Transmission Strategies and Resource Allocation for Fading Broadcast Relay Channels

Int. J. Electron. Commun. (AE) 69 (2015) 699707

Contents lists available at ScienceDirect

International Journal of Electronics andCommunications (AE)

j ourna l h om epage: www.elsev ier .com/ locate /aeue

Transm n frelay c

Arif OndTOBB ETU, Turk

a r t i c l

Article history:Received 4 JulAccepted 16 D

Keywords:Broadcast relaCooperationLong-term powOutage probabPower allocati

nnel, ed. Fiinati

In MH relayrm pon ouommnicay is li

1. Introduction

The four-terminal broadcast relay channel (BRC), which is espe-cially important for hierarchical downlink communications, is rststudied in [1]. In the four-terminal BRC model, there are two des-tinations, wsingle dedicfor the BRCgeneration Advanced senhanced d

When chsubstantial are adaptedpower consadaptation tion:

If an applegy, whicmaximize

If an appoption. In

CorresponE-mail add

transmission block, and only power is adjusted. If the target rateis high, an outage is inevitable for some transmission blocks.For such an application the optimal power allocation schemethat minimizes outage probability is of threshold-type [12]. Tomaintain a xed rate over time, channel inversion is performed.

http://dx.doi.o1434-8411/ hich communicate with the source with the help of aated relay. Various achievability schemes are proposed

in [18]. The BRC can be especially important for next-wireless standards such as 3GPP Long Term Evolutiontandard (LTE-A) [9,10], which proposes using relays forata rates.annel state information is available at the transmitter,gains can be achieved if transmission rate and power

according to the channel conditions. Under long-termtraint over multiple fading blocks, there are severaltechniques in the literature depending on the applica-

ication is delay tolerant, waterlling is the best strat-h adjusts both power and rate over all fading blocks to

the ergodic rate [11].lication is delay-limited, rate adaptation is not anstead there is a xed target transmission rate for each

ding author. Tel.: +90 5389440004.ress: [email protected] (A.O. Isikman).

However, it is best to cease transmission if too much power isrequired to invert the channel.

In this paper, we are interested in delay-limited applica-tions. Under long-term power constraint, optimal power allocationprotocols for minimum outage probability for fading broadcastchannels and relay channels are studied in [1316]. In [16], oppor-tunistic protocols, in which the relay is not utilized if cooperationconsumes more power with respect to direct transmission are pro-posed and proved to perform close to the cut-set bound.

In this paper we investigate relaying strategies and relatedpower allocation methods that minimize outage probability forthe BRC with N destinations under long-term power constraint fordelay-limited applications. Note that, the four-terminal BRC is dif-ferent from the two-receiver relay-broadcast channel [17,18]. Inthe latter, the source communicates with two destinations one ofwhich acts as a relay for the other. The relaying receiver conveysmessages to a single node only and does not encounter the problemof assisting two different receivers simultaneously.

In the single-antenna BRC under study, the source uses super-position coding at xed target rates to reach all destinationsreliably. We rst study the common outage probability for all of the

rg/10.1016/j.aeue.2014.12.0102014 Elsevier GmbH. All rights reserved.ission strategies and resource allocatiohannels

er Isikman , Melda Yukseley

e i n f o

y 2014ecember 2014

y channel

er constraintilityon

a b s t r a c t

In this paper the broadcast relay chawith the help of a single relay is studitihop (MH), multihop with link combcombination (PSLC) are investigated. both destinations. In PS and PSLC, theone of the destinations. Under long-tesion is performed to minimize commcomparison, lower bounds on both cresults suggest that path selection sighelp both destinations simultaneouslor fading broadcast

where the source communicates with multiple destinationsve different transmission protocols, direct transmission, mul-on (MHLC), path selection (PS) and path selection with link

and MHLC, the relay decodes the source message and assists can perform partial decoding and has the option to help onlyower constraint, power allocation for delay-limited transmis-tage probability and individual outage probability region. Foron and individual outage probabilities are found. Numericalntly lowers outage probabilities, while enforcing the relay tomiting the system performance.

2014 Elsevier GmbH. All rights reserved.

700 A.O. Isikman, M. Yuksel / Int. J. Electron. Commun. (AE) 69 (2015) 699707

destinations. In a broadcast channel, there is common outage,whenever any of the destinations is in outage [13]. Such an oper-ation mode is necessary if coordination among receivers is tobe established and transmission to all of the destinations has totake place anot requireresult, for probability,

In the Binvestigate link combinwith link corates at theindividual orate regionposition cothe N destiit consumeto decode adestinationtion that enof messagewhere the lar to MH, inot listen toPSLC, we stuintroduced the source aform betterreceivers an

In our pprobability paper, we ibilities. Mosource and relay was uof this work

Under lonsion the m2-user BRsolved sep

In additioMH, MHLare given is also foufor xed tmined thindividuamented wprobabilitvector.

The broadegradeddestinatioconditiontheir own

Computerthe effectof users. Oalso obsersetting.

The orgSection 2, sunder comm

he brtinatioed on

d, d1

3, tnumis con

tem

BRCD1, DtaneoR, a. It i

y at espoadinex Gaean

assuong

n of

syst B ap

tran1, . . s W1ates

X2 + . . ., aHLCned irelay decodes Wj for all j E(s), where E(s) {1, 2, . . ., N}.at the subset E(s) depends on the channel state s, and on theission protocol. The relay then reencodes Wj, j E(s) intog an independent codebook at power P(i)

Rj(s, t) and transmits

jE(s)Xj .ore explaining power and outage constraints, we next outlinensmission protocols, DT, MH, MHLC, PS and PSLC. Calculationinstantaneous achievable rates at the destinations and thed power levels will be presented in Section 3.

