On the Region of Feasibility of Interference Alignment in Underwater Sensor Networks

Transcription

1 On he Region of Feasibiliy of Inerference Alignmen in Underwaer Sensor Neworks Parul Pandey, Suden Member, IEEE, and Dario Pompili, Member, IEEE Absrac o enable underwaer applicaions such as coasal and acical surveillance, undersea exploraions, and picure/video acquisiion, here is a need o achieve high daarae underwaer acousic communicaions, which ranslaes ino aaining high acousic channel specral efficiencies. Inerference Alignmen (IA) echnique, which has recenly been proposed for radio-frequency MIMO erresrial communicaion sysems, aims a improving he specral efficiency by enabling nodes o ransmi daa simulaneously a a rae equal o half of he inerference-free channel capaciy. While promising, here are challenges o be solved for he use of IA underwaer, i.e., imperfec acousic channel knowledge, high compuaional complexiy, and high communicaion delay. In his paper, a feasibiliy sudy on he pracical employmen of IA underwaer is presened, and a novel disribued compuing framework for sharing processing resources in he nework so o parallelize an ieraive IA algorihm is proposed. Index erms Underwaer acousic neworks, MIMO echnology, inerference alignmen, channel esimaion. I. INRODUCION UnderWaer Acousic Sensor Neworks (UW-ASNs) [] consis of saic and mobile sensors deployed o perform collaboraive monioring asks over a body of waer. hese neworks enable oceanographic applicaions such as environmenal monioring, offshore exploraion, and video-assised navigaion. Due o propagaion limiaions of Radio Frequency (RF) and opical signals, i.e., high medium absorpion and scaering, respecively, acousic communicaion echnology is employed for ransfer of informaion beween underwaer sensors. owever, because of he limied acousic bandwidh available, here is a need o maximize he underwaer nework capaciy. his is essenial in order o enable high daa-rae mulimedia applicaions such as video/audio sream ransfer, ransfer of meadaa associaed wih hese sreams, and imecriical monioring processes. In erresrial sysems, Muliple Inpu Muliple Oupu (MIMO) sysems have been proposed o enable high daa-rae applicaions. hese sysems are able o exploi he scaering and mulipah fading in such a way as o provide higher specral efficiencies using he same ransmission oupu power. MIMO echnology can in fac ake advanage of he rich scaering and heavy mulipah of he underwaer acousic environmen so o increase daa ransmission raes and improve link reliabiliy in UW-ASNs [2], []. While sill no maure, he promise of his echnology has also being recognized by he auhors are wih he Deparmen of Elecrical and Compuer Engineering, Rugers Universiy, New Brunswick, NJ. heir s are parul, pompili@cac.rugers.edu. his work was suppored by he NSF CAREER Award No. OCI x x2 x Rx Rx2 Rx Sound Speed (m/s) Fig.. An UW-ASN wih K = users (i.e., x-rx pairs) wih N = N R = 2 (wo anennae on each node). For a clear visualizaion, we have shown he Bell-hop channel profile associaed only wih x. he ransmission loss of he channel is given in db. ere, we used he Munk sound speed profile (righ subfigure) wih he deph being he same as in he lef subfigure. he underwaer acousic communicaion communiy in recen years. In order o increase he specral efficiency of muli-user wireless erresrial neworks, a echnique called Inerference Alignmen (IA) has been proposed [4], [5]. his echnique enables he ransmier-receiver pairs ( users ) o ransmi daa simulaneously a a rae equal o half of heir inerference-free channel capaciy. he goal of IA is o design ransmi signals for all users in such a way ha he inerfering signals a each receiver fall in he subspace ha is linearly independen of he subspace of he desired signal. he receiver hen applies an inerference suppression filer o projec he desired signal ono he inerference-free dimension of he nework. his is a very promising echnique o enable high daa-rae applicaions by increasing he specral efficiency of he channel. o he bes of our knowledge, his is firs ime IA echnique is being proposed o improve underwaer acousic communicaions. here are a few research challenges ha need o be solved for he pracical use of IA underwaer, namely, imperfec channel knowledge, high compuaional complexiy, and high communicaion delay. Exising IA algorihms assume perfec knowledge of he channel a he communicaing nodes; however, he accurae esimaion of he ime- and spacevarying underwaer acousic channel is a challenging ask iself. he propagaion speed of acousic waves varies wih waer emperaure, saliniy, and pressure (i.e., deph), which causes wave pahs o bend owards regions of lower sound speed (as shown in Fig. ). Acousic waves are also refleced

