joint optimal resource allocation and papr reduction ... · joint optimal resource allocation and...

Joint Optimal Resource Allocation and PAPR Reduction Algorithm for OFDMA Systems 107

Joint Optimal Resource Allocation and PAPRReduction Algorithm for OFDMA Systems

Pattama Phoomchusak1 and Chaiyod Pirak2 , Non-members

ABSTRACT

One of the drawbacks of an orthogonal frequencydivision multiplexing (OFDM) system is the largerpeak to averaged power ratio (PAPR). The PAPR re-duction scheme is a complicated problem, especiallywhen a resource allocation is considered jointly. Inthis paper, a joint algorithm for determining an opti-mal resource allocation with PAPR awareness is pro-posed. Firstly, an adaptive tone reservation assign-ment is performed by optimally choosing a group ofsubcarriers, whose channel gains are sufficiently high,to be the data subcarriers and the remaining sub-carriers will be used as the reserved tones for reduc-ing PAPR to the desired level. Secondly, an adap-tive power adjustment for PAPR reduction techniqueis introduced for determining the allocated power ofdata subcarriers by using the water-filling approachwith the joint PAPR and capacity constraints. By us-ing the proposed joint algorithm, the PAPR thresholdlevel is satisfied while the desired capacity could beachieved. From the results, the proposed algorithmachieves the better results comparing with a con-ventional partial transmit sequence (PTS) techniqueand the tone reservation (TR) technique in termsof PAPR, and probability of error performances, inwhich the side information is not required, in con-trast with the other techniques.

Keywords: PAPR, Tone Reservation, OFDM, Re-source Allocation

1. INTRODUCTION

The OFDM has been chosen for high data ratecommunications due to considerable high spectral ef-ficiency, multipath delay spread tolerance, immunityto the frequency selective fading channels and powerefficiency. Thanks to its advantages, the OFDM is aninteresting option for high data rate wireless sensornetwork, Digital Video Broadcasting (DVB), mobileworldwide interoperability for microwave access (mo-bile WiMAX) and the future broadband radio system

Manuscript received on February 6, 2015 ; revised on August22, 2015.Final manuscript received on September 5, 2015.1,2 The authors are with Sirindhorn International Thai-

German Graduate School of Engineering (TGGS), KingMongkut’s University of Technology North Bangkok,Bangkok, Thailand, E-mail: [email protected] [email protected]

(5G) [1]. However, a major drawback in OFDM sys-tems is the high peak-to-average power ratio (PAPR)of transmitting signals due to the superposition ofmany subcarriers, in which the high dynamic rangesis required for a nonlinear device such as a poweramplifier (PA) to avoid the amplitude clipping of thesignal [2]. Different approaches have been designedto cope with the PAPR problem. An amplitude clip-ping technique has been proposed in [3], in which thebaseband signal from IFFT is clipped to the prede-fined threshold in the time domain. The amplitudeclipping is a simplest technique, but it could gener-ate both in-band and out-of-band distortions. For ablock coding technique proposed in [4], the usefulnessof this technique is limited to multicarrier systemswith a small number of subcarriers, and the requiredexhaustive search for a good code is computation-ally expensive. A selected mapping technique (SLM)proposed in [5] and a partial transmit sequence tech-nique (PTS) proposed in [6] can reduce the PAPR bycontrolling the phase of data subcarriers, which pro-vides an effective solution. However, they require atransmission of continuously side information to thereceiver, which degrades the capacity of the system.A tone reservation (TR) technique proposed in [7]and [8] is one of the most effective techniques whenthe number of subcarrier is large. In this technique,a portion of subcarriers (tone), not being used fordata transmission, are reserved to create a dummydata in time domain which can be used to minimizethe PAPR of the overall signal. Note that, since thedummy data on the reserved tone is separated (in fre-quency domain) from the data subcarriers, the datais not distorted and, hence, the probability-of-errorperformance will not be degraded. However, there isno rule for the tradition TR to define the number andposition of reserved tones.

In [9], an adaptive TR with subcarriers allocationawareness has been proposed. A non-selected toneresulted from the optimal subcarrier allocation algo-rithm, based on the maximum subcarrier’s channelgain approach, will be used as a reserved tone. Thistechnique could enhance the capacity while reducingPAPR of the OFDMA systems. However, an opti-mal number of reserved tones are not investigated.In [10], a cross-layer design between a TR-PAPR re-duction and a subcarrier allocation algorithm is pro-posed for determining the optimal number of reservedtones to achieve the throughput requirement. In [11],the joint optimization of subcarrier allocation and TR

108 ECTI TRANSACTIONS ON COMPUTER AND INFORMATION TECHNOLOGY VOL.9, NO.2 November 2015

PAPR reduction technique based on a fairness con-straint for all users is proposed. However, the powerallocation does not be mentioned in this technique.It is obvious that the existing techniques are investi-gated based on the equal power distribution for all ofdata subcarriers, which may not be valid in the realis-tic systems. Recently, some theoretical approaches todetermine the power distribution have been proposed.The water-filling policy is a well-known technique todetermine the required minimum power of subcarriersby using the channel gain and the data rate condition[12]. However, the different transmission powers allo-cated to different subcarriers could affect the perfor-mance of PAPR reduction, as shown in [13-14]. Dif-ferent techniques have been designed to minimize thePAPR by adjusting subcarrier power levels. In [15],the simple PAPR reduction technique by using the in-put sequence envelope scaling approach is proposedby modifying amplitude envelope of non-overlappinggroups of subcarriers with different weights in the fre-quency domain in which the PAPR is reduced. How-ever, the capacity performance awareness is not men-tioned in this technique. For [16-18], the PAPR re-duction technique are proposed based on the powervariance approach, the dynamically extension of theactive constellation points (ACE) approach, and thesubcarrier power window adjustment, respectively.

The previous techniques of the resource allocationand PAPR are optimized individually. In order todesign an efficient algorithm to jointly optimize theresource allocation while constraining the PAPR toa certain threshold, a new algorithm for multiple ob-jective optimizations has to be investigated. This isthe motivation of this paper to propose a joint op-timal resource allocation and PAPR reduction algo-rithm aiming at decreasing the PAPR level given theoptimum power distribution and capacity constraintsof the OFDMA systems. The contribution of this pa-per includes the adaptive power adjustment techniqueand the resource allocation and PAPR reduction al-gorithm, which can be jointly optimized for practi-cal application of OFDMA downlink systems; mean-while, the side information regarding the power leveladjustment is not needed to transmit to the receiver.Therefore, an additional processing is not required atthe receiver side.