verview of transmission protocols

T, the relay is not utilized and the system is equivalent to aast channel. The source node transmits all the time, t = 1.hat, DT will be a part of all other opportunistic protocolst the same time. On the other hand, if coordination isd, destinations can declare outage independently. As axed rates, each destination can have a different outage

dening a region.RC setting, in addition to direct transmission (DT), wefour different protocols: multihop (MH), multihop withation (MHLC), path selection (PS) and path selectionmbination (PSLC). We also upper bound the achievable

destinations and nd a lower bound on common andutage probabilities and an upper bound on -outage

s. In MH, MHLC, PS, and PSLC the source uses super-ding for the N independent messages it has for each ofnations and opportunistically resorts to DT, whenevers less power than using the relay. In MH, the relay hasll N messages to help all destinations. We assume thes only listen to the relay as this is a practical assump-ables simple receivers. In PS; we exploit superpositions, and allow the relay to assist a subset of destinations,other destinations directly listen to the source. Simi-n this case, the destinations that listen to the relay do

the source. Complementing MH and PS, in MHLC anddy the effect of link combination and explore the gainswhen the destinations can combine signals both fromnd the relay. Although, MHLC and PSLC are sure to per-

than MH and PS, respectively, they require complexd their use is limited.revious work [19], we only studied common outagefor the four-terminal BRC for DT, MH, PS and PSLC. In thisnclude MHLC and investigate individual outage proba-reover, in this work, the opportunistic behavior of thethe relay are determined optimally, whereas in [19], thetilized according to suboptimal rules. The contributions

are listed as follows:

g-term power constraint and delay-limited transmis-inimum outage probability problem is posed for the

C. Common and individual outage probability cases arearately.

n to DT, four different opportunistic relaying strategies,C, PS and PSLC are proposed and achievable rate regionsfor the 2-user BRC. An upper bound on achievable ratesnd. For these achievable schemes and the upper bound,arget rates, optimal power allocation policies are deter-at minimize the common outage probability and thel outage probability regions. The results are comple-ith -outage rate regions, for a xed common outagey value and for a xed individual outage probability

dcast relay channel under study is not necessarily [2]. For some channel conditions it is better if bothns decode both messages, and for some other channels, less power is consumed if both destinations decode

messages only. simulations are performed for N = 2 and N = 3 to reveals of partial decoding at the relay for increasing numberur results indicate that PS is very close to optimal. Weve that partial decoding has signicant gains in the BRC

anization of the rest of the paper is as follows. Inystem model and optimal power allocation principleson and individual outage constraints are introduced. In

Fig. 1. Ttwo desare locatequal to

Sectiontion 4, paper

2. Sys

Thetions (instanSDj, S2, . . ., Ngloballat corrstatic fComplzero m

Wesion amfractio1 t.

Thewheresourcerates RencodeIt allocX = X1 +s = (a1,MH, Mbe deX, the Note thtransm

Xj usin

the sumBef

the traof the require

2.1. O

In DbroadcNote toadcast relay channel (BRC), with one source (S), one relay (R), andns (D1, D2). For the numerical simulations in Section 4, all four nodes

a plane with SR, D1-point P and D2-point P distances are respectivelyand d2.

ransmission protocols are described in detail. In Sec-erical results are presented. Finally in Section 5, thecluded.

model

consists of one source (S), one relay (R), and N destina-2, . . ., DN). The model is illustrated for N = 2 in Fig. 1. Theus amplitude squares of complex channel gains amongnd RDj are respectively denoted by aj, b, and cj, j = 1,s assumed that the channel gain amplitudes are knownall nodes, whereas channel gain phases are known onlynding receivers. The channel coefcients have quasi-g [12] and are independent from one block to the other.ussian noise at the receivers are independent, and have

and unit variance.me that the relay is half-duplex and there is time divi-

the source and the relay. The source transmits for tthe block, 0 < t 1, and the relay transmits in the rest

em is delay-limited. Communication lasts for B blocks,proaches innity. Over each communication block, thesmits N independent messages W1, . . . WN at xed target., RN respectively to each destination. The source node, . . ., WN into X1, . . ., XN using superposition coding [20].

power P(i)Sj

(s, t) to send Xj, j = 1, . . ., N, and transmits + XN to reach all destinations simultaneously. HereN, b, c1, . . ., cN) is the channel state vector and i, i = DT,

, PS, PSLC, denotes the transmission protocol that willn the next subsection. Upon receiving the source signal

A.O. Isikman, M. Yuksel / Int. J. Electron. Commun. (AE) 69 (2015) 699707 701

Fig. 2. (a) Diresible, whereas(b) Operation transmission combination (DFLC modes a

under studyin less consDT for N = 2operation msimultaneodenoted as operation mor D1 and D

there will b

individual oThe two

and decodemon outageunder commThe relay bconsuming ten to the rare DT and MHLC protofrom both tand double

In PS, theis not requiof them. Thincreases itcally, for theof operation(RH2) and Dshown in Ficases appeasource can the relay (DDF2 modesthere are 2NN1

n=1

(Nn

)In PSLC,

four modesnation (RH1and DFLC. Umodes DT modes show

In MH anand W2. The

any of these two constraints is relaxed, MH and MHLC respectivelybecome equivalent to PS and PSLC. Therefore, for MH and MHLC,we do not study the individual outage probability region.

ection 3, we write achievable rates at each destination C(i)j

forse only for enhanced readability. We nd the instantaneous

able (i)

C anand fhe fo

ng-te

assuower

P(i)S (s

) = P

) = P

) de.C(i)j

(tinaLC, fomm(i)j

(s, protj asi)1(s, t

t of p

um tn as

= m

+

i)(s, tct transmission operation modes: for common outage, only DT is pos- for individual outage the system can be in DT, DT1 or DT2 modes.modes for MH and MHLC for common outage probability: direct

(DT), decode-and-forward (DF) and decode-and-forward with linkDFLC). In MH, DT and DF modes are available, while in MHLC DT andre in use.

, in which the relay is not employed, whenever it resultsumption. Fig. 2a represents the operation modes for. Under common outage constraint, there is only oneode: The source node transmits to both destinations

usly. With a slight abuse of notation, this mode is alsoDT. Under individual outage constraint, there are threeodes: The source can serve D1 only (DT1), D2 only (DT2)2 together (DT). When generalized to N destinations,

e a total ofN

n=1

(Nn

)= 2N 1 operation modes for

utage. modes of operation for MH, direct transmission (DT)-and-forward (DF), for the four-terminal BRC for com-

probability are shown in Fig. 2b. For N destinationson outage DT and DF are still the only mode options.

ehaves opportunistically and chooses the less powermode over the other. In MH the destinations only lis-elay in DF mode. In MHLC, the two modes of operationdecode-and-forward with link combination (DFLC). Incol in DFLC mode, the destinations listen to the signalshe source and the relay combining the incoming single

links in Fig. 2b. source transmits to all destinations. However, the relayred to decode all messages, but can decode any subsetis decreases the decoding constraint at the relay, ands chance to be more useful for the destinations. Speci-

four-terminal BRC for common outage the four modes are DT, relay helps only D1 (RH1), relay helps only D2