2 from he surface and boom. Such uneven propagaion of waves resuls in convergence (or shadow) zones, which are characerized by lower (or higher) ransmission loss. In his paper, we sudy he effec of inaccurae esimaion of underwaer acousic channel on he echnique of IA. We also sudy he radeoffs of muliplexing and link reliabiliy, power, and number of concurren users associaed wih IA. Also, o overcome he challenge of compuaional complexiy and communicaion delay, we inroduce a novel disribued compuing framework for sharing processing resources in he nework. We provide he compuing infrasrucure o suppor he disribued capabiliies of exising IA algorihms by forming an elasic resource pool; using he collecive compuaional capabiliy of his pool of neighboring nodes, parallel asks can be performed. We presen a sudy on he poenial increase in he region of feasibiliy of compue-inensive IA echniques in UW environmen hrough our framework. his involves sudying he rade-off beween compuaional gain (in erms of speed up over sand-alone compuaion) versus communicaion (and delay) overhead incurred as well as is effec on he performance in erms of specral efficiency for daa ransmission. his radeoff helps us define he scenarios in which he disribued realizaion of IA echnique is feasible in UW environmen. he following are he main conribuions of his paper. We sudy wheher i is feasible and pracical o use IA underwaer under differen channel and nework condiions. We also sudy he radeoff beween muliplexing and link reliabiliy, power, and number of concurren users associaed wih IA; We propose a disribued framework o parallelize he ieraive IA algorihm in underwaer environmen and show he gains via simulaions in erms of increase in nework capaciy. he res of he paper is organized as follows: in Sec. II, we provide he necessary background on IA and sudy he various radeoffs associaed wih his echnique; in Sec. III, we propose a disribued grid compuing framework and explain how we exploi i o realize disribued IA; in Sec. I, we evaluae he performance of our proposed approach; finally, in Sec., we draw he conclusions and provide a brief noe on fuure work. II. BACKGROUND In his secion, firsly we presen a brief background on IA and sudy he effec of imperfec channel condiions on he performance of IA. Secondly, we discuss he radeoff beween muliplexing and link reliabiliy in IA. We also sudy he need for power conrol, which is aimed a selecing an opimal ransmission power so o avoid impairing he ongoing communicaions of neighboring nodes while a he same ime guaraneeing minimum power requiremen for a ransmission o occur successfully. Finally, we discuss he compuaional complexiy of disribued IA algorihms. Inerference Alignmen: We consider a generic sysem model, a K-user inerference channel sysem as shown in Fig.. Each ransmier x is equipped wih N anennas, 2 2 U Fig. 2. Under perfec channel knowledge, inerfering signals 2 2 and align perfecly. and each receiver Rx is equipped wih N R anennas. Each x i is communicaing wih Rx i i =... K [6], [7]. When K = 2 and N = N R = 2, he channel beween ransmier i and receiver j is given as ij, which can be decomposed as ij = [ h ij h ij 2 h ij 2 h ij 22 ], () where each enry h ij kl is a complex number whose magniude represens he signal aenuaion from ransmier anenna k o receiver anenna l in a ime slo and whose phase represens he propagaion delay (in Fig., k, l {, 2}). A ransmier i, x i is a d i symbol vecor where d i is he number of independen informaion sreams or he degree of freedom for he i h ransmier. he goal of IA is o design ransmi precoding marices i of dimensions N d i for each ransmier. he