On the peak-to-average power ratio reduction in mobile WiMAX: A discrete cosine transform matrix precoding based random-interleaved orthogonal frequency division multiple access uplink system
Introduction
The mobile worldwide interoperability for microwave access (Mobile WiMAX) is a broadband wireless solution that enables the convergence of mobile and fixed broadband networks through a common wide area radio-access (RA) technology and flexible network architecture. Since January 2007, the IEEE 802.16 working group (WG) has been developing a new amendment of the IEEE 802.16 standard i.e. IEEE 802.16 m as an advanced air interface to meet the requirements of ITU-R/IMT-Advanced for 4 G systems. The mobile WiMAX air interface adopts orthogonal frequency division multiple access (OFDMA) as multiple access technique for its uplink (UL) and downlink (DL) to improve the multipath performance. The scalable OFDMA (SOFDMA) is introduced in the IEEE 802.16 e amendment to support scalable channel bandwidth.
OFDMA is a multiple access version of the orthogonal frequency division multiplexing (OFDM) systems. OFDMA system splits the high speed data stream into a number of parallel low data rate streams and these low rates data streams are transmitted simultaneously over a number of orthogonal subcarriers. The key difference between OFDM and OFDMA is that, instead of being allocated all of the available subcarriers, the base station assigns a subset of carriers to each user in order to accommodate several transmissions at the same time. An inherent gain of the OFDMA based systems is its ability to exploit the multiuser diversity through subchannel allocation. Additionally, OFDMA has the advantage of simple decoding at the receiver side due to the absence of inter-carrier-interference (ICI). Other benefits of OFDMA include better granularity and improved link budget in the uplink communications (Knopp and Humblet, 1995, Tse, 1997).
There are two different approaches to do subcarrier mapping in OFDMA systems, localized subcarrier mapping and distributed subcarrier mapping. The distributed subcarrier mapping can be further divided in to two modes, interleaved mode and random interleaved mode. The random interleaved subcarrier mapping is favorable for the mobile WiMAX because it increases the capacity in the frequency selective fading channels and offers maximum frequency diversity. Fig. 1 shows the subcarrier mapping in interleaved mode, where the subcarriers are mapped equidistant to each other's. Fig. 2 explains the subcarrier mapping in random interleaved mode, where the subcarriers are mapped randomly based on some permutation algorithm to each other's. Fig. 3 further explains the concept of localized subcarrier mapping, where the subcarrier mapping is done in adjacent.
OFDMA is widely adopted in the various communication standards like WiMAX, mobile broadband wireless access (MBWA), evolved UMTS terrestrial radio access (E-UTRA) and ultra mobile broadband (UMB). OFDMA is also a strong candidate for the wireless regional area networks (WRAN) and the long term evaluation advanced (LTE-Advanced). However, OFDMA has some drawbacks, among others; the peak-to-average power ratio (PAPR) is still one of the major drawbacks in the transmitted OFDMA signal (Wang and Chen, 2004). Therefore, for zero distortion of the OFDMA signal, the high-power-amplifier (HPA) must not only operate in its linear region but also with sufficient back-off. Thus, HPA with a large dynamic range is required for OFDMA systems. These amplifiers are very expensive and are major cost component of the OFDMA systems. Thus, if we reduce the PAPR it not only means that we are reducing the cost of OFDMA systems and reducing the complexity of analog-to-digital (A/D) and digital-to-analog (D/A) converters, but also increasing the transmit power, thus, for same range improving received signal-noise-ratio (SNR), or for the same SNR improving range.
A large number of PAPR reduction techniques have been proposed in the literature. Among them, schemes like phase optimization (Nikookar and Lidsheim 2002), constellation shaping (Kou et al., 2007), selective mapping (SLM) (Lim et al., 2005), nonlinear companding transforms (Jiang et al., 2006), tone reservation (TR), tone injection (TI) (Mourelo, 1999; Yoo et al., 2006), partial transmit sequence (PTS) (Han and Lee 2004), clipping and filtering (Wang and Tellambura 2005), precoding based techniques (Park et al., 2001, Baig and Jeoti, 2010a, Baig and Jeoti, 2010b, Baig and Jeoti, 2010c), precoding based selected mapping (PSLM) techniques (Jeoti and Baig, 2009; Baig and Jeoti, 2010d) and phase modulation transform (Tasi et al., 2006, Thompson et al., 2008) are popular. The precoding based techniques, however, show great promise as they are simple linear techniques to implement without the need of any side information.