In SN = 2 caachievPS, PSLstate s

In t

2.2. Lo

Wetotal p

[t

where

P(i)S (s, t

P(i)R (s, t

and f(sstate s

Let jth desPS, PSable crates Cfor allrates R

ing (P(Samoun

minimis give

P(i)req(s)

= t(P(

F. These additional operation modes, RH1 and RH2 are

g. 3a. In addition to these operation modes, 4 additionalr when individual outage declaration is allowed. Thetransmit to D1 individually either directly (DT1) or viaF1). Similarly, the source can transmit to D2 in DT2 or. DF1 and DF2 are shown in Fig. 3a. Then, for general Noperation modes for common outage, and an additional

2n number of modes for individual outage.

for the four-terminal BRC under common outage the of operation are DT, relay helps only D1 with link combi-LC), relay helps only D2 with link combination (RH2LC)nder individual outage, in addition to the operation

DFLC, RH1LC and RH2LC, there are DF1LC and DF2LCn in Fig. 3b.d MHLC protocols, the source sends both messages W1n the relay decodes and forwards both messages. When

S1

where t* is 1 t. Notefunction of

2.3. Commo

The comcast channecan either take place adestination

Given P(rallocation rates at each destination Cj

, j = 1, 2, i =DT, MH, MHLC,d an upper bound on achievable rates for each channelor a xed t. We will present results for N = 3 in Section 4.llowing, we explain power and outage constraints.

rm average total power constraint

me the source and the relay have a long-term average constraint Pavg over all communication blocks:

, t) + (1 t) P(i)R (s, t)] f (s) ds Pavg (1)

(i)S1(s, t) + P

(i)S2(s, t) + + P

(i)SN(s, t) (2)

(i)R1(s, t) + P

(i)R2(s, t) + + P

(i)RN(s, t) (3)

notes the probability density function of the channel

s, t) denote the instantaneous achievable rate at thetion j = 1, 2, . . ., N with protocol i, i = DT, MH, MHLC,or a xed t and channel state vector s. For reli-unication, we require the instantaneous achievable

t), which will be calculated for all destinations andocols in Section 3, to be larger than the xed target

the system is assumed to be delay-limited. Den-

), . . ., P(i)SN(s, t), P(i)R1(s, t), . . ., P

(i)RN(s, t)) as the minimum

ower levels that satisfy the condition C(i)j

(s, t) Rj , theotal amount of power required for protocol i,1 at state s

intt(P(i)S1(s, t) + + P

(i)SN(s, t)) + t(P

(i)R1(s, t) +

P(i)RN(s, t)), (4)

) + + P(i)SN(s, t)) + t(P(i)R1(s, t

) + + P(i)RN(s, t)),(5)

the best t, 0 < t 1 that minimizes (4), t = 1 t, and t = that the fraction of the time the relay listens, t*, is athe channel state vector s.

n outage probability

mon outage probability is introduced in [13]. In a broad-l, depending on the channel state, the broadcast channelnot be used at all, or transmission to all the receiverst the same time. In other words, whenever one of thes is in outage, there is system outage.i)eq(s) for the ith protocol at state s, the optimal resourcefunction that attains the minimum common outage


Fig. 3. (a) Addhelps user 1 (user 2 (RH2) acommon outaDT, RH1LC, RHoperation moddecode-and-foand decode-anoutage the opein PSLC, DT, Rfor individual

probability power leve

P(i)kj

(s, t) =

for k = S, R, satised.2

This thrthe applicatfor each chsion poweris equal to than requirpower levelto D1, . . ., Dpoor channand the totever, if tranbecome favFor those chP(i)req(s) Pth

Subject tmine Pth suP(i)out = P(P(irevector (R1, given as

P(i)out-min = m

In this poutage probMH, MHLC,are turned omon outageanalyze thecollection ocommon ouconstraint (

1 P(i)req(s) notRH1, RH2, RH1

2 From this p

tively with P(i)kj

probability problem of (7) and the -outage rate region problemare inherently the same [13].

2.4. Individual outage probability region

In a broadestinationThen, thereprobabilitie

PS, Piven ) deour s

regiissioual olay the oaneoer thte s,ationis is tomit touser r th

. To the he de

nsm

his sH, Ms on

irect

min prob. Heunis

Commen ty foitional operation modes for PS and PSLC for common outage: relayRH1), relay helps user 1 with link combination (RH1LC), relay helpsnd relay helps user 2 with link combination (RH2LC). Then, in PS, forge the operation modes are DT, RH1, RH2 and DF. Similarly, in PSLC,2LC and DFLC modes are possible for common outage. (b) Additionales for individual outage probability: decode-and-forward 1 (DF1),rward 1 with link combination (DF1LC), decode-and-forward 2 (DF2),d-forward 2 with link combination (DF2LC). Then, in PS, for individualration modes are DT, RH1, RH2, DF, DT1, DF1, DT2 and DF2. Similarly,H1LC, RH2LC, DFLC, DT1, DF1LC, DT2 and DF2LC modes are possibleoutage.

is of threshold type [12,13,16]. As a result, the requiredls are determined according to{

0 if P(i)req(s) PthP(i)kj

(s, t) if P(i)req(s) < Pth,(6)

j = 1, 2, . . ., N where Pth is determined such that (1) is

eshold type behavior can be explained as follows: Asion is delay-limited, reliable communication is neededannel state s. Then, one would choose the transmis-

levels such that the instantaneous achievable rate C(i)j

the target rate Rj: There is no point in achieving moreed. However, for very poor channel conditions, the total

required to send the target rates R1, . . ., RN respectivelyN is very high. If transmission is sustained during suchel conditions, power is wasted to invert the channelal average power constraint in (1) is violated. How-smission is discontinued until the channel conditionsorable, then power can be saved and (1) is satised.annel states during which transmission is off, or when, the system is in outage.o the total average power constraint Pavg, one can deter-ch that the common outage probability for protocol i,)q(s) Pth), is minimized. Then for a given target rate. . ., RN), the minimum common outage probability is

(i)

