502 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 4, OCTOBER 2011
Peer-Reviewed Technical Communication
Exploiting Space–Time–Frequency Diversity With MIMO–OFDMfor Underwater Acoustic Communications
Konstantinos Pelekanakis, Member, IEEE, and Arthur B. Baggeroer, Life Fellow, IEEE
Abstract—Underwater acoustic (UWA) channels exhibittime-varying fading statistics, thus a coded modulation schemeoptimally designed for a specific model (e.g., Rayleigh fading) willperform poorly when the channel statistics change. Exploitingdiversity via coded modulation is a robust approach to improve thereliability of the acoustic link in a variety of channel conditions.Two coded modulation schemes drawn from the terrestrial radioliterature are compared in terms of their bit error rate (BER). Thefirst scheme combines trellis coded modulation (TCM) based on an8-phase-shift keying (8-PSK) signal set and symbol interleaving.The second scheme is based on bit-interleaved coded modulation(BICM), which includes a convolutional encoder, a bit interleaver,and a 16-quadrature-amplitude-modulation (16-QAM) signalset. These schemes, which are designed to have the same bitrate and decoding complexity, are tested under two scenarios.In the first scenario, a single-input–multiple-output (SIMO)system is implemented by means of orthogonal frequency-divisionmultiplexing (OFDM) modulation. In the second scenario, amultiple-input–multiple-output (MIMO) system is implementedand each of the coded modulation scheme is coupled with a3/4-rate space–time block code (STBC) before applying OFDM.Analyzing both simulated and experimental data, the followingresults, which also hold for terrestrial radio, are confirmed: codedmodulation schemes emphasizing higher Hamming distance (suchas BICM) yield a lower error rate when spatial diversity is verylimited (first scenario). On the other hand, coded modulationschemes emphasizing higher free Euclidean distance (such asTCM) demonstrate a lower error rate when spatial diversity issufficiently high (second scenario).
D ESIGN of bandwidth-efficient coded modulationschemes, based on low-complexity, noniterative de-
coding, requires the knowledge of the channel fading statistics.
Manuscript received October 22, 2009; revised August 26, 2010, March 14,2011, and July 03, 2011; accepted August 12, 2011. Date of publication October03, 2011; date of current version October 21, 2011.
Associate Editor: U. Mitra.K. Pelekanakis is with the Acoustic Research Laboratory, Tropical Marine
Science Institute, National University of Singapore, Singapore 119223, Singa-pore (e-mail: [email protected]).
A. B. Baggeroer is with the Department of Mechanical and Electrical Engi-neering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA(e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JOE.2011.2165758
However, underwater acoustic (UWA) channels demonstratetime-varying fading statistics, which depend on a variety offactors, including the sea state, ocean depth, and the propaga-tion path length. Rayleigh fading models are proposed in [1]and [2]; in contrast, Rician fading models are proposed in [3]and [4]. These models presume a large number of scatterersallowing for the use of the central limit theorem, yet Preisiget al. [5] challenge the Gaussian assumption as intermittentdistinct arrivals were identified in the channel response of asurf zone environment.
Channels with time-varying fading statistics are often en-countered in the mobile radio community as well [6]. Theneed for a robust coded modulation scheme that will performwell in a variety of channel fading conditions motivated theidentification of schemes that provide good performance intwo extreme channel models: 1) additive white Gaussian noise(AWGN) (or Rician with high -factor)1 and 2) Rayleigh (orRician with low -factor). These kinds of schemes could bevery useful in UWA communications since the -factor is timevarying even when there is no platform motion [3], [4].
It is well known that efficient design of coded modulationfor the AWGN channel model focuses on maximizing the freeEuclidean distance (minimum Euclidean distance betweenany pair of codewords). On the other hand, maximizing theHamming distance (minimum number of bits per symbolsfor which two codewords differ) of any pair of codewords isessential to achieve good performance in fully interleaved, andthus effectively independent and identically distributed (i.i.d.),Rayleigh fading channels. Consequently, coded modulationschemes should exhibit both large free Euclidean and Ham-ming distances to ensure robust performance over a varietyof channel conditions. Towards this end, trellis coded mod-ulation (TCM) [7] has been the de facto standard for UWAcommunications [8]. An alternative approach, currently used invarious radio communications standards such as IEEE 802.11n[9] and DVB-T2 [10], is the bit-interleaved coded modulation(BICM) [11]. In contrast to TCM, BICM treats channel codingand modulation as two independent entities and hence, it ismore flexible in adjusting the data rate and/or the complexityof the communication system. Only recently, BICM has beenproposed in UWA communications [12], [13]. In particular,Shah et al. [13] used an iterative receiver structure, whichcombines BICM with decision feedback equalization (DFE).
1The Rician �-factor is defined as the ratio of the energy of the nonfadedsignal component to the energy of the diffused multipath component.
