J. Cent. South Univ. (2012) 19: 988-993

DOI: 10.1007/s11771-012-1101-7

PAPR reduction in mobile WiMAX:

A new ZCMT precoded random interleaved OFDMA system

I. Baig, V. Jeoti

Electrical and Electronic Engineering Department, Universiti Teknologi PETRONAS, Tronoh 31750, Perak, Malaysia

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Mobile WiMAX (worldwide interoperability for microwave access) 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. All OFDMA based networks, like mobile WiMAX, experience the problem of high peak-to-average power ratio (PAPR). The high PAPR increases the complexity of analog-to-digital (A/D) and digital-to-analog (D/A) convertors, and also reduces the efficiency of RF high-power-amplifier (HPA). In this work, a new zadoff-chu matrix transform (ZCMT) precoding based random interleaved orthogonal frequency division multiple access (OFDMA) system was proposed for PAPR reduction in mobile WiMAX system. The system is based on precoding the constellation symbols with the ZCMT precoder before subcarrier mapping. The PAPR of proposed system is analyzed with the root-raised-cosine (RRC) pulse shaping to keep out of band radiation low and meet the transmission spectrum mask requirement. Simulation results show that the proposed system has better PAPR gain than the hadamard transform (WHT) precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems. Symbol-error- rate (SER) performance of the system is also better than the conventional random interleaved OFDMA systems and the random interleaved OFDMA systems with WHT. The good improvement in PAPR significantly reduces the cost and the complexity of the transmitter.

Key words: peak to average power ratio; orthogonal frequency division multiple access; zadoff-chu matrix transform; mobile WiMAX; root-raised-cosine pulse shaping

1 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 developed a new amendment of the IEEE 802.16 standard, i.e. IEEE 802.16m, as an advanced air interface to meet the requirements of ITU-R/IMT-Advanced for 4G 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  802.16e amendment to support scalable channel bandwidth.

The OFDMA is a multiple access version of orthogonal frequency division multiplexing (OFDM) systems. It splits the high speed data stream into a number of parallel low rate data streams and these low rate 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 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 OFDMA based system is the 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 [1-2].

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 into two modes, interleaved mode and random interleaved mode. The random interleaved subcarrier mapping is favoured because it increases the capacity in the frequencyselective fading channels and offers maximum frequency diversity. Figure 1 shows the subcarrier mapping in interleaved mode, where the subcarriers are mapped equidistant to each other. Figure 2 explains the subcarrier mapping in random interleaved mode, where the subcarriers are mapped randomly based on some permutation algorithm to each other.

Fig. 1 Interleaved OFDMA

Fig. 2 Random interleaved OFDMA

Figure 3 further explains the concept of localized subcarrier mapping, where the subcarrier mapping is done in adjacent. The OFDMA is widely adopted in various communication standards like worldwide interoperability for microwave access (WiMAX), mobile broadband wireless access (MBWA), evolved UMTS terrestrial radio access (E-UTRA) and ultra mobile broadband (UMB). The OFDMA is also a strong candidate for the wireless regional area networks (WRAN) and the long term evaluation advanced (LTE-Advanced).

Fig. 3 Localized OFDMA

However, OFDMA has some drawbacks. The peak to average power ratio (PAPR) is still one of the major drawbacks in the transmitted OFDMA signal [3]. Therefore, for zero distortion of the OFDMA signal, the high power amplifier (HPA) must operate not only 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 components of the OFDMA systems. So, if the PAPR is reduced, it means that not only the cost of OFDMA systems and the complexity of A/D and D/A converters are reduced, but also the transmit power is increases, 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 previous researches. Among them, schemes like phase optimization [4], constellation shaping [5], selective mapping (SLM) [6], nonlinear companding transforms [7], tone reservation (TR), tone injection (TI) [8], partial transmit sequence (PTS) [9], clipping and filtering [10], precoding based techniques [11], precoding based selected mapping (PSLM) techniques [12] and phase modulation transform [13] 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.

