- Email: [email protected]
PAPR reduction for FBMC-OQAM systems using P-PTS scheme
The Journal of China Universities of Posts and Telecommunications December 2015, 22(6): 78–85 www.sciencedirect.com/science/journal/10058885
http://jcupt.xsw.bupt.cn
PAPR reduction for FBMC-OQAM systems using P-PTS scheme Liu Kaiming (
), Hou Jundan, Zhang Peng, Liu Yuan’an
School of Telecommunication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract Filter bank multi-carrier (FBMC) with offset quadrature amplitude modulation (OQAM) has been regarded as one of the candidates for next generation broadband wireless communication systems. Being a multi-carrier technique, FBMC suffers from the inherent drawback of high peak-to-average power ratio (PAPR). And it has been turned out that conventional PAPR reduction schemes for orthogonal frequency division multiplexing (OFDM) systems are ineffective for FBMC-OQAM systems, due to the overlapping structure of FBMC-OQAM signals. In this paper, we propose an efficient PAPR reduction scheme based on a two-step optimization structure, named pretreated partial transmit sequence (P-PTS). The first step uses a multiple overlapping symbols joint optimization scheme that the phase rotation sequences for current symbol is determined and optimized according to previous overlapped symbols. And in the second step, it employs a novel segment PAPR reduction scheme based on PTS technique. Simulation results indicate that the proposed P-PTS scheme can achieve better PAPR reduction performance than conventional methods with lower computational complexity and the complexity can be traded off more flexibly with PAPR reduction performance. Keywords FBMC-OQAM, PAPR, P-PTS
1 Introduction Constantly increasing demand of higher data rates, multimedia services support, and ever more bandwidth are creating unprecedented challenges for future mobile communication systems. There seems to be general consensus on the future fifth-generation (5G) radio access technology (RAT) for much better performance than today’s fourth-generation (4G) systems [1]. Although OFDM has been widely employed in long term evolution (LTE)/4G and other broadband wireless communication systems, it is not taken for granted for next generation communication systems. The drawbacks like limited spectral efficiency, spectral out-of-band radiation and strict frequency synchronization make OFDM less attractive [2]. FBMC has drawn increasing attention as it shows strong potential and is one of the promising candidates to replace OFDM as multicarrier transmission technique, due to the Received date: 07-07-2015 Corresponding author: Liu Kaiming, E-mail: [email protected] DOI: 10.1016/S1005-8885(15)60698-7
high spectral selectivity and robustness against synchronization offsets [3]. In addition, employing OQAM in FBMC systems can achieve higher spectral efficiency due to the extremely concentrated frequency localization and there is no need to insert any guard interval. We can employ several filters with different characters according to practical channel environments [4]. Then, the FBMC-OQAM systems can achieve better performance under the environments with higher frequency dispersion, and inherently provides better side-lobe characteristics. However, one of the common drawbacks of OFDM and FBMC-OQAM is the high PAPR. In OFDM systems, the distribution of PAPR has been derived by theoretical approaches, and there are various kinds of techniques to solve the problem of high PAPR [5], such as clipping and filtering, selective mapping (SLM), partial transmit sequence (PTS), companding transforms, tone reservation (TR) and so on. Because the signal scrambling techniques cause no distortion and create no out-of-band radiation (e.g. SLM, PTS, TR), they are key considerations for PAPR reduction. Besides, some hybrid techniques [6–7] have
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
been put forward for OFDM systems, and actually they add a pretreatment on the basis of original techniques. Because each technique can take full advantage of its own, the combination of several techniques can achieve better performance. Whereas, these techniques cannot be directly applied to FBMC-OQAM systems due to the inherent overlapping signals structure. Recently, different kinds of PAPR reduction techniques for FBMC-OQAM have been proposed. In Ref. [8], an alternative-signal (AS) method is proposed and it uses a sequential optimization procedure, which makes a joint optimization among the overlapped OFDM/OQAM symbols. An improved PTS scheme by employing multi-block joint optimization (MBJO) is proposed in Ref. [9]. Unlike existing schemes of independently optimizing the data blocks, it exploits the overlapping structure of the FBMC-OQAM signal and jointly optimizes multiple data blocks. In Ref. [10], a sliding window tone reservation (SW-TR) technique has been proposed. The SW-TR technique uses the peak reduction tones (PRTs) of several consecutive data blocks to cancel the peaks of the FBMC-OQAM signal inside a window for PAPR reduction. In Ref. [11], the A-law and µ-law companding is just directly employed in FBMC-OQAM system without any modifications, and is a try to employ the companding techniques. A method called as overlapped SLM was proposed in Ref. [12]. Although overlapped SLM improves the original SLM for FBMC-OQAM systems, it still uses step-by-step optimization that optimizes each data block separately, and it does not really take account into the overlapping of signals. In Ref. [13], the authors proposed a scheme named dispersive SLM which is an extended and generalized version of overlapped SLM. This technique regard complex symbols as the optimized objects, and changing to real symbols may be a better choice. However, it just uses one scheme for PAPR reduction and it has no obvious advantages to hybrid method. Ye et al. put forward a novel segmental (S-PTS) scheme to reduce PAPR in Ref. [14]. The key idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are divided and multiplied with different phase rotation factors in each segment. However, due to the inherent complexity of PTS scheme, only using PTS to reduce PAPR causes high computational complexity, and the complexity is hard to be reduced and be flexibly traded off with PAPR reduction performance. Besides, there are no hybrid
79
schemes proposed for FMBC-OQAM systems, though the hybrid schemes have inherent advantages over a single scheme. In this paper, we propose a P-PTS scheme based on a two-step optimization structure, termed as P-PTS for simplicity, to reduce the PAPR in FBMC-OQAM systems. Due to the overlapping structure of FBMC-OQAM signals, we take into account multiple data blocks when reducing the peak power, instead of each data block independently. The first step uses a multiple overlapping symbols joint optimization scheme that the phase rotation sequences for current symbol is determined and optimized according to previous overlapped symbols. And the second step uses a novel segment scheme based on PTS technique which is similar to Ref. [14]. The main idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are partitioned and multiplied with different phase rotation factors in each segment. The remainder of this paper is organized as follows. In Sect. 2, we briefly introduce the FBMC-OQAM system and the definition of PAPR. The proposed scheme is described in Sect. 3, as well as the analysis of computational complexity. Then, the simulation results are presented in Sect. 4, followed by conclusions and future work in Sect. 5.
2 FBMC-OQAM system In a baseband FBMC-OQAM system, we use real symbols that are modulated based on OQAM and then transmit them. As shown in Fig. 1, the data block number is M, the subcarrier number is N and subcarrier spacing is 1/T, where T is the complex symbol interval.
