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A Pilot Symbol Pattern Enabling Data Recovery Without Side Information in PTS-Based OFDM Systems Hyunju Kim, Student Member, IEEE, Eonpyo Hong, Member, IEEE, Changjun Ahn, and Dongsoo Har
Abstract—Partial transmit sequence (PTS) scheme is one of the most popular peak-to-average power ratio (PAPR) reduction schemes for orthogonal frequency division multiplexing (OFDM) systems. In the PTS scheme, one OFDM symbol is partitioned into disjointed sub-blocks, and each sub-block is multiplied by a phase factor to generate signals with low PAPR. For data recovery, receivers must have side information (SI), e.g., phase factors, from transmitters. In this letter, a novel data recovery scheme in PTS-based OFDM systems without SI is proposed. In the proposed scheme, an additional pilot symbol is intentionally inserted at the end of each sub-block, so that efficient data decoding based on channel estimation can be executed with known pilot symbols. Simulation results show that the BER performance of the proposed scheme without SI is approximately the same as those of the PTS scheme with perfect SI and a maximum likelihood decoding scheme. Considering the cost for SI encoding and decoding, the proposed scheme is practically more advantageous over the PTS scheme. Index Terms—Orthogonal frequency division multiplexing (OFDM), partial transmit sequence (PTS), peak-to-average power ratio (PAPR), side information.
I. INTRODUCTION RTHOGONAL frequency division multiplexing (OFDM) has been widely adopted in various application systems such as digital audio/video broadcasting systems, wireless LANs, and other emerging wireless broadband systems. However, OFDM systems suffer several drawbacks such as sensitivity of carrier frequency offset and high peak-to-average power ratio (PAPR). Of these drawbacks, high PAPR causes nonlinear distortion at high power amplifier and reduces its power efficiency. Therefore, many PAPR reduction schemes have been reported in the literature [1]. Among them, the partial transmit sequence (PTS) scheme [2] is an attractive solution to reduce PAPR without any distortion of transmitted signals. In the PTS scheme, input data symbols are divided into disjointed sub-blocks and the sub-blocks are separately phase-rotated by individually selected phase factors during PAPR optimization process. The phase factors are also
O
Manuscript received August 05, 2010; revised nulldate; accepted January 03, 2011. Date of publication February 04, 2011; date of current version May 25, 2011.This work was supported in part by the Center for Distributed Sensor Networks at the Gwangju Institute of Science and Technology (GIST) H. Kim, E. Hong, and D. Har are with the School of Information and Communications, GIST, Gwangju 500-712, Korea (e-mail:
[email protected];
[email protected];
[email protected]). C. Ahn is with the Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBC.2011.2105611
transmitted as side information (SI) when data symbols are sent. For successful data recovery, receivers must have the SI. Since SI is very critical for successful operation of the PTS scheme, it is protected by channel coding to combat frequency-selective fading. To do so requires increased system complexity, further loss in data transmission rate, and additional PAPR growth due to SI production following the PAPR optimization process. A variety of different methods for PTS-based OFDM systems have appeared in the literature to recover transmitted data without SI [3]–[8]. According to marking algorithm proposed in [3], phase factors are binary numbers. The phases of sub-blocks are rotated as much as predefined amount when the phase factor of the sub-blocks is one of such binary numbers and are unchanged when the phase factor is the other binary number. So, the receivers need the detection process checking whether the predefined phase rotation is placed. In [4], [5], the symbol positions in symbol constellation are determined by constellation mapping based on phase factors. The hexagonal constellation mapping [4] and square mapping [5] are respectively used for these schemes. Another PTS-based OFDM system without SI is discussed in [6]. According to the scheme in [6], pilot sub-channel is transformed into time domain and zero-padding is performed to get channel estimation for each sub-block. The scheme in [7] recovers data without SI by a maximum likelihood decoding. The scheme in [8] uses combined block-type and comb-type pilot symbol patterns for channel estimation and PTS phase factor estimation, respectively. The block-type pilot symbols enable robust BER performance even in extremely frequency-selective fading channels, but the scheme requires a large number of these additional pilot symbols causing a loss in data throughput. In this letter, an efficient data recovery scheme without SI is presented for adjacent partitioning PTS scheme. The adjacent partitioning PTS scheme can be more simply implemented and demonstrates similar PAPR performance in comparison with the interleaved or the randomized partitioning PTS scheme. The latter leads to the best PAPR reduction performance among three different partitioning types for the PTS schemes [9]. Based on the proposed scheme, an extra pilot symbol is placed at the end of each sub-block to facilitate simple and complete channel estimation for each and whole sub-block. The proposed scheme does not require any other additional process to embed or to extract SI. The rest of this letter is organized as follows. In Section II, the PTS scheme with perfect SI is discussed. In Section III, the proposed scheme is presented. Section IV shows the comparisons of computational complexity and the BER performance. Finally, conclusions are drawn in Section V.