This work presents a new zadoff-chu matrix transform (ZCMT) precoding based random interleaved OFDMA system for PAPR reduction in the mobile WiMAX systems. The PAPR of proposed system is analyzed with root raised cosine (RRC) pulse shaping.

2 Random interleaved OFDMA system

Figure 4 illustrates the block diagram of random interleaved OFDMA system, where the subcarriers are mapped randomly to each other. In random interleaved OFDMA system, the baseband modulated symbols are passed through serial-to-parallel (S/P) converter which generates complex vector of size L. Let the complex vector of size L as X=[X₀, X₁, X₂, …, X_L-1]^T. After N subcarrier mapping in random interleaved mode to the X, get  The complex baseband random interleaved OFDMA signal with N system subcarriers and L user subcarriers can be written as

                     (1)

where  is got after subcarrier mapping,  n=0, 1, 2, …, N-1,  is modulated signal on subcarrier l for the k-th user and users index k=1, 2, …, Q-1.

Fig. 4 Random interleaved OFDMA system

3 Proposed model

3.1 Zadoff-chu sequences and zadoff-chu matrix transform

Zadoff-chu (ZC) sequences are class of poly phase sequences having optimum correlation properties. The ZC sequences have an ideal periodic autocorrelation and constant magnitude. According to Ref. [14], ZC sequences of length L can be defined as

                 (2)

where k=0, 1, 2, …, L-1; q is any integer; r is any integer relatively prime to L.

The kernel of ZCMT is defined as Eq. (3). For N= L×L and  the ZCMT, A, of size N=L×L=L² is obtained by reshaping the ZC sequence by k=mL+l as

            (3)

where m is the row variable and l the column variable. In other words, the L² point long ZC sequence fills the kernel of the matrix transform row-wise.

3.2 ZCMT precoding based random interleaved OFDMA system

Figure 5 shows a ZCMT precoding based random interleaved OFDMA system. In this system, a precoding matrix A of dimension N=L×L is applied to constellations symbols before the subcarrier mapping and IFFT to reduce PAPR. In the ZCMT precoding based random interleaved OFDMA systems, baseband modulated data pass through S/P convertor which generates a complex vector of size L that can be written as X=[X₀, X₁, …, X_L-1]^T. Then, ZCMT precoding is applied to this complex vector which transforms this complex vector into new vector of length L that can be written as Y=AX=[Y₀, Y₁, Y₂, …, Y_L-1]^T, where A is a precoder matrix of size N=L×L and Y_m can be written as

 (m=0, 1, …, L-1)             (4)

Fig. 5 ZCMT precoded random interleaved OFDMA

a_m,l means the m-th row and the l-th column of precoder matrix. Expanding Eq. (4), using row wise sequence reshaping k=mL+l and putting q=0, r=1 in Eq. (2), it becomes

   (5)

Equation (5) represents the ZCMT precoded constellation symbols. The subcarrier mapping is performed on these ZCMT precoded constellation symbols in random interleaved mode. After the subcarrier mapping in random interleaved mode, the frequency domain samplesis obtained. Mathematically, the subcarrier mapping in random interleaved mode can be done as

                   (6)

where 0≤l≤N-1, N=Q·L and 0≤≤Q; N means system subcarriers; L means user subcarriers (for one user); Q means the ratio between subchannels and users (Q=N/L).

The k-th subcarrier of each group is assigned to the k-th user with index set {r_q,1, Q+r_q,2, …, (L-1)Q+r_q,L-1}, where {r_q,1, r_q,2, …, r_q,L-1} are independent and identically distributed random variables with uniform distribution on {q=0, 1, …, Q-1}. Suppose that the k-th user is assigned to subchannel k, then the complex baseband ZCMT precoded random interleaved OFDMA signal for k-th user can be written as

 (n=0, 1, …, L-1)       (7)

where users index k=q=0, 1, …, Q-1 and  is modulated signal on subcarrier l for the k-th user. The complex passband signal of ZCMT precoded random interleaved OFDMA after RRC pulse shaping can be written as

                    (8)

where ω_c is carrier frequency, r(t) is baseband pulse,  (M/N)·T is compressed symbol duration after IFFT and T is symbol duration in seconds. The RRC pulse shaping filter can be defined as

      (9)

where  is roll off factor (0≤≤1).