ransmied signal is hen given as s i = i x i of dimension N. hese marices are chosen such ha by encoding wih hem all he inerfering signals lie in a subspace ha is linearly independen of he subspace of he desired signal. he hear of IA in spaial domain lies in consrucing hese ransmi precoding vecors. o decode, he receiver projecs he received signal ono a vecor ha is orhogonal o he vecor of inerfering signal. he received signal vecor a receiver j is given as, r i = ii i x i + K j=,i j ji j x j + n i, (2) where he firs erm is he desired signal a Rx i and he second erm is he inerference from all oher ransmiers. ere, n i is he N R Addiive Whie Gaussian Noise (AWGN) or hermal noise vecor. Inerference Cancelaion o decode, he receiver projecs he received signal ono a decoding vecor, U i, ha is orhogonal o he daa vecor of inerfering signal. Such decoding vecor can be found by imposing U i = null( ji i ) = null([ ki k ] ), where represens he ermiian or conjugae ranspose and null represens he null space of a generic marix A, i.e., he se of all vecors x for which Ax = 0. Afer applying he inerference suppression filer, i.e., U i,

3 + U U U 2 + Fig.. Under imperfec channel knowledge, inerfering signals and + do no align, hus resuling in residual inerference (leakage). represens he rank of he desired signal, i.e., he number of parallel sreams (also known as degree of freedom). Imperfec channel knowledge: Now we consider he alignmen a Rx afer [s] from he las channel probing a insan. We assume ha he channel has changed wih ime and he new updaed channel marix is +. We also assume ha he nodes do no have updaed channel informaion. As a resul, hey coninue o use he precoding and decoding vecors esimaed a ime (i.e., i and U i ). Figure shows he inerference alignmen a Rx. he inerference signals ( and + ) no longer align perfecly as in he case of Fig. 2. his is because he channel has changed and he precoding/decoding used are esimaed based on he old channel knowledge +. ence, he inerfering signals no longer lie in he same subspace. Also, a new inerference suppression filer needs o be esimaed o cancel he inerference. As a resul, afer applying he inerference suppression filer U he inerference is no compleely canceled ou. he inerference leakage in his case is U i ji + j 0, j i. (6) he received signal a receiver i is given as, y i = U i ii i x i + K j=,j i U i ji j x j + U i n i. () he second erm in () is he oal inerference a receiver i, which is called inerference leakage. he inerference leakage a Rx i is defined as, K j=,j i U i ji j. In case of ideal IA, i.e., when he channel knowledge is perfec, he inerference signals lie in he same subspace and he inerference suppression filer eliminaes he inerference compleely. Channel informaion and inerference leakage: We now discuss abou he effec of perfec and imperfec channel knowledge a he communicaing nodes on he IA echnique. Perfec channel knowledge: Le us consider a K = user sysem wih N = N R = 2 and d i =, where d i is he number of independen sreams ransmied by x i. he channel from X i o RX i a ime is given as ii. According o IA, in he case of perfec channel knowledge he inerfering signals lie in he same subspace ha is independen of he subspace of he desired signal. Fig. 2 shows he signals received a Rx. Signals 2 2 and are inerference signals and is he desired signal. he dimension of he received signals is 2 d i (i.e., N in his example). We see ha boh he inerference signals align, i.e., overlap, perfecly. he inerference suppression filer is hen applied o hese inerference signals, which compleely cancels hese signals. In case of ideal inerference alignmen, he decoding vecor U = null( 2 2 ) = null([ ] ), i.e, i lies in he null space of he inerference signals. ence, in he case of perfec channel knowledge we have, U i ji j = 0, j i, (4) i.e., he inerference leakage is compleely removed by he inerference suppression filer and rank(u i ii i ) = d i (5) As a resul, he Bi Error Rae (BER) increases, which leads o he corresponding decrease in ne bi rae, given by D N = d i C x ( BER), where he capaciy C x is given as a produc of he used bandwidh, B [kz], and he specral efficiency of he modulaion, η [bps/z]. he capaciy of each individual daa sream is muliplied by he number of parallel sreams of he nework o obain he overall capaciy of he MIMO sysem. he higher d i (i.e., he higher he degree of muliplexing), he higher he specral efficiency of he MIMO sysem. We will now discuss he radeoffs associaed wih IA and how hey affec is performance. Muliplexing and link reliabiliy: In MIMO ransmissions, o increase he specral efficiency muliple daa sreams are sen ou in parallel. he increase in specral efficiency by ransmission of muliple independen parallel sreams in comparison o a single sream is called muliplexing gain. If d i is he number of independen sreams sen ou, hen he muliplexing gain is d i. he ransmied signal i x i a X i is of dimension N d i. A Rx i, he rank of he subspace of he desired signal is d i. For perfec alignmen, according o he heory of IA, he subspace of inerfering signals j x j should have a rank N d i and should span he same subspace, linearly independen from he desired-signal subspace. In case of imperfec channel esimaion, however, he inerference signals may no longer occupy he same inerference subspace. o overcome his effec, he number of independen sreams d i a he ransmier can/should be reduced. his allows he inerference o span across a higher dimension subspace, which leads o low inerference leakage and, hence, o a low BER. owever, alhough his low BER gives a high link reliabiliy, i comes a a cos of a lower muliplexing gain, which explains he muliplexing vs. link reliabiliy radeoff. Power conrol: o visualize he effec of ransmission power on IA, we consider wo ypes opologies. opology is similar o ha in Fig., where all ransmiers and receivers are equidisan from each oher; whereas opology 2 is given in Fig. 4(a). We see ha due o he proximiy of x o Rx 2

4 x Rx2 Rx x2 Sum Rae Capaciy [bps/z] opology opology 2 Sum Capaciy per user [bps/z] N = 2 N = N = x Rx P [W] Number of Users (a) (b) (c) Fig. 4. (a) opology o visualize he near-far effec on he echnique of IA; (b) ariaion of specral efficiency wih opology; (c) ariaion of nework capaciy wih number of users for differen number of anennae (N = 2,, 4). in Fig. 4(a) he signal received from x is sronger han ha received from x 2. his is an example of he near-far effec, which in general occurs when he signal received by a receiver from a sender near he receiver is sronger han he signal received from anoher sender locaed furher. In his case, he remoe sender will be dominaed by he close sender. In Fig. 4(a), we can see ha he signal from x 2 will cause inerference a Rx. he residual inerference a RX will be j=2,j i P j U j j. ence, he higher he power of X, he higher he inerference leakage will be. Figure 4(b) compares he specral efficiency of he sysem associaed wih he wo exreme opologies. We see ha he specral efficiency of he sysem for opology 2 is lower han ha for opology. his moivaes he need for a power-conrol mechanism ha avoids impairing he ongoing communicaions of neighboring nodes and a he same ime is able o guaranee he minimum power requiremen for he ransmission o occur successfully. Number of acive users: In he case of imperfec channel esimaion, he inerference leakage K j=,j i U i ji j canno be negleced. Specifically, as he number of users K increases, he inerference leakage also increases, leading o higher BER (i.e., lower link reliabiliy). In Fig. 4(c) we see ha as K increases he capaciy per user of he sysem decreases; on he oher hand, if K is oo low, he gain from IA is no exploied properly. Compuaional complexiy and communicaion delay: IA algorihms used for esimaing he precoding/decoding vecors (e.g.,[8], [9]) are compue inensive as hey involve muliple eigen-vecor calculaions and marix muliplicaions. hese calculaions need o be performed in a fracion of he channel coherence ime c (defined as he duraion over which he impulse response is considered o be ime invarian) so ha he esimaed precoding/decoding vecors are reusable for he remaining ime of he coherence ime. Also, he exising IA algorihms require exchange of informaion beween ransmier and receiver, which canno happen insananeously due o he large underwaer communicaion delay (due o propagaion and ransmission