Reduction of PAPR for FBMC-OQAM Systems using ... - IEEE Xplore

Reduction of PAPR for FBMC-OQAM Systems using Dispersive SLM Technique S. S. Krishna Chaitanya BULUSU† , Hmaied SHAIEK† , Daniel ROVIRAS† , Rafik ZAYANI†? † CEDRIC/LAETITIA, CNAM, Paris, France. ? Innov’Com, Sup’Com, Carthage University, Tunis, Tunisia. {krishna-chaitanya.bulusu, hmaied.shaiek, daniel.roviras, rafik.zayani}@cnam.fr Abstract—The Filter Bank Multi-Carrier (FBMC) based systems are being seriously considered for 5G Radio Access Technology (RAT). As FBMC-OQAM is a multi-carrier technique, it suffers from the high Peak-to-Average Power Ratio (PAPR) and directly applying the PAPR reduction schemes proposed for OFDM to FBMC-OQAM turns out to be ineffective, due to its overlapping structure. In this paper, a scheme named as Dispersive Selective Mapping (DSLM) is proposed, which is an extended and generalized version of Overlapped Selective Mapping (OSLM). Simulation results show that performance of this method is very closely trailing to that of OFDM. Keywords—FBMC-OQAM, PAPR, SLM, 5G.

I.

I NTRODUCTION

Increasingly, the Filter Bank Multi-Carrier (FBMC) based systems combined with Offset Quadrature Amplitude Modulation (OQAM) are gaining appeal to be the front runner to become the radio waveform in forthcoming 5G Radio Access Technology (RAT) [1]. This advanced modulation scheme offers numerous advantages such as excellent frequency localization, very low side lobes in its Power Spectral Density (PSD), robustness to phase noise and frequency offsets making it more suitable than OFDM for 5G RAT [2]. However, FBMC-OQAM system suffers from high PAPR by being a multi-carrier technique and it’s frequency localization property takes off beat in real communication systems consisting of non-linear High Power Amplifiers (HPAs) leading to spectral regrowth thereby abrogating much of it’s attractive appeal to be the ideal candidate for 5G RAT [3]. This crucial reason coerces us to probe for good PAPR reduction and HPA linearization techniques. Generally PAPR reduction techniques can be broadly classified into three varieties namely clip effect transformations (clipping), block coding techniques and probabilistic approaches (PTS, SLM). Probabilistic solutions such as partial transmit sequence (PTS) and Selective Mapping (SLM) schemes, instead of aiming at reducing the maximum signal amplitude; target on the occurrence of peak values which leads to reduction in the clipping noise. They gain upper hand in terms of relatively low complexity and don’t affect the Bit Error Rate (BER) when there is perfect Side Information (SI) recovery, making them more captivating. FBMC-OQAM by virtue of having an overlapping signal structure cannot afford to have the conventional PAPR reduction schemes that have been effectively applied for OFDM systems. A method named Overlapped SLM (OSLM) was c 2014 IEEE 978-1-4799-5863-4/14/$31.00

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introduced in [5] which takes into account the overlapping naturally emanating from the FBMC-OQAM symbols. Taking a leap ahead, a PTS scheme with Multi-block Joint optimization (MBJO) was introduced in [6], which has shown that FBMC outperforms OFDM when the overlapping nature of FBMCOQAM signals are exploited properly. A sub-optimal version of MBJO-PTS scheme with low complexity was also put forth in the same paper. In this paper, we have introduced a scheme named as Dispersive SLM, which is an extended and generalized version of OSLM as it can be applied for any prototype filter. In a classical SLM scheme, each symbol is rotated with different phase rotation vectors that are i.i.d and the optimally rotated symbol is chosen among the others based on least PAPR criterion [4]. Even though, it is a symbol-by-symbol optimization, it doesn’t impact the performance owing to the non-overlapping signal structure of OFDM signals. In the proposed algorithm, when calculating the PAPR, we take into account the whole interval upon which the FBMC symbol got spread. It is an extension to the OSLM algorithm, where only the current interval is considered for PAPR calculation of the phase rotated symbol. Rest of the paper is composed as follows: Section II deals with an overview of FBMC-OQAM signal structure and an effort is put to showcase the overlapping nature of the FBMC signals based on their power profile. Next, in Section III, the proposed DSLM scheme is presented. For a better comprehension, we elucidate the classical SLM scheme and ineptitude in it’s direct implementation for FBMC-OQAM system. This is followed by Section IV, which shows the simulation results. Finally, the conclusion is given in Section V, which is followed by the acknowledgment. II.