MHLC,for a g. . ., RNpaper abilitytransmindividsical reis still simult

Undnel stadestinthat thtem autransmactive level fostate sfollowleave t

3. Tra

In tcols Mbound

3.1. D

Theoutagein [13]opport

3.1.1. Wh

strateg

inPthPout subject to(1). (7)

aper our rst objective is to nd the minimum commonability dened in (7). We investigate ve protocols DT,

PS, and PSLC. In each of these protocols, all destinationsn or off simultaneously. In addition to minimum com-

probability for a given rate vector (R1, . . ., RN), we also -outage rate region. The -outage rate region is thef all achievable rate vectors (R1, . . ., RN), for which thetage probability is at most and the total average power1) is satised. Note that the minimum common outage

ation will also be used for operation modes DT1, DT2, DF, DF1, DF2,LC, RH2LC, DFLC, DF1LC and DF2LC.oint on, we will denote P(i)

kj(s, t), P(i)

kj(s, t), P(i)

k(s, t) and C(i)

j(s, t) respec-

, P(i)kj

, P(i)k

and C(i)j

for a simpler notation.

simultaneosame outagthe messag

Let () the point (channel for

C(DT)(1) = log

Solving C(DT(l

amount of pand R2. In tfor the fourdcast channel, instead of declaring system outage, every can go into outage independently from each other.

are N different outage probabilities for each user. Theses will be denoted as P(i)out,1, . . ., P

(i)out,N where i = DT, MH,

SLC. The collection of all achievable (P(i)out,1, . . ., P(i)out,N)

power allocation and for a given target rate vector (R1,nes the individual outage probability region. In thisecond objective is to nd the individual outage prob-on and the corresponding -outage rate region for then strategies DT, MH, MHLC, PS and PSLC. Note that theutage measure does not reduce the system to the clas-

channel with a single destination, as in the BRC thereption of broadcasting to all or a subset of destinationsusly.e individual outage probability measure, for each chan-

the source can choose to transmit to a subset of thes resulting in 2N 1 possible sets of active users. Notenot an option under common outage, in which the sys-atically goes into outage whenever the source does not

all destinations simultaneously. We will denote theset with Sl, l = 1, 2, . . ., 2N 1 and the required powere active user set Sl with P(i)req,l(s) for each protocol i fornd the best active user set for each channel state s, wealgorithm described in [13]. Due to lack of space, wetails to the reader.

ission protocols

ection we describe DT and the opportunistic proto-HLC, PS and PSLC in detail and also derive performanceoutage probability and -outage rate regions.

transmission

imum common outage probability and the individualability region for the broadcast channel for DT is solved

re, we restate the results, as DT is a part of all othertic protocols under study.

on outagehe performance metric is system outage, the bestr the source is to communicate with all destinationsusly. The source can only consume more power for thee probability if it chooses to transmit only a subset ofes.be a permutation on {1, 2} such that a(1) > a(2). ThenC(DT)1 , C

(DT)2 ) is on the capacity region of the broadcast

state s, where

(1 + a(1)P(DT)S(1)

), C(DT)

(2) = log(

1 +a(2)P

(DT)S(2)

1 + a(2)P(DT)S(1)

).

(8)

)) = R(l) for PS(l), l = 1, 2, one can calculate the minimumower required, P(DT)

S(l), to attain the xed target rates, R1he following we nd the required source powers for DT-terminal BRC.


Dene g as a function with three inputs and two outputs as

(y1, y2) g(x1, x2, x3) (9)

y1 =

2

2

y2 =

22

Then, P(DSas (P(DT)S1 , P

(S

(5) as

P(DT)req (s) = PUsing (10),(probability.

3.1.2. IndivUnlike t

age, the soutime. Depenone of the term. Whenpossible setDT2, and DTturns into awith only onis given by

nd P(DT1)S1 a

P(DT1)S1 =2R1

while P(DT1)S2thus P(DT)req,1(sbe found fortem is equivlevels are th

where P(DT)reqP(DT)req,1(s), P

(Dre

user set anddescribed in

3.2. Multih

For MH, there are 2 relay has to

The ach

is found as

relay to decthe target s

P(DF)S = (2R1

Using independent codebooks, the relay then reencodes W1 andW2, and forwards them to the destinations using superpositioncoding. As the destinations only listen to relay and the source andthe relay transmissions are orthogonal, the transmission from the

o theutatt the

t log

= t l

t = 1tinat

P(DF)R2

ubsti

ppor

) = m

P(DFreqon ou

ultih

HLCode

andW11 anng, tstinaer, td in [o recodi

ions l cosers

the ithoa deng Xe.

Case h dess W1

desti

log

(

log

(R1x3 1 1

x1if x1 x2

R1x3 1

( 1

x1+ y2

)if x1 < x2

R2x3 1

( 1

x2+ y1

)if x1 x2

R2x3 1

1x2

if x1 < x2

T)1 and P

(DT)S2 can be expressed in terms of the function g

DT)2 ) = g(a1, a2, 1). Then, P

(DT)req (s) can be calculated from

(DT)S1 + P

(DT)S2 . (10)

6) and (7) one can nd the minimum common outage

idual outagehe common outage case, when there is individual out-rce no longer has to serve both destinations at the sameding on the channel state, communicating with only

destinations can be more power efcient in the long- there is an individual outage constraint, there are 3s of active users, and thus 3 modes of operation: DT1,, shown in Fig. 2a. In DT1 and DT2 modes, the system

point-to-point channel as the source communicatese of the destinations. The achievable rate for DT1 modeC(DT1)1 = log(1 + a1P

(DT1)S1 ). Then, solving C

(DT1)1 = R1, we

s

1a1

. (11)

= 0. As the relay is not utilized, P(DT1)R1 = P(DT1)R2 = 0 and

) = P(DT1)req (s) = P(DT1)S1 is obtained. Similarly, P(DT)req,2(s) can

DT2 mode. Finally, when both users are active, the sys-alent to the broadcast channel and the required powere same as P(DT)S1 and P

(DT)S2 resulting in P

(DT)req,3(s) = P

(DT)req (s)

(s) computed for the common outage case in (10). GivenT)q,2(s) and P

(DT)req,3(s), one can determine the best active

nd the individual outage probabilities as in [13], as Section 2.4.