delays). If c is smaller han he ime aken o compue he precoding/decoding vecors, hen hese vecors will no be useful as he channel condiions will have changed. o overcome hese issues, we propose a disribued compuing framework ha reduces he compuaion ime for esimaing he precoding vecors by execuing in parallel he asks composing he IA algorihm. Such framework, however, inroduces some overhead, which needs o be absorbed by he gain i brings (i.e., reducing he overall execuion ime of he IA disribued algorihm): his is anoher radeoff involving compuaional complexiy and communicaion delay. III. DISRIBUED COMPUING FRAMEWORK Exising IA algorihms are compuaionally inensive and require exchange of informaion beween ransmier and receiver, which canno happen insananeously (as desirable ideally) due o he large underwaer propagaion delay. If he coherence ime of he channel ( c ) is smaller han he ime aken o compue he precoding/decoding vecors, hen hese vecors will no be useful as he channel condiions will have changed. o overcome his issue, we propose a disribued compuing grid framework [0] ha reduces he compuaion ime for esimaing he precoding vecors by execuing in parallel he asks composing he IA algorihm. Disribued IA Algorihm: We now presen an ieraive IA algorihm [8] for which our framework provides compuing infrasrucure o suppor is disribued capabiliies. his algorihm is compuaionally inensive as i involves muliple marix and eigen-vecor calculaions. he oal residual inerference a he receiver of user j due o inerference from all undesired ransmiers (k j) is given by, I j = r[u j Q j U j ], Q j = K k=,k j P k d k kj k k kj, where P k is he ransmi power a ransmier k. Each of he d j columns of U j are given by, U j[n] = ν n [Q j ], n =,..., d j, where ν n [Q j ] is he eigenvecor corresponding o he n h smalles eigenvalue of Q j. In he beginning of he ieraive algorihm, he ransmi precoding vecors are iniialized wih some random values and inerference suppression filer of he original nework are calculaed using (7). Afer deermining U j, he ransmier and receiver swich heir roles. his nework is called a reciprocal nework. he esimaed (7)

5 Daa providersproviding channel coefficien esimaes Maser (Addiional role of some service providers) Workflow manager Opimizer Ge service Accep Pu adverisemens workload/ asks/ Reurn Ge resuls resuls Submi workload/ Receive resuls Pu service adverisemens Coordinaion space Ge asks/ Submi resuls Sensor Nodes in he viciniy of daa providers AUs Resource providerssharing he workload by execuing algorihms (in parallel) wih differen iniial condiions Sensor nodes Fig. 5. An overview of he envisioned disribued compuing framework for opimizing compue-inensive IA algorihms inerference suppression filer (U j ) of he original nework now become he precoding vecors ( j ) for he reciprocal nework. he arrow a he op indicaes ha his vecor belongs o he reciprocal nework. Similarly o he original nework, in he reciprocal nework (wih ransmiers and receivers swiched) he oal inerference leakage a receiver j due o inerference from all undesired ransmiers (k j) is given by, I j = r[ U j Q juj ]. he inerference suppression filer ( U j ) for he receivers of he reciprocal nework are calculaed only o be used as he ransmi precoding vecors of he original nework in he nex ieraion. he ieraive algorihm alernaes beween he original and reciprocal neworks wih only he receivers updaing heir inerference suppression filer (in every ieraion) o minimize heir oal leakage inerference. Leveraging he disribued framework in UW-ASNs: In our framework, one of he node serves as he maser, i.e., i is responsible for parallelizing he asks beween ransmier/receiver pair and he nodes in he neighborhood, called Service Providers (SPs). We assume ha only he communicaing nodes are service providers. Our scenario is shown in Fig. 5. Each communicaing node esimaes he channel from iself o all oher communicaing nodes and broadcass his informaion. he maser chooses equally spaced iniial condiions for he ieraive IA algorihm so o ensure good coverage of he n-dimensional search space and o avoid choosing final precoding/decoding vecors suck in local minima, hence, subopimal. he