PELEKANAKIS AND BAGGEROER: EXPLOITING SPACE–TIME–FREQUENCY DIVERSITY WITH MIMO–OFDM 503
Orthogonal frequency-division multiplexing (OFDM) en-ables one-tap equalization in static multipath channels. IfOFDM is combined with channel coding and interleaving,termed as coded OFDM, then coded data are distributed overdifferent coherence bands (frequency interval over which twofrequencies of the signal are likely to experience correlatedamplitude fading) and coherence periods (time interval overwhich two samples of the signal are likely to experience corre-lated amplitude fading) and therefore, both frequency and timediversity are exploited. For instance, Chitre et al. [14] employconvolutional codes combined with bit interleaving in OFDMsystems over a shallow-water acoustic channel. Additionaldiversity gain in space is possible when a system employessufficiently separated multiple transmit transducers combinedwith space–time trellis codes (STTCs) [15] or space–timeblock codes (STBCs) [16]. In [17], Ormondroyd and Dhanoaemploy STBC for UWA communications; nevertheless, onlysimulated results were given. Recently, STTCs have becomenotable at-sea experiments [18].
Using low-complexity coded modulation schemes that fullyharvest the channel diversity in space, time, and frequency, hasnot yet been given the attention it deserves in UWA communi-cations. Towards this end, we exploit the strategies proposedin [21], [24]–[26] for terrestrial radio channels in the UWAenvironment and we compare two coded OFDM schemeswith the same bit rate and decoding complexity but differentfree Euclidean and Hamming distances. The first scheme usesTCM based on an 8-phase-shift keying (8-PSK) signal set. Thesecond scheme uses BICM based on a convolutional encoderand a 16-quadrature-amplitude-modulation (16-QAM) signalset. Both schemes are combined with a rate-3/4 STBC whenthe transmitter employs three transducers. The performancetrends we observed from a short-range shallow-water acousticlink echo those observed for terrestrial radio channels: schemeswith higher Hamming distance (such as BICM) should bepreferred when the total number of employed transducers isvery small (two or three). In contrast, schemes with higherfree Euclidean distance (such as TCM) become a better choicewhen employing many transducers is feasible.
The rest of this paper is organized as follows. Section IIprovides the OFDM system model and describes a robustchannel estimation algorithm. The proposed TCM–OFDM andBICM–OFDM systems, as well as their coupling with STBC,are described in Section III. Simulations and experimentalresults are reported in Sections IV and V, respectively. Finally,the paper is concluded in Section VI.
Notation: Superscripts , , and stand for transpose, Her-mitian transpose, and conjugate, respectively. Column vectors(matrices) are denoted by boldface lowercase (uppercase) let-ters. is the sinc function, is the Kro-necker delta function, and denotes expectation.
II. OFDM SYSTEM MODEL AND CHANNEL ESTIMATION
A. OFDM System Model
A cyclic-prefixed OFDM system with subcarriers isconsidered. Let , , and denote the incoming symbol
rate, the channel delay spread, and the maximum Dopplerfrequency of the channel, respectively. The subcarrier spacingis equal to and the cyclic prefix duration is equalto channel symbol periods, where isthe number of channel taps. In practice, it is desired that
to make Doppler spread tolerable. Assumethe vector is the input of theOFDM modulator, where stands for the data symboltransmitted over the th subcarrier during the th OFDMperiod. After an inverse fast Fourier transform (IFFT) oper-ation and cyclic prefix insertion, the resulting vector can beexpressed as , where is an
matrix, is the FFT matrix,and is the matrix formed by the lastcolumns of . Then, is serialized, upconverted, and sentthrough the channel.
If we denote , then is the transmissiontime for . By choosing small enough, we assume thatthe channel remains static over (one OFDM period)but may vary from period to period. This type of quasi-staticchannel can be encountered in short-range, shallow-water en-vironments after motion-induced Doppler compensation [19],[20]. In our case, both the transmitter and the receiver wereidle and the observed channel Doppler spread (mainly due tosurface wave motion) was much smaller than the subcarrierspacing . Let denote thechannel impulse response taps during the th OFDM period.Then, the received signal during the th OFDM block is givenby , where denotes a
lower triangular Toeplitzmatrix with its first column equal to and denotesthe additive noise vector. After cyclic prefix removal and FFTdemodulation, the effective channel matrix becomes diagonaland the received data symbol at the th subcarrier during the
th OFDM period can be written as
(1)
where is the channel fre-quency gain and is the resulting noise. Here, ismodeled as i.i.d. complex Gaussian random variable with zeromean and , wherestands for the power spectral density (psd) of the noise.
B. Robust Channel Estimation
In [21], a robust channel estimation algorithm is describedgiven that the time-varying frequency response of the channel
is modeled as a wide sense stationary (WSS) randomprocess in both frequency and time, i.e., the channel falls withinthe wide sense stationary uncorrelated scattering (WSSUS)framework. In our case, this model is valid because the rule ofthumb [8] ( 1500 m/s is the sound speedin the water and is the maximum propagation path velocityin meters per second) holds. Hence, a short-term stationarychannel is implicitly assumed when we characterize asa 2-D WSS process.