P RESENTATION OF FBMC-OQAM SYSTEMS

A. Overview of FBMC-OQAM signal structure In a FBMC-OQAM system we use complex symbols that are modulated based on OQAM and then transmitted [7]. The M complex input symbols with N sub-carriers at the transmitter can be written as n n Cm,n = Rm + j.Im , 0 ≤ n ≤ N − 1, 0 ≤ m ≤ M − 1 (1) n n where, Rm and Im are the real and imaginary parts of the mth symbol on the nth sub-carrier, respectively. The input symbols in mth data block can be grouped as a vector as shown below

Cm = (Cm,0 , Cm,1 , ...Cm,N −1 )T , 0 ≤ n ≤ N − 1

(2)

Fig. 1.

Impulse response for PHYDYAS and rectangular filters.

Fig. 2. symbols.

In OQAM, the real and imaginary parts of the symbols are time staggered by T /2, where T is the symbol period. It is done in such a way that, for every two adjacent sub-carriers, the timing offset of T /2 is introduced on the real part of the former symbol, whereas it will be on the imaginary part of the latter one. Then, these symbols are passed through a bank of synthesis filters to get modulated with N sub-carriers where the spacing between every two sub-carriers is 1/T [8]. Then a FBMC-OQAM modulated signal with M symbols can be written as

s(t) =

−1 N −1 2M X X n=0

2π

am0 ,n h(t − m0 T /2)ej T

nt jϕm0 ,n

e

(3)

m0 =0

where am0 ,n is a real symbol mapped from complex Cm,n with m varying from 0 to M − 1, as follows

am0 ,n

 n n (1 − δ).Rm + δ.Im = n n δ.Rm + (1 − δ).Im

0

m is even m0 is odd

(4)

where δ ∈ {0, 1} and is defined as n modulo 2. Also, h(t) is the impulse response of the prototype filter. The mathematical significance of this time-staggering rule appears in [9] that has got a phase term ϕm0 ,n , which is set to be π 0 0 2 (m +n)−πm n without loss of generality. PHYDYAS filter was originally designed by Bellanger [10] and later it was chosen to be the reference prototype filter of the European project PHYDYAS. In this paper, we have chosen to use PHYDYAS filter as the prototype filter. The design of this filter is based on frequency sampling technique. The analytical parameters involved in this filter design are the number of sub-carriers N , the overlapping factor K, the roll-off α and the length of the filter, L = KN with desired values F (k/L) where k = 0, 1, ...L − 1. √ Fo = 1, F1 = 0.97196, F2 = 1/ 2 q F3 = 1 − F12 , Fk = 0, 4 < k < L − 1

(5)

569

Illustration of mean-power overlapping among FBMC-OQAM

The impulse response of the PHYDYAS filter is given as [10]  K−1 P  √1 [1 + 2 (−1)k Fk cos( 2πkt KT )] t ∈ [0, KT ] A h(t) = k=1  0 elsewhere (6)   K−1 P 2 where the normalization constant, A = KT 1 + 2 Fk . k=1