Fig. 1
FBMC-OQAM signal model
The symbol am , n is real-valued at the time-frequency
80
The Journal of China Universities of Posts and Telecommunications
point (m, n) with the symbol interval τ 0 = T 2 . Thus, the baseband FBMC-OQAM signal is written as [15] M −1 N −1
s (t ) =
∑ ∑a
m,n
h(t − mτ 0 )e
j
2 πn t T
e
jφm ,n
(1)
m =0 n = 0
where φm , n is an additional phase term [16] which set to be φm , n = π(m + n) 2 − πmn . h(t) is the impulse response of the prototype filter with FT length ( F ∈ ℤ ), and the square-root raise cosine (SRRC) filter is employed in this paper. By using the filter, inter-symbol interference (ISI) and inter-carrier interference (ICI) can be easily avoided due to the well-localized pulse shape of the filter both in time domain and frequency domain. Since the length of the filter is FT, the spanning of each FBMC-OQAM signal lasts until FT, too. In another word, current signal is overlapped over by adjacent data blocks, and that is the reason why conventional PAPR reduction techniques cannot be directly applied to FBMC-OQAM systems. So, the concept of signals s(t) is different from the original OFDM signals, and the general definition of PAPR for OFDM systems is no longer useful for FBMC-OQAM systems, too. According to the whole length, we firstly divide the FBMC-OQAM signals into (M/2+F) intervals equally with the time duration T. Thus, the definition of PAPR for each interval can be expressed as [16]
max
DPAPR s ( t ) =
kT ≤t ≤( k +1)T
s (t )
2
; k = 0,1,…
E s (t ) where E[⋅] represents the expectation. 2
M + F −1 2
(2)
For the original PTS scheme used in OFDM systems, the signal in each data block is processed independently to reduce the PAPR. When the PTS scheme is directly employed in FBMC-OQAM systems, the peak power of the signal in each data block is decreased. However, FBMC-OQAM signals are overlapped, and in a certain time interval the actual PAPR depends on several consecutive data blocks. For the effect of multiple consecutive data blocks, the actual PAPR in a time interval might not be reduced.
PAPR for FBMC-OQAM systems. Due to the overlapping structure of FBMC-OQAM signals, we take into account multiple overlapped data blocks when reducing the peak power, instead of each data block independently. The first step is similar to conventional SLM scheme in OFDM systems, and the difference lies in the optimization of phase rotation sequence for current symbol is determined and optimized according to previous overlapped FBMC-OQAM symbols. In other words, all the symbols overlapped with the current symbol should be taken into account when selecting optimized phase rotation sequences to reduce PAPR. Besides, because the spanning of each FBMC-OQAM signal lasts until FT, to choose the optimally rotated symbols, the value of PAPR has been computed over [0, FT) instead of [0, T). The second step employs the scheme which is similar to S-PTS in Ref. [14]. The key idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are partitioned and multiplied with different phase rotation factors in each segment. However, due to the inherent complexity of PTS scheme, only using PTS to reduce PAPR causes high computational complexity, and the complexity is hard to be reduced and be flexibly traded off with PAPR reduction performance. The proposed P-PTS scheme uses the two-step optimization structure which is a more effective measure to deal with the problem of overlap. Compared with S-PTS, it can achieve much better PAPR reduction performance with lower computational complexity. Besides, the proposed P-PTS introduces two key parameters, so different parameter combinations can be used and computational complexity and performance can be traded off flexibly. The detail of two-step optimization structure is described in Fig. 2.
3 Proposed P-PTS scheme for PAPR reduction of FBMC-OQAM signals 3.1
Proposed P-PTS scheme
In this section, we propose a P-PTS scheme which is based on a two-step optimization structure to reduce the
2015
(a) The first step
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
81
Generate the FBMC-OQAM signals s ( u ) (t )
Step 3
by the following formula considering the overlap of previous symbols: N −1 m −1 m′T j 2πT n t jφm′,n u u ) s ( ) (t ) = ∑ ∑ am( ′min h t e − + ,n e 2 n = 0 m′ = 0 overlapping past symbols
N −1
∑ a( ) h t − u m,n
n=0
mT j 2πT n t jφm ,n e e 2
(6)
current symbols
( umin )
are from previous selected symbols C m(u ) .
where am′, n
Step 4 Use Eq. (7) to compute the PAPR of s(u)(t) on a certain interval T0.
max s (u ) (t )
DPAPR ( u ) =
2
t∈T0
(7) 2 E s (u ) (t ) where T0 is any arbitrary interval that includes [(mT)/2, (mT)/2+4T] interval. Among DPAPR ( u ) , the index u is chosen for the signal s (t )
s (t )
with least PAPR as per the below criterion. Then store the index and update the current overlapping input signal. umin = min DPAPR ( u ) (8) 0≤u≤U −1
s (t )
C m(umin ) = Pm( umin ) C m ( umin ) m
where P
(9)
represents the best phase rotation sequence
to achieve the least PAPR for C m .
Step 5 It is obvious that the filtered signal on the nth subcarrier can be represented by (b) The second step Fig. 2 Block diagrams of the first and second steps of the proposed P-PTS scheme
The main steps of the proposed P-PTS scheme can be summarized as the following steps: Step 1 Generate U phase rotation sequences {P (u ) ,
u = 1, 2, … , U } of length N, the uth sequence P(u) can be expressed by P (u ) = P0(u ) , P1( u ) , … , PN(u−)1 ; u = 1, 2, … , U
(3)
where Pi (u ) = exp( jϕi(u ) ), i = 0, 1, … , N − 1 , and ϕi( u ) is a random phase with uniform distribution between
[ 0, 2π ) .