The PAPR of ZCMT precoded random interleaved OFDMA signal in Eq. (8) with RRC pulse shaping can be written as

                   (10)

The PAPR of ZCMT precoded random interleaved OFDMA signal in Eq. (7) without pulse shaping can be written as

                    (11)

It should be pointed out that the orthogonality of the symbols after introducing precoding is maintained, as the precoding matrix is cyclic auto-orthogonal [13].

4 Simulation results

Extensive simulations in MATLAB software have been carried out to evaluate the performance of the proposed ZCMT precoded random interleaved OFDMA system with and without pulse shaping. To show PAPR analysis of the proposed system, the data are generated randomly then modulated by QPSK, 16-QAM and 64-QAM respectively. The PAPR was evaluated statistically by using complementary cumulative distribution function (CCDF). The CCDF of PAPR λ, is the probability that PAPR exceeds a given threshold λ₀, and it can be written as P (λ≥λ₀), where F(λ) is the CCDF of PAPR λ. Simulation parameters used are given in Table 1.

The simulation results of proposed system was compared with WHT precoded random interleaved OFDMA systems and conventional random interleaved OFDMA system. To show the PAPR analysis of proposed system with pulse shaping in MATLAB, we considered RRC rolloff factor 0.22 with system subcarriers L=256 and user subcarriers L=64. All the simulations have been performed on 10⁵ random data blocks.

Table 1 System parameters

Figure 6 shows the CCDF based comparison of the PAPR of the ZCMT precoded random interleaved OFDMA system with and without pulse shaping, with that of WHT precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems respectively. It can be seen that ZCMT precoded random interleaved OFDMA system without pulse shaping has best performance. However, realistically speaking, as the signals come through pulse shaping, the best performance can be seen for ZCMT with pulse shaping. For example, at clip rate of 10^-3, with user subcarriers L=64 and system subcarriers N=256, the PAPRs are 11, 9.6, 8 and 7 dB, respectively, for conventional random interleaved OFDMA systems, WHT precoded random interleaved OFDMA systems, ZCMT precoded random interleaved OFDMA system using RRC pulse and ZCMT precoded random interleaved OFDMA system without pulse shaping respectively, using QPSK modulation. It is observed that the proposed ZCMT precoding based system provides considerable PAPR gain for the OFDMA signal when compared to that of conventional random interleaved OFDMA signal, WHT precoded random interleaved OFDMA signal respectively using QPSK modulation.

Fig. 6 CCDF comparison of PAPR for QPSK modulation

Figure 7 shows the CCDF based comparison of the PAPR of the ZCMT precoded random interleaved OFDMA system with and without pulse shaping, with that of WHT precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems. It can be seen that ZCMT precoded random interleaved OFDMA system without pulse shaping has best performance. However, realistically speaking, as the signals come through pulse shaping, the best performance can be seen for ZCMT with pulse shaping. For example, at clip rate of 10^-3, with user subcarriers L=64 and system subcarriers N=256, the PAPRs are 10.5, 10, 9 and 7.8 dB, respectively, for conventional random interleaved OFDMA systems, WHT precoded random interleaved OFDMA systems, ZCMT precoded random interleaved OFDMA system using RRC pulse and ZCMT precoded random interleaved OFDMA system without pulse shaping respectively, using 16-QAM modulation. It is observed that the proposed ZCMT precoding based system provides considerable PAPR gain for the OFDMA signal when compared to that of conventional random interleaved OFDMA signal, WHT precoded random interleaved OFDMA signal respectively using 16-QAM modulation.

