Blind Algorithm Development for Peak to Average Power

192 Tanzania Journal of Engineering and Technology (Tanz. J. Engrg. Technol.), Vol. 38 (No. 2), Dec. 2019

Vol. 38(2), pp. 192-203, Dec. 2019ISSN 1821-536X (print)ISSN 2619-8789 (electronic)

Tanzania Journal of Engineering and TechnologyCopyright © 2019 College of Engineering andTechnology, University of Dar es Salaam

Full Length Research Paper

Blind Algorithm Development for Peak to Average Power Ratio Reduction inOFDM Systems under Frequency Selective Channels

Godwin M. Gadiel, Kwame S. Ibwe* and M. M. Kissaka

Department of Electronics and Telecom Engineering, University of Dar es Salaam,P. O. Box 33335, University of Dar es Salaam.

*Corresponding author: [email protected]

ABSTRACT

One major drawback of orthogonal frequency division multiplexing (OFDM) system is peak toaverage power ratio (PAPR). This effect causes high power amplifier (HPA) to introduceintermodulation and out of band radiation as the signal goes through, thus degrades theperformance of OFDM systems. This paper proposes blind algorithms which takes advantage ofsignal transformation technique and signal distortion technique. Simulation results show that atcomplementary cumulative distribution function (CCDF) level of 10-3, the proposed algorithmachieved 3.2 dB PAPR improvement compared to discrete Fourier transform with interleavedfrequency division multiple access (DFT-IFDMA) based algorithm. The bit error rate (BER)performance has degraded by 2 dB compared to the original OFDM signal with no distortionunder frequency selective channel (FCS) at BER of 10-4. These presented results, mark thisalgorithm as a better candidate for PAPR reduction algorithm in long term evolution (LTE)network. Under AWGN channels, the proposed algorithm performs better both in low and highsignal power values. Under frequency selective channels, the existing and proposed algorithmconverges after 10 dB of signal to noise power values. The low BER transmissions at low signalpower values signify energy efficiency, ideal for portable wireless devices with limited batterypower.

Keywords: Bit Error Rate, Frequency Selective Channel, High power amplifier, Orthogonalfrequency division multiplexing (OFDM), Peak to average power ratio (PAPR).

INTRODUCTION123

Orthogonal Frequency Division Multiplexing(OFDM) is a transmission scheme which usesmulti-carriers to overcome severeenvironmental challenges which affect wirelesscommunications spectral efficiencyperformance (Singh and Sharma, 2015). Itsmulticarrier nature has managed to attractseveral technologies, both wired and wirelesscommunication systems. These includes,Digital Audio and Video Broadcasting, Digitalsubscriber line using digital multitone,Wireless Local Area Network (WLAN) such as

IEEE 802.11, High Performance Radio LocalArea Network (HIPERLAN) and MultimediaMobile Access Communication (MMAC),wireless broadband service, WiMAX IEEE802.16 and other new generation cellularnetwork such as LTE (Singh and Sharma,2015; Kondamuri and Sundru, 2018; Liu et al.,2018). However, this technology has severaldrawbacks including high sensitivity tofrequency offset, spectral null in the channeland high peak to average power ratio (PAPR)(Yang, 2005). Since several transmissionschemes have adopted OFDM, it is of interestto address the mentioned drawbacks.

Godwin M. Gadiel, Kwame S. Ibwe and M. M. Kissaka

Tanzania Journal of Engineering and Technology (Tanz. J. Engrg. Technol.), Vol. 38 (No. 2), Dec. 2019 193

A transmitted OFDM signal is a superpositionof multiple orthogonal subcarriers which at agiven time can have the same phase thus, addup and generate peaks whose power is largewhen compared to average power of the signal.Signal with large PAPR require poweramplifier with large range of input backoff(IBO) for linear amplification. Linear high-power amplifier (L-HPA) is very expensiveand they are inefficient (Salah et al., 2009). Itis of interest to use non-linear HPA which hassmall range of IBO for wide spread oftechnology. Therefore, it is necessary to reducePAPR by appropriate methods while achievingclose to optimal system performance (Wetz etal., 2006; Litsyn, 2007). PAPR causes non-linear HPA to radiate in-band and out-of-bandradiation when the transmitted signal passesthrough it (Hao et al., 2019). The out-of-band(OOB) effect is of concern to a regulatoryauthority such as Tanzania CommunicationRegulatory Authority (TCRA) for the case ofTanzania since the licence of the broadcast isbreached. Also, at the receiver end, thedetection efficiency is highly sensitive todevices such as analog to digital converters(ADC) which is highly affected by largerPAPR.