504 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 4, OCTOBER 2011
Fig. 1. Pilot-symbol arrangement for the proposed OFDM system. The signalspace is partitioned in time–frequency cells. A subcarrier of duration � � �and bandwidth ��� is transmitted in one cell.
Estimation of is performed by dispersing unit-energypilot symbols into the data stream. A rectangular pilot-symbolarrangement is considered, as seen in Fig. 1. The 2-D samplingtheorem requires that
and (2)
where is the distance in subcarriers between two pilot sym-bols in frequency domain and is the distance in OFDM blocksbetween two pilot symbols in time domain. When multiple pro-jectors are used, the pilot symbols are transmitted in an orthog-onal manner: when a projector transmits a pilot symbol duringa specific time–frequency location all the other projectors aresilent at that location. This simple scheme avoids pilot symbolstransmitted from different projectors to interfere with each otherwhen channel estimation is performed.
Let the frequency and time locations of the pilot symbolsbe denoted as and , respectively, and is the set of all
pairs with . The minimum mean squared error(MMSE) estimate of is given by [21]
(3)
(4)
(5)
where is the estimated channel frequency gain at posi-tion , denotes the shift-variant 2-D impulseresponse of the filter with taps, stands for the
autocorrelation matrix with elementsand is the cross-correlation
vector with elements .In practice, the autocorrelation and cross correlation of the
channel gains are not known at the receiver. Keeping the re-ceiver at a low complexity, a robust, nonadaptive selection ofthe filter taps is considered that can cope with a wide variety ofpower density spectra. In [22], it is proved that when the MMSEfilter is matched to uniform Doppler and delay power densityspectrums and the filter bandwidths exceed the channel band-widths (delay and Doppler spread), then a model mismatch willslightly degrade the estimation performance. Following this line
of thought, the elements of the cross-correlation vector and theautocorrelation matrix are given by
(6)
and
(7)
respectively. Note that correspond to the averagepower of the channel impulse response.
III. PROPOSED CODED OFDM SYSTEMS
A. TCM Combined With OFDM
Here we describe a system that combines a TCM encoderwith OFDM modulation. The incoming bit stream is encodedby a 2/3-rate, 8-state, TCM encoder with octal generators(04,02,11) [7, p. 174] to produce a coded symbol stream whereeach symbol is drawn from an 8-PSK signal set with averageunit energy. Note that the information transmission rate is2 b/s/Hz and the number of the TCM decoder states at eachtrellis step is 4 8 32, where 4 is the number of branchesmerging at each state and 8 is the number of states at eachtrellis step. A symbol interleaver permutes the order of thecoded symbols before OFDM is applied. Since OFDMsubcarriers are expected to be heavily correlated ( aredefined in Section II-A), the depth of the symbol interleavermust be greater than to ensure that contiguous codedsymbols are transmitted over uncorrelated parts of the channelspectrum (different coherence bands of the channel).
At the receiver side, after CP removal, FFT demodulation andchannel estimation, the faded, noisy version of each transmittedsymbol as well as its associated channel gain are fedto the symbol deinterleaver. The deinterleaved output becomesthe input to the decoder, which uses the well-known Viterbi al-gorithm [7].
UWA channels often exhibit Rician fading statistics. It isknown that when the Rician parameter , the Ricianchannel behaves like the AWGN channel, while when ,the Rician fading reduces to Rayleigh fading. The error prob-ability of the TCM encoder for the AWGN channel behaveslike [7], where 4.59 is the squared free Euclideandistance of the TCM encoder and SNR stands for the averagereceived signal-to-noise ratio per symbol duration. On theother hand, the error probability of the TCM encoder for theRayleigh fading channel with independent taps behaves likeSNR [24], where is the Hamming distanceof the TCM encoder. Clearly, when the channel exhibits morethan two independent taps, the proposed system cannot exploitfull frequency diversity.