The organization of this paper is as follows: Weintroduce the system model in section 2, and PAPRreduction techniques for OFDM systems in section 3.The resource allocation scheme for OFDM systems isdescribed in section 4. In section 5 and 6, the pro-posed scheme and its simulation results are presented,respectively. The conclusion is given in section 7.

2. SYSTEM MODEL

In this section, we describe a system model used inthis research, regarding orthogonal frequency divisionmultiplex (OFDM) signal and PAPR problem. After

the modulated symbol Xn at the nth subcarrier inthe frequency domain is passed through a serial-to-parallel converter, this frequency component will beconverted to the time domain signal at the kth sam-ple point by IFFT processing in order to generate anOFDM signal. The baseband sample for OFDM sig-nals, with N subcarriers, at the output of IFFT isgiven by [1],

xk =1√N

N−1∑n=0

Xn · ej2πnk/N . (1)

The OFDM sample after adding a cyclic prefix isthen ordered by the parallel-to-serial converter, andconverted to the analog signal by the digital-to-analogconverter (D/A). Before transmitting to the chan-nel, the baseband OFDM signal is passed througha nonlinear power amplifier (PA). The peak powerof the OFDM signal could be distorted when passingthrough the D/A converter or PA, resulting in a sub-stantial amount of signal distortion. The PAPR ofthe signal is defined as [1],

PAPR(dB) = 10 log

max0≤k≤N−1

|xk|2

E [|xk|2]

. (2)

where E[] is the expectation operator, representingthe averaged power of the signal.

3. PEAK-TO-AVERAGE POWER RATIOREDUCTION TECHNIQUES

In this section, a summary of PAPR reductiontechniques is reviewed, including a tone reservationtechnique, a partial transmission sequence technique,and an input sequence envelop scaling technique.

3.1 Tone Reservation Technique

The tone reservation (TR) technique can reducethe PAPR value by utilizing the reserved subcarri-ers, which are not used for data transmission. Basedon the TR technique, the baseband signal in (1) ismodified as,

xk=1√N

(∑d∈D

Xd ·ej2πkd/N+∑r∈R

Cr ·ej2πkr/N). (3)

where D is the set of subcarriers used for the datatransmission, and R is the set of remaining subcarri-ers used for the reserved tones. Xd and Cr stand forthe modulated data signal on the dth subcarrier andthe dummy data signal on the rth subcarrier, respec-tively. Basically, Cr must be chosen in order to min-imize the maximum value of the time-domain signalxk. Then, a minimax PAPR optimization problem isdefined as [7],


C(opt)r = argmin

crmax

0≤k≤N−1|xk|2. (4)

One of the simple suboptimal techniques to definethe value of Cr without the frequency band expansionis the iterative clipping and filtering (ICF) [2]. Ineach of the iteration, the baseband signal obtainedfrom IFFT is clipped by a limiter to the predefinedthreshold in the time domain [3]. The clipped OFDMsignal, xclipped , becomes [7]

xclipped =

{xk , |xk| ≤ AAejϕk , |xk| > A

(5)

where A is the clipping level and ϕk is the phase ofxk. The xclipped is converted to frequency domain andthen filtered such that the clipping noise exists onlyon the reserved tones. In this approach, the frequencydomain signal is only changed at the reserved tonelocations.

3.2 Partial Transmission Sequence Technique

For a typical partial transmission sequence (PTS)approach, the input data block in X is partitionedinto Y disjoint sub-blocks, which are represented bythe vectors Xy = [Xy, 0 Xy, 1 . . . . . . Xy,N−1], where(0 ≤ y ≤ Y − 1) and N is the total number of sym-bols. Then, the sub-blocks Xy are transformed intoY time-domain partial transmit sequences by IFFTprocessing. These partial sequences are indepen-dently rotated by phase factors b = {by = ejθy , y =0, 1, . . . , Y − 1} in order to obtain the time domainOFDM signals with the lowest PAPR. It can be de-fined as [6],

x′ =Y−1∑y=0

byxy· (6)

The search complexity is depended on the numberof allowed phase factors W . Hence, WY−1 sets ofphase factors are searched to find the set of phasefactors.

3.3 Input Sequence Envelope Scaling Tech-nique

The idea of the envelope scaling technique is toscale the envelope of the input in some subcarriersin order to obtain the minimum PAPR at the outputof IFFT. First, the input data block X is partitionedinto Z disjoint sub-blocks or clusters, which are rep-resented by the vectors {Xz, z = 0, 1, . . . , Z − 1}.All vectors Xz are scaled with the scaling factorsszϵ(0, 1], z = 0, 1, . . . , Z − 1 and combined togetherbefore being sent to the IFFT. For single scaling fac-tor approach, only Z iterations have been done. Fi-nally, the scaling factors are chosen to minimize thePAPR of x′ [14], where

X ′ =Z−1∑z=0

szXz. (7)

x′ = IFFT{X ′}. (8)

4. SUBCARRIER AND OPTIMAL POWERALLOCATION TECHNIQUES

In this section, a summary of an adaptive sub-carrier allocation and water-filling technique are pre-sented.

4.1 Subcarrier Allocation Technique

For the frequency-selective fading channel in down-link OFDMA systems, the channel gains are differ-ent for each subcarrier. This characteristic is used toadaptively assign the subcarriers to all users. Assum-ing that there are U users and N subcarriers in thesystem, the maximum change in achieved data rateof the uth user can be defined by [19],

Vu =B

Nlog2

(1 + pu,n(Hu,mean + su)

2

1 + pu,n(Hu,mean − su)2

)(9)

where B is the total bandwidth of the system.Hu,mean is the average channel gain for all subcar-riers of the uth user, and su is the uth user’s channelgain standard deviation from the mean.

4.2 Power Allocation Technique

For the water-filling technique, the spectrum canbe considered as a vessel and the shape of the bot-tom of this vessel is determined by the inverse of Hn

values, H−1n . The additional power, which is the dis-

tance between the water level and the H−1n of each

subcarrier, can be defined as follows [20],

Pn =

{λ−H−1

n , ∀n : 1 ≤ n ≤ N0 , otherwise.

