A practical scheduling and power/constellation allocation for three relay networks

Transcription

1 RESEARCH Open Access A practcal schedulng and power/constellaton allocaton for three relay networks Paolo Baracca *, Stefano Tomasn and Nevo Benvenuto Abstract Relays are beng deployed n both fourth generaton cellular systems and wde metropoltan area networks n order to ncrease coverage and spectral effcency. In ths artcle, we consder a network wth three half-duplex relays assstng the transmsson from a source towards a destnaton. By assumng that transmsson tme conssts of a sequence of phases, we develop a transmsson scheme n whch spatal multplexng s acheved by alternatng the transmsson of a sngle relay n odd phases and a couple of relays employng Slepan-Wolf encodng n even phases. Moreover, to smplfy Slepan-Wolf decodng (consstng of a scheme wth successve nterference cancelaton, we propose a suboptmal scheme n whch cooperatve relays employ quantzed QAM constellatons to yeld at the destnaton the desred QAM constellaton wth no nterference. We formalze the problem of mzng network spectral effcency optmzng (a QAM sze, (b power allocaton, (c tme allocaton, and (d relays transmttng and recevng at each phase. The performance of the proposed scheme s compared aganst exstng technques n typcal wreless scenaros showng the merts of the proposed approach. Keywords: relay network, cooperatve systems, quadrature ampltude modulaton. Introducton Relays or cooperatve networks where the transmsson between a source and a destnaton s asssted by other nodes have shown to be an nterestng soluton to mplement dstrbuted multple nput multple output (MIMO systems. Intal works on relay networks have consdered a sngle relay node [] and varous transmsson technques, ncludng decode and forward, amplfy and forward, and compress and forward [-4]. As relay nodes are beng deployed, e.g., n forth generaton cellular networks and n wde metropoltan area networks [5], there s an ncreasng nterest n usng more than one relay. In fact beamformng can be used by cooperatve relays wth the am of transmttng coherently towards the destnaton. Networks wth multple relays have been wdely studed under the full-duplex assumpton n [6,7]. The achevable rates for varous technques have been derved n [8] for the case of half duplex relays n the absence of nterference for a network wth two relays. In ths artcle, we consder a network wth three relays operatng n half duplex mode. In order to lmt the * Correspondence: baraccap@de.unpd.t Department of Informaton Engneerng, Unversty of Padova, Padova, Italy complexty of the consdered scenaro, we assume that relays cannot communcate wth each other, but only wth the source and the destnaton. Furthermore, we consder that the transmsson tme s a sequence of phases, where n odd phases a subset of relays s transmttng and the rest s recevng, whle n the even phases the role of the relays s swapped. For ths scenaro we formulate the optmzaton problem that mzes the throughput from the source to the destnaton, consderng transmsson power constrants at each node. The optmzaton ncludes both the choce of the subset of relays transmttng and recevng at each phase and the duraton of even and odd phases. Two solutons are proposed. The frst s based on the Slepan-Wolf theorem [9] for the transmsson of prvate and common nformaton and requres successve nterference cancelaton at the destnaton. In the second soluton we adapt the technque developed n [0] for downlnk mult-cell scenaro by allowng the smultaneous transmsson of relays towards the destnaton n such a way that a sngle QAM symbol s receved, and thus not requrng successve nterference cancelaton. The performance of the proposed solutons s compared wth respect to exstng approaches, showng 0 Baracca et al; lcensee Sprnger. Ths s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted.