op

we only consider common outage. As mentioned before,modes of operation in MH: DT and DF. In DF mode, the

decode both messages, W1 and W2.ievable sum rate for W1 and W2 at the relay, C

(DF)R (s),

C(DF)R = t log(1 + bP(DF)S

). In DF mode, in order for the

ode both messages reliably, C(DF)R must be as large asum rate R1 + R2. Thus,

+R2t 1) 1

b. (12)

relay ta permrates a

C(DF)(1) =

C(DF)(2)

wherethe desas

(P(DF)R1 ,

Then s

is an o

P(MH)req (s

wherecomm

3.3. M

In MDFLC msourcesends both WdecodiThe deHowevdenewith twtion deconditchanneother uone ofsage wcases: (treatimessag

3.3.1. Bot

decodeat the

K1 = t

K2 = t destinations constitute a broadcast channel. Let () beion on {1, 2} such that c(1) > c(2). Then the achievable

destinations are

(1 + c(1)P(DF)R(1)

),

og

(1 +

c(2)P(DF)R(2)

1 + c(2)P(DF)R(1)

), (13)

t and the relay power needed for reliable reception ations can be found solving C(DF)

(1) = R(1) and C(DF)(2) = R(2)

) = g(c1, c2, 1 t). (14)

tuting (12) and (14) into (4), we obtain P(DF)req (s). As MH

tunistic protocol, P(MH)req (s) is calculated as

in{P(DF)req (s), P

(DT)req (s)

}, (15)

)(s) is given in (10). Using (15) and (6), the minimumtage probability of (7) is calculated.

op with link combination

, under common outage the system is either in DT ors. In DFLC mode, the destinations listen to both the

the relay. The source uses superposition coding andand W2 while the relay has to decode and forwardd W2. Thus P

(DFLC)S (s) is given by (12). Upon successful

he relay forwards both messages to both destinations.tions have two distinct observations about (W1, W2).he BRC under study is not necessarily degraded as2]. Note that in a degraded Gaussian broadcast channelceivers, superposition coding with successive cancella-ng is optimal [2]. While the user with worse channeldecodes its own message only, the user with betternditions decodes its own message after decoding the

message. However in a BRC we cannot conclude thatdestinations can always decode the other users mes-ut incurring an extra cost. Therefore, we study bothstination i can decode its message Wi either directlyj, i /= j as noise) or after decoding the other users

1tinations decode their messages directly, i.e., D1 directlyand D2 directly decodes W2. Then, the achievable rates

nations are C(DFLC-1)1 = K1 and C(DFLC-1)2 = K2, where

1 + a1P(DFLC)S1

1 + a1P(DFLC)S2

)+ (1 t) log

(1 + c1P

(DFLC)R1

1 + c1P(DFLC)R2

)(16)

1 + a2P(DFLC)S2

1 + a2P(DFLC)S1

)+ (1 t) log

(1 + c2P

(DFLC)R2

1 + c2P(DFLC)R1

).

(17)


3.3.2. Case 2D1 rst decodes W2. Subtracting X2 and X2 from its received sig-

nals respectively in the rst and the second slots, D1 then decodesW1. D2, on the other hand, directly decodes W2. As W2 has to bedecoded relC(DFLC-2)2 = mby

L2 = t log(

Once the efattain the r

M1 = t log(

3.3.3. Case Case 3 c

rst decodebe decodedachievable is dened in

L1 = t log(

Then, remoachieve the

M2 = t log(

3.3.4. Case In Case

achievable

and C(DFLC-42There is

imum totalall 4 cases n

As in M

as large as same as (12not affect th

levels P(DFLS1that will besource pow

P(DFLC)S , P(S

Substitu

(16)(21) adestinationpower levethe total reP(DFLC)S1 , P

(DFS2

power leve

P(MHLC)req (s) =

and the com(22) and (6)

3.4. Path selection

In the PS protocol, the four modes of operation for the four-terminal BRC are DT, RH1, RH2 and DF.

H1, the source transmits W1 to the relay with power P(RH1)S1

2 to D2 with power P(RH1)S2 using superposition coding. In other

, the transmission from S to R and D2 forms a broadcast chan- RH1e relarce s

he ac

=

hat i tran

at D reenstina

= (1

=

Comm req

are fH1), P(RH1)R1

1)/

into ( RH2, the, P(RHS2

requ usins

= m

can tility

IndivS, unode

T2, Dnly D1. In relayo (11F1 mtes aiably at both destinations, the achievable rate for W2 isin{K2, L2} where K2 is dened in (17) and L2 is given

1 + a1P(DFLC)S2

1 + a1P(DFLC)S1

)+ (1 t) log

(1 + c1P

(DFLC)R2

1 + c1P(DFLC)R1

).

(18)

fect of W2 is removed from D1s observations, D1 canate C(DFLC-2)1 = M1 where M1 is given by

1 + a1P(DFLC)S1)

+ (1 t) log(1 + c1P(DFLC)R1

). (19)

3omplements Case 2. D1 directly decodes W1 while D2s W1 and then decodes W2. In this case, W1 has to

reliably at both destinations. The constraints on therate at D1 are given by C

(DFLC-3)1 = min{K1, L1} where K1

(16) and L1 is given by

1 + a2P(DFLC)S1

1 + a2P(DFLC)S2

)+ (1 t) log

(1 + c2P

(DFLC)R1

1 + c2P(DFLC)R2

).

(20)

ving the effect of W1 from its observations, D2 can rate C(DFLC-3)2 = M2 where M2 is given by

1 + a2P(DFLC)S2)

+ (1 t) log(1 + c2P(DFLC)R2

). (21)

44, both receivers decode both messages. Then, therates at D1 and D2 are given by C

(DFLC-4)1 = min{L1, M1}

) = min{L2, M2}, respectively. no guarantee that Case 2 or Case 3 achieves the min-

required power in a communication block. Therefore,eed to be considered.H, for reliable decoding at the relay, C(DFLC)R must be

R1 + R2. Thus, the required source power P(DFLC)S is the

). Note that the superposition order at the source doese total source power P(DFLC)S , but the individual power

C) and P(DFLC)S2 have an effect on the relay power levels calculated shortly. Let [0, 1] denote the fraction ofer which is allocated to transmit W1. Then, P

(DFLC)S1 =

DFLC)2 = (1 )P

(DFLC)S .

ting the source power levels, P(DFLC)S1 , and P(DFLC)S2 , into

nd satisfying C(DFLC-n)m = Rm, m = 1, 2, n = 1, 2, 3, 4, thes nd the optimal case and calculate the required relayls P(DFLC)R1 and P

(DFLC)R2 and optimal that minimize

quired power for a communication block. SubstitutingLC), P(DFLC)R1 and P

(DFLC)R2 into (5), we obtain the required

l for DFLC denoted as P(DFLC)req (s). Finally,

min{P(DFLC)req (s), P

(DT)req (s)

}. (22)

mon outage probability of (7) can be computed using.

