be seen after expectation has been taken with respect to the transmitted symbols, resulting in
2
(14)
where 0 < α pp 1 controls the degree of averaging. This smoothing is important as it reduces the variance of the timing estimates, thus decreasing jitter caused by the channel and additive noise. The timing estimate is then finally obtained as
The amplitude distortion ξ and the phase disturbance (t) reflect the influence of the channel, is the residual timing misalignment, ω denotes a frequency offset due to Doppler effects and θ is a constant phase shift. The aim of timing recovery is to (i) estimate the timing misalignment ˆ and then (ii) adjust timing. The applied feed-forward non-data-aided timing estimator is based on the algorithm proposed in [13], which has been slightly modified. It is hang-up free and offers a constant acquisition time independent of initial timing error. The complete timing estimation algorithm is shown in Fig. 2. The signal
2 (9) x(t) = r (t)r ∗ (t − T )
{r(kTs)r*[(k−M)Ts]}
2π 1 M−1 |x ([nM + k]Ts )| e − j M k . M k=0
To improve the estimation of , planar filtering [14] is used to post-process the estimates prior to phase extraction:
t=kTs
r(kTs)
(13)
is formed, which shows the same spectral component at frequency 1/T as (9) if Ts < T2 is fulfilled. The expectation in (10) is substituted by the instantaneous value x(kT s ) to estimate the Fourier coefficient every T seconds:
For notational simplicity, only one channel is assumed in the following. Let the nominal oversampling factor with respect to the symbol duration be M = TTs . The received, fixed-rate sampled and filtered baseband communication signal is then given by . (8) r (kTs ) = ξ e (t) · e[ φ(t− T )+ωt+θ]
=
(12)
follows. To obtain an estimate of using the samples r (kT s ), the expression
3.1. Timing Recovery
x(t) ¯
1 arg {c1 } 2π
(17)
(18)
where x denotes the greatest integer less than or equal to x, and 0 ≤ µn < 1. Both m i and µˆ i may be computed recursively by 1 + ˆ i M m i+1 = m i + µˆ i + p 1 + ˆ i M µˆ i+1 = µˆ i + , (19) p mod 1
ε^ n
Fig. 2. Feed-forward Timing Estimator
3
y1,i
y2,i . . .
yN,i
which consists of the sample present at time instance nT and the previous L − 1 fractionally-spaced samples, and where (◦)T denotes transposition. Then, stacking the vectors corresponding to channels 1 to N into one large vector
c1,i
c2,i
+
y~n
yn
^ dn
T T , . . . , x N,n ]T , xn = [x1,n
. . .
PLL
cN,i
.
−j{ }
e
and considering the combined equalizer vector
^θ n
T w = [c1,i , . . . , cTN,i ]T ,
(24)
the symbol-spaced output of the equalizer is given as
CMA
yn = w H x n .
Fig. 3. Multichannel CMA-Equalizer and PLL where ˆ i = ˆi − ˆi−1 , and the rate sequence ˆi is obby repeating each tained from the symbol rate sequence value of the latter ( p − 1) times, which corresponds to a discrete sample-and-hold device. For initialization, m 0 = 0 and µˆ 0 = 0 can be used. Approximation of the samples r [(m i + µˆ i )Ts ] is carried out in two steps. First, interpolation using a finite impulse response (FIR) filter with time-varying coefficients is performed, followed by decimation, yielding rate Tp samples: LI
h l (µˆ i ) r ([m i − l]Ts ) .
with γ = 1 for our application. Taking the gradient with respect to w yields (27) ∇w JCMA (w) = E |yn |2 − γ xn yn∗ , where (◦)∗ denotes complex conjugation. It has been shown in [20] that replacing the expected value of the gradient in (27) by its instantaneous value yields the following iterative algorithm to find the minimum of (26): (28) wn+1 = wn + µ γ − |yn |2 xn yn∗ ,
(20)
l=0
It is well justified [17] to use a piece-wise parabolic interpolator α I µˆ 2i − α I µˆ i l=0 −α µˆ 2 + (α + 1)µ l=1 I i I i h l (µˆ i ) = , (21) 2 −α I µˆ i + (α I − 1)µi + 1 l = 2 α I µˆ 2i − α I µˆ i l=3
where µ is a small positive step-size parameter. An initial value w0 is obtained by common central tap initialization [19]. The output y n of the multichannel equalizer is then phase corrected using the phase-offset estimate θˆ :
with α I = 0.43 and L I = 3 in equation (20).