In Fig. 1, we can have a glance of the impulse responses for both OFDM which has a rectangular shape and FBMCOQAM that uses a PHYDYAS filter. We can notice that unlike the OFDM, the impulse response of the PHYDYAS filter has duration that spans over 4T . B. Power profile of FBMC-OQAM signals FBMC-OQAM signal spreads beyond one symbol period. The spreading length depends on the impulse response of the prototype filter (in our case it is 4T ). This is the reason behind the FBMC-OQAM signals of adjacent data blocks getting overlapped each other. For PHYDYAS filter, it’s energy lies mostly in the main lobe thus making symbol-by-symbol optimization incongruous. The mean-power profile of the FBMC-OQAM signal is defined as     Pavg s(t) = E |s(t)|2 (7) where E[.] is the expectation operator. A FBMC-OQAM signal has been simulated and the mean power profile of one symbol is shown in Fig. 2. In that figure, we can observe that most of the energy of the symbol lies in the succeeding two symbols period intervals in sharp contrast with that of an OFDM symbol. We can notice that even though the length of prototype filter is 4T , the time spanning of each FBMC-OQAM symbol lasts until 4.5T because of the OQAM modulation, where an additional spread by T2 is because of the offset of imaginary part. We can have a more elegant understanding about how FBMC-OQAM symbols overlap each other by viewing Fig. 2.

Since the prototype filter has a time period of 4T , a given FBMC-OQAM symbol overlaps over it’s next three symbols while it significantly impacts two symbols which are the immediate preceding and succeeding symbols as evident from the same figure. C. PAPR analysis The PAPR is a random variable that is an appurtenant parameter in measuring the sensitivity of a non-linear HPA when a non-constant envelop input need to be transmitted. Every multi-carrier modulation system have high PAPR, which poses a severe challenge to the RF design of HPAs. In order to obviate distortion, the HPA is made to operate in it’s linear region which means that the signal peaks should be within this region. This can be achieved by reducing the mean power of the input signal and is termed as input back-off (IBO). The IBO of a HPA is defined as the ratio between the 1dB compression point input-referred power and the input signal average power. Back-off dampens the power efficiency of a HPA. With this constraint, a real communication system design needs a HPA that has got longer linear region. Higher IBO results on energy wastage [11]. In order to fend off this, we ought to opt for PAPR reduction techniques. The PAPR of the continuous-time base-band signal s(t), transmitted during a symbol period T is defined by [12], P AP Rs(t) =

max0≤t≤T |s(t)|2 RT 1 |s(t)|2 .dt T

the optimally rotated symbol is chosen among others based on least PAPR criterion that has been computed over [0, 4T ) instead of [0, T ). The proposed scheme deals with the time dispersive nature of the FBMC-OQAM signals and hence termed as Dispersive SLM. This scheme can hold for any prototype filter such as IOTA (Isotropic Orthogonal Transform Algorithm). The algorithm of DSLM scheme involves the following steps, Step 1 - Initialization: Firstly, we generate U phase rotation vectors of length N as: (u)

θk

= ejψk ∈ CN , u ∈ {1, ..U }, k ∈ {1, ..N }, ψk ∈ [0, 2π) (9)

where, without loss of generality we choose θ (0) = 1. Step 2 - Rotation: Each input symbol vector Cm is (u) then phase rotated with U different input vectors giving Cm : (u) C(u) m = Cm θ

where implies carrier-wise point-to-point multiplication. (u) (u) Likewise the symbols, am0 ,n are chosen from Cm as per (4). Step 3 - Modulation: FBMC-OQAM modulation of the mth input symbol considering the overlap of previous symbols:

(8) s(u) (t) =

0

N −1 2m−1 X X

(u

2π

)

0 j T am0min ,n h(t − m T /2)e

nt jϕm0 ,n

e

n=0 m0 =0

Generally, most of the existing reduction PAPR techniques can be implemented on discrete-time signals only, despite our concern being a continuous-time FBMC-OQAM signal. If we sample the signal with Nyquist rate then we may miss some peaks; so we need to perform over-sampling. Beyond an oversampling factor L = 4, we cannot improve further in approximating the PAPR of the continuous-time signal [13]. The Complementary Cumulative Density Function (CCDF) of PAPR is a useful parameter to analyze the PAPR, which is defined as the probability that the PAPR of the discrete-time signal exceeds beyond a given threshold that is denoted by γ and thereby it can be evaluated as P r{P AP Rs[n] ≥ γ}. III.

