Clipping-Based Iterative PAPR-Reduction Techniques for FBMC - BME

Clipping-Based Iterative PAPR-Reduction Techniques for FBMC Zs. Koll´ar, L. Varga and K. Czimer Department of Broadband Infocommunications and Electromagnetic Theory Budapest University of Technology and Economics, Budapest, Hungary {kollar,varga}@mht.bme.hu

Abstract— Orthogonal Frequency Division Multiplexing (OFDM) is the most favored modulation technique in multicarrier wireless communications. Recently, the Filter Bank Multicarrier (FBMC) modulation scheme has drawn attention due its low Adjacent Channel Leakage Ratio (ACLR), which makes it especially suitable for Cognitive Radio (CR) applications. In multicarrier schemes the large dynamic range of the signal is a common problem, both FBMC and OFDM signals have high Peak-to-Average Power Ratio (PAPR). If nonlinear distortions are present, this large PAPR can lead to spectral regrowth causing harmful interference in the neighboring frequency bands. In this paper clippingbased PAPR-reduction schemes aided to reduce the PAPR of FBMC signal are presented. A comparison is given for both transmitter and receiver oriented methods. Index Terms— FBMC, PAPR-reduction, Clipping, Iterative.

I. I NTRODUCTION OFDM is a simple method for wide-band high-speed data transmission over multi-path channels. Modulation and demodulation can be performed by the IFFT and FFT operations respectively, with a cyclic prefix maintaining orthogonality over channels showing linearly distorting characteristics. Due to the digital switchover many frequency bands become available for CR [1] usage. The requirements posed in these opportunistic applications are rather strict [2], especially considering the Power Spectral Density (PSD). With OFDM modulation the required ACLR is only achievable with additional filtering which may cause degraded performance. The need for multicarrier modulation with extremely low ACLR triggered an intensive research of the FBMC scheme [3]. Due to the nature of OFDM being a sum of independent subcarrier signals, the amplitude-distribution of the composite signal is Gaussian. This amplitude distribution leads to a large PAPR of the OFDM signal. As the linearity of the signal must be guaranteed to meet the orthogonality conditions, the transmit signal must be amplified with an amplifier having a large linear dynamic range. These amplifiers are expensive to implement and operate, therefore it is preferred to reduce the PAPR of the transmit signal. Numerous techniques have been proposed for OFDM [4], [5] such as: amplitude clipping, coding, interleaving, Partial Transmit Sequence (PTS), Selected

Mapping (SM), Tone Injection (TI), Tone Reservation (TR) and Active Constellation Extension (ACE). FBMC signals suffer also from large PAPR. As it was shown in [6], this technique is also rather sensitive of nonlinearities, with a significant increase of ACLR in case of a nonlinear signal amplifier. This makes PAPR-reduction an increasingly important topic for FBMC modulation. Some solutions can be already found in the literature for FBMC such as clipping [7] and overlapped SLM technique [8], [9], but most of them (coding, interleaving, PTS, SM and TI) are not directly applicable to FBMC due to the fact that the time domain symbols overlap (unlike in OFDM, where each symbol can be treated separately) which implies a search involving highly complex calculations. The remaining three possibilities (clipping, TR and ACE) are investigated for FBMC scheme in this paper. All three possibilities combine time domain clipping with additional signal processing either on the transmitter or on the receiver side. Note that TR and ACE are also part of the DVB-T2 standard [10]. The organization of the paper is as follows. Section II introduces and briefly described the FBMC modulation and the applied transmitter model. The statistic properties of the transmitted signal are evaluated and the negative effects of nonlinearities on the PSD are shown. In Section III the basic model of baseband clipping is introduced. Section IV introduces two clipping aided, iterative, transmitter-oriented PAPR-reduction methods – TR and ACE – and their joint use in FBMC systems. Section V deals with the description and the properties of the receiver-oriented PAPR-reduction technique. In the next section the simulation results of the proposed PAPRreduction methods for FBMC are presented and discussed. Section VII summarizes the results and concludes the paper with an overall evaluation of the discussed PAPRreduction schemes. II. FBMC

MODULATION

The FBMC modulation scheme is a wide family of multicarrier schemes. The modulation of the subchannels is performed via IFFT – similar as to in OFDM systems – then each subchannel is filtered by a specially designed prototype filter. There is a wide range of filters presented in the literature, which can be adapted for FBMC [11]. The

key effect of this filter is that it has a positive influence on the spectral characteristics of the transmitted signal. In this section, first the transmitter block diagrams for FBMC are described than the statistical and spectral metric of the modulation signal is investigated.

