PAPR reduction scheme with efficient embedded signaling in MIMOOFDM systems
 Mouna Sghaier^{1}Email author,
 Fatma Abdelkefi^{1}Email author and
 Mohamed Siala^{1}Email author
https://doi.org/10.1186/s136380150443x
© Sghaier et al. 2015
Received: 6 March 2015
Accepted: 7 September 2015
Published: 4 November 2015
Abstract
Multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) is a promising transmission scheme for high performance broadband wireless communications. However, this technique suffers from a major drawback which is the high peak to average power ratio (PAPR) of the output signals. In order to overcome this issue, several methods requiring the transmission of explicit side information (SI) bits have been proposed in the literature. In fact, the transmitted bits must be channelencoded as they are particularly critical to the performance of the considered OFDM system. Consequently, this channelencoding highly increases the system complexity and decreases the transmission data rate. To overcome these problems, we propose in this paper two robust blind techniques that embed the SI implicitly into the OFDM frame. The first technique, referred to as Blind Space Time Bloc Codes (BSTBC), is inspired from the conventional selected mapping (SLM) approach. This technique banks on an adequate embedded signaling that mainly consists in a specific Space Time Bloc Codes (STBC) patterns and a precoding sequence codebook. In addition, in order to improve the signal detection process and the PAPR gain, we propose a new efficient combined Blind SLMSTBC (BSLMSTBC) method. Both methods propose an optimized scheme during the signal estimation process that is based on the maximum a posteriori (MAP) algorithm. A simulation study shows that our investigated approaches result in a spectacular PAPR reduction and furthermore lead to a perfect signal recovery at the receiver side.
Keywords
1 Introduction
Orthogonal frequency division multiplexing (OFDM) modulation technique is a multicarrier transmission scheme that recently has been widely adopted in various wireless communication standards (WLAN, DVBT…), thanks to its high spectral efficiency and robustness offered, especially for the frequency selective channels [1, 2]. This technique has also been combined with the multiple input multiple output (MIMO) systems [3] and has recently been adopted for many important wireless standards such as the Third Generation Partnership Project (3 GPP) of longterm evolution advanced (LTEA) [4]. However, the transmitted signals in OFDM systems may potentially have high peak values in the time domain since many independent subcarrier components are added via an inverse fast Fourier transform (IFFT) operation. This aspect may considerably increase the peak power at the output of the highpower amplifier (HPA) at the transmitter [5, 6].
Since high peak values can occur in any transmitted branch of the MIMOOFDM system, this issue becomes more serious mainly when using several transmitter antennas. It is for this reason that several research works were interested in the PAPR reduction by applying existing single input single output (SISO) algorithms separately on each transmit antenna such as ordinary selected mapping (SLM) [7] and partial transmit sequence (PTS) techniques [8]. Such techniques need a number of side information (SI) equal to the number of used sequence phase for each antenna. Therefore, the SI increases highly with the number of antenna which weakness this approach. To overcome this problem, interesting solutions are proposed in the literature such as crossantenna rotation and inversion [9], direct SLM [10], direct PTS (dPTS) [11], unitary rotation [12], optimal PAPR reduction [13], and polyphase interleaving and inversion [14]. These techniques consist of selecting the transmitted sequence with the lowest average PAPR over all transmit antennas. However, all these methods decrease the SI but imply an explicit SI transmission to recover the useful data at the receiver side. As such, these approaches cause a resource wasting (in terms of channel bandwidth) that can considerably decrease the data rate. Moreover, a wrong estimation of the SI at the received side could damage the total signal recovery which leads to significant performance deterioration in terms of bit error rate (BER). Thus, several recent research works, known as blind techniques [15–17], have been proposed to avoid the sending of the explicit SI. Some of these studies required the use of a special phase rotations of candidate signals (0 or π) [15], which degrade the PAPR performance. The other proposed approaches are only relevant for two antennas [16] or are too complex to be implemented [17].