(10)

{z

| +

N −1 2m+1 X X n=0

2π

(u)

am0 ,n h(t − m0 T /2)ej T {z

|

e

(11)

}

current symbol

where, • s(u) (t) 6= 0 from t = [0, (2m + 1) T2 + 4T ), (u ) (u ) • am0min are from previous selected symbols Cm min , ,n • m ∈ {0, 1, . . . M − 1}. Step 4 - PAPR Calculation: Then, we compute the PAPR of s(u) (t) on a certain interval To : (u)

P AP R(To ) =

In classical SLM scheme for OFDM, each symbol is rotated with different phase rotation vectors that are i.i.d and the optimally rotated symbol is chosen among others, based on the least PAPR criterion. The input symbol is phase rotated by U vectors of size LN each. These U rotated input symbols carry same information and pose identical constellation like the original input symbols. After the modulation, the PAPR is calculated over an OFDM symbol period and the symbol with the least PAPR is chosen, which is referred as optimally rotated symbol.

nt jϕm0 ,n

m0 =2m

PAPR REDUCTION BASED ON D ISPERSIVE SLM

A. Classical SLM

}

overlapping past symbols

maxt∈To |s(u) (t)|2 R 1 (u) (t)|2 .dt To To |s

(12)

where To is any arbitrary interval that includes [mT, mT +4T ] interval i.e. over 4T instead of 4.5T since almost all of the symbol energy lies within 4T interval, as evident from Fig. 2. (u)

Step 5 - Selection: Among P AP RTo , the index u is chosen for the signal with least PAPR as per the below criterion: umin =

min

0≤u≤U −1

(u)

P AP R(To )

(13)

Step 6 - Updation: We update the current overlapping input symbol vector:

B. Dispersive SLM Similar to the classical SLM scheme, each symbol is rotated with different phase rotation vectors that are i.i.d and

570

min ) C(u = Cm . θ (umin ) m

(14)

The input symbol that has been rotated with θ (umin ) is considered to be optimally rotated w.r.t DSLM scheme. The index umin will be stored in a vector USI in order to be transmitted as Side Information (SI) for perfect recovery of the signal at the receiver. The vector USI which is a null vector initially; will be updated for every mth symbol by row concatenation with the newly obtained umin , as follows   USI = USI umin (15) Then goto Step 2 to repeat the same for next input symbol vector Cm+1 .

Fig. 4. CCDF of PAPR plot for 105 FBMC-OQAM symbols with PAPR calculated over [0, T ), [T, 3T ) and [0, 4T ) with U = 4 to illustrate the impact of variation of To duration on the DSLM scheme.

the PAPR is calculated, we can see how it is affecting the efficiency of the DSLM scheme. ‘FBMC 1st’, ‘FBMC 23rd’ and ‘FBMC 1234th’ in the legend indicate that the duration considered for PAPR calculation of a given FBMC-OQAM symbol are [0, T ), [T, 3T ) and [0, 4T ) respectively. The phase rotation vector size is fixed for U = 4.

Fig. 3.

Block diagram of Dispersive SLM for FBMC-OQAM systems.

We can see the illustration of how the algorithm is implemented for 5th symbol in Fig. 3. When calculating PAPR for that symbol, we consider the overlapping of previous 4 symbols also. In the same figure ‘*’ on the current symbol denotes that it is a rotated symbol. IV.

S IMULATION R ESULTS

The objective of the simulations is to understand the impact of duration To while calculating PAPR and comparison with OFDM when classical SLM scheme is used. Simulations are done for a FBMC-OQAM signal that has been generated from 105 4-QAM symbols with 64 Sub-carriers (SCs). The PHYDYAS filter has been chosen to be the prototype filter was used in the simulation, which spans for 4T [10]. Nevertheless, the scheme holds for any prototype filter. The range of the complex phase rotation vector was chosen such as, θ (u) ∈ {1, −1, j, −j}. In general most of the PAPR reduction schemes are implemented over discrete-time signals. So, we need to sample the continuous-time FBMC-OQAM signal s(t), thereby obtaining it’s discrete-time signal s[n]. In order to well approximate the PAPR, we have over sampled the modulated signal by a factor of 4 and then implemented the Dispersive SLM scheme on the discrete-time signal s[n]. A. Impact of variation of To duration When computing the PAPR, the duration To seems to make a significant impact in the performance of DSLM scheme as depicted in Fig. 4. By varying the duration over which