Fig. 1.

Block diagram of the FBMC transmitter.

A. System model

where

θk = √

(

1, j,

if k is even , if k is odd

(2)

j = −1 and N represents the number of available subcarriers. The overlapping ratio of consecutive symbols is strongly related to the length of the prototype filter. For simplicity the filter is designed with an impulse response of length K ∗ N , meaning that the symbol duration is stretched and K symbols are overlapping in the time domain to prevent data rate loss. The block diagram of an FBMC transmitter can be seen in Fig. 1. The bitstream b is encoded to the coded bitstream c, then the bits are mapped to complex symbols X according to the modulation alphabet A. Finally Equation (1) is implemented computationally efficiently using an IFFT and a polyphase decomposition of the modulated prototype filters for the real and imaginary parts. Then the two output signals are time staggered and added. B. Signal metrics To properly design the analog circuits of the transceiver chain a deep understanding of the statistic properties of the transmitted signal must be gathered. Such investigations are especially important in case of the design of power amplifiers which have to work in an efficient manner and

0

10

−1

10

CCDF

In FBMC modulation, prototype filters having an impulse response of p0 are are applied on the subcarriers. These filters fulfill the Nyquist criterion. Due to the advantageous properties of the prototype filter, an FBMC signal will have better spectral efficiency than an OFDM signal. In the transmitter, first the binary information is encoded using a convolutional encoder and then interleaved. The bits are then mapped using the complex modulation alphabet A, where each symbol X represents M bits. With the use of offset-QAM modulation, the real (ℜ) and imaginary (ℑ) parts of the complex modulation symbol X are transmitted with a time offset of half a symbol duration. Finally, prior to transmission, the symbols are overlapped such that they can be separated in the receiver. No CP is used in FBMC systems to maintain orthogonality of the subcarriers. The discrete modulated baseband signal s[n] of FBMC can be expressed based on the complex modulation symbol Xm [k] at the k th subcarrier during the mth time slot as: ∞ NP −1 P s[n] = (θk ℜ{Xm [k]}p0 [n − mN ] + m=−∞ k=0  
2π θk+1 ℑ{Xm [k]}p0 n − mN − N2 ejk(n−mN ) N , (1)

N = 128 N = 1024 N = 8192

−2

10

−3

10

6

7

8

9

10

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12

PAPR0 [dB]

Fig. 2. CCDF of the PAPR of the transmitted symbols as a function of the number of subcarriers

as linearly as possible. A detailed investigation of such metrics for OFDM can be found in [12]. This section investigates the PAPR and kurtosis of the transmitted signal and and the negative effect of nonlinear distortion in presence of a nonlinear power amplifier are also shown. 1) PAPR: A simple technique to describe the dynamics of the transmission signal s[n] is to calculate the PAPR which is defined as γ1 =

max{|s[n]|2 } , E{|s[n]|2 }

(3)

where |s[n]| is the amplitude of the transmission signal and E{.} is the expectation value. The PAPR in dB is defined as: PAPR(s[n])dB = 10 log10 (γ1 ).

(4)

The Complimentary Cumulative Density Function (CCDF) of the PAPR as a function of the number of subcarriers can be seen in Fig. 2 for FBMC. It can be seen that with growing number of subcarriers the PAPR also increases similar to OFDM. 2) Kurtosis: In order to statistically describe the probability density function of an FBMC signal, the kurtosis denoted as γ2 of the random variable ξ will be employed in the following discussion. Parameter γ2 of ξ is commonly defined as  E ξ4 γ2 = (5) 2 − 3. [E {ξ 2 }] Note that for the Gaussian distributed signals, γ2 = 0. Fig. 3 shows γ2 of the real and imaginary parts of the FBMC signal employing different number of subcarriers.

domain FBMC signal is limited to a threshold Amax . As a result, the clipped signal sc [n] can be written as ( s[n], if |s[n]| ≤ Amax c , (6) s [n] = jϕ(s[n]) Amax e , if |s[n]| > Amax

0

10

Kurtosis of the imaginary part Kurtosis of the real part −1

Normalized kurtosis − γ

2

10

−2

10

−3

10

−4

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−5

10

0

1000

2000

3000

4000

5000

6000

7000

8000

Number of subcarriers (N)

Fig. 3. Normalized kurtosis of the real and imaginary part of the FBMC signal.

