Reducing Error Vector Magnitude of OFDM Signals UsingThreshold Vector Circle Method

Qingqing Wu1, Jingqi Wang1,2,Wen Wu11Nanjing University of Science and Technology Nanjing, 210094, China

2State Key Laboratory of Millimeter Waves, Nanjing, 210096, Chinawangjingqi@njust.edu.cn

Abstract: The main disadvantage of Orthogonal Frequency Division Multiplexing (OFDM) signal is the highpeak-to-average power ratio (PAPR) which influences the system power efficiency and system performance inthe presence of nonlinearities within the high power amplifier (HPA). The error vector magnitude (EVM) isone of the performance metrics by communications standards in OFDM system. In this paper, a novel EVMreduction method from geometric angle analysis is proposed which keeps the bit-error-rate (BER) performanceafter PAPR reduction. In our method, a threshold vector circle is designed in frequency domain in order to adjustthe amplitude and phase of the OFDM signal constellation points to near the ideal points. Simulation results showthat PAPR of a QPSK modulated OFDM signal is reduced from 10.56dB to 7.496dB with an EVM reduction of2.34%. This technique should vastly improve the performance of OFDM signal in communication system

Key–Words: Error vector magnitude (EVM), orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), threshold vector circle method

1 IntroductionOrthogonal Frequency Division Multiplexing (OFD-M), which has been adopted by many wireless com-munication standards [1]-[3], offers many advantagesfor multicarrier transmission such as high spectralefficiency and robustness against frequency-selectivefading channels. However, the main disadvantageof OFDM signal is the high time-domain peak-to-average power ratio which becomes a major obstaclein the implementation of power-efficient transmitters[4]. PAPR reduction is necessary to alleviate the con-tradiction between high power amplifier (HPA) linear-ity and power efficiency.

Various technologies have been developed to re-duce the PAPR of OFDM signals such as active con-stellation extension (ACE) with smart gradient-project(SGP) algorithm [5], repeated clipping and frequen-cy domain filtering [6], and etc. However, those PA-PR reduction technologies which aim to reduce thesignal peak value directly will cause distortions. Itis well known that error vector magnitude (EVM) isfrequently used in communication standards to quan-tify the amount of in-band distortion that occurs inthe communication system. For example, in [5], theSGP-ACE method which substantially reducing thepeak magnitude of an OFDM transmit block and re-quiring no side information offers fast PAPR reduc-

tion because of the step size setting. The simulationresults show that only two iterations of the SGP-ACEalgorithm are needed to make PAPR under 6dB. Un-fortunately, as the simulation results show in [7], themore PAPR is reduced, the higher EVM gets. In otherwords, the value of EVM in SGP-ACE method is un-controllable which greatly affects the implementationof power-efficient transmitters. Therefore it is neces-sary to control the balance between PAPR reductionand EVM which predefined by communication stan-dards.

In [8], a PAPR reduction method formulated intoan optimization problem to reduce EVM subject to de-terministic PAPR and interior-point method (IPM) isproposed. Our paper presents a novel EVM reductionmethod from geometric angle analysis which keepsBER performance. After PAPR reduction by SGP-ACE method which will simultaneously decreases thebit-error-rate (BER) slightly [5], a threshold vectorcircle is designed in frequency domain to adjust theamplitude and phase of the OFDM signal constella-tion points to near the ideal points. Detailed introduc-tion of the threshold vector circle method will be p-resented in part 3. Simulation results from MATLABsoftware show that PAPR of a QPSK modulated OFD-M signal is reduced from 10.56dB to 7.496dB with anEVM reduction of 2.34%.

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QINGQING WU, JINGQI WANG,WEN WUQINGQING WU, JINGQI WANG, WEN WU

2 DefinitionEFINITIONThis section defines the metric to quantify OFDM sys-tem performance—–Constellation Error Vector Mag-nitude.

Let c0 ∈ Cn be an ideal constellation and letc ∈ Cn be the constellation that is actually transmit-ted. Many OFDM standards transmit data on a subsetof available carriers ci , i = i1, ...id (where d < n)because of tone reservation or filtering limitations inthe receiver. The average EVM of c is defined as [2]:

EVM =

√1d

∑idi=i1

||ci − coi||2

P0(1)

Where d is the number of data carriers and P0 isthe average power of the carrier modulation scheme(QPSK, 16QAM, etc.).EVM can be reduced by min-imizing the difference between a collection of actu-ally transmitted symbols and ideal symbols from theformula (1) since P0 is a fixed value. The proposedthreshold vector circle method in this paper is derivedfrom this idea which aims at minimizing the molecu-lar value.

Mathematically, the goal of EVM reduction is [7]:

min||S(c− c0)|| (2)

Where S ∈ Rn×n is a diagonal carrier selection ma-trix defined to simplify notation as follows:

Sii =

{1, if carrier i contains data0, otherwise

(3)

Let the constellation c be c = c0 + ∆ , and ∆ ∈ Cn

stands for the difference between a collection of trans-mitted symbols and ideal symbols which aim to be re-duced under the tolerance of EVM by communicationstandards.

3 Customized USTOMIZED THRESHOLDVECTOR CIRCLE METHOD

Differ from the EVM reduction method in [8], thethreshold vector circle method is a novel constellationpoints adjustment method which is easily explainedwith geometric graph directly in the case of OFD-M with QPSK modulation. For an individual chan-nel, there are four possible constellation points, whichlie in each quadrant in the complex plane. Fig.1 andFig.2 show the principle of the threshold vector circlemethod.