2 Page of 8 a sgnfcant mprovement of the network throughput n typcal wreless scenaros. The rest of the artcle s organzed as follows. In Secton, we ntroduce the system model of the network wth three relays and brefly summarze exstng approaches for the cooperatve transmsson. In Secton 3, we propose the new solutons dervng the achevable network throughput. Numercal results are presented and dscussed n Secton 4. Lastly, conclusons are outlned n Secton 5.. System model We consder the relay network shown n Fgure consstng of three relays assstng a source S transmttng towards a destnaton D. All the nodes are equpped wth a sngle antenna, and we ndcate wth h Î C, g Î C, =,, 3, the flat-fadng channel between S and relay and between relay and D, respectvely. S transmts a sgnal x, and the sgnal receved by relay can be wrtten as y = h x + w, ( where w s the addtve whte complex Gaussan nose wth zero mean. We ndcate the sgnal transmtted by relay wth z and consder a untary power constrant for each node n the network,.e., E[ x ], E[ z ], =,,3.Byassumngchannelstatenformatonof the relay-destnaton lnk at the relay, the transmsson performed by relays can be done coherently adjustng the phases of z, =,,3.Forthsreasonandwthout loss of generalty, n the followng we only consder the channel gans H = h, G = g. (a (b Wthout loss of generalty, we assume that all noses have untary varance, whle the effectve sgnal to nose rato (SNR at the recever s obtaned by a proper scalng of the channel gans, see (9. We assume that a central controller knows all channels, correspondngly allocates resources to nodes, ncludng power, and constellaton szes. Hence, the determned network spectral effcency can be assumed as a bound for cases where only a partal channel state nformaton s avalable. Nodes operate n half-duplex mode,.e., they cannot transmt and receve smultaneously. Each relay alternates a phase n whch t receves data from the source and a phase when t transmts to the destnaton. No communcaton among relays s allowed. Moreover, we assume no drect transmsson from S to D because of shadowng or the long dstance between S and D. Let the tme used for two consecutve phases be untary. The odd phases are assgned a tme l, and the even phases are assgned a tme - l, where the parameter l wll be optmzed. The schedulng of transmsson s then fully characterzed by the varable δ = { 0, relay transmts durng even phases,, relay transmts durng odd phases, (3 S H H relay relay G G D for =,, 3. We wll see that the scheduler must know the channel gans for all relays and all phases n order to compute l and assgn δ. We frst revew transmsson schemes proposed n the lterature where all relays receve n odd phases and transmt n even phases,.e., δ =0, =,,3.Indetal, we consder the amplfy-and-forward (AF, the decodeand-forward (DF, and the broadcast-multaccess (BM technques. Let us denote the lnk spectral effcency for a gven SNR h as C(η =log ( + η. (4 H 3 relay 3 Fgure The consdered relay network wth 3 relays between S and D. G 3.. Amplfy-and-forward In AF each relay smply retransmts a scaled verson of the receved sgnal,.e., z = g y, observng the untary power constrant γ (H +. The sgnal receved at node D can be wrtten as r = G z + w D = x γ G H + w D + w γ G, (5

3 Page 3 of 8 where w D s complex Gaussan wth zero mean and untary varance. Note that wth AF no optmzaton of the tme-allocaton l s performed. Indeed, each relay retransmts the whole receved sgnal from S towards D, therefore equal-tme has to be assgned to both phases,.e., l = /. The spectral effcency s obtaned by (4, where from (5 the sgnal power s 3 G H γ and the nose power s + 3 G γ. Scalng factors g are selected n order to mze the network spectral effcency,.e., 3 G H γ R (AF = γ 0 C + 3 G γ (6a γ (H +, =,,3. (6b Note that the factor / n (6a s due to the equal duraton of phases. Moreover, we observe that (6 s a non-lnear nonconvex optmzaton problem n the three varables {g }... Decode-and-forward Wth DF a relay decodes the nformaton receved from S, whch s transmtted coherently wth the other relays towards D [4]. A bottleneck of ths scheme s the channel between S and each relay, as the spectral effcency s strongly lmted by the worst channel mn {H }. For ths reason, we also consder a selecton of the relays nvolved n the operatons. For each subset S {,, 3}, n order to mze the nformaton rate from S to D, we mpose the equalty of the spectral effcency n both phases,.e., ( R (DF (S =λc mn {H } ( =( λc G.