(10)

where λ = 2Rreq/NN∏

n=1

(H−1n )1/N is a water-filling

level.

5. THE PROPOSED JOINT OPTIMAL RE-SOURCE ALLOCATION AND PAPR RE-DUCTION ALGORITHM

As mentioned in the literature, the existing subcar-rier and power allocation does not consider the PAPRproblem. In this section, we propose the joint opti-mal resource allocation and PAPR reduction (JORP)algorithm design for OFDMA systems. Basically, thegoal of the proposed algorithm is to minimize thePAPR of OFDM systems by using the TR techniquewith the capacity constraint, Rreq. Specifically, the


PAPR will be minimized by optimally inserting thespecific complex signal Cr, determined by the TRtechnique, in the rth reserved subcarriers with thecapacity constraint, expressed as follows,

C(opt)r = argmin

Cr

max0≤k≤N−1

|xk|2,where (11)

xk=1√N

(∑d∈D

Xd ·Pd ·ej2πkd/N+∑r∈R

Cr ·ej2πkr/N)

Subject to

Rreq ≥ B

N

∑d∈D

log2

(1 +

Pd|Hd|2

N0(B/N)

)

where D is the set of subcarriers used for the datatransmission, and R is the set of remaining subcar-riers used for the reserved tones. In addition, Xd

denotes the modulated data signal of the dth datasubcarrier with the allocated power Pd ,Hd denotesthe channel’s frequency response of the dth data sub-carrier, and B is the total bandwidth of the sys-tem. Since the explicit solution for an optimal Cr

and Pd achieving a minimal PAPR with the capacityconstraint is not trivial, we propose a hybrid recur-sive search algorithm, called JORP, which consistsof two suboptimal algorithms, including an adaptivetone reservation assignment algorithm and an adap-tive power allocation algorithm with PAPR aware-ness. The structure of downlink OFDMA system withthe proposed JORP algorithm is illustrated in Figure1.

Fig.1: The Structure of Downlink OFDMA Systemswith the Proposed JORP Algorithm.

The proposed algorithm is described as follow.

The following notations are used in the JORP al-gorithm:

B is the total bandwidth of the OFDMA systemPAPRth is PAPR threshold used as the performance

benchmark of the systemQ={1, 2,. . .U} is a set of user, U = 2i, i ∈ Z+ where U

denotes the number of user in the systemD is a set of data subcarrier,R={1, 2,. . .N} is a set of reserved subcarrier, N=2i, i ∈ Z+

where N denotes the number of subcarriersCr is dummy data for the rth reserved subcarrierH(u,n) is the channel’s frequency response at the nth

subcarrier of the uth usersu is the uth user’s channel gain standard

deviation with respect to the meanZ is the number of subcarriers for each userXd is the data symbol of the dth data subcarrierXclipped is the clipped OFDM signal in frequency

domainxk is baseband OFDM signal at the kth sample

point of IFFT processing where k={1,. . ., N}xclipped is the clipped OFDM signal in time domaint is the number of ICF iterationA is the ICF clipping levelϕk = ∠xk is the phase of xk

Rreq is the capacity requirementλ is a water-filling level constantPd is the allocated power for the dth data

subcarrierHd is the channel’s frequency response at the dth

data subcarrierl(i) is the decision level at the ith order, where l(0)

denotes the initial decision leveli is the decision level index, where i={1, 2,. . ., I},

and I denotes the total number of thedifferent decision levels

∆ is a distance between the different decisionlevels

Wi is a set of non-modified power subcarrier atthe ith decision level

Mi is a set of modified power subcarrier at the ithdecision level

βϵ is a weight factor

P(i)w is the allocated power of the wth non-modifed

subcarrier at the ith decision level

P(i)m is the allocated power of the mth modifed

subcarrier at the ith decision levelXw is the data symbol of wth subcarrierXm is the data symbol at mth subcarrier

x(i)k is baseband OFDM signal at the kth sample

point of IFFT for the ith decision level andk={1, 2, . . . , N}, where N denotes the totalnumber of subcarriers

X(i)d is the data signal of the dth subcarrier in

frequency domain at the ith decision level

ϕk = ∠x(i)k is the phase of x

(i)k


5.1 An Adaptive Tone Reservation Assign-ment Algorithm (ATR)

For the JORP algorithm, the ATR algorithm isperformed firstly in order to assign subcarriers adap-tively for achieving the PAPR threshold. The ATRalgorithm is described below.

ATR AlgorithmStart:1: Z = N/U ,2: Do3: Q = {1, 2, . . . , U},4: R = {1, 2, . . . , N},5: D = ø, where ø denote an empty setStep 1: Subcarrier allocation6: while(Q ̸= ø)

7: u∗=arg max1≤n≤U

(B

Nlog2

(1+(|Hu|2+su

)21+(|Hu|2−su

)2))

, where

Hu = E[Hu,n]n denote a mean of Hu,n over allsubcarriers8: for m = 1 to Z9: n = arg max

1≤n≤N|Hu∗,n|2 ,

10: D = D ∪ {n}andR = R− {n},11: end for12: Q = Q− {u∗},13: end whileStep 2. PAPR reduction by ICF technique14: if R ̸= Ø then15: Cr = 0, ∀r where r ∈ R

16: xk=1√N

(∑d∈D


Cr ·ej2πkd/N), ∀k

17: for m = 1tot

18: xclipped,k =

{xk , |xk| ≤ AAejϕk , |xk| > A

, ∀k

19: Xclipped = FFT{xclipped,k}, ∀k20: Cr = Xclipped,r, ∀rwherer ∈ R

21:xk=1√N

(∑d∈D


Cr ·ej2πkr/N), ∀k

22: end for

23: PAPR(dB) = 100 log

max0≤k≤N−1

|xk|2

E[|xk|2]

,24: end if25: Z = Z − 1,26: while (PAPR > PAPRth)

The ATR algorithm can be described completelyas follows.