Step 2 Multiply the original data blocks by the above sequences. The FBMC-OQAM symbols Cm( u ) can be generated by C m = am,0 , am ,1 , … , am, N −1
(4)
C m(u ) = P (u ) C m = P0( u ) am,0 , P1(u ) am ,1 , … , PN( u−)1am , N −1
(5)
M −1
S n (t ) =
∑e
jφm ,n
) am(u,min n h(t − mτ 0 )
(10)
m=0
) where am(u,min are the updated symbols and can be n
calculated by Eq. (9). The length of S n (t ) is (M/2+F)T, and we divide S n (t ) into several segments with the same duration Ts(Ts =LT, L≥ F 2, L ∈ ℤ ). It is obvious that the number of segments is K = [ ( M 2 + F )T ] Ts . The signal on the nth subcarrier in the kth segment as Skn (t ) = S n (t ) RTs (t − kTs ); k = 0,1,… , K − 1
(11)
1; kTs ≤t≤( k + 1)Ts with R (t − kT ) = . Ts s 0; eles Step 6 Then, N signals in the kth segment Skv (t ) are
partitioned into V random disjoint Skv (t ) = {Skv , n (t ) | n = 0,1,… , N − 1} , satisfying N N n ( v − 1)≤ n≤ v − 1 S (t ); S kv , n (t ) = k V V 0; eles
sub-blocks
(12)
82
The Journal of China Universities of Posts and Telecommunications
Then modulating the signals to subcarriers, and V signals in the kth segment are obtained as N −1
skv (t ) = ∑ Skv , n (t )e
j
2πn t T
; v = 1, 2,… ,V
3.3
And the signal skv (t ) is multiplied with the
phase rotation factor bkv ∈ {1, −1} , since {1, −1} is easily implemented and as good as any other phase sequence in terms of the PAPR reducing capability. Obviously, the number of rotation factor is V. Then, the optimal phase factor combination of skv (t ) with the minimum PAPR is selected as V arg min max ∑ bkv skv (t ) v bk kTs ≤t ≤( k +1)Ts v =1 (14) s.t. bkv ∈ {1, −1} ; k = 1, 2,… , K − 1 The proposed P-PTS scheme introduces two key parameters V and U, so we can change the value of the two to achieve better PAPR reduction performance. Compared with S-PTS scheme, different parameter combinations can flexibly be traded off between computational complexity and PAPR reduction performance. 3.2
it will not affect the complexity. Analysis of computational complexity
(13)
n=0
Step 7
2015
Signal phase recovery
Because of the design, P-PTS scheme only change the phase of the signals. At the receiver, we should add a step to recover the original phases of the signals, and the side information (SI) must be transmitted. The SI is usually phase rotation sequences or phase rotation factors selected by PAPR reduction schemes. But actually, we always transmit the serial number of the selected sequence for simplicity, and the proposed P-PTS should transmit (lbU +V) bit for each data block. Compared with conventional scheme, for example S-PTS, the SI has a small increase. Because the proposed P-PTS is a two-step scheme including a pretreatment at the transmitter, the receiver should use the corresponding SI to recover original phase, and it needs two phase rotation sequences for each data block. To put it simply, we first convert the serial numbers into phase rotation sequences when SI arrives, and then multiply the frequency domain signals which are transformed from time domain with the two phase rotation sequences. The calculations of signal phase recovery only need several complex multiplications and the computational complexity is so small that can be ignored. Besides, the order of two phase rotation sequences can be changed and
The computational complexity is one of the restrictions for the practical implementation of a novel scheme. Because FBMC-OQAM systems can be implemented through fast Fourier transform (FFT)/inrerse fast Fourier transform (IFFT) module, the module exerts a significant effect on the whole complexity level. For the proposed P-PTS scheme, to find the best phase sequence in Eq. (6), NUTs complex multiplications and (N−1)UTs complex additions are required, and Ts is equal to N for simulation. To generate V signals in Eq. (13), NVTs complex multiplications and (N−1)VTs complex additions are required, too. Besides, the number of phase combinations is 2V for each segment, and VTs complex multiplications and (V−1)Ts complex additions are needed for one phase combination. Because the above three parts are different and important in the proposed P-PTS and S-PTS scheme, they are all taken into account. Other calculations are same and small in both schemes (e.g. the calculations in Eqs. (9)–(10)), so they are ignored. In addition, it is well known that one complex multiplication requires four real multiplications and two real additions, and one complex addition requires two real additions. Then, the numbers of required real multiplications and real additions for the P-PTS and S-PTS schemes are listed in Table 1. Table 1 Numbers of required real multiplication and real addition of the P-PTS and S-PTS schemes Scheme
Real multiplications V
Proposed P-PTS
4N(NU+NV+2 V)
S-PTS
4N(NV+2VV)
Real additions 2N(2NU+2NV+2× 2VV−U−V−2V) 2N(2NV+2× 2VV−V−2V)
From the table we can see that, if the parameters are determined, the real multiplications and additions can be calculated. Besides, at the receiver the computational complexity is so smaller that can be ignored compared with the transmitter.
4 Simulation results In this section we have done several simulations using the proposed P-PTS scheme with different conditions to analyze the PAPR reduction performances and bit error rate (BER) performances, compared with S-PTS [14]. And
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
the CCDF curves plot the probability versus the PAPR in dB. In all simulations, the number of sub-carriers is set to be 64 and the modulation scheme of 4-OQAM is adopted. For the simulation of complementary cumulative distribution function (CCDF) of the PAPR, 100 000 FBMC-OQAM blocks are generated randomly. Besides, the rolloff factor of the SRRC filter is set to be 1, and the length of the filter is generally set to 4T.
83
of the proposed P-PTS scheme with that of S-PTS scheme. If the probability is fixed at the value of 0.1%, the PAPR of P-PTS with V=4, U=2 is about 7.9 dB, smaller than 8.3 dB of S-PTS with V=4. Besides, the PAPR of P-PTS with V=4, U=16 is 7.1 dB, also better than S-PTS with V=8. It implies that we can flexibly use two parameters to achieve a better performance. However, S-PTS scheme can only change one parameter V, so its PAPR reductions just affected by V.
4.1 Simulation results of the proposed P-PTS scheme with different values of U From Fig. 3, it is clear that for a given value of V, the value of PAPR decreases as the increasing of U. For example, if V=4 and the probability is fixed at the value of 0.1%, and it is observed that the PAPR value for U=2 case is about 2.6 dB smaller than the original OFDM signal. Under the same condition, the PAPR values for U=4, 16 and 32 are about 7.5 dB, 7.5 dB and 6.7 dB, respectively. Besides, if the U is fixed, the value of PAPR decreases faster as the increasing of V. In another word, increasing V is more effective to decrease the value of PAPR. It implies that different combinations of U and V can achieve different PAPR reduction performances, and in a practical application we can flexibly choose the combinations as required.
Fig. 4
CCDFs of the proposed P-PTS and S-PTS schemes
From the two above simulation results, we can find that PAPR reduction performances of the proposed P-PTS scheme with certain parameters are better than S-PTS scheme. Furthermore, the computation complexity is also one of the restrictions for applying a novel scheme. In order to research the relationship between computational complexity and PAPR reduction performance, we can use the equations in Table 1 to calculate the numbers of the real multiplications and real additions. The calculation results are listed in Table 2. Table 2 The computational complexity comparison in terms of real multiplications and additions Scheme
V
4
Fig. 3 CCDFs of the proposed P-PTS scheme with different values of U and V
4.2 Simulation results of PAPR reduction performance between the proposed P-PTS and S-PTS schemes In Fig. 4, we compare the PAPR reduction performances
Proposed P-PTS
8
S-PTS
4 8 16
U
Real multiplications
Real additions
2 4 16 32 2 4 16 32 — — —
114 688 147 456 344 064 606 208 688 128 720 796 917 504 1 179 648 81 920 655 360 268 697 600
111 872 144 384 339 456 599 552 654 080 686 592 881 664 1 141 760 79 360 621 568 260 306 944
Value of PAPR at CCDF is 10−3 7.9 7.5 7.1 6.7 7.0 6.6 6.2 5.7 8.3 7.3 —
From the above analysis, it is obvious that both the
84
The Journal of China Universities of Posts and Telecommunications
proposed P-PTS and S-PTS schemes can reduce PAPR effectively. In the table, we can find that the complexity is lowest when using S-PTS with V=4, but the PAPR reduction is also the worst. When V = 4 and U = 2, the PAPR value of the proposed P-PTS is about 0.4 dB smaller than S-PTS scheme with a little increase in the computational complexity. The computational complexity has a significantly increase, when S-PTS uses V=8. The PAPR reduction performance of P-PTS with V = 4 and U = 16 is a little worse than S-PTS with V=8, however, the complexity considerably decreases. When U changes to 16 and 32, PAPR reduction performances get further ascent. Although the complexity has increased, it is still smaller than S-PTS with V=8. It implies that we can flexibly trade off between the computational complexity and the PAPR reduction performance.
2015
white Gaussian noise (AWGN) channel. For ideal situation, the three dotted lines denote the BER performance using different schemes without SSPA. Obviously, the BER of the original curve without SSPA is the best, because the signals are not affected by the nonlinear distortion. But actually, the nonlinear distortion is exist. On the other hand, because the introduced pretreatment does not destroy the structure of FBMC-OQAM symbols and causes no distortion, the two curves are almost same.