Linear IBO=9 dB IBO=6 dB IBO=3 dB

−10

PSD [dB]

−20 −30 −40 −50

(8)

Note that baseband clipping will be applied throughout the paper, so no out-of-band radiation will appear.

−60 −70 −80 −90 −0.5

sc [n] = αs[n] + d[n],

where α describes the attenuation and d[n] is the clipping noise, also called as Bussgang noise, which is assumed to be uncorrelated with s[n]. The attenuation factor α can be calculated as √ π −γ 2 + γ erfc(γ). (9) α=1−e 2 The power of the clipping noise can be calculated as   2 (10) Pd = 1 − e−γ − α2 Ps .

10 0

where ϕ(s[n]) is the phase of the complex signal s[n]. The limiter is characterized by the clipping ratio (CR) defined as (7) CRdB = 20 log10 (γ), √ with γ = Amax / Ps , where Ps is the average power of the transmitted signal s[n]. The mathematical model for clipping can be derived from the Bussgang Theorem for memoryless nonlinearities with Gaussian inputs. The clipped signal can be expressed as

IV. T RANSMITTER ORIENTED PAPR- REDUCTION 0

0.5

Normalized frequency [Hz]

Fig. 4. PSD function of FBMC in presence of nonlinear amplifiers with different IBOs.

It can be observed that γ2 converges with increasing N (in correspondance with the Central Limit Theorem) to zero rapidly. This means that the FBMC signal is also converging to Gaussian distribution as the number of subcarriers increase. 3) Effects of nonlinearity: Nonlinearities present in the transceiver chain – especially caused by amplifiers – can severely degrade the advantageous properties of FBMC signals’ low ACLR as shown in [2]. For comparison in Fig. 4 a PSD on FBMC signal is shown for N = 1024 subcarriers with amplifiers with different Input BackOff (IBO) values. As it can be seen with an IBO of 9 dB the strict ACLR-requirements for CR can not be fulfilled any more [2]. Based on the amplifier characteristics, the spectral distortion can be predicted with Bessel functions, as shown in [2]. III. BASEBAND CLIPPING Clipping is the simplest way to reduce the PAPR of an FBMC signal [13]. The discrete amplitude of the time

In this section we focus on methods which can be used in the transmitter to reduce the PAPR of the transmitted signal, and the receiver side can be left unaltered without performance degradation. In system identification multisines are often used as measurement signal where a similar PAPR reduction is required. The main difference is that while in measurement the amplitude and phase of the sines are used for evaluation purposes, in wireless communication the amplitude and phase carries the data. In system identification a clipping aided iterative scheme has been developed to reduce the PAPR of multisines, presented in [14]. A similar repeated clipping and filtering for OFDM was developed in [15], which can significantly reduce the PAPR but introduces significant amount of nonlinear distortion. Based on both ideas, incorporating their advantages, a similar algorithm suitable for FBMC is presented in this section. The general block diagram of the transmitter oriented PAPR-reduction scheme is presented in Fig. 5. Extra signal processing blocks are added to the signal path prior to transmission. Following a conventional FBMC modulation of the symbols X, the PAPR of the generated FBMC signal s[n] is measured. If it is below the predefined limit, it can be transmitted. If the amplitude is larger, clipping is applied. After clipping, the signal sc is demodulated. The demodulated symbols X c are then processed using a special selection and processing algorithm. Then the new

Fig. 5. Block diagram of the clipping based transmitter oriented iterative PAPR-reduction scheme for FBMC.