This paper focus on avoiding the transmission of the explicit SI in MIMOOFDM systems. To achieve this goal, we propose two efficient blind methods. In the first part, we propose a new blind technique, one inspired from classical SLM techniques, referred to as Blind Space Time Bloc Codes (BSTBC). This method requires, at the transmitter side, a special precoder codebook containing different configurations of two Space Time Bloc Codes (STBC) patterns. Among them, the one leading to the minimum PAPR will be kept in the PAPR reduction process. Consequently, this leads to an embedded signaling that guarantees a reliable and perfect signal recovery at the receiver side through a hard or a soft decision process. The second method consists of combining the BSTBC method with BSLM scheme already investigated in [18]. This combined method, referred to as Blind SLMSTBC (BSLMSTBC), exploits two forms of signaling which are the set of rotated and unrotated constellations and a precoders codebook containing different configurations of STBC patterns. In this paper, we show that BSLMSTBC approach does not only lead to significant reduce of the PAPR level but also enhances the recovery process at the receiver side. Furthermore, both methods consider a MAXLogMAP estimation technique which takes an optimal advantage from these embedded signaling. Compared to the existing works, our proposed methods have the advantage to consider an embedded signaling process that exploits both the transmitter and the receiver sides to jointly reduce the PAPR and guarantee a perfect signal reconstitution without use of an explicit SI.
The remainder of this paper is organized as follows. First, we define the system model in Section 3. Then, we review the conventional SLM technique used in SISOOFDM system. In Section 4, we describe our proposed blind techniques mainly BSTBC and BSLMSTBC and detail their improved version in Section 5. Subsequently, we present in Section 6 the simulation results to illustrate the performance of our proposed methods. Finally, Section 7 presents the conclusions of this study and makes some suggestions for future work.
2 Notations
Throughout this paper, the boldface lower case and upper cases letters denote vectors and matrices respectively. I _{ N } refers to the identity matrix of dimension N. The superscripts.^{ T } and.^{∗} denote the transpose and the element wise conjugation, respectively. Finally, \(\mathbb {E}\) refers to the expectation operator, . denotes the absolute value, and Pr refers to the probability.
3 MIMOOFDM system, PAPR metric, and SLM approach
Recently, OFDM combined with MIMO technology has received a great deal of attention since it represents an interesting candidate for mobile communication systems thanks to its robustness to multipath fading channels, ability to achieve high data rate and very high bandwidth efficiencies [20, 21]. Moreover, in order to attain optimum performance in MIMOOFDM systems, several kinds of diversity (time, frequency, channel coding) are often used. Furthermore, authors in [19] have shown that the performance of OFDM systems using SpaceTime Coding (STC) yielded significant gains (∼5 dB) in terms of BER in a multi path channel with a 30Hz Doppler spectrum and the absence of any timeinterleaving. These codes can be classified into STBC and spacetime trellis codes (STTCs) [22].
The STBC utilizes the orthogonality property of the used code to achieve full diversity, yet it cannot achieve fullrate transmission when the number of transmit antennas is greater than two [21]. On the other hand, the STBC can guarantee full diversity by the use of enough trellis coding, but the decoding complexity increases exponentially with the number of transmit antennas [34, 35]. For these reasons, we consider the STBC code in this work. The first and wellknown STBC is the Alamouti code, which is an orthogonal STC and has the advantage to be full rate contrarily to those proposed by Tarokh et al. [23, 24].
In the sequel, in order to simplify the description of our proposed methods, we focus on the Alamouti codes. Then, the code of rate \(\frac {3}{4}\) will be used for the related simulations. It is important to mention that the study of the blind PAPR reduction scheme described in this paper can be generalized to include both of the two previously cited categories of codes.
3.1 System model
For simplicity of presentation, we consider a multiple input single output (MISO) system with two transmit and one receive antennas using an Alamouti code [25] denoted as S T B C _{2}.