4.3 Simulation results of BER performance between the proposed P-PTS and S-PTS schemes To evaluate the performances of the BER with the proposed P-PTS in FBMC-OQAM systems, the typical solid-state power amplifier (SSPA) is employed. And the Rapp model is a widely used SSPA model and it commonly used to emulate the nonlinear behavior of SSPAs in mobile and cellular communications [17]. The time-domain samples at the SSPA input is sn = an e jθn , the amplifier output using the SSPA model can be expressed as j θ +φ ( a ) yn = A(an )e [ n n ] (14) where the operators
A(⋅)
and
φ (⋅)
represent the
amplitude modulation (AM)/AM and AM/ phase modulation (PM) conversion characteristics of the nonlinear amplifier, respectively. In general, SSPAs introduce AM/AM distortion, which can be described as −1
a 2 p 2 p A(an ) = an 1 + n (15) A0 where A0 denotes the maximum amplifier output, and the smoothness of the transition from the linear region to the limiting region can be controlled by the parameter p. The AM/PM distortion is very limited for most applications; hence, φ (an ) = 0 . In Fig. 5, the BER performances of the proposed P-PTS and S-PTS schemes are depicted. The channel between the transmitter and the receiver is modeled as an additive
Fig. 5 BERs of the proposed P-PTS and S-PTS schemes over AWGN channel
In practical applications, the BER performances reduced significantly due to the influence caused by nonlinear distortion, and both the proposed P-PTS and S-PTS can improve the BER performances. Besides, the signals operated by the proposed P-PTS scheme achieve better BER performances than the original signals with the SSPA. Specifically, to reach a BER of 10−4, the SNRs are 15.1 dB for S-PTS schemes with V=8, and 14.1 dB, 16.0 dB for the proposed P-PTS scheme with V=4, U=4 and 16, respectively. As the analysis in Sect. 4.2, the PAPR reduction performance for the proposed P-PTS scheme with above parameters is close to S-PTS schemes with V=8, but the computational complexity is much lower. And it is obvious that the order of the three BER performance curves is same as PAPR curves.
5 Conclusions In this paper, a novel P-PTS scheme was proposed to reducing the PAPR in FBMC-OQAM systems. To deal with the problem of overlap more effective, we take fully into account the overlapping structure of FBMC-OQAM symbols and use a two-step optimization structure. The
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
simulation results show that the proposed P-PTS scheme can achieve better PAPR reduction performance than the comparatively new scheme S-PTS with lower computational complexity. In addition, the signals operated by the proposed P-PTS scheme achieve better BER performances than S-PTS with the SSPA, and the computational complexity and performance can be traded off flexibly by using different parameter combinations. Acknowledgements This work was supported by the Beijing Higher Education Young Elite Teacher Project (YETP0440), the National Natural Science Foundation of China (61272518, 61302083)
References 1. Banelli P, Buzzi S, Colavolpe G, et al. Modulation formats and waveforms for 5G networks: who will be the heir of OFDM?: an overview of alternative modulation schemes for improved spectral efficiency. IEEE Signal Processing Magazine, 2014, 31(6): 80−93 2. Farhang-Boroujeny B. OFDM versus filter bank multicarrier. IEEE Signal Processing Magazine, 2011, 28(3): 92−112 3. Sahin A, Guvenc I, Arslan H. A survey on multicarrier communications: prototype filters, lattice structures, and implementation aspects. IEEE Communications Surveys & Tutorials, 2014, 16(3): 1312−1338 4. Sahin A, Guvenc I, Arslan H. A comparative study of FBMC prototype filters in doubly dispersive channels. Proceedings of the 2012 IEEE Globecom Workshops (GC’12 Wkshop’12), Dec 3−7, 2012, Anaheim, CA, USA. Piscataway, NJ, USA: IEEE, 2012: 197−203 5. Rahmatallah Y, Mohan S. Peak-to-average power ratio reduction in OFDM systems: a survey and taxonomy. IEEE Communications Surveys & Tutorials, 2013, 15(4): 1567−1592 6. Gokkul N A, Kumar A A, Kumar S H, et al. Performance improvement of OFDM using hybrid PAPR reduction technique. Proceedings of the 4th International Conference on Computing, Communications and Networking Technologies (ICCCNT’13), Jul 4−6, 2013, Tiruchengode, India.
85
Piscataway, NJ, USA: IEEE, 2013: 4p 7. Abbas M A, Gasser S, Aziz A M, et al. A new approach for PAPR reduction of OFDM signal based on SLM and PTS. Proceedings of the 3rd International Conference on e-Technologies and Networks for Development (ICeND’14), Apr 29−May 1, 2014. Piscataway, NJ, USA: IEEE, 2014: 58−63 8. Zhou Y, Jiang T, Huang C, et al. Peak-to-average power ratio reduction for OFDM/OQAM signals via alternative-signal method. IEEE Transactions on Vehicular Technology, 2014, 63(1): 494−499 9. Qu D M, Lu S X, Jiang T. Multi-block joint optimization for the peak-to-average power ratio reduction of FBMC-OQAM signals. IEEE Transactions on Signal Processing, 2013, 61(7): 1605−1613 10. Lu S X, Qu D M, He Y J. Sliding window tone reservation technique for the peak-to-average power ratio reduction of FBMC-OQAM signals. IEEE Wireless Communications Letters, 2012, 1(4): 268−2714 11. Varghese N, Chunkath J, Sheeba V S. Peak-to-average power ratio reduction in FBMC-OQAM system. Proceedings of the 4th International Conference on Advances in Computing and Communications (ICACC’14), Aug 27−29, 2014, Cochin, India. Piscataway, NJ, USA: IEEE, 2014: 286−290 12. Skrzypczak A, Javaudin J P, Siohan P. Reduction of the peak-to-average power ratio for the OFDM/OQAM modulation. Proceedings of the 63rd Vehicular Technology Conference (VTC-Spring’06): Vol 4, Mar 7−10, 2006, Melbourne, Australia. Piscataway, NJ, USA: IEEE, 2006: 2018−2022 13. Krishna Chaitanya Bulusu S S, Shaiek H, Roviras D, et al. Reduction of PAPR for FBMC-OQAM systems using dispersive SLM technique. Proceedings of the 11th International Conference on Wireless Communications Systems (ISWCS’14), Aug 26−29, 2014, Barcelona, Spain. Piscataway, NJ, USA: IEEE, 2014: 568−572 14. Ye C, Li Z J, Jiang T, et al. PAPR reduction of OQAM-OFDM signals using segmental PTS scheme with low complexity. IEEE Transactions on Broadcasting. 2014, 60(1): 141−147 15. Le Floch B, Alard M, Berrou C. Coded orthogonal frequency division multiplex. Proceedings of the IEEE, 1995, 83(6): 982−996 16. Ochiai H, Imai H. On the distribution of the peak-to-average power ratio in OFDM signals. IEEE Transactions on Communications, 2001, 49(2): 282−289 17. Al-Dalakta E, Al-Dweik A, Hazmi A, et al. Efficient BER reduction technique for nonlinear OFDM transmission using distortion prediction. IEEE Transactions on Vehicular Technology, 2012, 61(5): 2330−2336
(Editor: Wang Xuying)
http://jcupt.xsw.bupt.cn
PAPR reduction for FBMC-OQAM systems using P-PTS scheme Liu Kaiming (
), Hou Jundan, Zhang Peng, Liu Yuan’an
