Low-complexity data decoding using binary phase detection in SLM-OFDM systems S.A. Adegbite, S.G. McMeekin and B.G. Stewart High computational complexity associated with maximum-likelihood (ML) data decoding in orthogonal frequency division multiplexing (OFDM) systems that use selected mapping (SLM) for the reducing peak-to-average power ratio (PAPR) can be significantly reduced using modified SLM and data decoding techniques presented in this Letter. Simulations show that the proposed method achieves similar PAPR reduction capability and data recovery performance compared with standard SLM (with perfect data recovery) and an ML detection scheme.
Introduction: Although, selected mapping (SLM) [1] is an attractive method for reducing the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems, some form of highly computational complex maximum-likelihood (ML) estimation is required for successful data recovery. This may increase system complexity and design costs. Some examples of such ML schemes are presented in [2, 3]. The method in [3] is based on a hybrid of pilot-aided channel estimation and ML detection (H-PACEML). Although H-PACEML requires smaller computational complexity over [2], its computational complexity increases with modulation order, therefore it is unattractive in higher order modulation such as 64-QAM and 256-QAM. To address this problem, a very low complexity data recovery method that achieves similar data recovery performance as H-PACEML is presented in this Letter. Fig. 1 shows a block diagram representation of a form of SLM-OFDM, which involves both pilot and data symbols as in [3] as described in the following Section.
D QAM modulation
pilot insertion
1
S
S B
1
IFFT
S
2 2
S
2
IFFT S
U
B
QAM demodulation
data decoding
U
U
S
IFFT
S
u
select a timedomain signal with the lowest PAPR
CP insertion multipath fading channel
FFT
remove CP
Fig. 1 SLM in pilot-aided OFDM system
H-PACEML: In [3], an OFDM symbol block S of length N = Nd + Np is formed as S[k] = S[mL + l] 0≤l≤L−1
=
P[m],
l=0
D[mL − m + l],
otherwise
(1)
where L is the pilot spacing, P[m] and D[mL − m + l ] represent the pilot and data symbol, respectively, for 0 ≤ m ≤ Np − 1, Np is the number of pilots and Nd is the number of data symbols. Pilot symbol and their locations are referenced by the name ‘even pilots’ or ‘odd pilots’ when m is an even or odd number, respectively. Using SLM-PAPR reduction, elements of SLM phase rotation sequences Bu are defined as ⎧ u l = 0, m = 0, 2, 4, . . . ⎪ ⎨ Bp [mL + l] = 1, u (2) Bu [k] = Bup [mL + l] = e jf [k], l = 0, m = 1, 3, 5, . . . ⎪ u ⎩ u Bd [mL + l] = e jf [k], l = 0 where ϕu[k] is obtained from a randomly distributed set over [0, 2π). This particular set of sequences increases SLM complexity but this can be avoided using binary sequences chosen from the set {±1} [4]. Therefore, only binary sequences are considered in this Letter. A time domain signal su = su0 su1 . . . suM −1 is formed through an M point inverse fast Fourier transform (IFFT) of the point-wise multiplication of S with Bu as −1 1 N
sun = √ S[k] · Bu [k]e(j2pnk/M ) , M k=0
0≤n≤M −1
(4)
where Su = S · Bu and V are complex-valued additive white Gaussian noise (AWGN) sequences. Y can be further decomposed into data Yd and pilot Yp sequences, H is also divided into data Hd and pilot Hp subchannel responses. An estimate of u is obtained by uˆ = min
⌊(N
p /2)−1⌋
|Yp [2r + 1] − Hˆ p [2r + 1]Bup [2r + 1]P[2r + 1]|2
r=0
(5) where sub-channel estimates Hˆ p [2r + 1] are obtained through linear interpolation between sub-channel estimates Hˆ p [2r] = Yp [2r]/P[2r] for r = 0, 1…⌊(Np/2) − 1⌋. After obtaining uˆ , Hˆ p [2r + 1] is then recalculated through ˆ Hˆ p [2r + 1] = Yp [2r + 1]Bup∗ [2r + 1]/P[2r + 1]
(6)
where * is the complex conjugation operator. Estimates of data symbols are obtained by ML defined as ˆ ˆ D[mL + l] = min |Yd [mL + l]Bud∗ [mL + l] − Hˆ d [mL + l]Xˆ d [q]|2 Xˆ d [q][Q
(7)
Proposed method: An alternative method that performs data decoding through binary phase detection and channel equalisation is proposed. This involves partitioning of an OFDM symbol block X into Np/2 independent clusters where each cluster contains two pilot symbols and 2L-2 data symbols. For 0 ≤ c < (Np/2) − 1, elements of X are defined as follows
AWGN
S
SI detection and sequence de-mapping
Y = HSu + V
where Q is a set of Q constellation points of the chosen data modulation ˆ scheme, D[mL + l] [ Q, 1 ≤ q ≤ Q, Yd[mL + l ] is the received data sequence and Hˆ d [mL + l] is the data sub-channel response, obtained by linear interpolation between values of Hˆ p [2r] and Hˆ p [2r + 1].