maser ransmis a unique iniial condiion o each SP and he number of ieraions required o execue he ieraive algorihm. Once he SPs have compued he precoding vecors, hey send heir resuls o he maser, which selecs he vecor pair ha maximizes he nework specral efficiency. In his compuing grid framework, each node execues he ieraive algorihm locally: his way, by incurring only small communicaion overhead caused by message exchanged among he nodes of he mobile grid, we overcome he challenge of high communicaion delay. I. PERFORMANCE EALUAION In his secion we sudy he performance gains achieved hrough IA in erms of specral efficiency in UW environmen. We consider boh he scenarios of perfec and imperfec channel knowledge a he nodes. We also invesigae he effeciveness of he proposed framework for IA via simulaions. We presen a sudy on he poenial increase in he region of feasibiliy of compue-inensive IA echniques in UW environmen using our framework. We model he UW channel using he Urick model. he Urick model is used o esimae he ransmission loss L(l, f) [db] as, L(l, f) = κ0log(l) + α(f)l + A, (8) where l [m] is he disance beween he ransmier and receiver and f [z] is he carrier frequency. Spreading facor κ is aken o be.5 for pracical spreading, and α(f) [db/m] represens an absorpion coefficien ha increases wih f. he las erm, expressed by he quaniy A [db], is he ransmission anomaly. We adop he empirical ambien acousic noise model presened in [], where he srucure of he noise power specrum densiy (psd) is shown. We consider a deploymen region of (L) (W ) () km. he carrier frequency and bandwidh are assumed o be 0 kz and 20 kz respecively. Figure 6(a) depics he measured and he heoreical specral efficiency versus Signal o Noise Raio (SNR) for differen degrees of freedom (DoF), a capaciy characerizaion of he nework ha is accurae wihin O(log SNR). We observe ha he measured specral efficiency does no increase a he same rae as he heoreical one, which can herefore be used as an upper bound. We assume he channel knowledge o be perfec in his case. We now consider he effecs of imperfec channel knowledge, where he error in esimaion of channel coefficiens can be modeled as = + eω, where eω is he error (assumed uncorrelaed wih ). he enries of Ω are i.i.d. zero-mean complex Gaussian wih uniy variance and e is a parameer modeling how accurae he channel esimaion is [2]. Figure 6(b) shows he variaion of BER as he SNR varies. We see ha he BER increases as e increases. he value of e ranges from 0 o 0.2, where 0 indicaes perfec channel knowledge. ere, he DoF is assumed o be. As he channel error (e ) increases from 0 o 0.2, he specral efficiency decreases by 70%. his indicaes ha he pracical implemenaion of IA depends largely on he qualiy of our channel esimaes. We now consider he performance gains in erms of specral efficiency from our disribued framework. In Fig 6(c), we see he nework specral efficiency (sum of specral efficiency of all he users in he nework) versus power; as he number of service providers (SPs) increases, he nework specral efficiency increases. Specifically, as he number of SPs increases from o, he specral efficiency increases by 5 kbps/z. For a 20kz-sysem, he specral efficiency increases by 00 kbps. he number of ieraions for all service providers is assumed o be 0. Le us compare he case where he enire ieraive algorihm is execued a one node (one SP) wih he case where he number of compuing nodes, i.e., SPs, is greaer han wo. From Fig. 7, we see ha, for he same opology, as he number of SPs increases, he esimaion ime (sum of compuaion ime for calculaing precoding/decoding vecors and