School of Telecommunication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract Filter bank multi-carrier (FBMC) with offset quadrature amplitude modulation (OQAM) has been regarded as one of the candidates for next generation broadband wireless communication systems. Being a multi-carrier technique, FBMC suffers from the inherent drawback of high peak-to-average power ratio (PAPR). And it has been turned out that conventional PAPR reduction schemes for orthogonal frequency division multiplexing (OFDM) systems are ineffective for FBMC-OQAM systems, due to the overlapping structure of FBMC-OQAM signals. In this paper, we propose an efficient PAPR reduction scheme based on a two-step optimization structure, named pretreated partial transmit sequence (P-PTS). The first step uses a multiple overlapping symbols joint optimization scheme that the phase rotation sequences for current symbol is determined and optimized according to previous overlapped symbols. And in the second step, it employs a novel segment PAPR reduction scheme based on PTS technique. Simulation results indicate that the proposed P-PTS scheme can achieve better PAPR reduction performance than conventional methods with lower computational complexity and the complexity can be traded off more flexibly with PAPR reduction performance. Keywords FBMC-OQAM, PAPR, P-PTS
1 Introduction Constantly increasing demand of higher data rates, multimedia services support, and ever more bandwidth are creating unprecedented challenges for future mobile communication systems. There seems to be general consensus on the future fifth-generation (5G) radio access technology (RAT) for much better performance than today’s fourth-generation (4G) systems [1]. Although OFDM has been widely employed in long term evolution (LTE)/4G and other broadband wireless communication systems, it is not taken for granted for next generation communication systems. The drawbacks like limited spectral efficiency, spectral out-of-band radiation and strict frequency synchronization make OFDM less attractive [2]. FBMC has drawn increasing attention as it shows strong potential and is one of the promising candidates to replace OFDM as multicarrier transmission technique, due to the Received date: 07-07-2015 Corresponding author: Liu Kaiming, E-mail: [email protected] DOI: 10.1016/S1005-8885(15)60698-7
high spectral selectivity and robustness against synchronization offsets [3]. In addition, employing OQAM in FBMC systems can achieve higher spectral efficiency due to the extremely concentrated frequency localization and there is no need to insert any guard interval. We can employ several filters with different characters according to practical channel environments [4]. Then, the FBMC-OQAM systems can achieve better performance under the environments with higher frequency dispersion, and inherently provides better side-lobe characteristics. However, one of the common drawbacks of OFDM and FBMC-OQAM is the high PAPR. In OFDM systems, the distribution of PAPR has been derived by theoretical approaches, and there are various kinds of techniques to solve the problem of high PAPR [5], such as clipping and filtering, selective mapping (SLM), partial transmit sequence (PTS), companding transforms, tone reservation (TR) and so on. Because the signal scrambling techniques cause no distortion and create no out-of-band radiation (e.g. SLM, PTS, TR), they are key considerations for PAPR reduction. Besides, some hybrid techniques [6–7] have
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
been put forward for OFDM systems, and actually they add a pretreatment on the basis of original techniques. Because each technique can take full advantage of its own, the combination of several techniques can achieve better performance. Whereas, these techniques cannot be directly applied to FBMC-OQAM systems due to the inherent overlapping signals structure. Recently, different kinds of PAPR reduction techniques for FBMC-OQAM have been proposed. In Ref. [8], an alternative-signal (AS) method is proposed and it uses a sequential optimization procedure, which makes a joint optimization among the overlapped OFDM/OQAM symbols. An improved PTS scheme by employing multi-block joint optimization (MBJO) is proposed in Ref. [9]. Unlike existing schemes of independently optimizing the data blocks, it exploits the overlapping structure of the FBMC-OQAM signal and jointly optimizes multiple data blocks. In Ref. [10], a sliding window tone reservation (SW-TR) technique has been proposed. The SW-TR technique uses the peak reduction tones (PRTs) of several consecutive data blocks to cancel the peaks of the FBMC-OQAM signal inside a window for PAPR reduction. In Ref. [11], the A-law and µ-law companding is just directly employed in FBMC-OQAM system without any modifications, and is a try to employ the companding techniques. A method called as overlapped SLM was proposed in Ref. [12]. Although overlapped SLM improves the original SLM for FBMC-OQAM systems, it still uses step-by-step optimization that optimizes each data block separately, and it does not really take account into the overlapping of signals. In Ref. [13], the authors proposed a scheme named dispersive SLM which is an extended and generalized version of overlapped SLM. This technique regard complex symbols as the optimized objects, and changing to real symbols may be a better choice. However, it just uses one scheme for PAPR reduction and it has no obvious advantages to hybrid method. Ye et al. put forward a novel segmental (S-PTS) scheme to reduce PAPR in Ref. [14]. The key idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are divided and multiplied with different phase rotation factors in each segment. However, due to the inherent complexity of PTS scheme, only using PTS to reduce PAPR causes high computational complexity, and the complexity is hard to be reduced and be flexibly traded off with PAPR reduction performance. Besides, there are no hybrid
79
schemes proposed for FMBC-OQAM systems, though the hybrid schemes have inherent advantages over a single scheme. In this paper, we propose a P-PTS scheme based on a two-step optimization structure, termed as P-PTS for simplicity, to reduce the PAPR in FBMC-OQAM systems. Due to the overlapping structure of FBMC-OQAM signals, we take into account multiple data blocks when reducing the peak power, instead of each data block independently. The first step uses a multiple overlapping symbols joint optimization scheme that the phase rotation sequences for current symbol is determined and optimized according to previous overlapped symbols. And the second step uses a novel segment scheme based on PTS technique which is similar to Ref. [14]. The main idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are partitioned and multiplied with different phase rotation factors in each segment. The remainder of this paper is organized as follows. In Sect. 2, we briefly introduce the FBMC-OQAM system and the definition of PAPR. The proposed scheme is described in Sect. 3, as well as the analysis of computational complexity. Then, the simulation results are presented in Sect. 4, followed by conclusions and future work in Sect. 5.
2 FBMC-OQAM system In a baseband FBMC-OQAM system, we use real symbols that are modulated based on OQAM and then transmit them. As shown in Fig. 1, the data block number is M, the subcarrier number is N and subcarrier spacing is 1/T, where T is the complex symbol interval.