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Fig. 1. Block diagram of OFDM systems based on the PTS scheme with perfect SI.
II. PTS SCHEME WITH PERFECT SI for , The time domain OFDM sequence which is generated by the inverse fast Fourier transform (IFFT) of frequency domain OFDM symbols, is represented as
are illustrated, which leads to the same phase rotations as those . The by multiplications with frequency domain sequence is represented as transmitted OFDM sequence (4)
(1) where the frequency domain OFDM sequence for is modulated by phase shift keying (PSK) or quadrature amplitude modulation and is the number . The of valid sub-carriers, excluding null sub-carriers in PAPR is defined as the ratio of the peak power to its average and given as following power of (2) where denotes expectation. Fig. 1 shows the block diagram of the adjacent partitioning PTS scheme [9] to reduce PAPR. In is partitioned the adjacent partitioning PTS scheme, the into disjointed sub-blocks, and then the -th sub-block for is obtained as otherwise
(3)
where and denotes the number of valid sub-carriers in a sub-block. By the IFFT modules, the frequency domain sequence corresponding to -th sub-block , including pilot symbols and data symbols, is for transformed into the time domain sequence . For the PTS scheme, , where is the pilot symbol interval. The transmitted time domain OFDM sequence is obtained by adding up sequences of , each of which is multiplied by a phase factor to generate the OFDM sequence with low PAPR. In Fig. 1, multiplication of phase factors with time domain sequences for
where phase factors are denoted by and can be chosen among allowed phase angles within . The optimum phase factors minimizing PAPR can be chosen by optimization algorithms [10]–[12] and obtained by (5) Transmitters must send the set of the optimum phase factors as SI in order to decode data symbols at receivers. Since one of phase factors can be set to without loss of generbits per OFDM symbol are required for SI. ality, With a channel coding employed to protect SI against channel harshness, larger number of bits per OFDM symbol is needed, reducing data transmission efficiency while increasing system complexity. III. PROPOSED SCHEME WITHOUT SI Fig. 2 shows the pilot symbol pattern for pilot interval of the proposed scheme, where data and pilot symbols are respectively represented by small empty circles and big blackfilled circles. As shown in Fig. 2, an extra pilot symbol is added at the end of the -th sub-block. Without the extra pilot symbol, the data symbols between the last pilot symbol in -th sub-block -th sub-block are hard to be and the first pilot symbol in recovered from channel estimation, due to different phase fac. In the presence of the extra pilot symbol, comtors and plete channel estimation for each and whole sub-block including those data symbols is enabled. Let and be the number of valid symbols and the number of pilot symbols in a sub-block, respectively,
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Fig. 2. Pilot pattern (L = 3) of a frequency domain OFDM sequence for the proposed scheme with extra pilot symbols placed at the end of sub-blocks.