symbols X new are modulated again and the PAPR of the signal snew is measured. This process is repeated until the desired PAPR is reached or no reduction in the PAPR is achieved. After the iteration the signal sout is used to form the analogue transmission signal. A. Tone reservation As in OFDM the TR method can be applied to reduce the PAPR of FBMC signals as well. The idea is to reserve a certain number of subcarriers called Peak Reduction Tones (PRT) for PAPR-reduction, i.e. these are not used for data transmission. The TR technique can be applied in numerous ways, as shown in [16]. In this paper we apply the clipping-based TR, in which the clipping is applied to the time domain signal s to get the clipped signal sc . The clipped signal is demodulated to retrieve complex modulation symbols X c effected by clipping. The data subcarriers are restored to their original state, while the PRTs are left unchanged to form X new . Finally, modulation is applied to X new to get the new time domain signal snew . If this signal does not satisfy the PAPR criterion, s = snew is set and the next iteration is started. Basically the nonlinear noise is kept on the PRTs only, data carriers remain unchanged which leads to a peak regrowth when snew is formed. The disadvantage of this technique is that the data rate is reduced, in correspondence with the number of the number of applied PRTs. B. Active constellation extension ACE was proposed by Krongold and Jones [17] for PAPR-reduction. The idea behind the ACE technique is that the outer constellation points of the constellation alphabet A can be dynamically extended outwards of the original constellation, such that the PAPR of the data block is reduced [5].

Fig. 7.

Extension regions of ACE for 16-QAM modulation.

Clipping-based ACE method starts with the time domain signal s. Following clipping, the signal sc is demodulated to get X c . After the demodulation the constraints are applied to the constellation, so that the constellation points are allowed to penetrate areas only which do not result in BER degradation. Other demodulated symbols are set to their original value. For QPSK constellation the shaded area on Fig. 6 shows the region of the allowed extension. The figure also shows the restrictions to be made on constellation points regarding the maximal transmit power (Pmax ). With these restrictions applied to the set X c , X new is obtained. Following a modulation, the new time domain signal snew is formed. If the desired PAPR criteria is not met, s = snew is set and the next iteration is started again. For higher order modulations the initial conditions and extension criteria are more complex. Figure 7 shows the extension regions for 16-QAM modulation. The figure shows that only the outer constellation points can be extended without a degradation of the system performance. Also while the corner points can be extended to a larger territory, the non-corner points can only be extended along a line. So the distorted modulation values X c which fall outside the constellation and originate from an outer point – but not from a corner point – must be rotated to fall on the given line. The advantage of ACE is that it does not require the transmission of additional information, nor does it decrease the data rate so the receiver can remain unchanged. As disadvantage, this method requires increased power for transmission of a data since the extended constellation points represent a carrier with higher amplitude than the original one. Another disadvantage of ACE is that no soft decision based detection can be applied due to distorted constellation points. C. Joint use of TR and ACE

Fig. 6.

Extension regions of ACE for QPSK modulation.

TR and ACE can be used simultaneously, since the two methods are independent of each other. TR acts on the PRTs and leave the data carrying subcarriers unchanged, while ACE modifies only the data carrying subcarriers leaving the PRTs unchanged. A certain number of carriers are reserved as in the TR method. This method leads to a PAPR-reduction with fast convergence but with the

Fig. 8. Modified FBMC transmitter with clipping and filtering of the unused subcarriers.

(LLR) for channel observation Yˆ [k] is calculated as   P p Yˆ [k]|au = al al ∈A1u,v  , L(bu,v |Yˆ [k]) = ln P (12) p Yˆ [k]|au = al al ∈A0u,v

disadvantages of TR and ACE appearing at the same time: it leads to data rate loss and it requires extra transmission power. V. R ECEIVER ORIENTED PAPR- REDUCTION Another approach is to move the majority of the signal processing to the receiver side. The transmission signal is clipped and transmitted. In real-life systems not all subcarriers are used for data transmission. Usually the DC subcarrier and some carriers on the edge of the transmission band are not used due to technical difficulties and guard band purposes in the spectrum. Clipping introduces nonlinear distortions in the entire baseband, so the originally unused subcarriers will contain additional components introduced by clipping. This also negatively affects the spectral behavior of the transmission signal i.e. leakage will appear. These additional components have to be suppressed. Digital filtering is not sufficient to suppress the clipping components on the unused subcarriers and analog filtering introduces modulation errors. Instead of filtering, the clipped transmit signal is demodulated again. The modulation values for each symbol of the used subcarriers are selected and the unused subcarriers are set to zero and then the modulation procedure is repeated. The described modification of FBMC transmitter can be seen in Fig. 8. The distortion term in Eq. (8) negatively affects the demodulation procedure on the receiver side. An iterative decoding scheme using the Turbo Principle to mitigate the distortion term was developed for OFDM [18] which was then applied for FBMC [19]. The disadvantage of the scheme is that it requires extensive calculations due to the iterative soft demapping and decoding procedure. The convergence of this scheme can be simply shown and analyzed with the aid of EXIT charts [20]. The basic block diagram of the Bussgang Noise Cancelation (BNC) iterative detector for clipped FBMC signals is shown in Fig. 9. Brief description of the steps of the proposed scheme is provided in the following section. Detailed analysis and analytical formulas are for the sake of clarity and due to the limited space omitted, but can be found in [19]. The received symbols after FBMC demodulation can be expressed using (8) as Y [k] = αX[k] + D[k] + W [k], 0 ≤ k < N,