In R

and Wwordsnel. Inand ththe souThen t

C(RH1)R

Note trelaysno usedentlythe de

C(RH1)1

C(RH1)2

3.4.1. The

P(RH1)S2as (P(RSRrelay P

(2R11t

P(RH1)R2The

In RH2(P(RH2)S1

Theculatedgiven a

P(PS)req (s)

whichprobab

3.4.2. In P

ation mDT1, D

If oand DFof the equal t

In Dable raby, D1 does not listen to the source, but only to the relayy is only required to decode W1. In RH1 mode, if b > a2,uperimposes X1 on X2, and the opposite is true if b < a2.hievable rates at the relay is

t log(1 + bP(RH1)S1

)ifb > a2

t log

(1 + bP

(RH1)S1

1 + bP(RH1)S2

)otherwise

(23)

n RH1, D2 does not need to listen to the relay, as thesmission carries information only about W1 and is of2. Upon successfully decoding W1, the relay indepen-codes and forwards W1 to D1. The achievable rates attions are

t) log(1 + c1P(RH1)R1

)(24)

t log

(1 + a2P

(RH1)S2

1 + a2P(RH1)S1

)ifb > a2

t log(1 + a2P(RH1)S2

)otherwise

(25)

on outageuired power levels for the source in RH1, P(RH1)S1 and

ound by solving C(RH1)R = R1 and C(RH1)2 = R2 and given

(RH1)S2 ) = g(b, a2, t). The required power level for theis found by solving C(RH1)1 = R1 and given as P

(RH1)R1 =

c1 while P(RH1)R2 = 0. Substituting P

(RH1)S1 , P

(RH1)S2 , P

(RH1)R1 and

5), we obtain P(RH1)req (s). mode is similar to RH1 and the relay only assists D2.

required source and relay power levels are given as2)) = g(a1, b, t) and (P(RH2)R1 , P

(RH2)R2 ) = [0, (2

R21t 1)/c2].

ired power for DF is the same as in MH, P(DF)req (s) is cal-g (12) and (14). Then the required power level for PS is

in{P(DF)req (s), P

(RH1)req (s), P

(RH2)req (s), P

(DT)req (s)

}, (26)

hen be used to calculate the minimum common outage of (7).

idual outageder individual outage constraint, in addition to the oper-s DT, RH1, RH2, and DF, there are four operation modesF1 and DF2, as shown in Fig. 3b.1 is active, then the possible operation modes are DT1DT1, the source directly sends W1 to D1 without the help. The required power for reliable transmission P(DT1)req is).ode, the source sends W1 to D1 via the relay. The achiev-t the relay and the destination are respectively given


C(DF1)R = t log(1 + bP(DF1)S1

), C(DF1)1 = (1 t) log

(1 + c1P(DF1)R1

).

(27)

Solving

thus P(DF1)req

min{P(DT1)req (Replacin

steps as aboFinally,

levels are tstraints. Th

P(PS)req,3 we in Section 2

3.5. Path se

In PSLC, PSLC, the demode the aMHLC as detude square

with RH1LCfor all cases

3.5.1. CommIn PSLC,

as in the R

(16)(21) a

optimal casreliable recdoes not he

P(RH1LC)R2 , we

mode, P(RH2reqIn DFLC,

DFLC in MH

P(PSLC)req (s) = We then useprobability

3.5.2. IndivIn PSLC,

DF1LC modpower levelD1 now bec

C(DF1LC)1 = t

Solving C(RP(DF1LC)R1 (s), a

P(PSLC)req,1 (s) =

Similarly, PrThen, the inSection 2.4.

3.6. Performance bounds

In the following, we write upper bounds on the achievable ratesin the four-terminal BRC. Using these, we deduce a lower bound on

prob deri

destthe say ccomacitdestDFLC)

mulestin

upptes a

t log

t log

the a(2).resp

Comming

)(s), P

e usility

P(boout- PS an, C1)utag

Indiv bouare

le thas to ts for s on

og(1

og(1

ing )(s) =sult,

eri

the e a

var. There Sint P

= 1, 2tionC(DF1)R = R1 and C(DF1)1 = R1, P

(DF1)S1 , P

(DF1)R1 and

(s) are obtained. As P(DF1)S2 = P(DF1)R2 = 0, P

(PS)req,1(s) =

s), P(DF1)req (s)}.g the subscripts 1 with 2 and following the sameve P(PS)req,2(s) can be found for DF2.when both users are active, the required powerhe same under individual and common outage con-en, P(PS)req,3(s) = P

(PS)req (s) in (26). Given P

(PS)req,1, P

(PS)req,2 and

nd the individual outage probabilities as described.4.

lection with link combination

the operation modes are DT, RH1LC, RH2LC and DFLC. Instinations always listen to the source. Then, in RH1LCchievable rate at Dj, C

(RH1LC)j

is calculated similar toscribed in Section 3.3. Setting the channel gain magni-

c2 = 0, the power level P(RH1LC)R2 = 0 and replacing DFLC

in (16)(21), C(RH1LC-n)j

, j = 1, 2, n = 1, 2, 3, 4 is found.

on outagein RH1LC, the source sets (P(RH1LC)S1 , P

(RH1LC)S2 ) = g(b, a2, t)

H1 mode of PS. Substituting P(RH1LC)S1 and P(RH1LC)S2 in

nd satisfying C(RH1LC-n)1 = R1, n = 1, 2, 3, 4, D1 nds thee and calculates the required relay power P(RH1LC)R1 foreption when there is link combination. As the relaylp D2, P

(RH1LC)R2 = 0. Using P

(RH1LC)S1 , P

(RH1LC)S2 , P

(RH1LC)R1 and

obtain P(RH1LC)req (s). The required power levels for RH2LCLC)(s), are similarly obtained.

the required power level, P(DFLC)req (s), is the same with

LC. Therefore, P(PSLC)req (s) is given as

min{P(DT)req (s), P(RH1LC)req (s), P(RH2LC)req (s), P(DFLC)req (s)}. (28) (28) and (6) to compute the minimum common outageof (7).

idual outageif only D1 is active, the system can either be in DT1 ores. When compared with PS, the only change in requireds occur in DF1LC mode, for which the achievable rate atomes

log(1 + a1P(DF1LC)S1

)+ (1 t) log

(1 + c1P(DF1LC)R1

).