Fig. 7 CCDF comparison of PAPR for 16-QAM modulation

Figure 8 shows the CCDF based comparison of the PAPR of the ZCMT precoded random interleaved OFDMA system with and without pulse shaping, with that of WHT precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems. It can be seen that ZCMT precoded random interleaved OFDMA system without pulse shaping has best performance. However, realistically speaking, as the signals come through pulse shaping, the best performance can be seen for ZCMT with pulse shaping. For example, at clip rate of 10^-3, with user subcarriers L=64 and system subcarriers N=256, the PAPRs are 10.5, 10, 9 and 7.9 dB, respectively, for conventional random interleaved OFDMA systems, WHT precoded random interleaved OFDMA systems, ZCMT precoded random interleaved OFDMA system using RRC pulse and ZCMT precoded random interleaved OFDMA system without pulse shaping respectively, using 64-QAM modulation. It is observed that the proposed ZCMT precoding based system provides considerable PAPR gain for the OFDMA signal when compared to that of conventional random interleaved OFDMA signal, WHT precoded random interleaved OFDMA signal respectively using 64-QAM modulation.

Figure 9 shows the SER performance of the ZCMT precoded random interleaved OFDMA systems, WHT precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems over the ITU pedestrian A outdoor channel with additive white gaussian noise (AWGN) and MMSE equalization. It is concluded from Fig. 9 that the ZCMT precoded random interleaved OFDMA systems provides same SER performance as WHT precoded random interleaved OFDMA systems, but a significant SER gain of 14 dB is obtained when the proposed system is compared with the conventional interleaved OFDMA systems at clip rate of 10^-4 for the sub-band 0 using QPSK modulation.

Fig. 8 CCDF comparison of PAPR for 64-QAM modulation

Fig. 9 SER vs SNR comparison for sub-band 0 and QPSK modulation

Table 2 summarizes the PAPR of random interleaved OFDMA systems, WHT random interleaved OFDMA systems, ZCMT random interleaved OFDMA system using RRC pulse shaping (roll off factor α=0.22) and ZCMT random interleaved OFDMA system without pulse shaping using QPSK, 16-QAM and 64-QAM respectively. At clip rate of 10^-3, following conclusions can be made from Table 2 as: 1) The ZCMT precoded random interleaved OFDMA system with pulse shaping achieves a PAPR gain of 3 dB and the ZCMT precoded random interleaved OFDMA system without pulse shaping achieves a PAPR gain of 4 dB, respectively, when compared with the conventional random interleaved OFDMA systems; 2) The ZCMT precoded random interleaved OFDMA system with pulse shaping achieves a PAPR gain of 1.6 dB and the ZCMT precoded random interleaved OFDMA system without pulse shaping achieves a PAPR gain of 2.6 dB, respectively, when compared with the WHT precoded random interleaved OFDMA systems, using QPSK modulation. Table 2 also concludes that, the PAPR gain of proposed system, using 16-QAM and 64-QAM modulation is also better than the conventional random interleaved OFDMA systems and WHT precoded random interleaved OFDMA systems, respectively.

Table 2 PAPR comparisons of random interleaved OFDMA, WHT random interleaved OFDMA, ZCMT random interleaved OFDMA using RRC pulse shaping (roll-off factor α=0.22) and ZCMT random interleaved OFDMA without pulse shaping, for L=64 and N=256 (at CCDF of 10^-3)

5 Conclusions

1) A new ZCMT precoded random interleaved OFDMA system has been proposed which provides good PAPR reduction in mobile WiMAX systems.

2) Simulation results show that the PAPR gain of the proposed systems with and without RRC pulse shaping is better than that of the WHT precoded random interleaved OFDMA systems and the conventional random interleaved OFDMA systems.

3) Additionally, it is seen that ZCMT precoded random interleaved OFDMA system also takes advantage of the frequency variations of the communication channel. At clip rate of 10^-4, the SER gain of 14 dB is obtained when the proposed system is compared with the conventional interleaved OFDMA systems.

4) The proposed system is signal independent, distortionless, and efficient. Proposed systems do not require any complex optimizations.

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(Edited by DENG Lü-xiang)

Received date: 2011-02-25; Accepted date: 2011-06-20

Corresponding author: I. Baig, PhD Candidate; Tel: +60-125224957; E-mail: imran_baig_mirza@yahoo.com