6 Ne Specral Efficiency [bps/z] Ach Capaciy DoF= Ach Capaciy DoF=2 Ach Capaciy DoF h Capaciy DoF= h Capaciy DoF=2 h Capaciy DoF= SNR [db] BER Perfec Channel Knowledge, e=0 e=0.05 e=0. e= SNR [db] Nework Specral Efficiency [bps/z] SP SPs 5 SPs 7 SPs 9 SPs Power [W] (a) (b) (c) Fig. 6. (a): ariaion of he heoreical and ne specral efficiency wih SNR under perfec channel condiions; (c): BER vs SNR wih differen degrees of inaccuracy in channel knowledge; (c) ariaion of nework specral efficiency wih power for differen number of SPs. Esimaion ime [s] dis = 200m dis = 400m dis = 600m dis = 800m dis = km disribued compuing framework for he UW environmen o overcome he challenge of compuaional complexiy and communicaion delay faced by IA algorihms. We observed ha parallelism is no only possible (nowihsanding he large acousic propagaion delays) bu in fac increases he region of feasibiliy. As a fuure work, we plan o implemen our proposed soluion on an emulaor wih real WOI acousic modems, wih he UW acousic channel simulaed using he Bellhop model Number of SPs Fig. 7. ariaion of minimum esimaion ime of precoding/decoding marices wih number of SPs. he disance indicaes he maximum disance assumed beween a ransmier and receiver in he nework. he communicaion ime beween maser and SPs) decreases. For example, when he number of SPs increase from o 5 for a disance of 800 m, he esimaion ime reduces from 4.25 o 2 s, i.e, a reducion by more han 50%. ence, for a given coherence ime, a high enough number of SPs allows he use of precoding vecors for a longer duraion (hus bringing savings in erms of probing overhead). We can also see ha as he number of SPs increases beyond eigh, he esimaion ime sars o increase. his increase in compuaion ime can be aribued o he increase in coordinaion ime beween maser and SPs. Alhough he specral efficiency increases as he number of SPs increases (as shown in Fig. 6(c)), he esimaion ime also increases. As a resul, he esimaed precoding/decoding vecors will be useful for a shorer duraion of ime, which provides a quaniave example of he radeoff beween communicaion overhead and compuaional gain.. CONCLUSION AND FUURE WORK We sudied he effec of inaccurae channel esimaion on he echnique of Inerference Alignmen (IA). We showed via simulaions he radeoffs under differen UndeWaer (UW) acousic channels and nework opologies. We observed ha he performance gain (in erms of specral efficiency) depends on he qualiy of he channel esimaes. We proposed a REFERENCES [] D. Pompili and I. Akyildiz, A Cross-layer Communicaion Soluion for Mulimedia Applicaions in Underwaer Acousic Sensor Neworks, in Proc. of IEEE Inernaional Conference on Mobile Ad-hoc and Sensor Sysems (MASS), Alana, GA, Ocober [2] D. Kilfoyle, J. Preisig, and A. Baggeroer, Spaial Modulaion Experimens in he Underwaer Acousic Channel, IEEE Journal of Oceanic Engineering, vol. 0, no. 2, pp , April [] A. arris and M. Zorzi, On he Design of Energy-efficien Rouing Proocols in Underwaer Neworks, in Proc. of IEEE Inernaional Conference on Sensor, Mesh and Ad oc Communicaions and Neworks (SECON), San Diego, CA, June [4]. Cadambe and S. Jafar, Inerference Alignmen and Degrees of Freedom of he K-user Inerference Channel, IEEE ransacions on Informaion heory, vol. 54, no. 8, pp , Augus [5] A. Ghasemi, A. Moahari, and A. Khandani, Inerference Alignmen for he K-user MIMO Inerference Channel, in Proc. of IEEE Inernaional Symposium Informaion heory Proceedings (ISI), Ausin, X, June 200. [6] S. Jafar and M. Fakhereddin, Degrees of Freedom for he MIMO Inerference Channel, IEEE ransacions on Informaion heory, vol. 5, no. 7, pp , [7] S. Jafar and S. Shamai, Degrees of Freedom Region of he MIMO X Channel, IEEE ransacions on Informaion heory, vol. 54, no., pp. 5 70, [8] K. Gomadam,. Cadambe, and S. Jafar, A Disribued Numerical Approach o Inerference Alignmen and Applicaions o Wireless Inerference Neworks, IEEE ransacions on Informaion heory, vol. 57, no. 6, pp , June 20. [9] D. Papailiopoulos and A. Dimakis, Inerference Alignmen as a Rank Consrained Rank Minimizaion, in Proc. of IEEE Global elecommunicaions Conference (GLOBECOM), Miami, FL, Dec 200. [0]. iswanahan, E. K. Lee, I. Rodero, and D. Pompili, An Auonomic Resource Provisioning Framework for Mobile Compuing Grids, in Proc. of IEEE Inernaional Conference on Auonomic Compuing (ICAC), San Jose, CA, Sep [] M. Sojanovic, On he Relaionship Beween Capaciy and Disance in an Underwaer Acousic Communicaion Channel, SIGMOBILE Mob. Compu. Commun. Rev., vol., no. 4, pp. 4 4, Oc [2] C. Wang, E. Au, R. Murch, W. Mow, R. Cheng, and. Lau, On he Performance of he MIMO Zero-Forcing Receiver in he Presence of Channel Esimaion Error, IEEE ransacions on Wireless Communicaions, vol. 6, no., pp , 2007.