(7 The optmal value of l s obtaned by solvng (7 for each subset S,.e., ( ( C G λ = ( ( ( C mn {H. (8 } + C G The network spectral effcency s then computed optmzng the choce of S, yeldng R (DF = S {,,3} R(DF (S = S {,,3} ( C mn {H} ( C mn {H} ( ( C G ( ( + C G. (9 Note that (9 s an nteger optmzaton problem, whch can be easly solved by an exhaustve search among all the subsets of relay nodes..3. Broadcast-multaccess Only for ths secton, we assume for smplcty that H H H 3. In the BM scheme the frst phase s a Gaussan broadcast channel [], where S transmts three messages M, M,andM 3 at rates R, R,andR 3, respectvely, where M s decoded only by relay, M s decoded by both relay and relay, and M 3 s decoded by all three relays. The second phase s a Gaussan multple-access channel wth correlated nformaton [9], where relays send dfferent but not ndependent nformaton. We ndcate wth a, a,anda 3 the powers used by S to transmt the messages M, M,andM 3, respectvely, g, g,andg thepowersusedbyrelay to transmt M, M,andM 3, respectvely, g and g the powers used by relay to transmt M and M 3, respectvely, and g 3 the power used by relay 3 to transmt M 3. Note that here we are extendng the BM scheme wth two relays of [8] to the case of three relays. Therefore, the network spectral effcency s the soluton of the followng optmzaton problem: R (BM = α,γ u,λ 0 R + R + R 3 R λc(α H, (0a (0b ( α H R λc, (0c +α H ( R 3 λc α 3 H 3 +α H 3 + α H 3 R ( λc(γ G,, (0d (0e ( ( R + R ( λc γ G + γ G + γ G,(0f ( ( R + R + R 3 ( λc γ G + γ G + + γ G ( γ G + γ G + (0g γ 3 G 3,

4 Page 4 of 8 α + α + α 3, γ + γ + γ, γ + γ, γ 3, (0h (0 (0j (0k ( 3 R (B λc G δ, (b ( 3 R (B ( λc H δ, (c λ. (0l Note that ( constrants (0b-(0d represent the rate-regon of the Gaussan broadcast channel between S and the relays, ( constrants (0e-(0g represent the rate-regon of the Gaussan multple-access channel wth correlated nformaton between the relays and D, and ( constrants (0h-(0k represent the power constrants at node S and at the relays, respectvely. Smlarly to (6, (0 s a non-lnear non-convex optmzaton problem. 3. Proposed schemes We propose now two schemes where the three relays are not forced to receve smultaneously at the same phase. For a scenaro wth three relays and two phases, we consder a confguraton where two relays are transmttng to the destnaton, and the thrd s recevng from the source. We ndcate wth R (A the spectral effcency related to the couple of cooperatve relays and wth R (B the spectral effcency related to the remanng relay. Let r be the ndex of the relay wth the best channel H,.e., r =arg :δ =0H, and let r mn be the ndex of the relay wth the worst channel H,.e., r mn =argmn :δ =0H. 3.. Adaptve BM scheme We frst propose an extenson of the BM scheme where the couple of cooperatve relays operatng synchronously employ Slepan-Wolf encodng to jontly transmt a common message at rate R (C towards D, whle relay r also transmts a prvate message at rate R (P,.e., R (A = R (P + R (C. The resultng scheme s named adaptve BM (ABM. The prvate message s transmtted by S wth power a and by the selected relay wth power P r (P. Furthermore, the thrd relay decodes an ndependent message receved from S, whch s then retransmtted towards D at rate R (B.Werecallthatδ dentfes the phase n whch relay transmts. The achevable network spectral effcency wth ths scheme can be wrtten as R (ABM = R (P + R (C + R (B α,p r (P,λ,δ (a R (P λc(αh r, ( ( R (C αhrmn λc +αh rmn (d, (e ( R (P ( λc P r (P G r, (f ( R (P + R (C ( λc P (P r Gr + ( ( P (p r Gr + G rmn, (g 3 δ =, δ {0, }, =,,3, (h r =arg :δ =0 H, r mn = arg mn :δ =0 H, 0 λ, 0 α, 0 P (P r. ( (j The spectral effcency of the non-cooperatve relay (havng ndex, such that δ = s sutably bounded n (b and (c for the two phases, respectvely. For the cooperatve relays (both havng δ = 0 (d and (e bound the spectral effcency n the frst phase, whle (f and (g gve the bound for the common and prvate message n the second phase. Note that ( s a mxed nteger programmng problem. 