Step 1: Subcarrier allocation

• The maximum change in the achieved data rate ofeach user, Vu, is measured by using (9) based onthe equal power distribution in order to define thesensitivity of users. Generally, the most sensitiveuser has a small immunity to the frequency selec-tive fading channels because its variance of subcar-rier’s channel is very high [19]. (line 7)

• This weakest user, who has the highest Vu, is prior-

itized as the first user to select subcarriers, whichhas a highest channel gain, for data transmission.(line 7)

• The subcarrier allocation will be continuously per-formed until achieving the desired number of datasubcarriers for such user. There are a number ofunused subcarriers, which can be dedicated to bethe reserved tones for reducing the PAPR value,and then this user will be eliminated from the userset. (line 8-11)

• Likewise, this subcarrier allocation procedure isperformed iteratively for all users. Based on thisapproach, the total capacity is maximized, and therate proportionality among all users is maintained[19]. (line 12-13)

Step 2: PAPR reduction by ICF technique

• The iterative clipping and filtering (ICF) tech-nique, which is the simplest technique, is adoptedin order to determine Cr, inserted in the reservedtone. (line 14-22)

• The PAPR value is then calculated and comparedwith the desired PAPR level, PAPRth. If theachieved PAPR is higher than the target, the sub-carriers will be reallocated again, in which the num-ber of reserved subcarriers will be increased in or-der to gain the PAPR reduction performance. (line23-25)

• This algorithm will be performed iteratively untilachieving the desired PAPR value, and then passedthrough the power allocation process. (line 26)

Based on the adaptive TR used in the ATR al-gorithm, not only the PAPR target can be satisfied,but also subcarriers for data transmission are allo-cated efficiently compared with the traditional TRtechnique.

5.2 An Adaptive Power Allocation Algorithmwith PAPR Awareness

From the ATR algorithm, one could observe thata certain number of subcarriers being used as the re-served tones can minimize the PAPR value at theexpense of reducing the capacity efficiency. To copewith such problem, the conventional water-fillingtechnique is adopted in order to allocate the powerfor all data subcarriers for achieving the capacity re-quirement.

Step 1: Unequal power distribution by the tra-ditional water-filling technique for achievingRreq By applying the water-filling algorithm, thetypical baseband OFDM signal in (3) can be modi-fied as,

xk=1√N

(∑d∈D

Xd ·Pd ·ej2πkd/N+∑r∈R

Cr ·ej2πkd/N).(12)


where Pd=

(2Rreq/n(D)

D∏d=1

(H−1d )1/n(D)

)−H−1

d ,∀d

where d ∈ D, is the optimum power allocated for alldata subcarriers, and n() denotes the total numberof elements in a finite set, specified in the argument( ). This step is illustrated in line 1-2 of the adap-tive power allocation algorithm with PAPR awarenessshown below.

However, the different power distribution, resultedfrom the water-filling technique, could impact on theamplitude variation of the signals leading to the sever-ity of the PAPR problem. As a result, the PAPRthreshold level could not be satisfied. It implies thatthe solution of the problem cannot be found by usingonly the ATR and the conventional water-filling algo-rithm. Therefore, a better PAPR reduction techniqueis required for effectively achieving the target. Ac-tually, the existing PAPR reduction technique, suchas the PTS technique and the envelope scaling tech-nique, can be applied for the PAPR reduction pur-pose. However, a transmission of phase informationto the receiver is needed for the PTS technique; mean-while, the envelope scaling technique does not achievethe capacity requirement. Therefore, this motivatesus to design an adaptive power adjustment for PAPRreduction (APP) technique to determine the optimalpower allocation of a data subcarrier in order to re-duce the PAPR value while maintaining the capac-ity constraint of the OFDM system without any ad-dition side information requirement. The proposedAPP technique is described as below.

Step 2: Adaptive power adjustment for PAPRreduction (APP) technique As mentioned in theliteratures, a power variance of data sequence is aparameter that plays an important role in PAPR re-duction in the OFDM signal. Therefore, the mainidea of the APP technique is that we use an exceededpower level as a function of subcarrier’s power, whichis higher than a predefined level, and multiply it by aweight factor in such a way that the power varianceis reduced in order to minimize the PAPR value ofthe overall OFDM signal. Note that the phase of thedata is not affected by the APP technique; therefore,it does not need any side information or any receiveroperation.

The data baseband signal allocated with an un-equal power distribution for all data subcarriers in(12), expressed similarly as , is modified by theAPP technique. The modified OFDM signal, xk =IFFT{X + C}, is written as

x′k = IFFT{X ′ + C}. (13)

X ′ is the transmitting-data signal in frequency do-main, which can be defined as

X ′ =

{XmPm , |Pd| > lXwPw , otherwise.

(14)

where Xw and Xm denote the data symbol of the wthnon-modified subcarriers and the mth modified sub-carriers, respectively. Based on the APP algorithm,the power amplitude of the data subcarriers is onlyadjusted; therefore, the data symbol Xw and Xm isstill the same as the original one Xd. Pw denotes thepower of the wth non-modified subcarriers, which isequal to Pd, while Pm denotes the modified powerof the mth subcarrier, which is Pm = βPd, where βdenotes a weight factor. The decision levels can bedenoted as l utilized for classifying the exceed powersubcarriers that would be modified by the weight fac-tor in such a way that the variation of the data sub-carriers’ s amplitude is decreased, β ∈ [0.5,1]. Thedecision levels can be obtained from

li = l(i−1) −∆, (15)

∆ =1

l

∣∣∣∣∣max(Pd)− 1

n(D)

∑d∈D

Pd

∣∣∣∣∣ . (16)

where i denotes the decision level index, i =1, 2, . . . , I, and I is the total number of the differ-ent decision levels. ∆ is the distance between thedifferent decision levels. The maximum value of Pd

is used as an initial value of the decision levels, l(0).The data subcarriers in the set D of the ATR algo-rithm, which occupy the power level higher than theconsidered decision level, are modified by β accord-ing to (14). This scheme is executed iteratively untilthe last decision level is performed. As a result, a setof different candidate signals is generated in the timedomain, which represents the same data informationwith the different data power. In other words, I IFFToperation is needed for each data block and there areI×O alternative representations for the different can-didate OFDM signals, where O denotes the numberof β to be allowed. Finally, the signal that has thelowest PAPR value is selected for transmission.

Although, the PAPR value can be minimized ef-ficiently by this approach, the capacity could be de-graded due to the reduction of power by a factor ofβ. Hence, it would be developed for achieving thecapacity requirement by modifying the data signal infrequency domain in (14) as,

X ′=

XmPm , |Pd| > 1

Xw

(Pw+

1n(W )

(∑d∈M

(1−β)Pd

)), otherwise.