PELEKANAKIS AND BAGGEROER: EXPLOITING SPACE–TIME–FREQUENCY DIVERSITY WITH MIMO–OFDM 505
B. BICM Combined With OFDM
A straightforward way to design a BICM scheme with thesame throughput (2 b/s/Hz) and decoding complexity (32 de-coding states) but higher Hamming distance than its TCM coun-terpart is to concatenate a low-rate convolutional code with anexpanded signal set. Let us consider the following two choices:1) concatenation of a 2/3-rate, 8-state convolutional encoderwith an 8-PSK signal set; and 2) concatenation of a 1/2-rate,16-state convolutional encoder with a 16-QAM signal set. Inthe first case, the best convolutional code yields Hamming dis-tance of five while in the second case the best convolutionalcode yields Hamming distance of seven [23, p. 492]. Althoughthe second scheme enjoys higher diversity gain, it might not bepractical for the bit error rates (BERs) of interest since an ex-panded signal set suffers smaller minimum Euclidean distance.To verify that the combination of a 1/2-rate convolutional codewith 16-QAM is worth pursuing, we use the expression of theasymptotic bit error performance in fully interleaved, and thuseffectively i.i.d., Rayleigh fading channel of an arbitrary BICMscheme [11]
(8)
where stands for the bit error probability, is the Ham-ming distance of the convolutional code, is the informationrate, and is a constant which depends on the bit labeling ofthe signal constellation. Clearly, dictates the slope (diver-sity gain) of the bit error curve while dictates its hori-zontal offset (coding gain). The goal is to evaluate the point
at which the two considered bit errorcurves intersect. Assuming Gray mapping in both cases, weobtain a crossover at 2.97 dB. Thus, the 16-QAMscheme provides better performance at almost any BER of in-terest.
We now describe a system that combines a BICM en-coder with OFDM modulation. The incoming bit sequenceis encoded by a 1/2-rate convolutional encoder with octalgenerators (23,35) [23, p. 492]. A bit interleaver permutes theorder of the coded bits before they are broken into sub-blocksof 4 b each. Then, each sub-block is one-to-one mappedonto a complex symbol drawn from a 16-QAM signal set
with averageunit energy and Gray labeling. The resulting symbol sequenceis passed through the channel via OFDM modulation. Notethat the bit interleaver is designed such that consecutive codedbits are mapped onto different 16-QAM symbols, which inturn are transmitted over different coherence bands of thechannel. Hence, each bit (rather than each symbol) experiencesuncorrelated fading.
At the receiver side, after OFDM demodulation and channelestimation, each received symbol and its associatedchannel gain are used to generate eight soft bit metrics.Let denote the th bit of the label of a channel symbol
and denote the subset of
all the channel symbols whose label has the valuein position . Let us also define the following eight differentsubsets:
(9)
(10)
(11)
(12)
(13)
Then, the induced eight bit metrics from the pairare [11]
(14)
The bit metrics are deinterleaved and become the input to thedecoder. At each trellis step, the branch metrics for each pos-sible binary 2-tuple is the sum of the corresponding bitmetrics; the Viterbi algorithm is used to minimize the sum ofthe branch metrics.
Similarly to TCM–OFDM, the error probability of theBICM–OFDM for the Rayleigh fading channel with inde-pendent taps behaves like SNR [24], whereis the Hamming distance of the employed convolutional code.The increased diversity gain of the BICM encoder (seven asopposed to two for the TCM counterpart) comes at the expenseof reduced Euclidean distance between the codewords. Due torandom bit labeling caused by the bit interleaver, the effectivesquared Euclidean distance becomes , whereis the minimum squared Euclidean distance of the 16-QAMconstellation. Consequently, the proposed BICM–OFDMsystem has an SNR disadvantage for the AWGN channel sinceit has a smaller Euclidean distance (2.8 are opposed to 4.59 forthe TCM counterpart).
C. Extension to Multiple-Projector OFDM Systems
We now extend the two proposed systems to multiple-pro-jector systems so that full transmit diversity is exploited.Fig. 2(a) shows the block diagram of the transmitter. Afterperforming coded modulation and interleaving, a serial-to-par-allel converter breaks the codeword into vectors ofchannel symbols each. Letbe the output of the serial-to-parallel converter, where
and is the trans-mitted symbol using the th projector over the
th subcarrier during the th OFDM period. A rate-3/4 STBC
506 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 4, OCTOBER 2011
Fig. 2. Block diagram of system with three projectors: (a) transmitter; (b) re-ceiver.
[16] is applied to and the encoder output is anrow-orthogonal matrix
(15)where the index is dropped for notational simplicity. AllOFDM symbols in the first column of are simultaneouslytransmitted by all projectors and all OFDM symbols in thesame row of are transmitted in consecutive OFDM periods.Thus, the required time duration to transmit is four OFDMperiods. Note that the combination of a channel encoder (outercode), an interleaver, and an STBC (inner code) ensures thatdifferent parts of a codeword are mapped across all projectorsas well as across different coherence bands and periods. Hence,the proposed system should, in principle, be able to exploitspace, time, and frequency diversity [25].