3.. Adaptve BM wth QAM quantzaton We now propose an alternatve soluton to Slepan-Wolf encodng used by cooperatve relays n Secton 3.. In partcular, we assume that the couple of cooperatve relays employ QAM constellatons, and we denote ths scheme adaptve BM wth QAM quantzaton (ABM- QAM. In ths scheme the central controller schedules a certan QAM symbol a to be sent towards D. Inthe frst phase, we assume lnk H r s able to delver all the nformaton sent by S to relay r, whch s then able to reconstruct the full symbol a. At the same tme lnk H rmn s able to delver only a quantzed verson to relay r mn,.e.,

5 Page 5 of 8 a (q = a a (e, ( where a (e s the quantzaton error. Hence relay r mn has a knowledge of a (q only. By lettng b and b (q Î {0,, 4,..., b} be the szes of the full QAM and the quantzed QAM, respectvely, assumng E[ a ] = and followng the quantzed constellaton desgn of [0], where E [a (e ] = 0 and E [a (q *a (e ]=0,wehave f ( [ a b, b (q =E (e ] b b(q = b. (3 The sgnal transmtted by relay r mn can be wrtten as z rmn = P r (C mn a (q, (4 whle the sgnal transmtted by relay r s a sutable combnaton of a (q and a (e,.e., z r = P r (C a (q + P r (P a (e. (5 { } The powers P r (C, P r (P, P r (C mn are chosen to reconstruct the full QAM symbol a at node D by mposng G r P r (C + G rmn P r (C mn = G r P r (P. (6 By usng (6, the SNR at D turns out to be G r P (P r and we approxmate the upper bound on the spectral effcency from relays r and r mn to D as R (A ( λ mn{b, C(G r P (P r }, (7 whereweconsderamumspectraleffcencyb related to the sze of the constellaton. Note that the symbol transmtted by relay r and the quantzed QAM symbol transmtted by relay r mn combne at the destnaton nto a QAM symbol that can be detected usng conventonal methods; ndeed, node D s unaware of the prvate transmsson from relay r, although t obtans the beneft of an hgher SNR. Wth ths transmsson scheme the mplementaton complexty at node D s sgnfcantly reduced wth respect to the ABM scheme because t does not need successve nterference cancelaton to decode both prvate and common messages. The problem of fndng the exact values of the spectral effcences of sgnals a (q and a (e, whch are sent through the Gaussan broadcast channel from S to relays r and r mn, respectvely, s the problem of fndng the spectral effcences of the messages after channel codng, nterleavng, and constellaton quantzaton. Even f entropy codng could be used to compute these quanttes, ts complexty may be too hgh for a practcal system mplementaton. Hence we approxmate the spectral effcency of a (q wth mn {( - lb (q, R (A }and that of a (e wth mn {( - l(b - b (q, R (A }. Wth ths suboptmal method S makes the best choce between transmttng the full stream of nformaton bts (at rate R (A or only the sequence of bts after quantzaton, at rate ( - lb (q for a (q andatrate(-l(b - b (q fora (e. Denotng wth M the set of avalable QAM constellatons, the network spectral effcency from S to D can be wrtten as R (ABM QAM = α,λ,δ,p (P r,p(c r,p(c r mn R (A + R (B (8a ( 3 R (B λc G δ, (8b ( 3 R (B ( λc H δ, (8c R (A ( λ mn{b, C(G r P (P r }, (8d ( f (b, b (q P (C r + f (b, b (q P (P r, (8e ( f (b, b (q P (C r mn, (8f G r P r (C + G rmn P r (C mn = G r P r (P, mn{( λ(b b (q, R (A } λc(αh r, ( ( mn{( λb (q, R (A αhrmn } λc +αh rmn (8g (8h, (8 3 δ =, δ {0, }, =,,3, (8j r =arg :δ =0 H, r mn = arg mn :δ =0 H, (8k 0 α, 0 λ, (8l P (C r, P (P r, P (C r mn 0, (8m