(17)Based on this approach, the power loss resulted

from the weight-modification process is compensatedby adding the same amount of the lost power tothe remaining data subcarriers equally. As a result,the capacity could be improved approximately to theoriginal level. Consequently, the modified basebandsignal in (12) can be written as,


x′k =

1√N

(∑w∈W

Xw · Pw · ej2πkw/N +∑m∈M

Xm · Pm

·ej2πkw/N +∑r∈R

Cr · ej2πkw/N

)(18)

where W and M denotes the set of non-modified sub-carriers and modified subcarriers, respectively. Notethat D = M +W .

In summary, the APP technique can be describedas follows, see also the adaptive power allocation al-gorithm with PAPR awareness.

• An initial value of the decision levels, l(0) is definedby the maximum value of Pd. (line 3-4)

• The distance between the different decision levels(∆) is determined. (line 5)

• The data subcarriers in the set D of the ATR al-gorithm, which occupy the power level higher thanthe considered decision level, are modified by β ac-cording to (17). (line 9-16)

• The PAPR value of the candidate OFDM signal isthen calculated. (line 17-19)

• This scheme is executed iteratively with the nextdecision levels l(0) until the last one is performed.As a result, a set of different candidate signals isgenerated in the time domain. (line 20)

• Finally, the signal that has the lowest PAPR valueis selected for transmission.

By using the proposed APP technique, the PAPRof the OFDM signal with different power allocationfor all subcarriers can be reduced while the capac-ity performance could be maintained unlike the enve-lope scaling technique. Another benefit of the APPtechnique is that the computational complexity of theAPP technique for achieving the lowest PAPR signalis lower than that of the partial transmit sequence(PTS) techniques comparatively. Furthermore, anyside information regarding the power adjustment isnot required by the receiver, in contrast with the PTStechnique. Moreover, it can be further applied to thetraditional PAPR reduction technique easily such asthe TR-ICF technique, the PTS technique and theenvelope scaling technique in order to improve thePAPR reduction performance.

Step 3: PAPR additional improvement by ICFtechnique Finally, if the lowest PAPR signal ob-tained from the APP technique is not achieved bycomparing with the PAPR threshold, the traditionalICF technique can be further applied to gain thePAPR reduction performance by determining Cr,filled in the reserved tone. The ICF algorithm willbe performed iteratively until completing the pre-defined number of ICF iteration, or satisfying thePAPR threshold. This step is shown in line 22-31 ofthe adaptive power allocation algorithm with PAPR

awareness described below.

The Adaptive Power Allocation Algorithmwith PAPR Awareness

Start:

Step 1 : Unequal power distribution by the tradi-tional water-filling technique for achieving Rreq

1: λ = 2Rreq/n(D)∏d∈D

(H−1d )1/n(D), where n() denotes

the total number of elements in a finite set,specified in the argument ( ), and

∏denotes

a product operator2: Pd = λ−H−1

d ,Step 2 : The APP technique3: d∗ = argmax

d∈DPd,

4: l(0) = Pd∗ ,5: ∆ = 1

l |Pd∗ − Pd|, where Pd = E[Pd] denotes a meanof P d over all data subcarriers

6: for i = 1 to I7: l(i) = l(i−1) −∆, where ()(i) denotes the

iterative index at the ith decision level8: Wi = D and Mi = ∅, where ∅ denotes an empty set9: for d = 1 to n(D)10: if Pd ≥ l(i) then11: Wi = Wi − {d} and Mi = Mi ∪ {d},12: P i

m = βPd, where m ∈ Mi

13: end if14: end for

15: P(i)w =P

(i)w + 1

n(Wi)

(∑d∈Mi

(1−β)Pd

), where w ∈ Wi

16: X(i)d = XwP

(i)w +XmP

(i)m ,

17: x(i)k = IFFT{X(i)

d + Cr}, ∀k18: Cr = 0, ∀r where r ∈ R

19: PAPR(i) = 10 log

(max

0≤k≤N−1|x(i)

k |2

E[|x(i)k |2]

)20: end for

21: i∗ = argminPAPR(i). {x(i∗)k is selected}

Step 3 : PAPR additional improvement by ICFtechnique22: for a = 1tot

23: xclipped =

{x(i∗)k , |x(i∗)

k | ≤ A

Aejϕk, |x(i∗)k | > A

, ∀k

24: Xclipped = FFT{xclipped,k, ∀k}25: Cr = Xclipped,r, ∀r where r ∈ R

26: x(i∗)k = IFFT{X(i∗)

d + Cr}, ∀k

27: PAPR(i∗) = 10 log

(max

0≤k≤N−1|x(i∗)

k |2

E[|x(i∗)k |2]

)28: if PAPR(i∗) ≥ PAPRth then29: break,30: end if31: end forThe complexity of the ATR algorithm can be eval-

uated by counting the total number of operation(multiplication) per round in a recursive loop [19],


as follows. Let U denotes the total number of user inthe system, and N denotes the number of subcarri-ers. The subcarrier gain Hu,n for each user u requiresthe NU((1 + N)/2) operations, thus the complex-ity is O(UN2), in order to determine the data andreserved subcarriers. Next, the ICF process is re-quired iteratively for determining the dummy signalCr, filled in the reserved subcarriers with O(N) op-erations. Therefore, the complexity of the ATR algo-rithm is O(UN2). For the adaptive power allocationalgorithm with PAPR awareness, the water filling re-peatedly operates U times for distributing the powerinto the data subcarriers with the complexity of O(U)operations. The exceeded PAPR signal is executedby the APP process cooperated with the optional op-eration of the ICF approach, which requires O(N)operations. Therefore, the complexity of the JORPalgorithm has been shown to be O(UN2). It is worthnoticing that the proposed JORP algorithm offers agood result in the sense of the PAPR reduction andthe capacity at the expense of higher computationalcomplexity.