The block diagram of the receiver is shown in Fig. 2(b). Let usalso assume that the channel is essentially static over four con-secutive OFDM symbol periods (by choosing an appropriateagain). After CP removal and FFT demodulation, the receiveddata symbols over the th subcarrier during the four OFDM pe-riods can be written as
(16)
(17)
(18)
(19)
where , , denotes the channelfrequency gain seen by the th projector at the th subcarrier.Decoupling of the transmitted symbols from the above
system of equations is accomplished by performing linearoperations due to the orthogonality of . It is shown in [26] thatthe effective channel gain for each becomes .In addition, if hydrophones are used at the receiver, it isstraightforward to show that the effective channel gain for each
becomes where is the channelgain between the th projector and th hydrophone at the thsubcarrier. After STBC decoupling, the processed receivedsymbols and their associated channel gains are fed into theTCM/BICM decoder. Finally note that the error probability ofthe proposed system for the Rayleigh fading channel withindependent taps behaves like SNR [24], where
is the Hamming distance of the TCM/BICM code.
IV. SIMULATIONS RESULTS
Several papers compare the BER performances betweenTCM and BICM [27]–[30], yet the so-obtained results arebased on channels with fixed multipath spread. Consequently,the interaction of the code properties (Hamming and freeEuclidean distance) with the channel multipath spread is notrevealed. Moreover, [24] and [31] deal only with BICM–OFDMsystems while [32] deals only with TCM–OFDM systems andhence, a comparison between BICM and TCM in terms ofdiversity exploitation is not obvious.
In this section, a comparison between the proposedTCM–OFDM and BICM–OFDM systems is investigatedin terms of their BER performances. We consider variouscombinations of interleavers, multipath channels, and numberof receive hydrophones. In all the following simulations, in-formation bits are formed into packets of 30 OFDM symbolseach. The symbol rate is 4 kHz, the number of OFDMsubcarriers is , and the cyclic prefix duration is 25 ms
. The possible physical path delays are approxi-mated as integer multiples of , thus the number of physicalpaths is equal to the number of nonzero taps of the channelimpulse response. Each nonzero physical path is characterizedby a uniform Doppler power density with maximum one-sidedfrequency and is modeled as an independent, complexGaussian random variable with zero mean and variance ,where is the total number of physical paths. When receivehydrophones are employed, the transmit energy is divided by
to compensate for the array gain. Consequently, if isthe psd of the additive white complex Gaussian noise process,then the average received symbol SNR for any system-channelcombination is , where is the average symbol energy(recall that ). Perfect channel state information at thereceiver is assumed so no channel estimation is performed here.All BER results are plotted with respect to , which, indecibels, is given by
(20)
(code rate) (constellation size)
(21)
where denotes the bandwidth efficiency (b/s/Hz) of thecoded modulation scheme, and is the array gain dueto multiple receive hydrophones. When receive hydrophones
PELEKANAKIS AND BAGGEROER: EXPLOITING SPACE–TIME–FREQUENCY DIVERSITY WITH MIMO–OFDM 507
Fig. 3. BER performances of the proposed TCM–OFDM and BICM–OFDM systems over various Rayleigh fading channels.
Fig. 4. Setup of RACE’08.
are used, the TCM–OFDM and BICM–OFDM systems are de-noted as TCM1x and BICM1x , respectively.
1) Exploiting Frequency Diversity: The individual impactof frequency diversity on the code performance is investigated,therefore during each packet transmission the channel gains arefixed ( 0 Hz). However, the gains independently changeat different packet transmissions. The coded bits per symbolsare interleaved within the packet and the interleaving depth isfour subcarriers. Fig. 3(a) shows the BER performance of theTCM1x1 system. Note that as the number of physical pathsincreases, the slope of the BER reaches its maximum valuewhen the channel delay spread is 5 ms (four nonzero taps). This
means that the TCM1x1 cannot exploit full frequency diversitywhen the nonzero taps increase beyond four. Note also thatfor higher delay spreads, the system exhibits a slightly largercoding gain.2 Fig. 3(b) shows the BER performance of theBICM1x1 system. Note that as the number of physical paths in-creases, the slope of the BER reaches its maximum value whenthe channel delay spread is 15 ms (eight nonzero taps). Clearly,BICM1x1 harvests more frequency diversity than its TCMcounterpart due to its higher Hamming distance. Again notethat as the delay spread increases from 15 to 25 ms, BICM1x1demonstrates a slightly higher coding gain. Fig. 3(c) comparesthe BER performances between TCM1x1 and BICM1x1 overtwo different multipath, Rayleigh fading channels. AlthoughBICM1x1 outperforms TCM1x1 in both channels, the impactof higher Hamming distance in boosting the code performanceis best seen when the channel provides eight physical paths.Then, BICM1x1 needs 3 dB less power to achieve a BER of2 10 . In addition, Fig. 3(c) shows the BER rate of bothsystems over the AWGN channel, which indicates the ultimatesystem performance when diversity goes to infinity. TCM1x1has a 2-dB power advantage at high due to its higher
2The coding gain manifests itself by shifting the BER curve to the left withrespect to SNR.
508 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 4, OCTOBER 2011
Fig. 5. Temporal and spatial characterization of the RACE’08 channel: (a) snapshots of the estimated time-varying channel impulse response; (b) unbiased cross-correlation function between sensor outputs 2, 4, 6, 8, 10, 12, and output 1.