(11)

where X[k], D[k], and W [k] are the FBMC demodulated signals x[n], d[n], and w[n], respectively. Two main blocks are presented in Fig. 9: the BNC detector and the channel decoder. The BNC detector consists of a forward and feedback signal processing path. A) Forward-path: The extrinsic Log-Likelihood Ratio

where A1u,v and A0u,v , are the subsets of Au (1 < u ≤ M ). The vth bit in au can be either 1 or 0. The conditional probability density function p(Yˆ = al ) is given by ! ˆ [k] − αa)2 ( Y p(Yˆ [k]|a) = exp , (13) N0 + Pdi where Pdi is the power of the remaining clipping noise after the ith iteration. Taking into account the large number of samples and applying the central limit theorem, the clipping noise d[n] can be modeled as a Gaussian distributed random variable, which is independent of the channel noise w[n]. For the 0th iteration, with no feedback, Pd0 is calculated according to (10). As the receiver does not know d[n], the power of the remaining clipping noise is to be estimated as ˆ 2 }. Pdi = Pd0 − E{|d[n]|

(14)

B) Feedback-path: After interleaving the extrinsic LLRs provided by the channel decoder, the soft symbols are computed as ˜n = X

M 2X −1

l=0

al

M −1 Y

P (bl,u ),

u=0

al ∈ A,

(15)

i.e. each symbol is weighted by the probability of the mapped bits, then they are summed. Using these soft symbols a time domain estimation of the FBMC signal is performed. Then clipping is applied with a limit of Amax , and the signal is transformed back to frequency domain. The attenuation factor αi must be set in accordance with the output power of the soft mapper. The clipping √ ratio for the ith iteration can be calculated as γ i = Amax / Ps˜. The new attenuation factor can be calculated according to (9) as √ i 2 π i αi = 1 − e−(γ ) + γ erfc(γ i ). (16) 2 From iteration to iteration, the attenuation factor in the feedback loop will drop from 1 to α as the estimate becomes more and more accurate. Subtracting the attenuated signal from the clipped signal, the estimated clipping noise can be expressed as ˜ = s˜c [n] − αi s˜[n]. d[n]

(17)

ˆ yˆ[n] = αx[n] + (d[n] − d[n]) + w[n],

(18)

The estimated noise dˆ is then subtracted from the received signal to suppress the clipping noise

The modified signal can be then demodulated again. The 0th iteration is considered as the case when no feedback loop is used, i.e yˆ[n] = y[n]. As the attenuation factor αi is monotonously decreasing, the iteration process can stop

Fig. 9.

Block diagram of the BNC receiver suitable for clipped FBMC signal.

0

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FBMC − no compensation FBMC − 1. iteration FBMC − 3. iteration FBMC − no clipping

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BER

CCDF

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No PAPR−reduction Clipping and filtering TR − 1 iteration TR − 3 iteration ACE − 1 iteration ACE − 3 iteration TR & ACE − 1 iteration TR & ACE − 3 iteration

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Fig. 10. BER of the BNC receiver for FBMC signaling over AWGN channel.

when the change in αi is smaller than a given threshold between consecutive iterations. The BJCR channel soft decision decoder computes the extrinsic information of the deinterleaved LLRs provided by the BNC detector. These extrinsic LLRs will be used to suppress the clipping noise in the feedback path of the BNC detector. Bit Error Rate (BER) performance over additive white Gaussian channel with a clipping ratio of 1 dB can be seen in Fig. 10. 16-QAM modulation was used for 768 subcarriers of the available 1024. The bits were encoded using a 1 2 rate convolutional encoder. With iterative compensation the system performance can be improved, above a certain noise level the BER results approach the performance of the case without clipping.