6. SIMULATION RESULTS

This section presents computer simulation resultsto verify the performance of the proposed algorithmin terms of the PAPR reduction, capacity, and biterror rate performances for a single-cell downlinkOFDM-based multiple access systems. In this pa-per, we assume that the BPSK modulation with 64subcarriers is used for 2 users in the 1 MHz band-width systems. A six-independent frequency selectiveRayleigh fading multipath channel model with thetypical urban with exponential power profile (COST231) is modeled. The perfect knowledge of the chan-nel state information (CSI) for all users is assumed tobe known at the base station. The PAPR reductionis evaluated in terms of its complementary cumula-tive density function (CCDF) that is the probabilitythat PAPR exceeds a given the desired threshold γ;(CCDF = Prob (PAPR > γ)). In our simulation,5000 different channel realizations are used, and theresults are averaged. The subcarrier’s channels foreach user are generated following the Jake’s model[1], and the average SNR is ranged from 1-40 dB.The simulation parameters used in the following eval-uations are expressed as follows.

1) We assume that the PAPR threshold in the sim-ulation is 6.5 dB at CCDF of 10-2, which is less thanthe minimum PAPR for the 802.11 a/g WLAN stan-dard [21].

2) To simplify the comparison in the simula-tion, the capacity requirement is assumed to be 2.2bits/s/Hz (at SNR = 10 dB), which is sufficientlyhigh enough comparing with the maximum capacityfor the 802.11 a/g WLAN standard [21].

3) Basically, the computational complexity of alltechnique depends on the disjoint group of subcarrier,

which is modified by the factor. In this simulation,the total number of the disjoint decision levels I is 4for the APP technique, and the input data block ispartitioned into 4 disjoint clusters for both PTS andenvelope scaling techniques.

The JORP algorithm is firstly processed by theATR operation for determining the number and posi-tion of reserved tones that achieve the PAPR thresh-old. The PAPR reduction resulted from the ATRalgorithm by using the equal power distribution forall data subcarriers, is shown in Figure 2.

It is worth noticing that the PAPR reduction byusing 16 iteration of ICF technique with 8 reservedtones is about 7.6 dB at CCDF of 10-2, which is notachieve the PAPR target in contrast with using 14 re-served tones. However, the number of reserved tonesdirectly reduces the capacity shown in Figure 3.

Specifically, it can be seen that using 14 reservedtones provide the capacity of 1.8 bits/s/Hz at SNR =10 dB, which is lower than using 8 reserved tones by0.5 bits/s/Hz at SNR = 10 dB. From these results, thesubcarrier assignment, which is solely based on thePAPR target criterion, could not satisfy the desiredcapacity. To cope with such problem, the adaptivepower allocation algorithm with PAPR awareness isthen performed. Firstly, the traditional water-fillingtechnique is applied for allocating the different powerto the data subcarriers given the capacity require-ment, which is 2.2 bits/s/Hz (at SNR = 10 dB). ThePAPR reduction by using the TR-ICF technique com-paring between the equal power distribution case andthe unequal power distribution case obtained fromthe traditional water-filling technique is shown in Fig-ure 4. From the figure, the PAPR level of the unequalpower distribution case can be reduced increasinglyfrom 9 dB to 6.9 dB at CCDF of 10-2 by using 16iteration of ICF technique. However, it is worse thanthat of the equal power distribution case about 0.4dB at CCDF of 10-2. From this result, we have foundthat the different power distribution affects the PAPRreduction performance, even when applying the TR-ICF technique for the PAPR reduction.

Subsequently, the APP technique is introduced forreducing the PAPR value by adjusting the power ofsome data subcarriers, which have the power levelhigher than the considered decision level l, with amultiplicative factor β . The experimental result ofthe trade-off curve between the PAPR and the ca-pacity with different β values of the APP techniqueis shown in Figure 5. Basically, the power varianceof the data subcarriers is minimized according to βvalue, which leads to PAPR reduction. Therefore, wecould observe that PAPR is greatly reduced when β isdecreasing. At β = 0.5, the lowest PAPR is reached,which is about 4.5 dB; whereas the capacity is mostdegraded, which is about 4.3 bits/s/Hz. However,the capacity is also depending on an amount of sub-carriers’ modified power, which are classified by the


decision level. Therefore, β = 0.5 is used in the follow-ing simulation because it provides the lowest PAPRexperimentally. A trade-off curve between the PAPRand the capacity with the different decision levels atβ = 0.5 is shown in Figure 6. From this figure, thedecision level l(6) provides the lowest PAPR, which isabout 4.5 dB whereas the highest PAPR at the deci-sion level l(1) is about 6.3 dB. However, the capacityat the decision level l(6) is worse, which is about 4.3bits/s/Hz, due to a large amount of data power is de-creased for the PAPR reduction propose. From theseresults, we have found that the PAPR reduction per-formance increases when the decision level tends tobe decreasing; meanwhile, the capacity is degradedgradually. However, the power compensation strat-egy is adopted in the APP technique to deal with thedegradation of the capacity performance.

The PAPR reduction of the JORP algorithm isshown in Figure 7. By using the total number of thedifferent decision levels I is 4, hence, 4 IFFT iterativeoperations are executed for each data block in orderto obtain the lowest PAPR level for the APP scheme.From this figure, the JORP algorithm achieve thePAPR target value (6.5 dB at CCDF of 10-2) by con-verges at 3 additional ICF iterations; meanwhile, thePAPR level of the water-filling distribution case is re-duced from 9 dB to 7 dB at CCDF of 10-2 by the tra-ditional TR-ICF technique with 16 iterations. Fromthis result, it implies that solely applying the TR-ICF technique cannot achieve the target value evenwhen applying 16 iterations. Therefore, it is possi-ble to combine the ICF and APP techniques to makethe convergence of the traditional TR much faster.Note that, the PAPR reduction of the TR-ICF tech-nique proportionally depends on the number of re-served tones in contrast with the JORP algorithm.Therefore, the PAPR reduction performance of theJORP algorithm could be better than the TR-ICFtechnique notably in the system that uses a smallnumber of reserved tones.

The capacity performance comparison of theJORP, the water-filling and the equal power distri-bution case by using the TR-ICF technique with 16iterations is shown in Figure 8. From this figure,the capacity performance of the JORP algorithm isnearly close to that of the water-filling distribution by2.2 bits/s/Hz at SNR of 10 dB, which is the capacityrequirement. This is due to the JORP algorithm em-ploys a power-penalty approach for the unmodified-data subcarriers equally. Certainly, the capacity re-quirement could not be achieved by distributing equalpower for all data subcarriers. By using the JORPalgorithm, the capacity requirement and the PAPRtarget could be jointly achieved.