At the transmitter side, IFFT processing is usually followed by a cyclic prefix (CP) insertion in order to mitigate the intersymbol interference (ISI). Finally, x ^{(1)} and x ^{(2)} are transmitted from the first and the second antennas, respectively.
Regarding the receiver side, we assume that the channel over the two consecutive data symbols is constant during two time slots T s, hence \(H_{2n}^{(i)}=H_{2n+1}^{(i)},\,i=1,2.\)
3.2 PAPR metric
where N _{ t } denotes the number of the transmitter antennas.
3.3 SLM technique
To guarantee that the input signal will be in the linear region of the HPA, many techniques were proposed [5]. Among these solutions, the first and the simplest one is the clipping of the signal to be amplified [26]. Other methods including coding techniques [27] or based on the relationship between some coding properties and OFDM modulator [28] have been proposed to reduce PAPR. Challenging solutions were proposed such as tone reservation (TR) [29], selected mapping [30], partial transmit sequence [31], etc. Among the cited techniques, we considered in this study the SLM technique due to its ability to reduce the PAPR without causing signal degradation in OFDM system and also thanks to its reduced complexity. Basically, the SLM generates, first, a special D×N phase matrix denoted as \( \mathbf {\mathcal {Z}}= \left [e^{j{\boldsymbol {\phi }}^{(0)}},\ldots,e^{j{\boldsymbol {\phi }}^{(D1)}}\right ]^{T}, \) where, \(\boldsymbol {\phi }^{(d)}=\left [\phi _{0}^{(d)},\phi _{i}^{(d)}\ldots,\phi _{N1}^{(d)}\right ] \), \( \phi _{i}^{(d)} \in [\!0, 2\pi [ \), and i=0,…,N−1. Then, the input data r is multiplied by the D independent phase sequences which produce a modified data block denoted by \(\textbf {r}^{(d)}= \textbf {r}.e^{j\,{\boldsymbol {\phi }}^{(d)}},\, d = 0,\ldots,D1. \label {Slmvector} \phantom {\dot {i}\!}\)
The main steps of the conventional algorithm are summarized according the following Algorithm 1
To perform the appropriate inverse operation, the receiver should know which phase sequence is used at the transmitter side. Thus, a portion of the bandwidth must be allocated for the transmission of the SI index. Obviously, l o g _{2}(D) bits are required to explicitly represent this SI. Hence, a wrong estimation of it at the received side leads to a damage on the total signal recovery. One alternative may be to protect the SI with some forms of coding techniques, but this will result in further bandwidth loss and resources waste.
where \( LLR_{n} \approx \min _{l \in \mathcal {Q}} S_{n}H_{n} q_{l}^{'}^{2}  \min _{l\in \mathcal {Q}^{'}} S_{n}H_{n} q_{l}^{2},\) with H _{ n } is the frequency response of the multipath channel.
In the next section, we detail our powerful blind method which is an extension of the Blind SLM method conceived to protect the SI. This proposed technique banks on an adequate embedded signaling that mainly consists on a specific STBC patterns and a precoding sequences codebook.
4 Blind PAPR reduction scheme for MIMOOFDM systems
The proposed PAPR reduction technique is based on specific STBC patterns from which we construct precoding sequences forming a codebook that ensures the role of an inherent embedded signaling for the MIMOOFDM system. This technique is blind and banks on the SLM principle. To achieve this objective, first, we start by explaining the construction of this codebook banking on the STBC class. Then, we detail the investigated technique dedicated to reduce the PAPR level. Finally, we illustrate the processing of estimating the SI.