(29)

DF1) = R1 and C(DF1LC)1 = R1, we obtain P(DF1LC)S1 (s),

nd P(DF1LC)req (s). Then

min{P(DT1)req (s), P(DF1LC)req (s)}. (30)(PSLC)eq,2 (s) is obtained. Finally, P

(PSLC)req,3 (s) = P

(PSLC)req (s) in (28).

dividual outage probabilities are found as explained in

outageWe

at thegiven the reltem bethe capat the

Cj = C(jThe

each dsecondable ra

C(1) =

C(2) =

wherea(1) > D2 are

3.6.1. Solv

P(boundS1Then wprobababilityMHLC,min(C1the -o

3.6.2. The

and D2possibreduceboundbound

Cj = t l

Cj = t l

Solv

P(boundreq,3As a re

4. Num

Forcases. Wrandoma planeP, wheand poas dj, jdestinaability and an upper bound on -outage rate region.ve two different upper bounds on the achievable ratesinations. In the rst bound, we assume the relay isource messages W1 and W2 for free, or equivalentlyan always decode W1 and W2 reliably. Then the sys-es equivalent to parallel broadcast channels, for whichy region is given in [21]. For a xed t, achievable ratesinations are respectively upper bounded by Cj, where

, j = 1, 2 and C(DFLC)j

are calculated as in Section 3.3.tiple antenna broadcast channel with two antennas atation and a single antenna at the source constitutes theer bound on the BRC under study [7]. Then, the achiev-t the destinations for a xed t are upper bounded with(

1 + (a(1) + b)P(bound)S(1))

(31)(1 +

(a(2) + b)P(bound)S(2)1 + (a(2) + b)P(bound)S(1)

), (32)

permutation (l) is a permutation on {1, 2} such that Combining the two bounds, achievable rates at D1 andectively upper bounded by min(C1, C1) and min(C2, C2).

on outagemin(C1, C1) = R1 and min(C2, C2) = R2, we calculate (bound)S2 (s), P

(bound)R1 (s) and P

(bound)R2 (s) to obtain P

(bound)req (s).

e P(bound)req (s) to obtain the minimum common outage dened in (7). This minimum common outage prob-und)min is a lower bound on all other protocols DT, MH,d PSLC. Based on the upper bounds on achievable rates,

and min(C2, C2), we also compute an upper bound one rate region in the next section.

idual outagends calculated in Section 3.6.1 are useful when both D1active. However, when there is individual outage, it ist only one of the destinations is active. In that case, BRChe three terminal relay channel [22]. Using the cut-setthe relay channel [16,20] we can write two additionalthe achievable rate at Dj, j = 1, 2, as

+ ajP(bound)Sj ) + (1 t) log(1 + cjP(bound)Rj

)(33)

+ (aj + b)P(bound)Sj). (34)

min(Cj, Cj) = Rj , P(bound)req,j (s) can be obtained. Moreover, P(bound)req (s), where the latter is found in Section 3.6.1.the individual outage probabilities are computed.

cal results

numerical results, we will investigate N = 2 and N = 3ssume a1, a2, a3, b, c1, c2, c3 are independent exponentialiables. For N = 2 we assume all terminals are located on

relay is located on the line joining the source and pointR distance is d and the distance between the source

is normalized to 1. In Fig. 1 DjP distance is denoted. Similarly, for general BRC with N destinations, each

is located on the plane which is orthogonal to the SP


Fig. 4. (a) The 0.2, dvs. average tot

Fig. 5. (a) Thexed minimum

Fig. 6. (a) E{d = 0.2, d1 = 0.2

line in threing DjP di

j = 1, 2, . . .,

and [(1 d)Fig. 4a il

average totd = 0.2, d1 = limited systtotal averagis far from oMH. On theonly 0.2 dB minimum common outage probability vs. average total power, N = 2, R1 = 1, R2 = 1, d =al power, N = 3, R1 = 1, R2 = 1, R3 = 1, d = 0.2, d1 = 0.25, d2 = 0.25, d3 = 0.25 and = 4. -outage rate region for xed minimum common outage probability of 0.01, N = 2, Pavg common outage probability of 0.01 and for xed individual outage probability Pout,1 = P

} and E{} (dened in (35)) vs. d2 for N = 2, Pavg = 0.5 dB, R1 = 1, R2 = 1, d1 = 0.5 and = 4 f5, d2 = 0.25, R1 = 1, R2 = 1, and = 4.

e dimensional space with dj, j = 1, 2, . . ., N represent-stance. As a result, the random variables aj, b, and cj,

N respectively have the mean values (1 + d2j) 2 , d

2 + d2j] 2 , where is the path loss exponent.

lustrates the minimum common outage probability vs.al power for all protocols for N = 2 with R1 = 1, R2 = 1,0.25, d2 = 0.25 and = 4. We observe that for the delay-em under study, MH requires approximately 4 dB lesse power with respect to DT at Pout = 101. However, itptimal. Link combination, MHLC, adds 0.3 dB gain upon

other hand, PS signicantly improves upon MH and isaway from the lower bound. This shows that enforcing

the relay toand path sewe can say rather thanimplies thato the sourPSLC in DFLsystem is econclude thmission schobservationboth receivtheir own.1 = 0.25, d2 = 0.25, = 4. (b) The minimum common outage probability= 1 dB, d = 0.3, d1 = 0.2, d2 = 0.4 and = 4. (b) The -outage region forout,2 = 0.01, N = 2, Pavg = 1 dB, d = 0.3, d1 = 0.2, d2 = 0.4 and = 4.

or PSLC. (b) Individual outage probability region for N = 2, Pavg = 4 dB,

help both destinations simultaneously is quite limiting,lection is necessary. As PS performs very close to PSLC,that the gains obtained are mainly due to path selection

link combination at the destinations when d = 0.2. Thist simple receivers are sufcient when the relay is closece. In the simulations it is observed that in MHLC andC mode, in approximately 1% of all channel states the

ither in Case 1 or Case 4 as described in Section 3.3. Weat in the resultant BRC implementing the given trans-emes, one of the receivers does not always have a better

than the other. Although rarely, it can be benecial ifers decode both messages, or both receivers decode only


Fig. 4b illustrates the minimum common outage probability vs.average total power for three users for all protocols for R1 = 1, R2 = 1,R3 = 1, d = 0.2, d1 = 0.25, d2 = 0.25, d3 = 0.25 and = 4. When com-pared with Fig. 4a, we observe that all protocols and the lowerbound require more power to attain the same common outageprobability for the loweover, the diof PS is eveincreases. Inbecomes m

Fig. 5a sminimum cd1 = 0.2, d2 =achieve a mthe -outagto the uppethe destinatlink combinsource.