In comparison to other techniques, the standardPTS technique and the envelope scaling technique areapplied to the unequal power distribution signal in afrequency domain for reducing the PAPR level. To be

fair in the process of adjusting the phase or amplitudefor all techniques, the scaling factors = {0.5, 1} areused in the envelope scaling technique, and the phasefactors = {1, -1} are used in the PTS technique. Forthe PTS technique, the partial sequences are indepen-dently rotated by phase factors after IFFT process inorder to obtain the time domain OFDM signals withthe lowest PAPR. Therefore, the computational ex-pense is further required by 8 iterations for searchingthe optimum set of phase factors unless 4 IFFT oper-ations. As a result, the PTS technique yields highercomputational complexity than that of both the enve-lope scaling and the APP techniques, needing only 4IFFT iterative operations. The PAPR reduction per-formance comparison is illustrated in Figure 9. Fromthe figure, the PTS technique and the envelop scalingtechnique can reduce the PAPR level from 9 dB to7 dB and 8 dB at CCDF of 10−2 respectively, whichcould not achieve the PAPR threshold level unlike theJORP algorithm. From the result, it is clear that thePAPR reduction performance of the JORP techniqueis better than that of both PTS and envelope scalingtechnique by 0.5 dB and 1.5 dB at CCDF of 10−2,respectively.

In Figure 10, the investigation of the capac-ity performance for these techniques is illustrated.As a result of the power-compensated procedure inthe JORP algorithm, the capacity performance ofthe JORP algorithm is almost close to that of thewater-filling technique. It imply that the JORP al-gorithm achieve the capacity requirement approxi-mately. Moreover, the capacity of the PTS techniqueis also equal to the capacity requirement because thephase of data subcarriers is only changed withoutany power distribution disturbance. For the envelopescaling technique, which is based on the amplitudelevel reduction without the compensation scheme, thecapacity performance is worse than the requirementabout 0.5 bits/s/Hz. The bit error rate (BER) perfor-mance comparison in the non-linear channel is inves-tigated in Figure 11. We could observe that the BERof the JORP algorithm yields less distortion than thatof the TR-ICF technique with 16 iterations, the PTStechnique and the envelope scaling technique for agiven SNR.

The PAPR reduction performance of the JORPalgorithm comparing to the TR-ICF technique, thetraditional PTS technique and the envelope scalingtechniques based on the 8QAM modulation is shownin Figure 12. From the figure, we could observe thatthe PAPR in the case of 8QAM is larger than that ofBPSK. Nonetheless, the JORP algorithm can reducethe PAPR value of the unequal power distributionfrom 11 dB to 6.5 dB at CCDF of 10−2, which isbetter than that of the TR-ICF technique with 16iterations, the traditional PTS technique and the en-velope scaling techniques by 1.5 dB 2 dB and 2.5 dBat CCDF of 10−2, respectively. Last but not least, the


PAPR reduction performance of the JORP algorithmfor BPSK, QPSK, and 8QAM modulation with thedifferent number of subcarrier are shown in Figure 13.From the figure, we could observe that the PAPR inthe case of 8QAM is larger than that of both BPSKand QPSK when the number of subcarrier tends to beincreasing. Moreover, the PAPR reduction gains areobtained by using the JORP algorithm in differentmodulation scheme.

7. CONCLUSION

In this paper, a joint optimal resource allocationand PAPR reduction algorithm, called the JORP al-gorithm, has been proposed. It consists of two sub-optimal algorithms, which are an adaptive tone reser-vation assignments algorithm used for achieving thePAPR target, and an adaptive power allocation algo-rithm with PAPR awareness used for achieving thecapacity constraint. Specially, the APP technique,which is applied in the JORP algorithm, is newlydesigned for reducing the exceeded PAPR value ofthe unequal power distribution of the water-fillingoperation without capacity degradation. Based onthe JORP algorithm, the optimal allocated powerfor data subcarriers are investigated for reducingthe PAPR to the threshold value while the capacitycould be achieved approximately to the requirementof OFDMA systems. From the simulation results, theJORP algorithm can reduce the PAPR level from 9dB to 6.5 at CCDF of 10−2, which is better than thatof the TR-ICF technique, the PTS technique and theenvelope scaling technique by 0.5 dB, 0.5 dB and 1.5dB at CCDF of 10−2, respectively. Another benefit ofthe JORP algorithm is that none of the side informa-tion is required by the proposed technique in contrastwith the PTS technique. It is worth noticing thatthe proposed JORP algorithm offers a good result inthe sense of the PAPR reduction, the capacity, andprobability of error performances at the expense ofhigher computational complexity, which is O(UN2).Finally, the JORP algorithm can be easily applied toboth PTS and envelope scaling techniques in variousmodulation types with different size of subcarriers.

References

[1] A. Goldsmith, Wireless Communications, Cam-bridge University Press, 2005, ch. 1.

[2] T. Jiang and Y. Wu, “An Overview : Peak-to-Average Power Ratio Reduction Techniques forOFDM Signals,” IEEE Transactions on Broad-casting, Vol. 54, No. 2, pp. 257-268, 2008.

[3] Z. Xiaodong et al, “Simplified Approach to Opti-mized Iterative Clipping and Filtering for PAPRReduction of OFDM Signals,” IEEE Transac-tions on Communications, Vol. 61, No. 5, pp.1891-1901, 2013.

[4] D. Qu, L. Li and T. Jiang, “Invertible SubsetLDPC Code for PAPR Reduction in OFDM Sys-

tems with Low Complexity,” IEEE Transactionson Wireless Communications, Vol. 13, No. 4, pp.2204-2213, 2014.

[5] E. Hong and D. Har, “Peak-to-Average PowerRatio Reduction for MISO OFDM Systems withAdaptive All-Pass Filters,” IEEE Transactionson Wireless Communications, Vol. 10, No. 10,pp. 163-167, 2011.

[6] S. J. Ku, “Low-Complexity PTS-Based Schemesfor PAPR Reduction in SFBC MIMO-OFDMSystems,” IEEE Transactions on Broadcasting,Vol. 60, No. 4, pp. 650-658, 2014.