ˆ
y˜n = yn e− j θn . 3.2. CMA Equalizer and Carrier Recovery
(29)
Estimates dˆn of the transmitted symbols are finally obtained via the time-variant nonlinearity
Possibly the most successful blind equalization method is the constant modulus algorithm (CMA) [18]. While it is also applicable to signal constellations showing a constant modulus like PSK [19], performance might however be substantially degraded due to unavoidable synchronization errors that lead to symbol samples that lie not on a circle anymore. We apply the CMA to MSK signals where - contrary to PSK modulation - the transmitted waveform is also of constant modulus so that symbol samples at the receiver lie on a circle regardless of a slight miss-synchronization, thus promising better results in using the CMA. The structure of the CMA-receiver is shown in Fig. 3. Consider the (T / p)-spaced signal y ν,i of channel ν, 1 ≤ ν ≤ N. These signals enter a bank of N adaptive FIR filters c ν,i , each of length L. To obtain a compact expression for the output of the multichannel equalizer, consider first the L-variate vector xν,n = [yν,nT , yν,nT −T / p , . . . , yν,nT −(L−1)T / p ]T ,
(25)
Equalization using the constant modulus algorithm (CMA) is performed by optimizing the following cost function [19]: 2 1 JCMA (w) = E |yn |2 − γ , (26) 4
p T ˆ n
yi := y(m i Ts ) =
(23)
dˆn = g[ y˜n , n]
(30)
by simply deciding on the QPSK symbol which is closest to y˜n . The toggling slicer g exploits the redundancy (7), introduced at the transmitter: it distinguishes between even and odd indexed symbols, toggling its decision regions between two perpendicular binary PSK constellations, see Fig. 4. It is apparent from the cost function (26) that the CMA only uses information about the magnitude of the received signal and not the phase. An existing phase-offset has therefore to be compensated after multichannel equalization. An estimate of the current phase error can be obtained by the phase difference between the signals y˜ n and dˆn before and after the slicer: (31) θˆn = Im y˜n dˆn∗ ,
(22)
4
where Im{◦} denotes the imaginary part of the argument. This quantity is processed in a loop filter and integrated to obtain an update of the phase estimate for the next iteration. For our application, where both transmitter and receiver are fixed, a first-order discrete-time PLL with positive parameter α seems to be sufficient, θˆn+1 = θˆn + αθˆn ,
toggling slicer
DD−PLL
c 1,i
+
y~n
^
dn
+
y 1,i
e
−j( )
phase comput. & loop filt.
(32) y (N−1),i
as a small residual constant phase-error can be neglected due to the differential encoding of the transmitted symbols. The iteration (32) is initialized by θˆ0 = 0.
c (N−1),i
+ ^ θn
y N,i
3.3. Decision-Directed Equalizer and Carrier Recovery Blind decision-directed (DD) equalization and carrier recovery has been examined in [8]. The proposed receiver structure is based on a multichannel extension of the scheme introduced in [21] and is depicted in Fig. 5. The time synchronized signals of the N-element sensor array enter a bank of N adaptive FIR filters cν,i , 1 ≤ ν ≤ N, each of length L. The combined and phase corrected T -spaced output y n of the fractionallyspaced multichannel equalizer is then given by
c N,i
e
j( )
+
en +
−
Fig. 5. Multichannel DD Equalizer with DPLL
ˆ is the carwhere (◦) H denotes Hermitian transposition, θ(n) rier phase estimate, and w n , xn are given in equations (23) and (24), respectively. Let the approximation error be
initialization. Equation (37) again represents a first-order decision-directed PLL with starting value θˆ0 = 0. To obtain a good dynamical behavior of the coupled system, the phase synchronizer should be able to track time variations more rapidly than the equalizer to provide the latter with reasonably phase-compensated symbol decisions. Therefore, the stepsize parameter α is ususally chosen roughly 10 times the value of µ.
en = dˆn − y˜n
4. SEA TRIAL
ˆ
y˜n = e − j θn wnH xn ,
(33)
(34)
and consider the cost function
JDD (w, θ ) = E |en |2 ,
Within the EC-funded project ROBLINKS, in spring 1999, a sea trial for underwater communication was conducted in the North Sea about 10 km off the Dutch coast. At the transmitting side, an almost omnidirectional acoustic source was deployed from the stern of a support ship and lowered to a depth of approximately 9 m. The total water depth in this shallow water area is about 20 m. The signals were received by either of two vertical arrays, consisting of 20 and 6 hydrophones, respectively. The arrays were fixed to an oceanographic platform, which also hosted all recording facilities. The 20-element array sampled the sound field from a depth of 4.4 m to 15.8 m with equally spaced sensors. The smaller array consisted of three pairs of hydrophones, separated horizontally by 15 cm at depths of approximately 7, 11, and 15 m below the sea surface. The support ship anchored at various positions with distances of 1, 2, 5, and 10 km from the platform. In addition, the ship was sailing at moderate speed the last two days to obtain measurements with a moving source. More details on the ROBLINKS experiments can be found in [22].