then
due to an extra pilot symbol and , . Also from the and , the number of data symbols relationship between . For the proposed scheme, non-zero compoof are decomposed nents in for and data into pilot symbols as following symbols (6)
, respecwhere , are quotient, remainder of tively. Note that PAPR performance of the proposed scheme for small number of sub-blocks in an OFDM symbol is approximately the same as that of the adjacent partitioning PTS scheme, because of negligible number of extra pilot symbols( 5 for ) compared with the number of valid sub-carriers( 2000 for DVB-T or alike). At receivers, according to the process of the general pilotaided channel estimation in [13], pilot sub-channels are estimated, and then data sub-channels are interpolated based on and neighbored pilot sub-channels. Let be -th received pilot symbol and -th received data symbol in -th sub-block, respectively, then these can be expressed as
(7) and are -th pilot sub-channel where response and -th data sub-channel response in -th are independent and identisub-block, respectively, and cally distributed (i.i.d.) complex additive white Gaussian noise (AWGN). The channel estimation of the proposed scheme is performed for each sub-block based on the pilot pattern described in (6). The estimated composite pilot sub-channel of -th sub-block including phase factor is as following (8) where
is a known pilot symbol and is the estimated pilot sub-channel, and is also an i.i.d. complex AWGN random variable. The composite data sub-channel is obtained by an interpolation from the neighbored
composite pilot sub-channels. In [14], cubic spline interpolation is discussed for better BER performance in comparison with a linear interpolation. When a linear interpolation is applied to obtain the composite data sub-channels
(9) where denotes the estimated data sub-channel. is obtained From (9), the estimated data symbol by
(10) where is phase shifted ver. With tightly spaced two consecutive pilot sion of symbols in most practical OFDM systems, the estimated data obtained by an interpolation is close to sub-channel . When , . If , the error term in (10) becomes significant, leading to degraded BER performance. Since the phase factor is removed as in (10), arbitrary values of the phase factors can be used. The proposed scheme does not need any other processes to protect and to extract SI. With an extra pilot symbol at the end of each sub-block, complete channel estimation including data symbols between the and is readily last two pilot symbols made. As a result, because of different phase factors for different sub-blocks in PTS-based OFDM systems, the presence of the extra pilot symbol at the end of a sub-block enables consistent channel estimation throughout the sub-block. Several parameters for the proposed scheme are indicated in Table I, compared with the adjacent partitioning PTS scheme of equi-spaced pilot pattern. For both schemes, the same number of data symbols and an identical pilot symbol interval are considered for each sub-block. Comparing the amount of SI according
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TABLE I COMPARISON OF PARAMETERS FOR THE PROPOSED SCHEME WITH THE PTS SCHEME OF EQUI-SPACED PILOT PATTERN AND PERFECT SI
to the number of sub-blocks and the number of allowed phase factors, the PTS scheme without any channel coding requires bits as SI, whereas only extra bits for pilot symbols, assuming practical Binary PSK is used for pilot symbols, are needed for the proposed scheme. or In the proposed scheme, the decoded symbol in (10) is obtained by (i) pilot sub-channel estimation, (ii) data sub-channel estimation, and (iii) decoding based on the decision metric as in Fig. 1. The FFT operation at front-end of receiver is not considered here. The decision metric for each data symbol can be described as , where is the constellation. The computational complexity in terms of real multiplications and real additions is as follows • # of complex multiplications for pilot symbols in (8) for (i), where a division by a complex number is a multiplication by its • # of complex additions for data symbols in the first equality of (9) for • # of real multiplications in the first equality of (9) for • # of complex multiplications in (10) for • # of complex additions for of , of the constellation • # of real multiplications for of • # of real additions for of The decision metric is only applied to data symbols. A complex multiplication is equivalent to four real multiplications and two real additions and a complex addition is equivalent to two real additions. Therefore, the required numbers of real multipli, cations and real additions are given as , and , respectively. where IV. COMPUTATIONAL COMPLEXITY AND SIMULATION RESULTS Comparisons of computational complexity are made for the procedures after the common FFT operation at front-end of -point and the receiver. In [6], IFFT modules of FFT modules of -point, other than the FFT module at front-end of receiver, replace (i) pilot sub-channel estimation module and (ii) data sub-channel estimation module of the proposed scheme in Fig. 1. The procedure (iii) as the final decoding step including the division in (10) to choose the closest data symbol in constellation is assumed to be the same as that of the proposed scheme. The computational complexity, excluding several intermediate steps for the scheme in [6], is as follows
# of complex multiplications of (i) and [15] # of complex additions of (i) and [15] Overall, the required numbers of real multiplications and real additions are given as and , respectively. The phase factors chosen as
where are used in [7]. The decision metric in [7] is modified as used for data symbols in -th sub-block following
in order to separate the division in (10) from the original decision metric in [7]. The procedures for channel estimation are assumed to be the same as (i) and (ii) of the proposed scheme, except that phase factor is not used for pilot symbol transmisobtained from an interpolation of adjacent sion, so in (10). Thus, the pilot symbols is used for in (10) contains a phase factor. Considering the first sub-block using , the computational complexity for the decision metric can be decomposed into several parts as following , for # of complex multiplications, when # of complex # of real multiplications for # of real additions for # of real additions for where , . Overall complexity of the scheme in [7] including (i), (ii), and real the division in (10) is multiplications and real additions. Computational complexity of the proposed scheme is evaluated in terms of computational complexity reduction ratio (CCRR) defined as following
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TABLE II CCRR OF THE PROPOSED SCHEME IN COMPARISON WITH THE SCHEME IN [6] AND THE S CHEME IN [7]
3
N = 1728, N = 1584, L = 12, V = 4, U = 4, and QPSK for
data symbols.