6 Page 6 of 8 b M, b (q {0,, 4,..., b}. (8n Note that (8e and (8f represent the power constrants at relays r and r mn, respectvely. Smlarly to (, (8 s a mxed nteger programmng problem. 4. Numercal results We consder that all nodes are located n a plane. Channel gans are related to the path loss, hence can be wrtten as H = κ d, G = κ S d, (9 D where d S and d D are the dstances between S and relay and between relay and D, respectvely, and s a normalzaton factor that determnes the receve SNR for a untary dstance. We assume that source node S s located at (-d MAX, 0 and destnaton node D at (0, d MAX. For ABM- QAM we consder the constellatons used n 3GPP LTE [],.e., M = {QPSK, 6QAM, 64QAM}. Developed schemes are compared n terms of network spectral effcency also consderng the cut-set upper bound computed n Appendx. Problems (6, (0, (, and (8 belong to NP-hard class and we compute ther soluton by usng standard global solver tools n GAMS [3], thanks to the lmted sze of the consdered scenaro. Fgure shows the network spectral effcency n terms of -d MAX <d <d MAX,byassumngthatrelaynodesmove from S to D on a set of ellpses centered n (0, 0 wth the sem-major axes long d MAX and dfferent values for the sem-mnor axes. In detal, relay s located at (d, d MAX /3 (d/d MAX, relay at (d, 0, and relay AF DF BM ABM QAM ABM cut set b. at (d, d MAX (d/d MAX (see also Fgure 3 and we mpose a reference sgnal to nose rato at dstance d MAX as Γ REF = /(d MAX = db. We observe that schemes as ABM and ABM-QAM sgnfcantly outperform the other schemes, whch do not acheve spatal multplexng, and ABM strctly outperforms ABM-QAM. As expected (see also [8] BM strctly outperforms DF and DF outperforms AF when the relays are clustered around S, whereas AF strctly outperforms DF when the relays are half way between S and D. Fgure 4 shows the average network spectral effcency n terms of Γ REF by assumng that relay nodes are randomly dropped n a square centered n (0, 0 and whose sdes have length (d Max - d MIN, where d MIN s the mnmum dstance between S or D and each relay (see also Fgure 5. We set κ/d MIN =30 db whch determnes the mum value assumed by H and G. Note that wth ths value of d MIN the saturaton of the spectral effcency due to the use of a fnte set of QAM constellatons n ABM-QAM s neglgble. As expected, the spectral effcency acheved by all the schemes s an ncreasng functon of Γ REF.Both ABM and ABM-QAM stll outperform DF and AF, whle ABM strctly outperforms ABM-QAM. Moreover, the performance of AF and DF are now qute close. We then consder a Raylegh fadng channel where each varable n (9 s multpled by an ndependent exponental random varable wth untary mean. Fgure 6 shows the cumulatve dstrbuton functon (CDF of the spectral effcency for the varous schemes by mposng Γ REF = db and settng d = 0 n the network of Fgure 3. We observe that the spectral effcency of the ABM schemes has a larger varance than that of AF, DF, and BM schemes as ABM are adaptve and thus are able to explot the best channel condtons. We also observe that the average values of the spectral effcences are 3 relay R [bt/s/hz].5 ( d MAX,0 relay (0,d MAX /3 (d MAX,0 S d D d/d MAX relay 3 (0, d MAX Fgure Network spectral effcency n terms of d for the network model descrbed n Fgure 3 assumng Γ REF =db. Fgure 3 Network model consdered n Fgure.

7 Page 7 of AF DF BM ABM QAM ABM cut set b R [bt/s/hz] 3.5 CDF [db] REF Fgure 4 Average network spectral effcency n terms of Γ REF for the network model descrbed n Fgure 5. qute close to that obtaned for non-fadng channels wth the same average SNR. Note that the solutons of both ABM and ABM-QAM optmzatons requre a hgh computaton tme as most mxed nteger programmng problems. However, even f ABM strctly outperforms ABM-QAM, the mplementaton complexty of ABM-QAM s consderably lower as the destnaton does not requre successve nterference cancelaton. Note that f we consder for example a cellular system, the complexty constrants are tghter at the moble termnals wth respect to base and relay statons. 