TABLE IPACKET PARAMETERS AND CORRESPONDING BIT RATES FOR SYSTEMS WITH ONE PROJECTOR
Euclidean distance. Note that the performance gap betweenAWGN and Rayleigh fading indicates that further improvementcan be accomplished if other types of diversity are exploited(e.g., spatial or time diversity).
2) Exploiting Space and Frequency Diversity: The benefit ofemploying many receive hydrophones on improving the BERperformance of the link is now examined. We assume inde-pendent channel fading among the receive hydrophones. Onceagain, the channel gains are fixed during each packet transmis-sion. In every subcarrier, the received signals from each hy-drophone are combined via maximal ratio combining (MRC).
In Fig. 3(d), we compare the BER results between TCM1x6and TCM1x6 over 1- and 10-ms-length, delay spread channels.Note that the BER performances of both systems approach theircorresponding “AWGN” performances as the frequency diver-sity increases. This result implies that each frequency-selectivefading channel turns into an AWGN-like channel before de-coding due to the ability of both systems to average out thechannel fade by exploiting full space and frequency diversity. In[33], a similar result was obtained for Rayleigh flat fading chan-nels with receive diversity. Since the free Euclidean distanceis the key parameter to achieve better performance in AWGN
PELEKANAKIS AND BAGGEROER: EXPLOITING SPACE–TIME–FREQUENCY DIVERSITY WITH MIMO–OFDM 509
Fig. 6. BER results corresponding to date 65 (March 5): (a) TCM/BICM systems with one transmit and one receive hydrophone (1x1); (b) TCM/BICM systemswith one transmit and two receive hydrophones (1x2); (c) TCM/BICM systems with one transmit and three receive hydrophones (1x3).
channels, TCM1x6 outperforms BICM1x6 in both channels.For example, the performance improvement of TCM1x6 is ap-proximately 1.5 dB at a BER of 10 for the six-tap Rayleighfading channel.
3) Exploiting Time and Frequency Diversity: The effect oftime diversity on the BER performance is now addressed. To-wards this end, we let the channel to become time varying withineach packet period. Channels with 2 Hz and 5 Hzare simulated. The interleaving depth is 32 subcarriers ensuringthat all codewords span both different coherence bands and dif-ferent coherence time periods, i.e., both time and frequency di-versities are exploited. We stress that the proposed systems donot account for the SNR loss due to the intercarrier interference(ICI). Fig. 3(e) illustrates the BER performance of TCM1x1over 1-ms-length delay spread channels. Note the channel with
5 Hz performs better than zero-Doppler channel sincethe time diversity offered by the channel leads to performanceimprovement despite the ICI. On the other hand, as Fig. 3(f)manifests, the TCM scheme cannot exploit the time diversitygiven by the Doppler spread channels and therefore, the zero-Doppler channel gives the best performance since it has no ICI.Fig. 3(g) shows that BICM1x1 can exploit time diversity whenthe channel has four physical paths. For instance, 3 dB lesspower is needed for a BER of 10 when increases from0 to 2 Hz. Observe also that the 5-Hz channel demonstrates anerror floor due to high ICI power. As the number of nonzerotaps increases from four to eight, BICM1x1 fails to exploit fulltime and frequency diversity, as seen in Fig. 3(h). As a result,the channel characterized by 10-ms delay spread and no Dopplerspread yields the best performance since it is not affected by ICI.
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Fig. 7. BER results corresponding to date 81 (March 21): (a) TCM/BICM systems with three transmit and one receive hydrophone (3x1); (b) TCM/BICM systemswith three transmit and two receive hydrophones (3x2); (c) TCM/BICM systems with three transmit and three receive hydrophones (3x3).
V. EXPERIMENTAL RESULTS
A. Description of RACE’08
The Rescheduled Acoustic Communications Experiment(RACE) took place in Narragansett Bay, RI, in March 2008.The experimental setup is shown in Fig. 4. The transmitterconsisted of a three-sensor line array with 60-cm intersensorspacing and a separate primary transducer, which was 1 mabove the uppermost element of the line array and 4 m abovethe sea bottom. The transmitter was mounted on a rigid tripodand the depth at the transmitter site was 9 m. The receiver con-sisted of a 12-sensor line array with 12-cm intersensor spacing.The receiver was mounted on a 2-m-height rigid tripod and thedepth at the receiver site was 10 m. The horizontal range ofthe link was 1 km. The total emitted signal level was 185 dBre 1 Pa at 1 m away from the source(s). Both the transmittingand receiving systems incorporated antialiasing filters with
18.5-kHz cutoff frequency and their sampling frequency was39062.5 samples/s.