Fig. 1
FBMC-OQAM signal model
The symbol am , n is real-valued at the time-frequency
80
The Journal of China Universities of Posts and Telecommunications
point (m, n) with the symbol interval τ 0 = T 2 . Thus, the baseband FBMC-OQAM signal is written as [15] M −1 N −1
s (t ) =
∑ ∑a
m,n
h(t − mτ 0 )e
j
2 πn t T
e
jφm ,n
(1)
m =0 n = 0
where φm , n is an additional phase term [16] which set to be φm , n = π(m + n) 2 − πmn . h(t) is the impulse response of the prototype filter with FT length ( F ∈ ℤ ), and the square-root raise cosine (SRRC) filter is employed in this paper. By using the filter, inter-symbol interference (ISI) and inter-carrier interference (ICI) can be easily avoided due to the well-localized pulse shape of the filter both in time domain and frequency domain. Since the length of the filter is FT, the spanning of each FBMC-OQAM signal lasts until FT, too. In another word, current signal is overlapped over by adjacent data blocks, and that is the reason why conventional PAPR reduction techniques cannot be directly applied to FBMC-OQAM systems. So, the concept of signals s(t) is different from the original OFDM signals, and the general definition of PAPR for OFDM systems is no longer useful for FBMC-OQAM systems, too. According to the whole length, we firstly divide the FBMC-OQAM signals into (M/2+F) intervals equally with the time duration T. Thus, the definition of PAPR for each interval can be expressed as [16]
max
DPAPR s ( t ) =
kT ≤t ≤( k +1)T
s (t )
2
; k = 0,1,…
E s (t ) where E[⋅] represents the expectation. 2
M + F −1 2
(2)
For the original PTS scheme used in OFDM systems, the signal in each data block is processed independently to reduce the PAPR. When the PTS scheme is directly employed in FBMC-OQAM systems, the peak power of the signal in each data block is decreased. However, FBMC-OQAM signals are overlapped, and in a certain time interval the actual PAPR depends on several consecutive data blocks. For the effect of multiple consecutive data blocks, the actual PAPR in a time interval might not be reduced.
PAPR for FBMC-OQAM systems. Due to the overlapping structure of FBMC-OQAM signals, we take into account multiple overlapped data blocks when reducing the peak power, instead of each data block independently. The first step is similar to conventional SLM scheme in OFDM systems, and the difference lies in the optimization of phase rotation sequence for current symbol is determined and optimized according to previous overlapped FBMC-OQAM symbols. In other words, all the symbols overlapped with the current symbol should be taken into account when selecting optimized phase rotation sequences to reduce PAPR. Besides, because the spanning of each FBMC-OQAM signal lasts until FT, to choose the optimally rotated symbols, the value of PAPR has been computed over [0, FT) instead of [0, T). The second step employs the scheme which is similar to S-PTS in Ref. [14]. The key idea is to divide the overlapped FBMC-OQAM signals into a number of segments, and then some disjoint sub-blocks are partitioned and multiplied with different phase rotation factors in each segment. However, due to the inherent complexity of PTS scheme, only using PTS to reduce PAPR causes high computational complexity, and the complexity is hard to be reduced and be flexibly traded off with PAPR reduction performance. The proposed P-PTS scheme uses the two-step optimization structure which is a more effective measure to deal with the problem of overlap. Compared with S-PTS, it can achieve much better PAPR reduction performance with lower computational complexity. Besides, the proposed P-PTS introduces two key parameters, so different parameter combinations can be used and computational complexity and performance can be traded off flexibly. The detail of two-step optimization structure is described in Fig. 2.
3 Proposed P-PTS scheme for PAPR reduction of FBMC-OQAM signals 3.1
Proposed P-PTS scheme
In this section, we propose a P-PTS scheme which is based on a two-step optimization structure to reduce the
2015
(a) The first step
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
81
Generate the FBMC-OQAM signals s ( u ) (t )
Step 3
by the following formula considering the overlap of previous symbols: N −1 m −1 m′T j 2πT n t jφm′,n u u ) s ( ) (t ) = ∑ ∑ am( ′min h t e − + ,n e 2 n = 0 m′ = 0 overlapping past symbols
N −1
∑ a( ) h t − u m,n
n=0
mT j 2πT n t jφm ,n e e 2
(6)
current symbols
( umin )
are from previous selected symbols C m(u ) .
where am′, n
Step 4 Use Eq. (7) to compute the PAPR of s(u)(t) on a certain interval T0.
max s (u ) (t )
DPAPR ( u ) =
2
t∈T0
(7) 2 E s (u ) (t ) where T0 is any arbitrary interval that includes [(mT)/2, (mT)/2+4T] interval. Among DPAPR ( u ) , the index u is chosen for the signal s (t )
s (t )
with least PAPR as per the below criterion. Then store the index and update the current overlapping input signal. umin = min DPAPR ( u ) (8) 0≤u≤U −1
s (t )
C m(umin ) = Pm( umin ) C m ( umin ) m
where P
(9)
represents the best phase rotation sequence
to achieve the least PAPR for C m .
Step 5 It is obvious that the filtered signal on the nth subcarrier can be represented by (b) The second step Fig. 2 Block diagrams of the first and second steps of the proposed P-PTS scheme
The main steps of the proposed P-PTS scheme can be summarized as the following steps: Step 1 Generate U phase rotation sequences {P (u ) ,
u = 1, 2, … , U } of length N, the uth sequence P(u) can be expressed by P (u ) = P0(u ) , P1( u ) , … , PN(u−)1 ; u = 1, 2, … , U
(3)
where Pi (u ) = exp( jϕi(u ) ), i = 0, 1, … , N − 1 , and ϕi( u ) is a random phase with uniform distribution between
[ 0, 2π ) .
Step 2 Multiply the original data blocks by the above sequences. The FBMC-OQAM symbols Cm( u ) can be generated by C m = am,0 , am ,1 , … , am, N −1
(4)
C m(u ) = P (u ) C m = P0( u ) am,0 , P1(u ) am ,1 , … , PN( u−)1am , N −1
(5)
M −1
S n (t ) =
∑e
jφm ,n
) am(u,min n h(t − mτ 0 )
(10)
m=0
) where am(u,min are the updated symbols and can be n
calculated by Eq. (9). The length of S n (t ) is (M/2+F)T, and we divide S n (t ) into several segments with the same duration Ts(Ts =LT, L≥ F 2, L ∈ ℤ ). It is obvious that the number of segments is K = [ ( M 2 + F )T ] Ts . The signal on the nth subcarrier in the kth segment as Skn (t ) = S n (t ) RTs (t − kTs ); k = 0,1,… , K − 1
(11)
1; kTs ≤t≤( k + 1)Ts with R (t − kT ) = . Ts s 0; eles Step 6 Then, N signals in the kth segment Skv (t ) are
partitioned into V random disjoint Skv (t ) = {Skv , n (t ) | n = 0,1,… , N − 1} , satisfying N N n ( v − 1)≤ n≤ v − 1 S (t ); S kv , n (t ) = k V V 0; eles
sub-blocks
(12)
82
The Journal of China Universities of Posts and Telecommunications
Then modulating the signals to subcarriers, and V signals in the kth segment are obtained as N −1
skv (t ) = ∑ Skv , n (t )e
j
2πn t T
; v = 1, 2,… ,V
3.3
And the signal skv (t ) is multiplied with the
phase rotation factor bkv ∈ {1, −1} , since {1, −1} is easily implemented and as good as any other phase sequence in terms of the PAPR reducing capability. Obviously, the number of rotation factor is V. Then, the optimal phase factor combination of skv (t ) with the minimum PAPR is selected as V arg min max ∑ bkv skv (t ) v bk kTs ≤t ≤( k +1)Ts v =1 (14) s.t. bkv ∈ {1, −1} ; k = 1, 2,… , K − 1 The proposed P-PTS scheme introduces two key parameters V and U, so we can change the value of the two to achieve better PAPR reduction performance. Compared with S-PTS scheme, different parameter combinations can flexibly be traded off between computational complexity and PAPR reduction performance. 3.2
it will not affect the complexity. Analysis of computational complexity
(13)
n=0
Step 7
2015
Signal phase recovery