4.1 Principle of the codebook construction
where K presents the number of precoding sequence. We call a precoding sequence a \( 1\times \frac {N}{2} \) binary vector which refers to the way to decode the original data according to the two different Alamouti codes (Sch _{0} and Sch _{1}). To explain more, if \( { Seq}^{(k)}_{n}=0 \), then the Sch _{0} will be used to decode (X _{2n },X _{2n+1}). Otherwise, we will exploit the other scheme Sch _{1}. This can be summarized as follows:

First, we kept only the nonequivalent schemas. For example, for two antennas [25], we can define the nonequivalent schemes as follows:$$\textbf{A} = \left[ {\begin{array}{*{20}{c}} {X_{2n}}&{  X_{2n+1}^{*}}\\ {X_{2n+1}}&{X_{2n}^{*}} \end{array}} \right], \, \textbf{B} = \left[ {\begin{array}{*{20}{c}} {X_{2n}}&{X_{2n+1}^{*}}\\ {X_{2n+1}}&{ X_{2n}^{*}} \end{array}} \right], $$$$\textbf{C} = \left[{\begin{array}{*{20}{c}} {X_{2n}}&{X_{2n+1}}\\ { X_{2n+1}^{*}}&{X_{2n}^{*}} \end{array}} \right], \, \textbf{D} = \left[{ \begin{array}{*{20}{c}} {X_{2n}}&{{X_{2n+1}}}\\ {X_{2n+1}^{*}}&{  X_{2n}^{*}} \end{array}} \right]. $$

Then, for each combination (for two antennas we define six possibilities AB, AC, AD, BC, BD, and C D), we perform the proposed coded scheme (see Eq. (13)) and calculate the PAPR according to the Eq. (7)).

Finally, we keep the two schemes that lead to the minimum PAPR.
This can be justified by the fact that these two schemes offer more diversity at the antennas level (see Eq. (14)).
4.2 PAPR reduction algorithm
Then, we kept the precoding sequence \(\textbf {Seq}^{(k_{0})} \phantom {\dot {i}\!}\) corresponding to the \({k_{0}^{th}} \phantom {\dot {i}\!}\) row of the precoding matrix leading to the minimum PAPR level according to Eq. (7). Finally, the proposed precoding technique is detailed in Algorithm 2.
Regarding the receiver side, we propose an efficient decision technique based on the MAP estimator to recover the transmitted sequence X as it will be explained in the next section.
4.3 Decoding of the side information k _{0}
In the following paragraph, we explain the hard decision process dedicated to detect the used index \(\tilde {k}_{0}\) in an efficient way.
4.3.1 Hard decision process
Indeed, the hard decision criteria ensures good decision performance, but when it is close to zero (for low signal to noise ratio (SNR) values), making a hard decision based on \(\mathcal {H}_{0}\) or \(\mathcal {H}_{1}\) could lead to a wrong estimation of the code vector and subsequently introduce a major decision error. To resolve this issue, we investigate, in the following paragraph the soft decision criteria.
4.3.2 Soft decision process
where \({\overline {{ Seq}^{(k)}_{n}}}\) is the complementary of \({ Seq}^{(k)}_{n}\).
5 Blind SLMSTBC technique
5.1 Embedding the SI into the OFDM symbol
The main steps of the improved algorithm performed at the transmitter side are summarized according to the following steps. First, we multiply the original data X by independent phase sequences to obtain X ^{ ϕ }. Then, each couple \(\left (X_{2n}^{\phi },X_{2n+1}^{\phi }\right)\) will be encoded according to the Alamouti codebook \(\mathbf {\mathcal {M}}\). Finally, the sequence that has the lowest PAPR is kept and then transmitted.
 1.
The first bit indicates if the X _{2n } belongs to the rotated set i.e., \( {\mathcal {E}}_{2}\) or not i.e., \({\mathcal {E}}_{1}\). Thus, If S e q _{ n } ^{(k)}=0, then \(X_{2n }^{\varphi } = X_{2n}.e^{j\varphi _{1}},\, \varphi _{1} \in E_{1}\), otherwise \( \, X_{2n}^{\varphi } = X_{2n}.e^{j\varphi 2},\varphi _{2} \in E_{2}\).
 2.