Uncoded OFDMA cannot exploit multipath diversity so that protection against fading in the form of error control coding is usually employed. Multicarrier systems employing precoding, albeit without outer codes, have attracted considerable attention. In the literature, precoding has been observed as a way of taking full advantage of the diversity gain of multicarrier signals and of trying to take advantage of the frequency selectivity of the multipath fading channel (Liu et al., 2003, Goeckel and Ananthaswamy, 2002, Hero and Marzetta, 2001). In general, precoding based OFDMA systems linearly mix the information symbols across the subcarriers and create a diversity effect by distributing the effect of channel fades across all the information symbols. For example, linear-constellation-precoding (LCP), together with subcarrier grouping has been designed to exploit both diversity and coding gains (Liu et al., 2003). It has been exposed that subcarrier grouping can reduce the complexity of the receiver without affecting the utmost achievable diversity and coding gains. In (Goeckel and Ananthaswamy 2002), the numerical results showed that the lowest PAPR ratio is obtained when only one group is used. On the other hand, using LCP with only one group will make the receiver too complex and limits the number of subcarriers that can be used. Indeed, the precoder proposed in (Goeckel and Ananthaswamy 2002) was designed for maximizing the diversity gain and minimizing the PAPR of the multicarrier signal simultaneously. However, their design procedure is quite different from the methods proposed in this paper.
This paper presents two precoding based OFDMA uplink systems for the PAPR reduction in the mobile WiMAX: Discrete-Cosine transform matrix (DCTM) precoding based random-interleaved OFDMA uplink system and SLM based DCTM precoded random-interleaved OFDMA uplink system. Precoding in OFDMA uplink systems consists of multiplying the modulated data of each OFDMA block by a precoding matrix before subcarrier mapping and OFDMA modulation. A predefined DCTM precoding matrix is used in the OFDMA uplink systems, and thus, no handshake is needed between the transmitter and the receiver. PAPR of the proposed system is analyzed with root-raised-cosine (RRC) pulse shaping. DCTM can be efficiently implemented via fast DCT algorithms which remarkably reduce the number of real multiplications from to, where represents the number of subcarriers.
This paper is organized as follows: Section 2 describes the basics of the Walsh-Hadamard Transform (WHT), Random Interleaved OFDMA Uplink Systems and Selected Mapping (SLM) based Random Interleaved OFDMA Uplink Systems, Section 3 presents the proposed system models with improved PAPR, Section 4 presents the computer simulation results and Section 5 concludes the paper.
Section snippets
Hadamard transform
Walsh-Hadamard transform (WHT) is an orthogonal linear transform and can be implemented by a butterfly structure as in FFT. This means that applying WHT does not require the extensive increase of system complexity. According to (Park et al., 2001), the kernel of the WHT can be written as follows:where denotes the binary complement of .
Random interleaved OFDMA uplink Systems
Fig. 4 illustrates the block diagram of the random-interleaved OFDMA uplink systems, where the subcarriers are mapped
Discrete cosine transform (DCT) and discrete cosine transform matrix (DCTM)
DCT (Ahmed et al., 1974) can be defined as:
DCTM (Pei and Hsue 2008) D of size L-by-L can be created by using Eq. (15)
The DCTM precoding matrix must fulfill the following criteria:
- 1.
All the elements of the precoding matrix must have the same magnitude.
- 2.
The magnitude must be equal to .
- 3.
The DCTM precoding matrix must be non-singular.
The first requirement ensures that every output symbol has the same amount of information of
Simulation Results
Extensive simulations in MATLAB(R) have been carried out to evaluate the performance of the proposed uplink systems with pulse shaping. To show PAPR analysis of the proposed system, the data is generated randomly then modulated by QPSK, 16-QAM and 64-QAM respectively. We evaluate the PAPR statistically by using complementary cumulative distribution function (CCDF). The CCDF of PAPR for the DCTM precoded random-interleaved OFDMA signal and the SLM based DCTM precoded random-interleaved OFDMA
Conclusion
In this paper, two precoding based systems: DCTM precoded random-interleaved OFDMA uplink system and SLM based DCTM precoded random-interleaved OFDMA uplink system have been proposed for PAPR reduction in mobile WiMAX systems. Computer simulation shows that, the PAPR of the both proposed uplink systems have low PAPR than the WHT precoded random-interleaved OFDMA uplink systems and conventional random-interleaved OFDMA uplink systems. Proposed systems are also efficient, signal independent,
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