There are two methods to mitigate thisproblem, signal processing technique and linearHPA (Chakrapani and Palanisamy, 2012;Myung et al., 2006). The latter is not advisableas it is very sensitive and it has poor efficiencyas stated earlier. It is better to choose signalprocessing techniques. Signal processingtechniques are in three categories. These aretransmitter-based technique, signaltransformation technique and receiver-basedtechnique. Transmitter based technique has twocategories; distortion technique and distortion-less techniques (Welden and Steendam, 2008;Chakrapani and Palanisamy, 2012). In receiver-based technique, there are maximum likelihoodand signal reconstruction (Hei et al., 2017).Signal transformation technique involvestransforming the signal before HPA intransmission, and the inverse is performedbefore demodulation.

In literature, researches have presented a lot ofsignal processing techniques. These includes,clipping (Mounir et al., 2017; Ibwe, 2019),peak windowing, non-linear compandingtechnique (NTC), partial transmit sequence(PTS), selected mapping (SLM), selectivemapping, tone reservation (TR), tone injection(TI), clipping and filtering (CF), discretefourier transform spreading, discrete cosinetransform, peak windowing (Cha et al., 2008;van Welden and Steendam, 2008; Chen et al.,2009; Sharma and Verma, 2011; Vittal, 2012;Chakrapani and Palanisamy, 2012; Wang et al.,2016). But still, a 0 dB PAPR system is farwithin reach. Most of the proposed algorithmsuse side information, which consumessignificant part of the bandwidth to transferdummy information. A 0 dB PAPR signifiesthat, HPA can operate at an optimal point,maximizing the average transmit power andmaximizing HPA efficiency (Chakrapani et al.,2012). This paper proposes a blind algorithm inwhich, by applying signal transformationbefore signal distortion, it will cause lessdistortion to the resulting signal. The PAPRreduction is characterized by considering thecumulative distribution function (CCDF)metric in accordance with the general way ofpresenting results on the subject (Ann and Jose,2016). The proposed algorithm has shownimproved PAPR with less distortion in BERperformance. The error rate performance isassessed in terms of bit mean squared error tonoise power ratio. These results are obtainedusing simulation platform, MATLAB®. To testfor the performance of the resultant transmitsignal AWGN and frequency selective wirelesschannel environments are used. The channelmodels used are from Proakis (2001).

METHODS AND MATERIALS

OFDM Signal

In OFDM a group of binary data is firstmodulated by a modulation scheme chosen for

Blind Algorithm Development for Peak to Average Power Ratio Reduction in OFDM Systems Under FrequencySelective Channels


a specific environment. A fast serial data isconverted to low data rate parallel bits oflength where is the number of samples of agiven data stream. The chunks of parallel bitsare expressed as shown in equation (1) and (2)

(1)whereby each symbol modulating one of sub-carriers , where N is thenumber of subcarriers. N subcarriers are chosento be orthogonal, that is where

and is the original symbol

period. Mapping of data into subcarriers isperformed by a unitary transformation functionIFFT and the resulting time domain signal isgiven in equation (2).

(2)

PAPR Definition

Continuous time PAPR of OFDM signal isdefined as the ratio between the maximuminstantaneous power and its average power. Inpractice, it is more concerned in reducingPAPR of a continuous signal since the cost andpower dissipation of analog componentsalways dominates. But most systems are indiscrete time signal model. Therefore, it isrequired to sample continuous time signalwith an overlapping factor L. The resultingequation is given in equation (3).

(3)

In the literature (Sharif et al., 2002) issufficient enough to accurately estimate thePAPR of a continuous signal from the digitalsignal. The PAPR reduction performance isevaluated by complementary cumulativedistribution function (CCDF), which is definedas the probability that the PAPR of x exceeds agiven clip level i.e

DFT Spreading

DFT spreading is an algorithm that performspre-conditioning/spreading of data at thetransmitter and resulting in diminished value ofPAPR system as the pre-coding is DFT based.The notion of introducing DFT before IDFTcreates an identity matrix which is a propertyof a single carrier and thus reduced PAPR. AnM point DFT spread is performed tosignal by using a block matrix defined byequation (4).

(4)

The resulting vector signal from DFTspreading is given by equation (5).

(5)

The resulting PAPR value highly depends onthe type of subcarrier mapping scheme. Thereare three types of subcarrier mapping. Theseare interleaved frequency division multipleaccess (IFDMA), localized frequency divisionmultiple access (LFDMA), and distributedfrequency division multiple access (DFDMA)(Sohl and Klein, 2007). Figure 1 describe thethree subcarrier mapping schemes.