1
B
The signal su has the lowest PAPR and u corresponds to the SLM sequence vector Bu which produce su . Therefore, elements of the optimum vector Bu or value of u, often referred to as side information (SI), must be known at the receiver for successful data recovery. After transmission over a fading channel with frequency response H, the received OFDM sequences Y are expressed as
(3)
X [k ] = X [cW + w] = Xc [w], where W = 2L, 0 ≤ w ≤ W − 1 ⎧ w = 0 = we for even pilots ⎪ ⎨ P[cW ], (8) = P[cW + w], w = L = wo for odd pilots ⎪ ⎩ D[cW − c + w], otherwise, w = wd To reduce PAPR, a clustered SLM (C-SLM) is applied. C-SLM involves phase rotation of all data subcarrier symbols and the odd pilot in a given cluster with the same phase rotation factor. Thus, application of C-SLM sequences Ju to X will produce Xu as X u [k] = X u [cW + w] ⎧ u ⎪ ⎨ X [cW + we ] = X [cW + we ] = X u [cW + wo ] = X [cW + wo ] · J u [cW + wo ] ⎪ ⎩ u X [cW + wd ] = X [cW + wd ] · J u [cW + wd ]
(9)
where J u [cW + wo ] = J u [cW + wd ] = Jcu and Jcu [ +1. A low PAPR signal xu obtained through the new C-SLM approach is −1 1 N
xun = √ X u [k]e(j2pnk/M ) , M k=0 u
0≤n≤M −1
(10)
where Xu = X · Ju and Ju = eja denotes the optimum C-SLM sequence vector. Let the received OFDM sequences be Z = HXu + V. At the receiver, estimates of sub-channel responses at even and odd pilots are ˆ ˆ and H[cW + we ] = Z[cW + we ]/X [cW + we ] H[cW + wo ] = ˆ + wo ] = Z[cW + wo ]/X [cW + wo ], respectively, where H[cW u H[cW + wo ] ejac . Assuming a slow fading channel, an estimate of Jcuˆ
ELECTRONICS LETTERS 27th March 2014 Vol. 50 No. 7 pp. 560–562
is obtained as ˆ Jcu
2 = min ej a˜ c − li , where a˜ c li [+1
⎞ ⎛ ˆ ˆ Re H[cW + we ] + wo ]/H[cW
⎠ = tan−1 ⎝ ˆ ˆ Im H[cW + wo ]/H[cW + we ]
(11)
ˆ Data sub-channel estimates H[cW + wd ] can be obtained by linear ˆ ˆ + wo ] where interpolation between values of H[cW + we ] and H[cW ˆ ˆ H[cW + wo ] = H[cW + wo ] × Jcuˆ . Data decoding is achieved as ˆ Z[cW + wd ] H[cW + wo ] Xˆ [cW + wd ] = × ˆ ˆ H[cW + wo ] H[cW + wd ]
u ˆ H[cW + wd ]X [cW + wd ] ejac H[cW + wo ] × u ˆ H[cW + wo ] ejac H[cW + wd ] ˆ H[cW + wd ]X [cW + wd ] H[cW + wo ] (12) × = ˆ H[cW + wo ] H[cW + wd ]
=
Simulation results: Simulations show that the proposed method has similar PAPR reduction capabilities (see Fig. 2) and data recovery performance (see Fig. 3) compared with conventional SLM-OFDM and H-PACEML. Simulations use the LTE standard with an OFDM subcarrier spacing of 15 kHz, FFT size of 2048, N = 1200, L = 6, Np = 200, guard interval of 5.21 μs and sampling frequency of 30.72 MHz. Data and pilot symbols are obtained using the 16/64-QAM modulation scheme and QPSK-modulated Gold codes, respectively. SLM is performed using chaotic binary sequences [5], and PAPR reduction performance is evaluated using the complementary cumulative distribution function (CCDF) of the PAPR. The CCDF gives the probability that the calculated PAPR of an OFDM signal exceeds a certain threshold denoted as γ.