The two components in the rectangular coordi-nate system represent the in-phase and quadrature (Iand Q) components. Every point in the figures stands

Figure 1: Principle of the Threshold Vector CircleMethod by adjusting amplitude only

Figure 2: Principle of the Threshold Vector CircleMethod by adjusting phase only

for a complex signal in frequency domain after PAPRreduction by SGP-ACE method. As show in Fig.1, athreshold vector circle is first drawn with its radius ofR at point O’. The R is the predefined threshold whichbased on c − c0 in formula (2) and O’ stands for theideal constellation point (1 + i). The points in thecircle were kept unchanged because of the distortionrestriction and others were adjusted according to thefollowing three cases.

Case1: In this situation, only amplitude was ad-justed in Fig.1. From the rectangular coordinate sys-tem original point O, we can draw two tangent lines(L1,L2) in each side to the circle O’ with the tangentpoint G1 and G2. From the points between two tan-gent lines like A, draw a line which goes through thepoint O. Meanwhile, two intersection points of theline with the circle O’ can be obtained, i.e., B, C in

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3 Customized Threshold Vector Circle Method

Fig.1, which are the new possible locations that pointA can be moved to. To keep the amplitude changeas small as possible, the closest point B is normallychosen to be the new location of the point A.

Case2: Since the sampling points are random-ly distributed on the constellation plane, some pointscan also be seen outside the two tangent lines such asshadows S1 and S2 in Fig.2, which also need to beconsidered. In this situation, we draw two circles (R1,R2) at the point O which contact with the circle O’.For the points in the shadow S2 such as point E, drawa circle at the point O which goes through point E andtwo intersection points with the circle O’ can be ob-tained, i.e., F, G. The closest point F is chosen to bethe new location of the point E.

Case3: The rest constellation points in the firstquadrant can be divided two situations. For the pointsin the shadows S3 and S4, we move them to point G2,because the change of phase and amplitude can getsmall as well as the amount of the rest points are less.At the same time, the points in the shadows S5 and S6can be moved to point G1.

The points in the other three quadrants can be ad-justed in the same way. Its worth reminding that se-vere distortion to the signal and great influence on PA-PR reduction can be introduced with large changes inphase and amplitude. As a result, we only adjust am-plitude in case1 and phase in case2.

4 Simulation ResultsIMULATION RESULTSIn this paper, simulation parameters are chosen as fol-lows: 100 QPSK OFDM symbols with 512 carrierseach symbol are taken as the input signal. L = 4 is ac-cepted as the oversampling rate. Additive white Gaus-sian noise (AWGN) channel model has been used inthe simulation. We select the radius R=0.6 for thresh-old vector circle.

Fig.3 compares the constellation diagram af-ter SGP-ACE algorithm and threshold vector circlemethod. From the comparison diagram, we can drawthat after adjustment the constellation points get muchcloser to the ideal points and a clearly threshold circlewas created.

Fig.4 shows PAPR versus EVM performanceof SGP-ACE algorithm and threshold vector circlemethod. The simulation results show that after 5 timesiteration, the PAPR convergence rate of SGP-ACEalgorithm gets slow with EVM greater than 21.23%which exceed the communication standard with SNRdesigned as 16dB. But after threshold vector circlemethod, the EVM and PAPR performance becomescontrollable by setting the radius of the circle from0.05 to 0.6 and the step size is 0.05. We got a balance

Figure 3: Constellation Diagram after SGP-ACE Al-gorithm and Threshold Vector Circle Method

Figure 4: PAPR Versus EVM Performance of SGP-ACE Algorithm and Threshold Vector Circle Method

between PAPR reduction and EVM performance.Fig.5 shows EVM versus SNR performance of

threshold vector circle method. Since the constella-tion points which stand outside the threshold vectorcircle has been adjusted on the circle which means thevalue of ∆ gets smaller, EVM can be reduced direct-ly based on the formula (1). When SNR is 16 dB,the EVM can be reduced below the communication s-tandard 18.5% of QPSK OFDM signals after AWGNchannel.

Fig.6 shows BER performance of threshold vec-tor circle method. It shows that BER performance gotimproved slightly after EVM reduced, because the pa-per [9] shows the inverse relationship that exists be-tween BER and EVM (with power term in log scale)based on a given equation.

5 ConclusionsONCLUSIONSIn this paper, a novel threshold vector circle approachfor EVM reduction from geometric angle analysis isdeveloped. From the simulation results, substantialEVM reduction is obtained while simultaneously im-proves BER performance slightly. Besides, the EVM

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Figure 5: EVM Versus SNR Performance of SGP-ACE Algorithm and Threshold Vector Circle Methodbefore and after AWGN channel

Figure 6: BER Versus SNR Performance of SGP-ACEAlgorithm and Threshold Vector Circle Method afterAWGN channel

value becomes controllable in comparison with SGP-ACE method. Furthermore, our method can employ acombination of any clipping PAPR reduction methodand has a practical application in communication sys-tem.

Acknowledgements: The research was supported bythe National Natural Science Foundation of China un-der Grant 61301020, the Natural Science Foundationof Jiangsu under Grant BK20130772, the Priority A-cademic Program Development of Jiangsu Higher E-ducation Institutions and the Open Research Programof State Key Laboratory of Millimeter Waves underGrant K201410.

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