(35)
which is now a function of both the filter coefficients and the carrier-phase offset. Taking the gradient of (35) with respect to w and θ and replacing the expected values by their instantaneous estimates yields the iterations wn+1
=
θˆn+1
=
ˆ
wn + µ e − j θn xn en∗ θˆn + α Im y˜n en∗
(36) (37)
to minimize the mean-squared error (MSE). The recursion (36) for the equalizer coefficients is initialized by central tap Im{d n} d 2l d 2l+1
+j
−1
1 Re{d n}
5. EXPERIMENTAL RESULTS −j
To examine the performance of the proposed receiver structures we analyzed data at rates 514.32 bit/s and 3233.81 bit/s, respectively, that had been recorded while the ship moored at
Fig. 4. Toggling Slicer
5
Error occurrences vs. time
Est. a−priori MSE vs. time
16
−6
14
−7
2
12 Bit error percentage
|en|2 in dB
Hydrophone
−8 −9
−10 −11
4
−14 0
50
100 Time (s)
6 10 15 Delay (ms)
20
25
6
2
−13
5
8
4
−12
0
10
0 0
150
50
100 Time (s)
150
30
(a) CMA: A-priori MSE
(b) CMA: Bit-Error Rate
Fig. 6. Initial Channel Responses Error occurrences vs. time
Estimated a−priori Mean−Squared Error vs. time
1.5
−2
a distance of 2 km from the platform. In both cases the carrier frequency was 3079 Hz and approximately 100000 data bits were continuously transmitted. The signals received at the hydrophones 2, 4, and 6 (corresponding to water depths 7, 11, and 15 m) of the smaller array were jointly processed in the multichannel receiver. Prior to the information-bearing signals, a linear FM sweep of 200 ms duration spanning the frequency band from 1 to 5 kHz was transmitted to obtain initial information about the channel responses. Fig. 6 shows the results of matched-filter analysis of the FM sweeps received at the three hydrophones. It is apparent, that the delay spread of the channels is at least 5-10 ms, giving some guidelines for choosing a proper length of the multichannel equalizer filters [23]. For a detailed channel analysis, see [24]. During time synchronization, an oversampling factor p = 2 was used and the post-processing constant α pp of the planar filtering (15) was set to 10−3 in both cases.
−4
1 1 Ns
,
−12 −14
1
0.5
−16 −18 −20 0
20
40
60
80 100 120 140 160 180 Time(s)
(c) DD: A-priori MSE
0 0
20
40
60
80 100 120 140 160 180 Time(s)
(d) DD: Bit-Error Rate
Fig. 7. Equalization results at Rate 514.32 bit/s all bit error rate based on 100000 transmitted bits was 0.5% with the CMA and 0.006% in the DD case, demonstrating the good performance of both receiver structures. It is, however, also interesting to look at the error history over time as shown in Figs. 7(b) and 7(d). To obtain the plots, segments of 500 received symbols were considered, in which the relative error was computed. In both cases, the majority of errors occurred during start-up: with the CMA, 409 out of a total of 491 bit errors occurred in the first 40 seconds, while with the DD algorithm all 6 errors appeared within the first block of 500 symbols.
The measured input signal-to-noise ratio (SNR) at the three hydrophones was 34.017 db, 34.380 dB, and 38.165 dB, respectively. The length of the three equalizer filters was set to L = 42. The step-size for the filter coefficient updates (28) and (36) was µ = 5 · 10 −3 and the filter parameter in the discrete-time first-order PLLs (32) and (37) was chosen to α = 10−1 . The results obtained with both equalizer structures are shown in Fig. 7. Comparing the runs of the a-priori MSE in Figs. 7(a) and 7(c), it is obvious that the CMA shows slow convergence, while the DD equalizer converges rapidly. The slower convergence of the CMA compared to the DD equalizer is also reflected in the output SNR, which is defined as [4] Ns
−10
n
|e |2 in dB
−8
5.1. Rate 514.32 bit/s
SNRout = 10 log10
Bit error percentage
−6
5.2. Rate 3233.81 bit/s The input signal-to-noise ratio (SNR) at the three hydrophones was now 23.680 db, 25.181 dB, and 26.877 dB, respectively, indicating more hostile channel conditions. The length of the three equalizer filters was set to L = 62. The step-size for the filter coefficient updates in equations (28) and (36) was chosen to µ = 10−3 and the filter constant used in the discrete-time first-order PLLs (32) and (37) was α = 5 · 10 −2 . The results at this higher data rate are shown in Fig. 8. From the runs of the a-priori MSE in Figs. 8(a) and 8(c) the large gap between the CMA and the DD receiver is obvious, again indicating the rather long convergence time of the CMA. The output SNRs in this case are 6.0 dB for the CMA and 10.6 dB for the DD algorithm. With an overall bit error rate of 3.6%, the CMA still shows a satisfactory performance. Again, the majority of errors occur during the first few seconds, as can be seen in Fig. 8(b). The overall bit error rate with the DD equalizer is
(38)
|dˆn − yn |2
n=1
where Ns is the number of received symbols. For the CMA equalizer it is 7.9 dB, while it is 12.9 dB for the DD equalizer. While the usual strategy is to switch from CMA to a decisiondirected mode as soon as a reasonable a-priori MSE is reached to decrease the MSE further [23], the results demonstrate that blind start-up with a DD equalizer is also possible. The over-
6
[2] M. Stojanovic, “Recent Advances in High-Speed Underwater Acoustic Communications”, IEEE J. Oceanic Eng., Vol. 21, No. 2, pp. 125-136, Apr. 1996.