The second bit indicates if the X _{2n } belongs \( {\mathcal {E}}_{2}\) or \({\mathcal {E}}_{1}\). If S e q _{ n+1} ^{(k)}=0, then \(X_{2n + 1}^{\varphi } = X_{2n + 1}.e^{j\varphi _{1}},\varphi _{1} \in E_{1}\), otherwise \( X_{2n + 1}^{\varphi } = X_{2n + 1}.e^{j\varphi 2},\varphi _{2} \in E_{2}\).
 3.
The third bit refers to Sch _{ i }, i=0,1. If S e q _{ n+2} ^{(k)}=0, then \(\left (X_{2n}^{\varphi },X_{2n + 1}^{\varphi } \right)\) will be coded by using the scheme code S c h _{0}. If it is not the case, we consider S c h _{1}.
In the following section, we analyze how the actually transmitted side information index will be estimated.
5.2 Precoder sequence \(\mathbf {Cseq}^{(k_{0})}\protect \phantom {\dot {i}\!}\) estimation
where \({\mathcal {Q}}=\{q_{0},\ldots,q_{M1}\}\) and \({\mathcal {Q}}^{'}=\{q_{0}^{'},\ldots,q_{M1}^{'}\}\) represent the coordinates of the rotated and the unrotated constellation points, respectively.
Finally, the transmitted sequence is deduced.
It should be noted that the complexity of our proposed methods at the receiver side is based mainly on the choice of the used STBC decoder. In our study, we consider a conventional decoder, where authors in [33] showed that the complexity of STBC detection algorithms is equal to O(N ^{ Q }), where N denotes the number of subcarriers and Q denotes the number of transmitted symbols per STBC block. Thus, since we exploit in our estimation process two conventional STBC schemes, we can conclude that the complexity of our proposed methods is equal to 2∗O(N ^{ Q }).
6 Simulation results
The performance of the proposed blind methods in MIMOOFDM systems is evaluated through simulation results. These simulations are performed for both the transmitter and the receiver sides. At the transmitter side, the performance is evaluated in terms of the CCDF of the PAPR versus its threshold. At the receiver side, the performances are highlighted in terms of the side information error rate (SIER) that indicates the percentage of failure detection of the phase sequence and the BER.
6.1 Simulation parameters
Parameters of simulations
Parameters  Specifications 

MIMOOFDM system]  LTE downlink 
Constellation  4,16−QAM 
Mobile Speed (Km/h)  10 
Ts(μs)  72 
fc(GHz)  2.15 
δf(KHz)  15 
B (MHz)  2.5 
size of IFFT  256 
6.2 Transmitter side
In order to evaluate the performance of the proposed blind methods, we first consider the case of STBC with a full rate i.e., the rate is set to 1, and then the case of a rate equal to \(\frac {3}{4}\).
6.3 Receiver side
Moreover, to evaluate the performance of the receiver side in terms of BER, first, we consider two cases: the case where we perform a Blind technique (BSTBC, BSLMSTBC) and the one where the phase sequence is perfectly known at the receiver side. Second, we consider a conventional Viterbi decoder with a rate equal to \(\frac {1}{2} \) and a hard decoder at the receiver side.
7 Conclusions
In this paper, we investigate an efficient PAPR reduction technique dedicated to the MIMOOFDM systems using STBC precoders codebook. The main feature of our proposed method is to induce an embedded signaling through the advanced precoders codebook. This form of signaling leads to a powerful recovery of the transmitted signal and guarantees a very low failure decision rate. To further improve the decision process, we proposed an additional embedded signaling that consists of a set of rotated and unrotated QAM constellations. Indeed, when this latter is used in the decision process (using a hard decision deduced from a MaxLogMAP decoding), it improves the MIMOOFDM system performances in terms of the CCDF, PAPR, SIER, and BER. The work perspective will be devoted to the applicability of our proposed technique in the spectrum sensing case for the cognitive radio systems.
Declarations
Acknowledgements
Parts of this paper were published in the IEEE Wireless Communications and Networking (WCNC) 2013 conference [37].
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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