B. Channel Characterization
The channel probing signal was approximately 1 min long,continuous repetition of a binary amplitude modulated, 4095-symbol length, -sequence. The bandwidth of the -sequencewas 10 kHz and the carrier frequency was 13 kHz. A prec-ompensation filter was applied before transmission to yield a“flat” response system between the transmitting and receivingtransducers. The probing signal was transmitted every 2 h forabout 20 days of the experiment. The received probing signalwas translated into baseband and lowpass filtered before crosscorrelating it with the transmitted -sequence to produce anestimate of the time-varying impulse response. Since both thetransmitter and the receiver were stationary, any rapid amplitudefluctuations of the received signal (signal fading) are attributedto environmental changes.
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TABLE IINUMBER OF ERROR-FREE PACKETS RECEIVED FOR TCM1xN AND BICM1xN SYSTEMS
TABLE IIIPACKET PARAMETERS AND CORRESPONDING BIT RATES FOR SYSTEMS WITH THREE PROJECTORS
Fig. 5(a) shows the amplitude of the estimated channel im-pulse response over a 16-h interval. The horizontal axis repre-sents delay, the vertical axis represents absolute time, and thecolorbar represents the amplitude. The channel estimates werecomputed by processing six data sets, received during Juliandate 75. This date is chosen because a correlation between theenvironmental conditions and the time variability of channel im-pulse response is obvious. Note that the multipath arrival struc-ture appears stable at 4:00 A.M. and 7:00 A.M. In addition, a con-structive/destructive interference pattern due to surface-bouncemultipaths (i.e., reflections from wave troughs and crests) isclearly seen. On the contrary, the multipath arrival structure ap-pears random and the impulse response is highly time varyingafter 12:00 P.M. This is because strong winds induced an in-crease of the sea surface height and roughness, which in turncaused the following two effects: 1) a random change in the dis-tance of surface-bounced paths due to rapid motion of the spec-ular reflection point above and/or below the average sea level;and 2) an additional random attenuation of surface-bounce mul-tipaths due to acoustic scattering off the rough sea surface. Fur-thermore, the hourly changes of sound speed result in shifting ofthe multipath arrival times. Fig. 5(b) illustrates the spatial coher-ence of the channel based on cross correlating the output of dif-ferent sensors of the receive array. The magnitude of cross-cor-relation functions is plotted. The averaging window was 0.8 s.Note that significant decorrelation happens when sensors areseparated by more than 48 cm, which corresponds to approx-imately at 13 kHz, being the acoustic wavelength. Con-sequently, using consecutive sensors is inefficient in terms ofexploiting receive diversity.
C. Decoding Results
Here, we provide an extensive set of BER results for theTCM-based and BICM-based systems by decoding field data
received during RACE’08. Information bits were groupedinto blocks of different sizes and each block generated aTCM–OFDM packet followed by its BICM–OFDM counter-part. Symbol per bit interleaving was chosen to be randomacross the entire length of each packet to ensure both time andfrequency diversities. A 2-min-long waveform was created afterputting all packets together. This waveform was transmittedevery 4 h during the same day for several days of the experi-ment. The bandwidth was 3906.25 Hz centered at 12 kHz.
1) Single Projector Systems: Packets with various combi-nations of number of subcarriers, (expected delay spread),and (expected one-sided Doppler spread) were tested. Thesecombinations, the pilot-symbol distances in time and frequency,the number of information bits in each packet, and the corre-sponding packet bit rate (after excluding pilot symbols and ac-counting for coding) are organized in Table I. Acoustic wave-forms were transmitted from the primary transducer only.
We now compare the BER performances of TCM–OFDMand BICM–OFDM based on the packets received. A selected setof BER results is presented in Fig. 6. For an extensive set of BERplots, the reader is directed to [34]. In all the BER plots, BER
is plotted as BER 10 for visualization purposes. Label1x1 indicates that one transmit and one receive hydrophone (the12th sensor) were used for decoding each packet. Similarly, la-bels 1x2 and 1x3 indicate that a combination of two (6th and12th) and three (1st, 6th, and 12th) receive sensors were used todecode the packets, respectively. From all the BER plots, BICMclearly performs better than TCM, especially when one receivesensor is employed. When two or three sensors were employed,BICM performs only marginally better. The success of BICMrelative to TCM is also evident in Table II, which shows thenumber of error-free packets for each system, based on datafrom eight different days of the experiment.
512 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 4, OCTOBER 2011
TABLE IVNUMBER OF ERROR-FREE PACKETS RECEIVED FOR TCM3xN AND BICM3xN SYSTEMS
These experimental results show that the advantage of havinga higher Hamming distance is a key parameter for obtaining ro-bust performance over UWA channels with low spatial diver-sity. This result is in accord with the simulation results shownin Fig. 3(a), which have also proven the superiority of BICMin multipath Rayleigh fading channels. Moreover, this result isconsistent with what is seen in terrestrial radio channels [24].
2) Multiple Projector Systems: Table III shows the packet pa-rameters and their corresponding data rates. Signals were trans-mitted from the primary transducer and the first two projectorsof the line array.