Error occurrences vs. time Est. a−priori MSE vs. time
20
−6.5 −7
Bit error percentage
15
−8
2
|en| in dB
−7.5
−8.5
[3] J.G. Proakis, Digital Communications, 3rd edition, McGraw-Hill, Boston, 1995.
10
5
[4] M. Stojanovic, J. Catipovic, and J.G. Proakis, “Adaptive Multi-Channel Combining and Equalization for Underwater Acoustic Communications”, J. Acoust. Soc. Amer., Vol. 94, No. 3, pp. 1621-1631, Sep. 1993.
−9 −9.5 0
5
10
15 Time (s)
20
0 0
25
(a) CMA: A-priori MSE
5
10
15 Time (s)
20
25
(b) CMA: Bit-Error Rate
[5] B.S. Sharif, J. Neasham, D. Thompson, O.R. Hinton, and A.E. Adams, “A Blind Multichannel Combiner for Long Range Underwater Communications”, in Proc. ICASSP’97, pp. 579-582, Munich, Apr. 1997.
Error occurrences vs. time
Est. a−priori MSE vs. time 0
3 −2
2.5 Bit error percentage
|en|2 in dB
−4 −6 −8
−10 −12
[6] J. Labat, O. Macchi, and C. Laot, “Adaptive Decision Feedback Equalization: Can You Skip the Training Period?”, IEEE Trans. Com., Vol. 46, No. 7, pp. 921-930, Jul. 1998.
2 1.5 1 0.5
−14 0
5
10
15 Time(s)
20
(c) DD: A-priori MSE
25
0 0
5
10
15 Time(s)
20
25
[7] J. Gomes, and V. Barroso, “Blind Decision-Feedback Equalization of Underwater Acoustic Channels”, in Proc. Oceans 1998 MTS/IEEE Conf., pp. 810-814, Nice, Sep./Oct. 1998.
(d) DD: Bit-Error Rate
Fig. 8. Equalization results at Rate 3233.81 bit/s
[8] A. Waldhorst, R. Weber, and J.F. B¨ohme, “A Blind Receiver for Digital Communications in Shallow Water”, in Proc. Oceans 2000 MTS/IEEE Conf., pp. 1839-1846, Providence, RI, Sep. 2000.
0.018%, again demonstrating the capability of this algorithm even during blind start-up.
[9] D. Cano, M.B. van Gijzen, and A. Waldhorst, “Long Range Shallow Water Robust Acoustic Communication Links: Roblinks”, in Proc. Third European Marine Science and Technology Conference, pp. 1133-1136, Lisbon, 1998.
6. CONCLUSIONS We examined blind receiver structures for MSK modulated transmitted signals. MSK appears to be a suitable modulation scheme for UWA communication systems due to its attractive properties. The explicit use of non-data-aided timing recovery together with joint blind equalization and phase synchronization led to the development of receiver structures that operate properly without any training symbols inserted into the data stream. The performance of both proposed receivers with measured data shows excellent behavior, thus supporting the feasibility of blind processing in the UWA communication context.
[10] M.B. van Gijzen, and P.A. van Walree, “Shallow-Water Acoustic Communication with High Bit Rate BPSK Signals”, in Proc. Oceans 2000 MTS/IEEE Conf., pp. 16211624, Providence, RI, Sep. 2000. [11] J.-M. Passerieux, and D. Cano, “Robust Shallow Water Acoustic Communication Based Upon Orthogonal Sequences”, in Proc. Oceans 2000 MTS/IEEE Conf., pp. 1825-1828, Providence, RI, Sep. 2000. [12] G. Ungerboeck, “Fractional Tap-Spacing Equalizer and Consequences for Clock Recovery in Data Modems”, IEEE Trans. Com., Vol. 24, No. 8, pp. 856-864, Aug. 1976.
7. ACKNOWLEDGEMENT We greatly acknowledge the teams of TNO Fysisch en Elektronisch Laboratorium and Thomson Marconi Sonar S.A.S. as well as the crews on board the HNLMS Tydeman and on the Meetpost Nordwijk for their valuable work and collaboration that led to the successful execution of the ROBLINKS project. 8. REFERENCES
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