CCDF(g ) = Pr(PAPR >g )
100
original OFDM conventional SLM H-PACEML proposed
10−1
U = 16
10−3
10−4 7.5
8
8.5
9
9.5
Comparisons of computational complexity: Since H-PACEML and the proposed method use the same standard pilot-aided channel estimation method but differ in their approaches for detecting SI and data decoding, their computational complexities are compared using their respective detection techniques. Table 1 shows comparisons of the number of mathematical operations required in H-PACEML using (5) and (7) compared with the proposed detection scheme using (11) and (12). Numerically, the reduction in complexity of the proposed method relative to H-PACEML is measured by evaluating the computational complexity reduction ratio (CCRR) metric defined [3] as complexity of the proposed method CCRR = 1 − × 100% (13) complexity of H-PACEML
Table 1: Number of computations: H-PACEML against proposed method Type of operations H-PACEML Proposed Multiplications/divisions Nd(1 + 2Q) + 3UNp/2 3Nd + 3Np/2 Additions/subtractions (UNp/2) + QNd Np
With [U, Q, Nd and Np] set to (16, 64, 1000 and 200), respectively, the total number of multiplications/divisions and additions/subtractions are, respectively, (133 800 and 65 600) in H-PACEML and (3300 and 200) in the proposed method. These corresponds to CCRR values of 97.53 and 99.69% for multiplications/divisions and additions/subtractions, respectively. These high CCRR values show that the proposed method has significantly reduced complexity over the existing H-PACEML method. Conclusion: An alternative method for SI detection and data recovery in OFDM systems is proposed. Simulation proves that the proposed method has significantly reduced computational complexity and offers similar PAPR reduction capability and data recovery performance to that of H-PACEML and SLM with perfect SI.
U=4 10−2
H-PACEML for each value of U. Assuming perfect knowledge of SI for the case of conventional SLM-OFDM, the results in Fig. 3 show that the proposed method produces the same bit error rate (BER) performance as an SLM-OFDM and H-PACEML for an OFDM transmission over the LTE defined Extended Pedestrian Channel-A (EPA) and the 3GPP rural (3GPP-RA) channels.
10
10.5
11
11.5
12
g , dB
Fig. 2 CCDF of PAPR (64-QAM): conventional SLM, H-PACEML and proposed method
© The Institution of Engineering and Technology 2014 13 December 2013 doi: 10.1049/el.2013.4030 S.A. Adegbite, S.G. McMeekin and B.G. Stewart (SEBE, Glasgow Caledonian University, Glasgow, G4 0BA, United Kingdom) E-mail:
[email protected]
100
100 SLM-OFDM (with perfect SI) H-PACEML proposed
10–1
10–2
10–2 64-QAM
LTE-EPA
64-QAM 16-QAM
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BER
BER
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10–3
References
3GPP-RA
10–3
10–4 10–4 0 [30] 3 [27] 6 [24] 9 [21] 12 [18] 15 [15] 18 [12] 21 [9] 24 [6] 27 [3] 30 [0] Eb/No, dB
Fig. 3 BER: OFDM (with perfect SI), H-PACEML and proposed method
1 Bauml, R.W., Fischer, R.F.H., and Huber, J.B.: ‘Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping’, Electron. Lett., 1996, 32, (22), pp. 2056–2057 2 Jayalath, A.D.S., and Tellambura, C.: ‘SLM and PTS peak-power reduction of OFDM signals without side information’, IEEE Trans. Wirel. Commun., 2005, 4, (5), pp. 2006–2013 3 Jihan, P., Eonpyo, H., and Dongsoo, H.: ‘Low complexity data decoding for SLM-based OFDM systems without side information’, IEEE Commun. Lett., 2011, 15, (6), pp. 611–613 4 Zhou, G.T., and Liang, P.: ‘Optimality condition for selected mapping in OFDM’, IEEE Trans. Signal Process., 2006, 54, (8), pp. 3159–3165 5 Cheng, P., Xiao, Y., Dan, L., and Li, S.: ‘Improved SLM for PAPR reduction in OFDM system’. 18th IEEE Int. Symp. Personal, Indoor and Mobile Radio Communications (PIMRC), Athens, Greece, September 2007, pp. 1–5
The results in Fig. 2 show that the proposed method gives the same PAPR reduction performance as the conventional SLM and
ELECTRONICS LETTERS
27th March 2014 Vol. 50 No. 7 pp. 560–562