The three-subcarrier mapping, IFDMA,DFDMA and LFDMA are mathematicallyrepresented by equation (6) through (8)respectively.

(6)

(7)

(8)

The resulting time domain signal after IFFTprocess for IFDMA, DFDMA and LFDMA aregiven by equation 9 through 11, respectively.

(9)



(10)

(11)

Figure 1: IFDMA, DFDMA and LFDMA DFT spreading mapping (Gouda et al.,2013)

It can be realized from equation 9 through 11that, the resulting time domain signal afterIFFT process is the scaled version of theoriginal signal (Gouda et al., 2013).

Peak Windowing

Peak windowing is applied to the output of theIFFT process to further reduce the PAPR to asignificant value. A signal is compared with athreshold, then a window which smoothes thepeaks according to the limit is applied. Thewidth of the window plays a significant role inBER performance, thus checking on the size ofthe window is a significant concern in thesystem. The peak windowing algorithm isdescribed in Table 1 (Chen et al., 2009).

Figure 2 gives a brief description of PeakWindowing algorithm. The smoothing function

can be realized as a FIR filter generatedfrom a convolution of the produced impulseresponse and the selected window function.The function is given by equation (12)(Cha et al., 2008).

(12)

Figure 3 shows the simulation results ofequation (11), when a Kaiser window of length8, together with a clipping threshold ofand shape parameter .

Blind Algorithm Development for Peak to Average Power Ratio Reduction in OFDM Systems Under FrequencySelective Channels


Figure 2: Block Diagram of Peak Windowing (Cha et al., 2008)

Figure 3: Peak windowing signal

Proposed Algorithm

This paper proposes an algorithm thatcombines two techniques, DFT spreading andpeak windowing whose block diagram ispresented in Figure 4. The resulting timedomain signal of a DFT based OFDM is ascaled version of the original signal. Then if adistortion technique is applied to improvePAPR further, the performance degradation is

less compared to if only distortion technique isused to the system. With this assumption inmind, it is expected the proposed algorithmwill have improved performance. The proposedalgorithm is blind, which ensures high spectralefficiency since no side information is requiredat the receiver for decoding purposes. Table 2shows the signal flow model of the proposedalgorithm.



Figure 4: OFDM signal flow diagram with DFT spreading and peak windowing

Table 2: Proposed algorithm

Step 1: The sequence from the modulator is transformed using a DFT matrix followed byzero insertion depending on IFDMA, DFDMA and LFDMA.Step 2: An IFFT is performed and resulting in equations 8,9, or 10 for interleaved, distributedand localized mapping respectively.Step 3: After the addition of a cyclic prefix, the peak windowing algorithm is then applied tothe resulting time domain signal to further minimize high peaks further.Step 4: At the receiver, the cyclic prefix is removed, and the FFT transform is applied to thereceived signal.Step 5: Padded zeros removed, followed by inverse DFT spreading. Then the signal is de-mapped to the bit stream.

RESULTS AND DISCUSSION

In this section, the proposed algorithm issimulated in OFDM system underfrequency selective fading channel. Thechannel is modelled as a FIR filter withsufficient taps to accommodate differentpath delays for the worst-case transmissionscenarios. The system specification isprovided in Table 3. The MATLAB®software is used to simulate the setexperiments and results of the performanceof the proposed algorithm presented in plotforms.

Table 3: System Specification

Parameter(s) Values(s)MappingIFFT PointOversamplingBandwidthCarrier FrequencyCyclic Prefix

QPSK512420 MHz3 GHz25%

First, the performance gain of the twoindependent algorithms which have beenused in the proposed system is established.Figure 5 shows a comparison of CCDFbetween the OFDM and DFT spreadingOFDM system. Original OFDM system

Blind Algorithm Development for Peak to Average Power Ratio Reduction in OFDM Systems UnderFrequency Selective Channels


has a PAPR value of 9.9 dB at CCDF of10-3, while that of DFT spreading has thevalues 7.6 dB, 7.1 dB and 6.5 dB forDFDMA, LFDMA and IFDMA,respectively. The maximum improvementof 3.4 dB form IFDMA and a minimumvalue of 2.3 dB from DFDMA is observed.