Because of the design, P-PTS scheme only change the phase of the signals. At the receiver, we should add a step to recover the original phases of the signals, and the side information (SI) must be transmitted. The SI is usually phase rotation sequences or phase rotation factors selected by PAPR reduction schemes. But actually, we always transmit the serial number of the selected sequence for simplicity, and the proposed P-PTS should transmit (lbU +V) bit for each data block. Compared with conventional scheme, for example S-PTS, the SI has a small increase. Because the proposed P-PTS is a two-step scheme including a pretreatment at the transmitter, the receiver should use the corresponding SI to recover original phase, and it needs two phase rotation sequences for each data block. To put it simply, we first convert the serial numbers into phase rotation sequences when SI arrives, and then multiply the frequency domain signals which are transformed from time domain with the two phase rotation sequences. The calculations of signal phase recovery only need several complex multiplications and the computational complexity is so small that can be ignored. Besides, the order of two phase rotation sequences can be changed and
The computational complexity is one of the restrictions for the practical implementation of a novel scheme. Because FBMC-OQAM systems can be implemented through fast Fourier transform (FFT)/inrerse fast Fourier transform (IFFT) module, the module exerts a significant effect on the whole complexity level. For the proposed P-PTS scheme, to find the best phase sequence in Eq. (6), NUTs complex multiplications and (N−1)UTs complex additions are required, and Ts is equal to N for simulation. To generate V signals in Eq. (13), NVTs complex multiplications and (N−1)VTs complex additions are required, too. Besides, the number of phase combinations is 2V for each segment, and VTs complex multiplications and (V−1)Ts complex additions are needed for one phase combination. Because the above three parts are different and important in the proposed P-PTS and S-PTS scheme, they are all taken into account. Other calculations are same and small in both schemes (e.g. the calculations in Eqs. (9)–(10)), so they are ignored. In addition, it is well known that one complex multiplication requires four real multiplications and two real additions, and one complex addition requires two real additions. Then, the numbers of required real multiplications and real additions for the P-PTS and S-PTS schemes are listed in Table 1. Table 1 Numbers of required real multiplication and real addition of the P-PTS and S-PTS schemes Scheme
Real multiplications V
Proposed P-PTS
4N(NU+NV+2 V)
S-PTS
4N(NV+2VV)
Real additions 2N(2NU+2NV+2× 2VV−U−V−2V) 2N(2NV+2× 2VV−V−2V)
From the table we can see that, if the parameters are determined, the real multiplications and additions can be calculated. Besides, at the receiver the computational complexity is so smaller that can be ignored compared with the transmitter.
4 Simulation results In this section we have done several simulations using the proposed P-PTS scheme with different conditions to analyze the PAPR reduction performances and bit error rate (BER) performances, compared with S-PTS [14]. And
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
the CCDF curves plot the probability versus the PAPR in dB. In all simulations, the number of sub-carriers is set to be 64 and the modulation scheme of 4-OQAM is adopted. For the simulation of complementary cumulative distribution function (CCDF) of the PAPR, 100 000 FBMC-OQAM blocks are generated randomly. Besides, the rolloff factor of the SRRC filter is set to be 1, and the length of the filter is generally set to 4T.
83
of the proposed P-PTS scheme with that of S-PTS scheme. If the probability is fixed at the value of 0.1%, the PAPR of P-PTS with V=4, U=2 is about 7.9 dB, smaller than 8.3 dB of S-PTS with V=4. Besides, the PAPR of P-PTS with V=4, U=16 is 7.1 dB, also better than S-PTS with V=8. It implies that we can flexibly use two parameters to achieve a better performance. However, S-PTS scheme can only change one parameter V, so its PAPR reductions just affected by V.
4.1 Simulation results of the proposed P-PTS scheme with different values of U From Fig. 3, it is clear that for a given value of V, the value of PAPR decreases as the increasing of U. For example, if V=4 and the probability is fixed at the value of 0.1%, and it is observed that the PAPR value for U=2 case is about 2.6 dB smaller than the original OFDM signal. Under the same condition, the PAPR values for U=4, 16 and 32 are about 7.5 dB, 7.5 dB and 6.7 dB, respectively. Besides, if the U is fixed, the value of PAPR decreases faster as the increasing of V. In another word, increasing V is more effective to decrease the value of PAPR. It implies that different combinations of U and V can achieve different PAPR reduction performances, and in a practical application we can flexibly choose the combinations as required.
Fig. 4
CCDFs of the proposed P-PTS and S-PTS schemes
From the two above simulation results, we can find that PAPR reduction performances of the proposed P-PTS scheme with certain parameters are better than S-PTS scheme. Furthermore, the computation complexity is also one of the restrictions for applying a novel scheme. In order to research the relationship between computational complexity and PAPR reduction performance, we can use the equations in Table 1 to calculate the numbers of the real multiplications and real additions. The calculation results are listed in Table 2. Table 2 The computational complexity comparison in terms of real multiplications and additions Scheme
V
4
Fig. 3 CCDFs of the proposed P-PTS scheme with different values of U and V
4.2 Simulation results of PAPR reduction performance between the proposed P-PTS and S-PTS schemes In Fig. 4, we compare the PAPR reduction performances
Proposed P-PTS
8
S-PTS
4 8 16
U
Real multiplications
Real additions
2 4 16 32 2 4 16 32 — — —
114 688 147 456 344 064 606 208 688 128 720 796 917 504 1 179 648 81 920 655 360 268 697 600
111 872 144 384 339 456 599 552 654 080 686 592 881 664 1 141 760 79 360 621 568 260 306 944
Value of PAPR at CCDF is 10−3 7.9 7.5 7.1 6.7 7.0 6.6 6.2 5.7 8.3 7.3 —
From the above analysis, it is obvious that both the
84
The Journal of China Universities of Posts and Telecommunications
proposed P-PTS and S-PTS schemes can reduce PAPR effectively. In the table, we can find that the complexity is lowest when using S-PTS with V=4, but the PAPR reduction is also the worst. When V = 4 and U = 2, the PAPR value of the proposed P-PTS is about 0.4 dB smaller than S-PTS scheme with a little increase in the computational complexity. The computational complexity has a significantly increase, when S-PTS uses V=8. The PAPR reduction performance of P-PTS with V = 4 and U = 16 is a little worse than S-PTS with V=8, however, the complexity considerably decreases. When U changes to 16 and 32, PAPR reduction performances get further ascent. Although the complexity has increased, it is still smaller than S-PTS with V=8. It implies that we can flexibly trade off between the computational complexity and the PAPR reduction performance.
2015
white Gaussian noise (AWGN) channel. For ideal situation, the three dotted lines denote the BER performance using different schemes without SSPA. Obviously, the BER of the original curve without SSPA is the best, because the signals are not affected by the nonlinear distortion. But actually, the nonlinear distortion is exist. On the other hand, because the introduced pretreatment does not destroy the structure of FBMC-OQAM symbols and causes no distortion, the two curves are almost same.