Allowingof freedomobtained antocols undeindividual otarget rates(1, . . ., N)imately equor R2 is zero

In Fig. 6a

P(PSS1

P(PSLC)S1 +for Pavg = 0.5that, whenand the reand E{} = Ebecause theues for a1 amore poweopposite is their maximthat the relacurve is hig

When thoutage decpairs becomthe individuPSLC and thupon the wthe lower b

5. Conclus

In this pof probabildelay-limitedirect transpath selectilyze both sminimum age probabprotocols. Fachievable

bound on outage probability and an upper bound on -outage rateregion. Our results indicate that enforcing the relay to help all desti-nations simultaneously is limiting the system performance. Partialdecoding brings in signicant gains in the BRC setting.

wled

s matlogiE05

ernaence

nces

mer the

p://dxskara8;54(boodadcasp://dxn L. O44th p://dxng Y, Vs. In: P4. p. 4o L, Cceedin26, hirim -forwrnatio

p://dxirim ed comtion thP furthnicailableg Y,advanp://dx

D, Vissity Prre G, Tns Inf, Goldnnelsp://dxna M,leigh-p://dxsel Mer in

p://dxduz

ource p://dxnik Ands. I. 2005ng Y, ory 2man adcas

comp://dxer TMnicati

D. Opceedin

http:/er TMory 1for an additional user. This loss is approximately 3 dBr bound, PS and PSLC, and 4 dB for MH and MHLC. More-fference between PS and MH is enlarged, and the valuen more emphasized when the number of destinations

other words, forcing the relay to decode all messagesore costly when there are more destinations.hows the -outage rate region for R1 and R2 for a xedommon outage probability of 0.01, Pavg = 1 dB, d = 0.3,

0.4 and = 4 for N = 2. It can be seen that MH and MHLCuch larger -outage rate region with respect to DT ande rate regions achievable with PS and PSLC are very closer bound. Therefore, allowing the relay to help each ofions individually is almost optimal without the need ofation at the destinations, when the relay is close to the

individual outage events brings in an extra degrees into the system. Fig. 5b shows the amount of gainsd compares -outage rate regions for DT and PSLC pro-r common and individual outage constraints. Underutage setup, the -outage rate region is the set of all

(R1, . . ., RN) such that a xed outage probability vector is satised. The gains are more emphasized for approx-al target rates R1 and R2, and diminish when either R1., we plot the expected values of the ratios

LC)

P(PSLC)S2

, P(PSLC)R1

P(PSLC)R1 + P(PSLC)R2

(35)

dB, R1 = 1, R2 = 1, d1 = 0.5, and = 4 for N = 2. We observe D2 is colocated with D1 (d2 = 0.5), both the sourcelay allot their power equally among the two users,{} = 0.5. When 0.5 < d2 < 0.5, E{}, E{} > 0.5. This is

mean values for a2 and c2 are larger than the mean val-nd c1. Therefore, both the source and the relay allocater for D1 to decrease the common outage probability. Thetrue for d2 > 0.5. It can be seen that E{} and E{} reachum values for d2 = 0. In addition to these, we observey location d has limited effect on E{} curve, while E{}hly dependent on the relay location.e system outage constraint is removed and individuallarations are possible, a range of (P(i)out,1-min, P

(i)out,2-min)

e feasible for xed target rates R1 and R2. Fig. 6b showsal outage probability region P(i)out,2 vs P

(i)out,1 for i = DT, PS,

e lower bound for N = 2. It is seen that PSLC improveshole region PS attains. Moreover, PSLC is very close toound for a range of (P(i)out,1, P

(i)out,2) around (0.01, 0.01).

ion

aper, we study the broadcast relay channel in termsity of outage under long-term power constraint andd transmission. We propose ve different protocols,mission, multihop, multihop with link combination,on and path selection with link combination. We ana-ystem outage and individual outage events and ndcommon outage probability and the individual out-ility region. We also nd -outage rate regions for allinally, for comparison we write upper bounds on therates in the broadcast relay channel and derive a lower

Ackno

ThiTechnoNo. 1127th IntConfer

Refere

[1] Kraity htt

[2] Bha200

[3] Behbrohtt

[4] Cheof htt

[5] Lianel200

[6] ZhaPro128

[7] Yildandintehtt

[8] Yildbasma

[9] 3GPTecAva

[10] Yanlte-htt

[11] Tsever

[12] CaiTra

[13] Li Lchahtt

[14] HasRayhtt

[15] Yukundhtt

[16] Gunreshtt

[17] Rezbouory

[18] LiaThe

[19] Isikbrolesshtt

[20] Covmu

[21] TsePro27,

[22] CovThegements

erial is based upon work supported by the Scientic andcal Research Council of Turkey, TUBITAK, under Grant9. The material in this paper was presented in part at thetional Wireless Communications and Mobile Computing, Istanbul, Turkey, July 2011.

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Transmission strategies and resource allocation for fading broadcast relay channels1 Introduction2 System model2.1 Overview of transmission protocols2.2 Long-term average total power constraint2.3 Common outage probability2.4 Individual outage probability region

3 Transmission protocols3.1 Direct transmission3.1.1 Common outage3.1.2 Individual outage

3.2 Multihop3.3 Multihop with link combination3.3.1 Case 13.3.2 Case 23.3.3 Case 33.3.4 Case 4

3.4 Path selection3.4.1 Common outage3.4.2 Individual outage

3.5 Path selection with link combination3.5.1 Common outage3.5.2 Individual outage

3.6 Performance bounds3.6.1 Common outage3.6.2 Individual outage

4 Numerical results5 ConclusionAcknowledgementsReferences

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Transmission Strategies and Resource Allocation for Fading Broadcast Relay Channels