Figure 6 shows PAPR reductionperformance of peak windowing algorithmfor different windowing, for the systemspecification in Table 3. A constant value

of window-length, set to 100, was used forHamming, Hanning and Kaiser windows.In the case of the Kaiser window, spectralshaper (β = 3.5) is used. There is animprovement of PAPR at CCDF = 10-3 asfollows; for Hamming window, there is animprovement of 1.2 dB, for Hanningwindow there is an improvement of 1.1dB, and for Kaiser window, there is animprovement of 1.3 dB compared to anoriginal OFDM system.

1 2 3 4 5 6 7 8PAPR [dB]

10-4

10-3

10-2

10-1

100

CC

DF

IFDMALFDMADFDMA

Figure 5: PAPR reduction performance of DFT-spreading algorithms for the systemspecifications in Table 3



Figure 6: PAPR reduction performance of peak windowing algorithm for differentwindowing, for the system specification in Table 3

Figure 7 shows the CCDF performance ofthe proposed algorithm for the systemspecified in Table 1. At CCDF = 10-3,LFDMA-DFT-spreading and peakwindowing have improved PAPR to 6.4dB, DFDMA-DFT-spreading and peakwindowing have improved PAPR to 6 dB,and the best performance is observed byIFDMA-DFT-spreading and peakwindowing which achieved a PAPR of3.35 dB. The proposed algorithms have byfar improve the value of PAPR comparedto DFT-spreading and peak windowingalgorithms. In this simulation, KaiserWindow, with window-length of 100 andspectral shaper of β = 3.5 have been usedsince it has better performance in anextensive range of CCDF compared toother windows as can be seen in Figure 6.

The BER performance of the proposedalgorithm is compared with theconventional algorithms. Figure 8 shows,BER performance for a system describedin Table 1, with different PAPR reduction

algorithms. The proposed algorithm,IFDMA/PW-k, has higher performancecompared to PW algorithm, and lessperformance compared to DFT-OFDMalgorithm. The proposed algorithm hasless performance compared to the latter,due to the distortion effect introduced byPW in the proposed algorithm. Theperformance of proposed IFDMA-PWalgorithm is compared with the work doneby Mounir et al. (2017) under AWGN andfrequency selective channel conditions.Figure 9 shows the better performance ofproposed algorithm for both small andlarger values of signal power. In Figure 10,the performance of proposed algorithmand that proposed in Mounir et al. (2017)both converge after 10 dB of signal tonoise power values. This results from thefact that Mounir et al. (2017) used adeliberate clipping with rectangularwindowing method whose effects aresimilarly countered as the proposedalgorithm at higher signal power values.



Figure 7: PAPR reduction performance of the proposed algorithm for the systemspecified in Table 3

Figure 8: BER performance versus signal to noise ratio for different algorithms



Figure 9: Performance of the proposed algorithm over AWGN channel

Figure 10: Performance of the proposed algorithm over Frequency Selective channel

MSE

0 5 10 15 20 25 30 35 40SNR [dB]

10-6

10-5

10-4

10-3

10-2

10-1

MS

E

Proposed IFDMA/PW

Mounir, 2017



CONCLUSIONS

This paper has presented a blind algorithmwhich employs DFT spreading and peakwindowing for PAPR reduction. Theproposed algorithm achieves low PAPR inlow signal power values compared to DFTspreading as well as peak windowingalgorithm. In particular, at a CCDF of 10-4,the proposed algorithm achieves a PAPRof 3.5 dB, while DFT spreading and PW-kachieves 6.8 dB and 9.3 dB, respectively.Furthermore, the proposed algorithm haslow BER performance compared to thePW algorithm. Specifically, at an SNR of14 dB, the proposed algorithmIFDMA/PW-k achieves a BER of 10-5

while PW achieves BER of 10-4. Low BERsignifies the suitability of the algorithm tobe used in harsh environments likefrequency selective channels withoutdegrading the battery efficiency ofportable wireless devices. The DFTspreading is gaining popularity in LTEsystems as one of the suitable radiotechnologies for uplink transmissions.Therefore, the proposed algorithm will bea useful alternative for energy efficienttransmissions. Furthermore, theperformance of the proposed algorithm,IFDMA-PW outperformed the existingone presented in Mounir et al. (2017)under AWGN channel. In frequencyselective channels, the performance ofboth algorithms converged after 10 dB ofsignal to noise power ratio values. Infuture, optimization of the performance ofthe proposed algorithm for highly time andfrequency changing channels could beresearched. This will shed more lighttowards the characterization of bothdoubly dispersive channels andmulticarrier transmission techniques.

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Blind Algorithm Development for Peak to Average Power