571

We can infer from this figure that, when only current symbol period is considered (i.e [0, T ) w.r.t the current symbol), then it won’t lead to any improvement. It implies that because of the overlapping nature of FBMC-OQAM symbols, direct implementation of classical SLM i.e. To = [0, T ) is ineffective. Whereas when 2nd and 3rd symbol periods (i.e [T, 3T ) w.r.t the current symbol) and when 1st , 2nd , 3rd and 4th symbol periods (i.e [0, 4T ) w.r.t the current symbol) are taken into account, then the performance of PAPR reduction with DSLM implementation seems to be trailing very closely to that of the OFDM with classical SLM as we can see from Fig. 5. The reason behind this is well understood from the earlier Fig. 2 which shows that for a given FBMC-OQAM symbol much of it’s energy lies in 2nd and 3rd time intervals rather than in it’s own interval. By taking the time dispersion of FBMC-OQAM symbols in to account, To = [0, T ) has been varied and we have found out that intervals [T, 3T ), [T, 4T ) and [0, 4T ) offer notable PAPR reduction when compared to the case of To = [0, T ). B. Impact of size of U Like any SLM scheme, the size of phase rotation vector impacts the performance of the PAPR reduction. For an illustration of impact of the U , we have considered To = [0, 4T ). The different sizes considered are U = {2, 4, 8}. We can see from Fig. 5, that the CCDF of PAPR for FBMCOQAM with DSLM is very closely trailing that of OFDM. It implies that when the overlapping nature of the FBMCOQAM signals is well exploited then it can significantly impact the PAPR reduction. Another observation is that

of the DSLM based scheme remains almost same as shown in Fig. 6. We can observe that in comparison with the original PAPR, the PAPR reduction is around 2.16 dB and 2.37 dB when N is 64 and 128 respectively. V.

Fig. 5. CCDF of PAPR plot for 105 FBMC-OQAM symbols with PAPR calculated over [0, 4T ) with U = {2, 4, 8} to illustrate the impact of size of U on the DSLM scheme in comparison with SLM scheme for OFDM.

C ONCLUSION

This paper proposes a SLM based scheme that is suitable for FBMC-OQAM systems. It is named as ‘Dispersive SLM’ since it takes into account the time dispersive nature of the FBMC-OQAM symbols leading to their mutual overlapping. If PAPR calculation is done in only the current symbol period duration then it won’t yield any improvement irrespective of the probabilistic scheme employed as most of the symbol energy lies in the two successive symbol periods. In terms of PAPR reduction, the DSLM with FBMC-OQAM is very close to the performance of OFDM with classical SLM and difference is in around of 0.05 dB, 0.25 dB and 0.32 dB at 10−3 value of CCDF of PAPR when U = 2, U = 4 and U = 8 respectively. ACKNOWLEDGMENT The work done in this paper is supported by European project EMPhAtiC, ICT 318362. R EFERENCES [1]

[2]

[3]

[4]

Fig. 6. CCDF of PAPR plot for 105 FBMC-OQAM symbols with PAPR calculated over [0, 4T ) with U = 4 and N = {64, 128} to illustrate the impact of FFT size on the DSLM scheme.

as phase rotation vector size U is getting increased; we can see the trail gap between CCDF curves of OFDM and FBMC-OQAM is getting increased. Both OSLM and DSLM schemes are compared. In the implementation of OSLM [5], oversampling was not done and IOTA filter has been used as the prototype filter. So, as a matter of coherence during comparison, we have implemented the DSLM scheme without oversampling and replacing PHYDYAS filter with the IOTA filter. In terms of PAPR reduction, the DSLM with FBMC-OQAM outperforms the OSLM and difference is in around of 0.26 dB, 0.67 dB and 1.46 dB at 10−3 value of CCDF of PAPR when U = 2, U = 4 and U = 8 respectively.

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C. Impact of FFT size When the FFT size is increased, then we observe that the original PAPR increases, while the PAPR reduction capability

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