4.3 Simulation results of BER performance between the proposed P-PTS and S-PTS schemes To evaluate the performances of the BER with the proposed P-PTS in FBMC-OQAM systems, the typical solid-state power amplifier (SSPA) is employed. And the Rapp model is a widely used SSPA model and it commonly used to emulate the nonlinear behavior of SSPAs in mobile and cellular communications [17]. The time-domain samples at the SSPA input is sn = an e jθn , the amplifier output using the SSPA model can be expressed as j θ +φ ( a ) yn = A(an )e [ n n ] (14) where the operators
A(⋅)
and
φ (⋅)
represent the
amplitude modulation (AM)/AM and AM/ phase modulation (PM) conversion characteristics of the nonlinear amplifier, respectively. In general, SSPAs introduce AM/AM distortion, which can be described as −1
a 2 p 2 p A(an ) = an 1 + n (15) A0 where A0 denotes the maximum amplifier output, and the smoothness of the transition from the linear region to the limiting region can be controlled by the parameter p. The AM/PM distortion is very limited for most applications; hence, φ (an ) = 0 . In Fig. 5, the BER performances of the proposed P-PTS and S-PTS schemes are depicted. The channel between the transmitter and the receiver is modeled as an additive
Fig. 5 BERs of the proposed P-PTS and S-PTS schemes over AWGN channel
In practical applications, the BER performances reduced significantly due to the influence caused by nonlinear distortion, and both the proposed P-PTS and S-PTS can improve the BER performances. Besides, the signals operated by the proposed P-PTS scheme achieve better BER performances than the original signals with the SSPA. Specifically, to reach a BER of 10−4, the SNRs are 15.1 dB for S-PTS schemes with V=8, and 14.1 dB, 16.0 dB for the proposed P-PTS scheme with V=4, U=4 and 16, respectively. As the analysis in Sect. 4.2, the PAPR reduction performance for the proposed P-PTS scheme with above parameters is close to S-PTS schemes with V=8, but the computational complexity is much lower. And it is obvious that the order of the three BER performance curves is same as PAPR curves.
5 Conclusions In this paper, a novel P-PTS scheme was proposed to reducing the PAPR in FBMC-OQAM systems. To deal with the problem of overlap more effective, we take fully into account the overlapping structure of FBMC-OQAM symbols and use a two-step optimization structure. The
Issue 6
Liu Kaiming, et al. / PAPR reduction for FBMC-OQAM systems using P-PTS scheme
simulation results show that the proposed P-PTS scheme can achieve better PAPR reduction performance than the comparatively new scheme S-PTS with lower computational complexity. In addition, the signals operated by the proposed P-PTS scheme achieve better BER performances than S-PTS with the SSPA, and the computational complexity and performance can be traded off flexibly by using different parameter combinations. Acknowledgements This work was supported by the Beijing Higher Education Young Elite Teacher Project (YETP0440), the National Natural Science Foundation of China (61272518, 61302083)
References 1. Banelli P, Buzzi S, Colavolpe G, et al. Modulation formats and waveforms for 5G networks: who will be the heir of OFDM?: an overview of alternative modulation schemes for improved spectral efficiency. IEEE Signal Processing Magazine, 2014, 31(6): 80−93 2. Farhang-Boroujeny B. OFDM versus filter bank multicarrier. IEEE Signal Processing Magazine, 2011, 28(3): 92−112 3. Sahin A, Guvenc I, Arslan H. A survey on multicarrier communications: prototype filters, lattice structures, and implementation aspects. IEEE Communications Surveys & Tutorials, 2014, 16(3): 1312−1338 4. Sahin A, Guvenc I, Arslan H. A comparative study of FBMC prototype filters in doubly dispersive channels. Proceedings of the 2012 IEEE Globecom Workshops (GC’12 Wkshop’12), Dec 3−7, 2012, Anaheim, CA, USA. Piscataway, NJ, USA: IEEE, 2012: 197−203 5. Rahmatallah Y, Mohan S. Peak-to-average power ratio reduction in OFDM systems: a survey and taxonomy. IEEE Communications Surveys & Tutorials, 2013, 15(4): 1567−1592 6. Gokkul N A, Kumar A A, Kumar S H, et al. Performance improvement of OFDM using hybrid PAPR reduction technique. Proceedings of the 4th International Conference on Computing, Communications and Networking Technologies (ICCCNT’13), Jul 4−6, 2013, Tiruchengode, India.
85
Piscataway, NJ, USA: IEEE, 2013: 4p 7. Abbas M A, Gasser S, Aziz A M, et al. A new approach for PAPR reduction of OFDM signal based on SLM and PTS. Proceedings of the 3rd International Conference on e-Technologies and Networks for Development (ICeND’14), Apr 29−May 1, 2014. Piscataway, NJ, USA: IEEE, 2014: 58−63 8. Zhou Y, Jiang T, Huang C, et al. Peak-to-average power ratio reduction for OFDM/OQAM signals via alternative-signal method. IEEE Transactions on Vehicular Technology, 2014, 63(1): 494−499 9. Qu D M, Lu S X, Jiang T. Multi-block joint optimization for the peak-to-average power ratio reduction of FBMC-OQAM signals. IEEE Transactions on Signal Processing, 2013, 61(7): 1605−1613 10. Lu S X, Qu D M, He Y J. Sliding window tone reservation technique for the peak-to-average power ratio reduction of FBMC-OQAM signals. IEEE Wireless Communications Letters, 2012, 1(4): 268−2714 11. Varghese N, Chunkath J, Sheeba V S. Peak-to-average power ratio reduction in FBMC-OQAM system. Proceedings of the 4th International Conference on Advances in Computing and Communications (ICACC’14), Aug 27−29, 2014, Cochin, India. Piscataway, NJ, USA: IEEE, 2014: 286−290 12. Skrzypczak A, Javaudin J P, Siohan P. Reduction of the peak-to-average power ratio for the OFDM/OQAM modulation. Proceedings of the 63rd Vehicular Technology Conference (VTC-Spring’06): Vol 4, Mar 7−10, 2006, Melbourne, Australia. Piscataway, NJ, USA: IEEE, 2006: 2018−2022 13. Krishna Chaitanya Bulusu S S, Shaiek H, Roviras D, et al. Reduction of PAPR for FBMC-OQAM systems using dispersive SLM technique. Proceedings of the 11th International Conference on Wireless Communications Systems (ISWCS’14), Aug 26−29, 2014, Barcelona, Spain. Piscataway, NJ, USA: IEEE, 2014: 568−572 14. Ye C, Li Z J, Jiang T, et al. PAPR reduction of OQAM-OFDM signals using segmental PTS scheme with low complexity. IEEE Transactions on Broadcasting. 2014, 60(1): 141−147 15. Le Floch B, Alard M, Berrou C. Coded orthogonal frequency division multiplex. Proceedings of the IEEE, 1995, 83(6): 982−996 16. Ochiai H, Imai H. On the distribution of the peak-to-average power ratio in OFDM signals. IEEE Transactions on Communications, 2001, 49(2): 282−289 17. Al-Dalakta E, Al-Dweik A, Hazmi A, et al. Efficient BER reduction technique for nonlinear OFDM transmission using distortion prediction. IEEE Transactions on Vehicular Technology, 2012, 61(5): 2330−2336
(Editor: Wang Xuying)