5. Conclusons In ths artcle, we have consdered a network wth three half-duplex relays assstng the transmsson of a source ( (d d,0 S MAX MIN (0,d MAX d MIN relay ( d relay 3 MAX,0 (d MAX,0 (d MAX d MIN,0 D AF 0. DF BM 0. ABM QAM ABM cut set b R [bt/s/hz] Fgure 6 CDF of the network spectral effcency wth Γ REF = db, relay located at (0, d MAX /3, relay at (0, 0, and relay 3 at (0, -d MAX. towards a destnaton. Spatal multplexng s acheved by allowng a sngle relay to transmt n odd phases and the other two relays to transmt n even phases. We have formalzed the problem of mzng network spectral effcency when the cooperatve relays employ (a Slepan-Wolf encodng and (b a suboptmal scheme based on QAM quantzaton. We have shown that n typcal wreless scenaros ABM-QAM acheves the performance of ABM and outperforms other exstng technques such as DF and AF. Appendx : cut-set upper bound Snce S and D are always transmttng and recevng, respectvely, there are at most 3 = 8 confguratons of {δ }. Only for ths appendx, we denote wth λ the fracton of the total untary tme when no relay s transmttng, l when all relays are transmttng, l when only relay s transmttng and λ when only relay s not transmttng. Moreover, there are eght dfferent cuts that separate S from D, and each one s related to a constrant on the nformaton-rate. The cut-set upper bound for the consdered relay network can be expressed as [4] relay R (cut - set b. = R {λ,λ,λ,λ} 0 (0a (0, (d MAX d MIN Fgure 5 Network model consdered n Fgure 4. ( R λc H + λ C H j + λ C(H, (0b

8 Page 8 of 8 R λc H j + λ C H j + C(G + λ j C(H k:k =,j + λ j [C(H j +C(G ] + λc(g, =,,3, (0c do:0.86/ Cte ths artcle as: Baracca et al.: A practcal schedulng and power/ constellaton allocaton for three relay networks. EURASIP Journal on Wreless Communcatons and Networkng 0 0:8. R λc(h + λ j[c(h +C(G j] + λ C(H +C G j + λ jc(g k:k =,j+λc G j, =,,3, (0d R λ C(G + λ C ( G j + λc G, (0e λ + (λ + λ +λ. (0f Note that (0 s a convex optmzaton problem. Competng nterests The authors declare that they have no competng nterests. Receved: 4 June 0 Accepted: 9 March 0 Publshed: 9 March 0 References. TM Cover, A El Gamal, Capacty theorems for the relay channel. IEEE Trans Inf Theory. 5(5, (979. do:0.09/tit A Sendonars, E Erkp, B Aazhang, User cooperaton dversty-part I and part II. IEEE Trans Commun. 5(, (003. do:0.09/ TCOMM A Høst-Madsen, J Zhang, Capacty bounds and power allocaton for wreless relay channels. IEEE Trans Inf Theory. 5(6, (005. do:0.09/tit B Rankov, A Wttneben, Spectral effcent protocols for half-duplex fadng relay channels. IEEE J Sel Areas Commun. 5(, (007. do:0.09/jsac Y Yang, H Hu, J Xu, G Mao, Relay technologes for WMax and LTEadvanced moble systems. IEEE Commun Mag. 47(0, (009. do:0.09/mcom A Reznk, SR Kulkarn, S Verdu, Degraded Gaussan multrelay channel: capacty and optmal power allocaton. IEEE Trans Inf Theory. 50(, (004. do:0.09/tit G Kramer, M Gastpar, P Gupta, Cooperatve strateges and capacty theorems for relay networks. IEEE Trans Inf Theory. 5(9, (005. do:0.09/tit F Xue, S Sandhu, Cooperaton n a half-duplex Gaussan damond relay channel. IEEE Trans Inf Theory. 53(0, (007. do:0.09/ TIT D Slepan, JK Wolf, A codng theorem for multple access channels wth correlated sources. Bell Syst Tech J. 5, ( P Baracca, S Tomasn, N Benvenuto, Downlnk multcell processng employng QAM quantzaton under a constraned backhaul. n Proc IEEE Sgnal Processng Advances n Wreless Communcatons (SPAWC., 5 (0. do:0.09/spawc TM Cover, JA Thomas, Elements of Informaton Theory (John Wley & Sons, New York, 006. S Sesa, I Toufk, M Baker, LTE: The UMTS Long Term Evoluton (John Wley & Sons, New York, General algebrac modelng system (GAMS 4. MA Khojastepour, A Sabharwal, B Aazhang, Bounds on achevable rates for general mult-termnal networks wth practcal constrants. n Proc Inf Process Sens Netw Second Int Work. 634, 46 6 (003 Submt your manuscrpt to a journal and beneft from: 7 Convenent onlne submsson 7 Rgorous peer revew 7 Immedate publcaton on acceptance 7 Open access: artcles freely avalable onlne 7 Hgh vsblty wthn the feld 7 Retanng the copyrght to your artcle Submt your next manuscrpt at 7 sprngeropen.com