A selected set of decoding results are presented in Fig. 7. Foran extensive set of BER plots, the reader is directed to [34].Once again, BER is plotted as BER 10 for visual-ization purposes. Label 3x1 indicates that two transmit and onereceive hydrophone (the 12th sensor) were used for decodingeach packet. Similarly, labels 3x2 and 3x3 indicate that a combi-nation of two (6th and 12th) and three (1st, 6th and 12th) receivesensors, respectively, were used to decode the packets. From allBER plots, it is clear that TCM performs better than BICM, es-pecially when two or more receive sensors are employed. Thesuperiority of TCM is also evident from Table IV, which showsthe number of error-free packets for each system based on datafrom five different days of the experiment.
These experimental results suggest a strong connection be-tween a higher free Euclidean distance and improved perfor-mance in UWA channels with high spatial diversity. However,there are also some unexplained results. If we compare the 1x3and the 3x1 results we see that despite the same spatial diversity,BICM modestly outperforms TCM in the 1x3 case. It should beunderscored that the environmental conditions were differentin these two experiments. Thus, further experimentation andchannel modeling is needed to gain additional insight into thedependence of the coding scheme performance and the spatialdiversity in UWA channels.
VI. CONCLUSION
Two systems with the same bit rate and decoding complexitywere designed based on methods popularized for terrestrialradio systems. The first system is based on TCM, while thesecond system is based on BICM using a convolutional code.Comparing the BER of these schemes by using SIMO andMIMO experimental channels, the following result, whichalso holds in radio communications, was obtained: the BICMscheme performs better when the channel exhibits a low di-versity order (which is usually the case when spatial diversityis very limited). This is because BICM has a higher Hamming
distance, which is a key parameter for achieving robust perfor-mance in fading channels. The TCM scheme, on the other hand,becomes a better choice when the channel demonstrates a highdiversity order (which is usually the case when spatial diversityis sufficient). The reason for TCM’s superiority is twofold: 1)spatial diversity averages out the channel fade, and thereforethe effective channel seen by the decoder is an AWGN-likechannel; and 2) TCM has a higher coding gain, which is thekey parameter for achieving better performance in the AWGNchannel. The results of this work were obtained by using afixed transmitter and a fixed receiver; however, investigatingthe proposed systems in a mobile scenario makes the problemmore challenging since ICI becomes a limiting factor for theperformance of OFDM systems. We leave this challenge as afuture research direction.
ACKNOWLEDGMENT
The authors would like to thank Dr. J. C. Preisig for con-ducting the RACE’08 experiment.
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Konstantinos Pelekanakis (S’06–M’09) receivedthe Diploma from the Department of Electronicand Computer Engineering, Technical University ofCrete, Chania, Greece, in 2001 and the M.Sc. andPh.D. degrees in mechanical and ocean engineeringfrom the Massachusetts Institute of Technology(MIT), Cambridge, in 2004 and 2009, respectively.
Currently, he is a Postdoctoral Associate withthe Acoustic Research Laboratory (ARL), Na-tional University of Singapore (NUS), Singapore.His current research interests lie in the areas of
multiple-input–multiple-output (MIMO) underwater acoustic communicationsystems, coded orthogonal frequency-division multiplexing (OFDM), statisticalsignal processing in non-Gaussian noise, and adaptive algorithms for sparsesystem identification.
Arthur B. Baggeroer (S’62–M’68–SM’87–F’89–LF’08) received the B.S.E.E degree from PurdueUniversity, West Lafayette, IN, in 1963 and theSc.D. degree from the Massachusetts Institute ofTechnology (MIT), Cambridge, in 1968.
He is a Ford Professor of Engineering with theDepartments of Ocean Engineering and ElectricalEngineering and Computer Science, MIT. He hasalso been a consultant to the Chief of Naval Researchat the NATO SACLANT Center, La Spezia, Italy,in 1977 and a Cecil and Ida Green Scholar at the
Scripps Institution of Oceanography, San Diego, CA, in 1990, while onsabbatical leaves. His research has concerned sonar array processing, acoustictelemetry, and most recently, global acoustics and matched field array pro-cessing. He also has had a long affiliation with the Woods Hole OceanographicInstitution, Woods Hole, MA and was Director of the MIT/Woods Hole JointProgram from 1983 to 1988.
Dr. Baggeroer is a Fellow of the Acoustical Society of America. He receivedthe IEEE Oceanic Engineering Society Distinguished Technical AchievementAward in 1991, was an elected member of the Executive Council of the Acous-tical Society from 1994 to 1997, and was awarded the Rayleigh–HelmholtzMedal from the Acoustical Society in 2003. He was elected to the NationalAcademy of Engineering in 1995 and awarded a Secretary of the Navy/Chief ofNaval Operations Chair in Oceanographic Science in 1998.