[7] L. Wang and C. Tellambura, “Analysis of Clip-ping Noise and Tone-Reservation Algorithmsfor Peak Reduction in OFDM Systems,” IEEETransactions on Vehicular Technology, Vol. 57,No. 3, pp. 1675-1694, 2008.

[8] H. Li et al., “An Improved Tone ReservationScheme with Fast Convergence for PAPR Reduc-tion in OFDM Systems,” IEEE Transactions onBroadcasting, Vol. 57, No. 4, pp. 902-906, 2011.

[9] P.Phoomchusak and C.Pirak, “Adaptive Tone-Reservation PAPR Technique with Optimal Sub-carriers Allocation Awareness for Multi-UserOFDMA Systems,” Proceeding of IEEE Interna-tional Conference on Advanced CommunicationTechnology (ICACT), Feb. 2011, Korea, pp. 814-818.

[10] P.Phoomchusak and C.Pirak, “Smart AdaptiveTone-Reservation for PAPR Reduction Tech-nique with Throughput Constraint for Multi-User OFDMA Systems,” Proceeding of IEEE In-ternational Congress on Ultra Modern Telecom-munication (ICUMT), Oct. 2011, Hungary, pp.1-5.

[11] L. Gao et al, “Joint Optimization of SubcarriersAllocation and Tone Reservation PAPR Reduc-tion for OFDMA Systems,” Proceeding of IEEE14th International Conference on Communica-tion Technology (ICCT), Nov. 2012, Chaina, pp.1172-1176.

[12] H. Wang et al, “Optimal Cooperative Water-Filling Power Allocation for OFDM System,”Proceeding of IEEE International Conferenceon Wireless Communications and Networking(WCNC), Apr. 2013, Chaina, pp. 3742-3747.

[13] T. Jiang, M. Guizani, H. H. Chen, W. Xiangand Y. Wu, “Derivation of PAPR Distributionfor OFDM Wireless Systems Based on ExtremeValue Theory,” IEEE Transactions on WirelessCommunications, Vol. 7, No. 4, pp. 1298-1305,2008.

[14] V. Mehmet et al, “Effect of Water-FillingMethod on the PAPR for OFDM and MIMOSystems,” Proceeding of 15th IEEE InternationalConference on Signal Processing and Communi-cations Applications, Jun. 2007, Turkey, pp.1-4.

[15] P. Foomooljareon, W. A.C. Femando and K. M.


Ahmed, “PAPR Reduction of OFDM Systemsusing Input Sequence Envelope Scaling,” Pro-ceeding of 57th IEEE International SemiannualConference on Vehicular Technology, Apr. 2003,pp. 1243-1247.

[16] I. M. Hussain and I. A. Mohammad, “PAPRReduction of OFDM Signals using Autocorre-lation based SLM without Side Information,”Proceeding of IEEE International Conference onElectrical and Computer Engineering, May 2008,Canada, pp. 71-76.

[17] B. S. Krongold and D. L. Jones, “PAR Reductionin OFDM via Active Constellation Extension,”IEEE Transactions on Broadcast, Vol. 49, pp.258-268, 2003.

[18] R. Rajbanshi, A. M. Wyglinski and G. J. Min-den, “Subcarrier Power Adjustment Techniquefor Peak-to-Average Power Ratio Reduction ofODFM Systems,” Proceeding of IEEE Interna-tional Conference on Military Communication,Oct. 2006, USA, pp.1-6.

[19] S. Sadr, A. Anpalagan and K. Rasshemifar,“Suboptimal Rate Adaptive Resource Allocationfor Downlink OFDMA Systems,” InternationalJournal of Vehicular, Vol. 2009, 2009.

[20] N. Papandreou and T. Antonakopoulos, “Bitand Power Allocation in Constrained Multicar-rier Systems: The Single-User Case,” Interna-tional Journal on Advances in Signal Processing,Vol. 2008, 2007.

[21] IEEE Std. 802.11a, “Wireless LAN Medium Ac-cess Control (MAC) and Physical Layer (PHY)Specifications: High-Speed Physical Layer in the5 Ghz Band”, 1999.

Fig.2: The PAPR Reduction Performance with theDifferent Number of the Reserved Tones.

Fig.3: The Capacity vs. SNR.

Fig.4: The PAPR Reduction Comparison betweenthe Equal Power Distribution Case and the Water-filling Distribution Case.

Fig.5: Trade-off Curve between the PAPR vs. theCapacity with the Different Weight Factors.

Fig.6: Trade-off Curve between the PAPR vs. theCapacity with the Different Decision Levels.


Fig.7: The PAPR Reduction Performance by theJORP Algorithm.

Fig.8: The Capacity vs. SNR of the JORP Algo-rithm.

Fig.9: The PAPR Reduction Performance by theJORP Algorithm.

Fig.10: The Capacity Performance Comparison.

Fig.11: BER Performance Comparison.

Fig.12: The PAPR Reduction Performance Com-parison of the 8QAM Modulation.

Fig.13: The PAPR Reduction of the JORP Algo-rithm for BPSK, QPSK, and 8QAM Modulation.

Pattama Phoomchusak received theB.Eng and M.Eng degree in Telecommu-nication Engineering from King Mong-kut’s Institute of Technology Ladkra-bang, Thailand, in 2000 and 2004, re-spectively. Currently, she is a Ph.D.candidate in wireless communicationengineering laboratory of The Sirind-horn International Thai-German Grad-uate School of Engineering (TGGS),King Mongkut’s University of Technol-

ogy North Bangkok, Thailand.


Chaiyod Pirak received the B.Eng.degree in Telecommunication Engineer-ing in 2000 from King Mongkut’s Insti-tute of Technology Ladkrabang, Thai-land. In 2005, he received the Ph.D de-gree in Electrical Engineering from Chu-lalongkorn University, Thailand in as-sociation with University of MarylandCollege Park, USA. In 2009, he was ap-pointed as the head of mobile communi-cations and embedded systems labora-

tory in the department of electrical and software system en-gineering, The Sirindhorn International Thai-German Grad-uate School of Engineering (TGGS). At present, he is a lec-turer at communication engineering department of TGGS. Hisresearch are in wireless sensor network; embedded system,FPGA, DSP, and microcontroller; broadband wireless access:WiMax, WCDMA, and CDMA2000; digital signal processingfor wireless communications.

joint optimal resource allocation and papr reduction ... · joint optimal resource allocation and...

Documents