Fig. 4. BER performances of the proposed scheme, the scheme in [7] ( = 30 ), and the PTS scheme for a typical urban (TU-6) channel, according to the number of partitioned sub-blocks. V = 4, 6, and 8 with four allowed phase factors, when cubic spline interpolation is used for data sub-channel.
( =
Fig. 3. BER performances of the proposed scheme, the scheme in [7] , and the PTS scheme for a typical urban (TU-6) channel, according to the number of partitioned sub-blocks. , 6, and 8 with four allowed phase factors, when linear interpolation is used for data sub-channel.
30 )
V =4
The CCRR( [6]) and CCRR( [7]) are separately evaluated in terms of real multiplications and real additions as in Table II. As seen in Table II, the proposed scheme has considerably lower computational complexity than the scheme in [6] and the scheme in [7]. In general, the proposed scheme has the lowest computational complexity with practical ranges of , , , and , considering the parameterized expressions of computational complexity for three schemes. OFDM system parameters used in the simulation are following the DVB-T standard [16]. The total number of sub-car, the interval between pilot sub-carriers rier , and OFDM . Binary PSK for pilot sub-carriers and quadrature PSK for data sub-carriers are valid sub-carriers are used adopted. While of the proposed scheme is obfor the PTS scheme, the tained according to the number of sub-blocks as in Table I. For simulation, a pilot symbol is assumed to be located at the valid sub-carriers even for the PTS scheme, so that end of , , and for . Figs. 3 and 4 show the BER performances of the PTS scheme with SI, the scheme in [7], and the proposed scheme with a 6-tap typical urban (TU-6) channel [17], according to the , 6, and 8. The phase factors number of sub-blocks are used in the proposed scheme and the PTS scheme with perfect SI. For the scheme in [7], four
phase factors with are used. Simulation results of the PTS scheme with SI, the scheme in [7], and the proposed scheme are obtained with conditions that (i) pilot symbol power is equal to data symbol power and (ii) pilot symbols, including extra pilot symbols in the proposed scheme, are taken into value in . The degree consideration for adjustment of of noise perturbation in (7) is varied according to . The estimation of composite data sub-channels is made by a linear interpolation and a cubic spline interpolation in Figs. 3 and 4, respectively. Typical urban channel demonstrates more frequency-selective fading in comparison with rural channel. Based on simulation results with a rural area (RA-6) channel, BER performance of the proposed scheme is indistinguishable from that of the over the range of PTS scheme with two different aforementioned interpolation methods, though not shown in this letter. As shown in Figs. 3 and 4, both the proposed scheme and the scheme in [7] without SI achieve approximately the same BER performance with high values. With low , the scheme in [7] is worse than the proposed scheme, since errors in SI decision for each sub-block cause substantial detection errors of data in the sub-block. The BER performance of the scheme in [7] is also getting a little worse when the number of sub-blocks is increased, because of less robust decision on SI is more likely made with the smaller sub-block. Based on the BER performance of the scheme in [6] in comparison with the PTS scheme with perfect SI and the BER performance of the proposed scheme close to the PTS scheme as shown in this letter, the scheme in [6] and the proposed scheme are believed to perform closely. For the PTS scheme, since channel estimation is made when phase factors are removed beforehand, the BER performance does not depend on the number of sub-blocks . In case of linear interpolation using only two neighboring pilot sub-channels, notable difference between the performances of the proposed scheme and the PTS scheme is not observed. The BER performances are improved by cubic spline interpolation that enables the more precise estimation of data sub-channels.
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V. CONCLUSION In this letter, an efficient data recovery without SI transmission in PTS-based OFDM systems is discussed. At the cost of an additional pilot symbol placed at the end of each sub-block, complete channel estimation even for data symbols around the end of each sub-block is performed without SI. Simulation results show that the proposed scheme without any SI transmission achieves approximately the same BER performance compared with the PTS scheme with perfect SI. Moreover, the proposed scheme has significantly lower computational complexity compared with the schemes in [6] and in [7].
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