Fig. 11. Comparison of the various PAPR-reduction techniques using a clipping ratio of 3 dB.

of iterations. In Fig. 12 the same parameters are used, with the only difference of the target PAPR for clipping being 1 dB in this case. It can be observed that for both cases the clipping with additional filtering provides the best performance. The price is the high computation complexity of the applied BNC receiver. The TR technique achieves the smallest PAPR gain, the performance is not strongly dependent on the chosen clipping level. ACE outperforms TR in both cases, with a performance affected by the chosen clipping ratio. The joint use of TR & ACE outperforms the cases where only ACE or TR is used. The performance of clipping with filtering can reach up to 1.5 dB by the joint use of TR and ACE after the third iteration. VII. C ONCLUSIONS

VI. S IMULATION RESULTS FOR THE PAPR- REDUCTION TECHNIQUES In this section simulation result are parented for the previously described PAPR-reduction methods in case of FBMC signals. During the simulations N=1024 carriers were implemented, from which 768 were used with 16QAM modulation. In case of TR, 10% of the subcarriers were used as PRTs. In Fig. 11 the results of ACE, TR, ACE & TR and simple clipping with filtering are presented with a target PAPR of 3 dB over the number

In this paper we have presented clipping-based PAPRreduction schemes suitable for FBMC. We have shown that the FBMC signal also has a large PAPR. We have presented transmitter and receiver oriented iterative schemes which can be applied to FBMC without considerable performance degradation. The PAPR-reduction schemes were compared through simulations. A summary and comparison of the advantages and disadvantages of the presented schemes are given in Table I by means of transmitter (Tx) and receiver (Rx) complexity,

TABLE I C OMPARISON OF THE PRESENTED CLIPPING - BASED PAPR- REDUCTION METHODS FOR FBMC.

PAPR-reduction Technique

Complexity

Data Rate Loss

Constellation Distortion

Power Increase

ACE

Tx: high

No

Yes

Yes

TR

Tx: moderate

Yes

No

Yes

ACE & TR

Tx: high

Yes

Yes

Yes

Clipping with filtering & BNC

Tx: low/ Rx: high

No

Yes

No

0

10

CCDF

−1

10

No PAPR−reduction Clipping and filtering TR − 1 iteration TR − 3 iteration ACE − 1 iteration ACE − 3 iteration TR & ACE − 1 iteration TR & ACE − 3 iteration

−2

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2

3

4

5

6

7

8

9

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11

PAPR [dB] 0

Fig. 12. Comparison of the various PAPR-reduction techniques using a clipping ratio of 1 dB.

data rate loss, constellation distortion and power increase. Depending on the specific application requirements, the most suitable PAPR-reduction technique can be chosen. As a future work the tradeoff between the power increase and the PAPR-reduction must be investigated. A possible dynamic setting of the clipping level should also be analyzed. ACKNOWLEDGMENT The research leading to these results was derived from the European Communitys Seventh Framework Programme (FP7) under Grant Agreement number 248454 (QoSMOS). R EFERENCES [1] S. Haykin, “Cognitive radio: Brain empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp. 201–220, 2005. [2] V. Berg, Zs. Koll´ar, R. Datta, P. Horv´ath, D. Noguet, and G. Fettweis, “Low ACLR communication systems for TVWS operation.,” in Future Network & Mobile Summit 2012. Berlin, Germany, June 2012. [3] B. Farhang-Boroujeny, “OFDM versus filter bank multicarrier,” IEEE Signal Processing Magazine, vol. 28, no. 3, pp. 92–112, 2011. [4] S. H. Han and J.-H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Communication, pp. 56–65, Apr. 2005. [5] V. Vijayarangan and R. Sukanesh, “An overview of techniques for reducing peak to average power ratio and its selection criteria for orthogonal frequency division multiplexing radio systems,” Journal of Theoretical and Applied Information Technology, vol. 5, no. 1, pp. 25–36, 2005.

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